diff --git a/.env.example b/.env.example
new file mode 100644
index 00000000..0a5d8b49
--- /dev/null
+++ b/.env.example
@@ -0,0 +1,3 @@
+# Google Gemini API Key for LLM TODO solver
+# Get your API key from: https://ai.google.dev/gemini-api/docs/api-key
+GOOGLE_API_KEY=your_google_api_key_here
diff --git a/.gitignore b/.gitignore
index 81ff4f9b..e3d81231 100644
--- a/.gitignore
+++ b/.gitignore
@@ -10,6 +10,9 @@ LICENSE
 yarn.lock
 package-lock.json
 
+# Environment variables (contains API keys)
+.env
+.env.local
 
 compiled
 /doc
diff --git a/LLM_SETUP.md b/LLM_SETUP.md
new file mode 100644
index 00000000..92b876ed
--- /dev/null
+++ b/LLM_SETUP.md
@@ -0,0 +1,44 @@
+# LLM TODO Solver Setup
+
+This project uses Google's Gemini API for LLM-powered TODO solving in Pie code.
+
+## Setup Instructions
+
+1. **Get a Google Gemini API Key**
+   - Visit: https://ai.google.dev/gemini-api/docs/api-key
+   - Sign in with your Google account
+   - Create a new API key
+
+2. **Configure the API Key**
+   - Copy `.env.example` to `.env`:
+     ```bash
+     cp .env.example .env
+     ```
+   - Edit `.env` and replace `your_google_api_key_here` with your actual API key:
+     ```
+     GOOGLE_API_KEY=your_actual_api_key_here
+     ```
+
+3. **Run Tests**
+   ```bash
+   npm test -- test_llm.ts
+   ```
+
+## Important Notes
+
+- **Never commit `.env` file to git** - it's already in `.gitignore`
+- The `.env.example` file is safe to commit (it has no real key)
+- If you get an error about missing API key, make sure `.env` file exists and contains your key
+
+## Free Tier Limits
+
+Google Gemini free tier has rate limits:
+- 10 requests per minute
+- If you hit the limit, tests will fail with quota errors
+- Wait a minute and try again
+
+## Security
+
+- Keep your API key private
+- Don't share it in commits, screenshots, or public channels
+- If accidentally exposed, regenerate a new key immediately
diff --git a/dist/index.js b/dist/index.js
index 1fcb0e47..87e571f6 100644
--- a/dist/index.js
+++ b/dist/index.js
@@ -1,2 +1,2 @@
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instanceof Ft||n instanceof Vt&&r instanceof Vt&&ht(n.smaller,r.smaller)}function lt(t,e,n){const r=e.now(),s=n.now();if(r instanceof ce)return n.readBackType(t);if(r instanceof Qt&&s instanceof Ft)return new me;if(r instanceof Qt&&s instanceof Vt)return new ge(lt(t,new Qt,s.smaller));if(r instanceof Gt){const e=q(t,s instanceof Xt?s.argName:r.argName);return new Ne(e,lt(W(t,e,r.argType),r.resultType.valOfClosure(new oe(r.argType,new wt(e))),J(s,new oe(r.argType,new wt(e)))))}if(r instanceof Kt){const e=rt(n),s=st(n);return new Se(lt(t,r.carType,e),lt(t,r.cdrType.valOfClosure(e),s))}if(r instanceof ue&&s instanceof zt)return new _e(s.name);if(r instanceof he)return new qe;if(r instanceof Zt&&s instanceof jt)return new Ae;if(r instanceof Zt&&s instanceof Wt)return new Se(lt(t,r.entryType,s.head),lt(t,new Zt(r.entryType),s.tail));if(r instanceof pe&&s instanceof oe)return new we(new Me,s.neutral.readBackNeutral(t));if(r instanceof Jt&&s instanceof te)return new De(lt(t,r.type,s.value));if(r instanceof ee&&r.length.now()instanceof Ft)return new Ye;if(r instanceof ee&&r.length.now()instanceof Vt&&s instanceof re){const e=r.length.now();return new Ke(lt(t,r.entryType,s.head),lt(t,new ee(r.entryType,e.smaller),s.tail))}if(r instanceof se&&s instanceof ie)return new tn(lt(t,r.leftType,s.value));if(r instanceof se&&s instanceof ae)return new en(lt(t,r.rightType,s.value));if(s instanceof oe)return s.neutral.readBackNeutral(t);throw new Error(`Cannot read back ${s} : ${r}`)}class pt{type;value;constructor(t,e){this.type=t,this.value=e}}let ft=class{constructor(){}toString(){return this.prettyPrint()}};class wt extends ft{name;constructor(t){super(),this.name=t}readBackNeutral(t){return new an(this.name)}prettyPrint(){return`N-${this.name}`}}let yt=class extends ft{where;type;constructor(t,e){super(),this.where=t,this.type=e}readBackNeutral(t){return new rn(this.where,this.type.readBackType(t))}prettyPrint(){return"N-TODO"}},dt=class extends ft{target;base;step;constructor(t,e,n){super(),this.target=t,this.base=e,this.step=n}readBackNeutral(t){return new ve(this.target.readBackNeutral(t),new we(this.base.type.readBackType(t),lt(t,this.base.type,this.base.value)),lt(t,this.step.type,this.step.value))}prettyPrint(){return"N-WhichNat"}},mt=class extends ft{target;base;step;constructor(t,e,n){super(),this.target=t,this.base=e,this.step=n}readBackNeutral(t){return new Ee(this.target.readBackNeutral(t),new we(this.base.type.readBackType(t),lt(t,this.base.type,this.base.value)),lt(t,this.step.type,this.step.value))}prettyPrint(){return"N-IterNat"}},gt=class extends ft{target;base;step;constructor(t,e,n){super(),this.target=t,this.base=e,this.step=n}readBackNeutral(t){return new Pe(this.target.readBackNeutral(t),new we(this.base.type.readBackType(t),lt(t,this.base.type,this.base.value)),lt(t,this.step.type,this.step.value))}prettyPrint(){return"N-RecNat"}},vt=class extends ft{target;motive;base;step;constructor(t,e,n,r){super(),this.target=t,this.motive=e,this.base=n,this.step=r}readBackNeutral(t){return new Te(this.target.readBackNeutral(t),lt(t,this.motive.type,this.motive.value),lt(t,this.base.type,this.base.value),lt(t,this.step.type,this.step.value))}prettyPrint(){return"N-IndNat"}},Et=class extends ft{target;constructor(t){super(),this.target=t}readBackNeutral(t){return new $e(this.target.readBackNeutral(t))}prettyPrint(){return"N-Car"}},Pt=class extends ft{target;constructor(t){super(),this.target=t}readBackNeutral(t){return new Oe(this.target.readBackNeutral(t))}prettyPrint(){return"N-Cdr"}},Tt=class extends ft{target;base;step;constructor(t,e,n){super(),this.target=t,this.base=e,this.step=n}readBackNeutral(t){return new Be(this.target.readBackNeutral(t),new we(this.base.type.readBackType(t),lt(t,this.base.type,this.base.value)),lt(t,this.step.type,this.step.value))}prettyPrint(){return"N-RecList"}},bt=class extends ft{target;motive;base;step;constructor(t,e,n,r){super(),this.target=t,this.motive=e,this.base=n,this.step=r}readBackNeutral(t){return new Ce(this.target.readBackNeutral(t),lt(t,this.motive.type,this.motive.value),lt(t,this.base.type,this.base.value),lt(t,this.step.type,this.step.value))}prettyPrint(){return"N-IndList"}},Nt=class extends ft{target;motive;constructor(t,e){super(),this.target=t,this.motive=e}readBackNeutral(t){return new Ue(new we(new Me,this.target.readBackNeutral(t)),lt(t,this.motive.type,this.motive.value))}prettyPrint(){return"N-IndAbsurd"}},xt=class extends ft{target;motive;base;constructor(t,e,n){super(),this.target=t,this.motive=e,this.base=n}readBackNeutral(t){return new ze(this.target.readBackNeutral(t),lt(t,this.motive.type,this.motive.value),lt(t,this.base.type,this.base.value))}prettyPrint(){return"N-Replace"}};class _t extends ft{target1;target2;constructor(t,e){super(),this.target1=t,this.target2=e}readBackNeutral(t){return new Qe(this.target1.readBackNeutral(t),lt(t,this.target2.type,this.target2.value))}prettyPrint(){return"N-Trans1"}}class kt extends ft{target1;target2;constructor(t,e){super(),this.target1=t,this.target2=e}readBackNeutral(t){return new Qe(lt(t,this.target1.type,this.target1.value),this.target2.readBackNeutral(t))}prettyPrint(){return"N-Trans2"}}class St extends ft{target1;target2;constructor(t,e){super(),this.target1=t,this.target2=e}readBackNeutral(t){return new Qe(this.target1.readBackNeutral(t),this.target2.readBackNeutral(t))}prettyPrint(){return"N-Trans12"}}let $t=class extends ft{target;func;constructor(t,e){super(),this.target=t,this.func=e}readBackNeutral(t){const e=this.func.type;if(e instanceof Gt){const n=e.resultType;return new Fe(this.target.readBackNeutral(t),n.valOfClosure(new pe).readBackType(t),lt(t,this.func.type,this.func.value))}throw new Error("Cong applied to non-Pi type.")}prettyPrint(){return"N-Cong"}},Ot=class extends ft{target;constructor(t){super(),this.target=t}readBackNeutral(t){return new Ve(this.target.readBackNeutral(t))}prettyPrint(){return"N-Symm"}},Lt=class extends ft{target;motive;base;constructor(t,e,n){super(),this.target=t,this.motive=e,this.base=n}readBackNeutral(t){return new Ge(this.target.readBackNeutral(t),lt(t,this.motive.type,this.motive.value),lt(t,this.base.type,this.base.value))}prettyPrint(){return"N-IndEqual"}},At=class extends ft{target;constructor(t){super(),this.target=t}readBackNeutral(t){return new Ze(this.target.readBackNeutral(t))}prettyPrint(){return"N-Head"}},It=class extends ft{target;constructor(t){super(),this.target=t}readBackNeutral(t){return new je(this.target.readBackNeutral(t))}prettyPrint(){return"N-Tail"}};class Bt extends ft{length;target;motive;base;step;constructor(t,e,n,r,s){super(),this.length=t,this.target=e,this.motive=n,this.base=r,this.step=s}readBackNeutral(t){return new We(lt(t,this.length.type,this.length.value),this.target.readBackNeutral(t),lt(t,this.motive.type,this.motive.value),lt(t,this.base.type,this.base.value),lt(t,this.step.type,this.step.value))}prettyPrint(){return"N-IndVec2"}}class Ct extends ft{length;target;motive;base;step;constructor(t,e,n,r,s){super(),this.length=t,this.target=e,this.motive=n,this.base=r,this.step=s}readBackNeutral(t){return new We(this.length.readBackNeutral(t),this.target.readBackNeutral(t),lt(t,this.motive.type,this.motive.value),lt(t,this.base.type,this.base.value),lt(t,this.step.type,this.step.value))}prettyPrint(){return"N-IndVec12"}}let Rt=class extends ft{target;motive;baseLeft;baseRight;constructor(t,e,n,r){super(),this.target=t,this.motive=e,this.baseLeft=n,this.baseRight=r}readBackNeutral(t){return new nn(this.target.readBackNeutral(t),lt(t,this.motive.type,this.motive.value),lt(t,this.baseLeft.type,this.baseLeft.value),lt(t,this.baseRight.type,this.baseRight.value))}prettyPrint(){return"N-IndEither"}},qt=class extends ft{operator;operand;constructor(t,e){super(),this.operator=t,this.operand=e}readBackNeutral(t){return new sn(this.operator.readBackNeutral(t),lt(t,this.operand.type,this.operand.value))}prettyPrint(){return"N-Application"}};class Mt{now(){return this}}class Ut{env;expr;constructor(t,e){this.env=t,this.expr=e}undelay(){return this.expr.valOf(this.env).now()}toString(){return`DelayClosure(${this.env}, ${this.expr})`}}class Ht{content;constructor(t){this.content=t}get(){return this.content}set(t){this.content=t}}class Dt extends Mt{val;constructor(t){super(),this.val=t}now(){const t=this.val.get();if(t instanceof Ut){let e=t.undelay();return this.val.set(e),e}return t}readBackType(t){return this.now().readBackType(t)}prettyPrint(){return this.now().prettyPrint()}toString(){return`Delay(${this.val})`}}let zt=class extends Mt{name;constructor(t){super(),this.name=t}readBackType(t){throw new Error("No readBackType for Quote.")}prettyPrint(){return`'${this.name}`}toString(){return this.prettyPrint()}},Qt=class extends Mt{constructor(){super()}readBackType(t){return new de}prettyPrint(){return"Nat"}toString(){return this.prettyPrint()}},Ft=class extends Mt{constructor(){super()}readBackType(t){throw new Error("No readBackType for Zero.")}prettyPrint(){return"zero"}toString(){return this.prettyPrint()}},Vt=class extends Mt{smaller;constructor(t){super(),this.smaller=t}readBackType(t){throw new Error("No readBackType for Add1.")}prettyPrint(){return`(add1 ${this.smaller.prettyPrint()})`}toString(){return this.prettyPrint()}},Gt=class extends Mt{argName;argType;resultType;constructor(t,e,n){super(),this.argName=t,this.argType=e,this.resultType=n}readBackType(t){const e=this.argType.readBackType(t),n=q(t,this.argName),r=W(t,n,this.argType);return new be(n,e,this.resultType.valOfClosure(new oe(this.argType,new wt(n))).readBackType(r))}prettyPrint(){return`(Π ${this.argName} ${this.argType.prettyPrint()} ${this.resultType.prettyPrint()})`}toString(){return this.prettyPrint()}},Xt=class extends Mt{argName;body;constructor(t,e){super(),this.argName=t,this.body=e}readBackType(t){throw new Error("No readBackType for Lambda.")}prettyPrint(){return`(lambda ${this.argName} ${this.body.prettyPrint()})`}toString(){return this.prettyPrint()}},Kt=class extends Mt{carName;carType;cdrType;constructor(t,e,n){super(),this.carName=t,this.carType=e,this.cdrType=n}readBackType(t){const e=this.carType.readBackType(t),n=q(t,this.carName),r=W(t,n,this.carType);return new ke(n,e,this.cdrType.valOfClosure(new oe(this.carType,new wt(n))).readBackType(r))}prettyPrint(){return`(Σ ${this.carName} ${this.carType.prettyPrint()} ${this.cdrType.prettyPrint()})`}toString(){return this.prettyPrint()}},Yt=class extends Mt{car;cdr;constructor(t,e){super(),this.car=t,this.cdr=e}readBackType(t){throw new Error("No readBackType for Cons.")}prettyPrint(){return`(cons ${this.car.prettyPrint()} ${this.cdr.prettyPrint()})`}toString(){return this.prettyPrint()}},Zt=class extends Mt{entryType;constructor(t){super(),this.entryType=t}readBackType(t){return new Ie(this.entryType.readBackType(t))}prettyPrint(){return`(List ${this.entryType.prettyPrint()})`}toString(){return this.prettyPrint()}},jt=class extends Mt{constructor(){super()}readBackType(t){throw new Error("No readBackType for Nil.")}prettyPrint(){return"nil"}toString(){return this.prettyPrint()}},Wt=class extends Mt{head;tail;constructor(t,e){super(),this.head=t,this.tail=e}readBackType(t){throw new Error("No readBackType for ListCons.")}prettyPrint(){return`(:: ${this.head.prettyPrint()} ${this.tail.prettyPrint()})`}toString(){return this.prettyPrint()}},Jt=class extends Mt{type;from;to;constructor(t,e,n){super(),this.type=t,this.from=e,this.to=n}readBackType(t){return new He(this.type.readBackType(t),lt(t,this.type,this.from),lt(t,this.type,this.to))}prettyPrint(){return`(= ${this.type.prettyPrint()} ${this.from.prettyPrint()} ${this.to.prettyPrint()})`}toString(){return this.prettyPrint()}},te=class extends Mt{value;constructor(t){super(),this.value=t}readBackType(t){throw new Error("No readBackType for Same.")}prettyPrint(){return`(same ${this.value.prettyPrint()})`}toString(){return this.prettyPrint()}},ee=class extends Mt{entryType;length;constructor(t,e){super(),this.entryType=t,this.length=e}readBackType(t){return new Xe(this.entryType.readBackType(t),lt(t,new Qt,this.length))}prettyPrint(){return`(Vec ${this.entryType.prettyPrint()} ${this.length.prettyPrint()})`}},ne=class extends Mt{constructor(){super()}readBackType(t){throw new Error("No readBackType for VecNil.")}prettyPrint(){return"vecnil"}toString(){return this.prettyPrint()}},re=class extends Mt{head;tail;constructor(t,e){super(),this.head=t,this.tail=e}readBackType(t){throw new Error("No readBackType for VecCons.")}prettyPrint(){return`(vec:: ${this.head.prettyPrint()} ${this.tail.prettyPrint()})`}toString(){return this.prettyPrint()}},se=class extends Mt{leftType;rightType;constructor(t,e){super(),this.leftType=t,this.rightType=e}readBackType(t){return new Je(this.leftType.readBackType(t),this.rightType.readBackType(t))}prettyPrint(){return`(Either ${this.leftType.prettyPrint()} ${this.rightType.prettyPrint()})`}toString(){return this.prettyPrint()}},ie=class extends Mt{value;constructor(t){super(),this.value=t}readBackType(t){throw new Error("No readBackType for Left.")}prettyPrint(){return`(left ${this.value.prettyPrint()})`}toString(){return this.prettyPrint()}},ae=class extends Mt{value;constructor(t){super(),this.value=t}readBackType(t){throw new Error("No readBackType for Right.")}prettyPrint(){return`(right ${this.value.prettyPrint()})`}toString(){return this.prettyPrint()}};class oe extends Mt{type;neutral;constructor(t,e){super(),this.type=t,this.neutral=e}readBackType(t){return this.neutral.readBackNeutral(t)}prettyPrint(){return`(Neutral ${this.type.prettyPrint()} ${this.neutral.prettyPrint()})`}toString(){return this.prettyPrint()}}let ce=class extends Mt{constructor(){super()}readBackType(t){return new ye}prettyPrint(){return"U"}toString(){return this.prettyPrint()}},ue=class extends Mt{constructor(){super()}readBackType(t){return new xe}prettyPrint(){return"Atom"}toString(){return this.prettyPrint()}},he=class extends Mt{constructor(){super()}readBackType(t){return new Re}prettyPrint(){return"Trivial"}toString(){return this.prettyPrint()}},le=class extends Mt{constructor(){super()}readBackType(t){throw new Error("No readBackType for Sole.")}prettyPrint(){return"sole"}toString(){return this.prettyPrint()}},pe=class extends Mt{constructor(){super()}readBackType(t){return new Me}prettyPrint(){return"Absurd"}toString(){return this.prettyPrint()}};class fe{toLazy(t){return new Dt(new Ht(new Ut(t,this)))}}let we=class extends fe{type;expr;constructor(t,e){super(),this.type=t,this.expr=e}valOf(t){return this.expr.valOf(t)}prettyPrint(){return`(the ${this.type.prettyPrint()} ${this.expr.prettyPrint()})`}toString(){return this.prettyPrint()}},ye=class extends fe{valOf(t){return new ce}prettyPrint(){return"U"}toString(){return this.prettyPrint()}},de=class extends fe{valOf(t){return new Qt}prettyPrint(){return"Nat"}toString(){return this.prettyPrint()}},me=class extends fe{valOf(t){return new Ft}prettyPrint(){return"0"}toString(){return this.prettyPrint()}},ge=class extends fe{n;constructor(t){super(),this.n=t}valOf(t){return new Vt(this.n.toLazy(t))}prettyPrint(){return isNaN(Number(this.n.prettyPrint()))?`(add1 ${this.n.prettyPrint()})`:`${Number(this.n.prettyPrint())+1}`}toString(){return this.prettyPrint()}},ve=class extends fe{target;base;step;constructor(t,e,n){super(),this.target=t,this.base=e,this.step=n}valOf(t){return function(t,e,n,r){const s=t.now();if(s instanceof Ft)return n;if(s instanceof Vt)return J(r,s.smaller);if(s instanceof oe&&s.type.now()instanceof Qt)return new oe(e,new dt(s.neutral,new pt(e,n),new pt(new Gt("n",new Qt,new B((t=>e))),r)));throw new Error(`invalid input for whichNat ${[t,e,n,r]}`)}(this.target.toLazy(t),this.base.type.toLazy(t),this.base.expr.toLazy(t),this.step.toLazy(t))}prettyPrint(){return`(which-Nat ${this.target.prettyPrint()} \n              ${this.base.prettyPrint()} \n              ${this.step.prettyPrint()})`}toString(){return this.prettyPrint()}},Ee=class extends fe{target;base;step;constructor(t,e,n){super(),this.target=t,this.base=e,this.step=n}valOf(t){return tt(this.target.toLazy(t),this.base.type.toLazy(t),this.base.expr.toLazy(t),this.step.toLazy(t))}prettyPrint(){return`(iter-Nat ${this.target.prettyPrint()} \n              ${this.base.prettyPrint()} \n              ${this.step.prettyPrint()})`}toString(){return this.prettyPrint()}},Pe=class extends fe{target;base;step;constructor(t,e,n){super(),this.target=t,this.base=e,this.step=n}valOf(t){return et(this.target.toLazy(t),this.base.type.toLazy(t),this.base.expr.toLazy(t),this.step.toLazy(t))}prettyPrint(){return`(rec-Nat ${this.target.prettyPrint()} \n              ${this.base.prettyPrint()} \n              ${this.step.prettyPrint()})`}toString(){return this.prettyPrint()}},Te=class extends fe{target;motive;base;step;constructor(t,e,n,r){super(),this.target=t,this.motive=e,this.base=n,this.step=r}valOf(t){return nt(this.target.toLazy(t),this.motive.toLazy(t),this.base.toLazy(t),this.step.toLazy(t))}prettyPrint(){return`(ind-Nat ${this.target.prettyPrint()} \n              ${this.motive.prettyPrint()} \n              ${this.base.prettyPrint()} \n              ${this.step.prettyPrint()})`}toString(){return this.prettyPrint()}},be=class extends fe{name;type;body;constructor(t,e,n){super(),this.name=t,this.type=e,this.body=n}valOf(t){const e=this.type.toLazy(t);return new Gt(this.name,e,new I(t,this.name,this.body))}prettyPrint(){return`(Π (${this.name} ${this.type.prettyPrint()}) \n          ${this.body.prettyPrint()})`}toString(){return this.prettyPrint()}},Ne=class extends fe{param;body;constructor(t,e){super(),this.param=t,this.body=e}valOf(t){return new Xt(this.param,new I(t,this.param,this.body))}prettyPrint(){return`(λ (${this.param}) ${this.body.prettyPrint()})`}toString(){return this.prettyPrint()}},xe=class extends fe{valOf(t){return new ue}prettyPrint(){return"Atom"}toString(){return this.prettyPrint()}},_e=class extends fe{sym;constructor(t){super(),this.sym=t}valOf(t){return new zt(this.sym)}prettyPrint(){return`'${this.sym}`}toString(){return this.prettyPrint()}},ke=class extends fe{name;type;body;constructor(t,e,n){super(),this.name=t,this.type=e,this.body=n}valOf(t){const e=this.type.toLazy(t);return new Kt(this.name,e,new I(t,this.name,this.body))}prettyPrint(){return`(Σ (${this.name} ${this.type.prettyPrint()}) \n              ${this.body.prettyPrint()})`}toString(){return this.prettyPrint()}},Se=class extends fe{first;second;constructor(t,e){super(),this.first=t,this.second=e}valOf(t){const e=this.first.toLazy(t),n=this.second.toLazy(t);return new Yt(e,n)}prettyPrint(){return`(cons ${this.first.prettyPrint()} ${this.second.prettyPrint()})`}toString(){return this.prettyPrint()}},$e=class extends fe{pair;constructor(t){super(),this.pair=t}valOf(t){return rt(this.pair.toLazy(t))}prettyPrint(){return`(car ${this.pair.prettyPrint()})`}toString(){return this.prettyPrint()}},Oe=class extends fe{pair;constructor(t){super(),this.pair=t}valOf(t){return st(this.pair.toLazy(t))}prettyPrint(){return`(cdr ${this.pair.prettyPrint()})`}toString(){return this.prettyPrint()}},Le=class extends fe{head;tail;constructor(t,e){super(),this.head=t,this.tail=e}valOf(t){const e=this.head.toLazy(t),n=this.tail.toLazy(t);return new Wt(e,n)}prettyPrint(){return`(:: ${this.head.prettyPrint()} ${this.tail.prettyPrint()})`}toString(){return this.prettyPrint()}},Ae=class extends fe{valOf(t){return new jt}prettyPrint(){return"nil"}toString(){return this.prettyPrint()}},Ie=class extends fe{elemType;constructor(t){super(),this.elemType=t}valOf(t){return new Zt(this.elemType.toLazy(t))}prettyPrint(){return`(List ${this.elemType.prettyPrint()})`}toString(){return this.prettyPrint()}},Be=class extends fe{target;base;step;constructor(t,e,n){super(),this.target=t,this.base=e,this.step=n}valOf(t){return at(this.target.toLazy(t),this.base.type.toLazy(t),this.base.expr.toLazy(t),this.step.toLazy(t))}prettyPrint(){return`(rec-List ${this.target.prettyPrint()} \n              ${this.base.prettyPrint()} \n              ${this.step.prettyPrint()})`}toString(){return this.prettyPrint()}},Ce=class extends fe{target;motive;base;step;constructor(t,e,n,r){super(),this.target=t,this.motive=e,this.base=n,this.step=r}valOf(t){return it(this.target.toLazy(t),this.motive.toLazy(t),this.base.toLazy(t),this.step.toLazy(t))}prettyPrint(){return`(ind-List ${this.target.prettyPrint()} \n              ${this.motive.prettyPrint()} \n              ${this.base.prettyPrint()} \n              ${this.step.prettyPrint()})`}toString(){return this.prettyPrint()}},Re=class extends fe{valOf(t){return new he}prettyPrint(){return"Trivial"}toString(){return this.prettyPrint()}},qe=class extends fe{valOf(t){return new le}prettyPrint(){return"sole"}toString(){return this.prettyPrint()}},Me=class extends fe{valOf(t){return new pe}prettyPrint(){return"Absurd"}toString(){return this.prettyPrint()}},Ue=class extends fe{target;motive;constructor(t,e){super(),this.target=t,this.motive=e}valOf(t){return function(t,e){const n=t.now();if(n instanceof oe&&n.type.now()instanceof pe)return new oe(e,new Nt(n.neutral,new pt(new ce,e)));throw new Error(`invalid input for indAbsurd ${[t,e]}`)}(this.target.toLazy(t),this.motive.toLazy(t))}prettyPrint(){return`(ind-Absurd \n              ${this.target.prettyPrint()} \n              ${this.motive.prettyPrint()})`}toString(){return this.prettyPrint()}},He=class extends fe{type;left;right;constructor(t,e,n){super(),this.type=t,this.left=e,this.right=n}valOf(t){return new Jt(this.type.toLazy(t),this.left.toLazy(t),this.right.toLazy(t))}prettyPrint(){return`(= ${this.type.prettyPrint()} \n              ${this.left.prettyPrint()} \n              ${this.right.prettyPrint()})`}toString(){return this.prettyPrint()}},De=class extends fe{type;constructor(t){super(),this.type=t}valOf(t){return new te(this.type.toLazy(t))}prettyPrint(){return`(same ${this.type.prettyPrint()})`}toString(){return this.prettyPrint()}},ze=class extends fe{target;motive;base;constructor(t,e,n){super(),this.target=t,this.motive=e,this.base=n}valOf(t){return function(t,e,n){const r=t.now();if(r instanceof te)return n;if(r instanceof oe){const t=r.type.now();if(t instanceof Jt){const s=r.neutral,i=t.type,a=t.from,o=t.to;return new oe(J(e,o),new xt(s,new pt(new Gt("x",i,new B((t=>new ce))),e),new pt(J(e,a),n)))}}throw new Error(`invalid input for replace ${[t,e,n]}`)}(this.target.toLazy(t),this.motive.toLazy(t),this.base.toLazy(t))}prettyPrint(){return`(replace ${this.target.prettyPrint()} \n              ${this.motive.prettyPrint()} \n              ${this.base.prettyPrint()})`}toString(){return this.prettyPrint()}},Qe=class extends fe{left;right;constructor(t,e){super(),this.left=t,this.right=e}valOf(t){return function(t,e){const n=t.now(),r=e.now();if(n instanceof te&&r instanceof te)return new te(n.value);if(n instanceof te&&r instanceof oe){const t=r.type.now();if(t instanceof Jt){const e=n.value,s=t.to,i=t.type,a=r.neutral;return new oe(new Jt(i,e,s),new kt(new pt(new Jt(i,e,e),new te(e)),a))}}else if(n instanceof oe&&r instanceof te){const t=n.type.now();if(t instanceof Jt){const e=t.from,s=r.value,i=t.type,a=n.neutral;return new oe(new Jt(i,e,s),new _t(a,new pt(new Jt(i,s,s),new te(s))))}}else if(n instanceof oe&&r instanceof oe){const t=n.type.now(),e=r.type.now();if(t instanceof Jt&&e instanceof Jt){const s=t.from,i=e.to,a=t.type,o=n.neutral,c=r.neutral;return new oe(new Jt(a,s,i),new St(o,c))}}throw new Error(`invalid input for do-trans: ${[t,e]}`)}(this.left.toLazy(t),this.right.toLazy(t))}prettyPrint(){return`(trans ${this.left.prettyPrint()} ${this.right.prettyPrint()})`}toString(){return this.prettyPrint()}},Fe=class extends fe{target;base;fun;constructor(t,e,n){super(),this.target=t,this.base=e,this.fun=n}valOf(t){return function(t,e,n){const r=t.now();if(r instanceof te)return new te(J(n,r.value));if(r instanceof oe){const t=r.type.now();if(t instanceof Jt){const s=t.type,i=t.from,a=t.to,o=r.neutral;return new oe(new Jt(e,J(n,i),J(n,a)),new $t(o,new pt(new Gt("x",s,new B((t=>e))),n)))}}throw new Error(`invalid input for cong ${[t,e,n]}`)}(this.target.toLazy(t),this.base.toLazy(t),this.fun.toLazy(t))}prettyPrint(){return`(cong ${this.target.prettyPrint()} ${this.fun.prettyPrint()})`}toString(){return this.prettyPrint()}},Ve=class extends fe{equality;constructor(t){super(),this.equality=t}valOf(t){return function(t){const e=t.now();if(e instanceof te)return new te(e.value);if(e instanceof oe){const t=e.type.now();if(t instanceof Jt)return new oe(new Jt(t.type,t.to,t.from),new Ot(e.neutral))}throw new Error(`invalid input for symm ${t}`)}(this.equality.toLazy(t))}prettyPrint(){return`(symm ${this.equality.prettyPrint()})`}toString(){return this.prettyPrint()}},Ge=class extends fe{target;motive;base;constructor(t,e,n){super(),this.target=t,this.motive=e,this.base=n}valOf(t){return function(t,e,n){const r=t.now();if(r instanceof te)return n;if(r instanceof oe){const s=r.type.now();if(s instanceof Jt){const i=s.type,a=s.from,o=s.to,c=r.neutral;return new oe(J(J(e,o),t),new Lt(c,new pt(new Gt("to",i,new B((t=>new Gt("p",new Jt(i,a,t),new B((t=>new ce)))))),e),new pt(J(J(e,a),new te(a)),n)))}}throw new Error(`invalid input for indEqual ${[t,e,n]}`)}(this.target.toLazy(t),this.motive.toLazy(t),this.base.toLazy(t))}prettyPrint(){return`(ind-= ${this.target.prettyPrint()} \n              ${this.motive.prettyPrint()} \n              ${this.base.prettyPrint()})`}toString(){return this.prettyPrint()}},Xe=class extends fe{type;length;constructor(t,e){super(),this.type=t,this.length=e}valOf(t){return new ee(this.type.toLazy(t),this.length.toLazy(t))}prettyPrint(){return`(Vec ${this.type.prettyPrint()} ${this.length.prettyPrint()})`}toString(){return this.prettyPrint()}},Ke=class extends fe{head;tail;constructor(t,e){super(),this.head=t,this.tail=e}valOf(t){return new re(this.head.toLazy(t),this.tail.toLazy(t))}prettyPrint(){return`(vec:: ${this.head.prettyPrint()} ${this.tail.prettyPrint()})`}toString(){return this.prettyPrint()}},Ye=class extends fe{valOf(t){return new ne}prettyPrint(){return"vecnil"}toString(){return this.prettyPrint()}},Ze=class extends fe{vec;constructor(t){super(),this.vec=t}valOf(t){return function(t){const e=t.now();if(e instanceof re)return e.head;if(e instanceof oe){const t=e.type.now();if(t instanceof ee&&t.length.now()instanceof Vt)return new oe(t.entryType,new At(e.neutral))}throw new Error(`invalid input for head ${t}`)}(this.vec.toLazy(t))}prettyPrint(){return`(head ${this.vec.prettyPrint()})`}toString(){return this.prettyPrint()}},je=class extends fe{vec;constructor(t){super(),this.vec=t}valOf(t){return ot(this.vec.toLazy(t))}prettyPrint(){return`(tail ${this.vec.prettyPrint()})`}toString(){return this.prettyPrint()}},We=class extends fe{length;target;motive;base;step;constructor(t,e,n,r,s){super(),this.length=t,this.target=e,this.motive=n,this.base=r,this.step=s}valOf(t){return ut(this.length.toLazy(t),this.target.toLazy(t),this.motive.toLazy(t),this.base.toLazy(t),this.step.toLazy(t))}prettyPrint(){return`ind-Vec ${this.length.prettyPrint()}\n              ${this.target.prettyPrint()}\n              ${this.motive.prettyPrint()}\n              ${this.base.prettyPrint()}\n              ${this.step.prettyPrint()}`}toString(){return this.prettyPrint()}},Je=class extends fe{left;right;constructor(t,e){super(),this.left=t,this.right=e}valOf(t){return new se(this.left.toLazy(t),this.right.toLazy(t))}prettyPrint(){return`(Either ${this.left.prettyPrint()} ${this.right.prettyPrint()})`}toString(){return this.prettyPrint()}},tn=class extends fe{value;constructor(t){super(),this.value=t}valOf(t){return new ie(this.value.toLazy(t))}prettyPrint(){return`(left ${this.value.prettyPrint()})`}toString(){return this.prettyPrint()}},en=class extends fe{value;constructor(t){super(),this.value=t}valOf(t){return new ae(this.value.toLazy(t))}prettyPrint(){return`(right ${this.value.prettyPrint()})`}toString(){return this.prettyPrint()}},nn=class extends fe{target;motive;baseLeft;baseRight;constructor(t,e,n,r){super(),this.target=t,this.motive=e,this.baseLeft=n,this.baseRight=r}valOf(t){return function(t,e,n,r){const s=t.now();if(s instanceof ie)return J(n,s.value);if(s instanceof ae)return J(r,s.value);if(s instanceof oe){const i=s.type.now();if(i instanceof se){const a=i.leftType,o=i.rightType,c=new Gt("x",new se(a,o),new B((t=>new ce)));return new oe(J(e,t),new Rt(s.neutral,new pt(c,e),new pt(new Gt("x",a,new B((t=>J(e,new ie(t))))),n),new pt(new Gt("x",o,new B((t=>J(e,new ae(t))))),r)))}}throw new Error(`invalid input for indEither: ${[t,e,n,r]}`)}(this.target.toLazy(t),this.motive.toLazy(t),this.baseLeft.toLazy(t),this.baseRight.toLazy(t))}prettyPrint(){return`(ind-Either ${this.target.prettyPrint()} \n              ${this.motive.prettyPrint()} \n              ${this.baseLeft.prettyPrint()} \n              ${this.baseRight.prettyPrint()})`}toString(){return this.prettyPrint()}},rn=class extends fe{loc;type;constructor(t,e){super(),this.loc=t,this.type=e}valOf(t){return new oe(this.type.toLazy(t),new yt(this.loc,this.type.toLazy(t)))}prettyPrint(){return`TODO ${this.type.prettyPrint()}`}toString(){return this.prettyPrint()}},sn=class extends fe{fun;arg;constructor(t,e){super(),this.fun=t,this.arg=e}valOf(t){return J(this.fun.toLazy(t),this.arg.toLazy(t))}prettyPrint(){return`(${this.fun.prettyPrint()} ${this.arg.prettyPrint()})`}toString(){return this.prettyPrint()}};class an extends fe{name;constructor(t){super(),this.name=t}valOf(t){if(C(this.name))return function(t,e){if(t.has(e))return t.get(e);throw new Error(`Variable ${e} not found in environment`)}(t,this.name);throw new Error("{this.name} is not a valid variable name")}prettyPrint(){return this.name}toString(){return this.prettyPrint()}}function on(t,e){return ln(0,new Map,new Map,t,e)}const cn=-1;function un(t,e,n){return new Map([[e,n],...t])}function hn(t,e){return e.has(t)?e.get(t):cn}function ln(t,e,n,r,s){if(r instanceof an&&s instanceof an){const t=r.name,i=s.name;if(C(t)&&C(i)){const r=hn(t,e),s=hn(i,n);return r!==cn&&s!==cn?r===s:r===cn&&s===cn&&t===i}return!1}return r instanceof _e&&s instanceof _e?r.sym===s.sym:r instanceof be&&s instanceof be||r instanceof ke&&s instanceof ke?ln(t,e,n,r.type,s.type)&&ln(t+1,un(e,r.name,t),un(n,s.name,t),r.body,s.body):r instanceof Ne&&s instanceof Ne?ln(t+1,un(e,r.param,t),un(n,s.param,t),r.body,s.body):r instanceof we&&s instanceof we&&r.type instanceof Me&&s.type instanceof Me||(r instanceof sn&&s instanceof sn?ln(t,e,n,r.fun,s.fun)&&ln(t,e,n,r.arg,s.arg):r instanceof ye&&s instanceof ye||r instanceof de&&s instanceof de||r instanceof me&&s instanceof me||r instanceof xe&&s instanceof xe||r instanceof Me&&s instanceof Me||r instanceof qe&&s instanceof qe||r instanceof Ae&&s instanceof Ae||r instanceof Ye&&s instanceof Ye||r instanceof Re&&s instanceof Re||(r instanceof we&&s instanceof we?ln(t,e,n,r.type,s.type)&&ln(t,e,n,r.expr,s.expr):r instanceof Ie&&s instanceof Ie?ln(t,e,n,r.elemType,s.elemType):r instanceof ge&&s instanceof ge?ln(t,e,n,r.n,s.n):r instanceof ve&&s instanceof ve||r instanceof Ee&&s instanceof Ee||r instanceof Pe&&s instanceof Pe?ln(t,e,n,r.target,s.target)&&ln(t,e,n,r.base,s.base)&&ln(t,e,n,r.step,s.step):r instanceof Te&&s instanceof Te?ln(t,e,n,r.target,s.target)&&ln(t,e,n,r.motive,s.motive)&&ln(t,e,n,r.base,s.base)&&ln(t,e,n,r.step,s.step):r instanceof Se&&s instanceof Se?ln(t,e,n,r.first,s.first)&&ln(t,e,n,r.second,s.second):r instanceof $e&&s instanceof $e||r instanceof Oe&&s instanceof Oe?ln(t,e,n,r.pair,s.pair):r instanceof Le&&s instanceof Le?ln(t,e,n,r.head,s.head)&&ln(t,e,n,r.tail,s.tail):r instanceof Be&&s instanceof Be?ln(t,e,n,r.target,s.target)&&ln(t,e,n,r.base,s.base)&&ln(t,e,n,r.step,s.step):r instanceof Ce&&s instanceof Ce?ln(t,e,n,r.target,s.target)&&ln(t,e,n,r.motive,s.motive)&&ln(t,e,n,r.base,s.base)&&ln(t,e,n,r.step,s.step):r instanceof Ue&&s instanceof Ue?ln(t,e,n,r.target,s.target)&&ln(t,e,n,r.motive,s.motive):r instanceof He&&s instanceof He?ln(t,e,n,r.type,s.type)&&ln(t,e,n,r.left,s.left)&&ln(t,e,n,r.right,s.right):r instanceof De&&s instanceof De?ln(t,e,n,r.type,s.type):r instanceof ze&&s instanceof ze?ln(t,e,n,r.target,s.target)&&ln(t,e,n,r.motive,s.motive)&&ln(t,e,n,r.base,s.base):r instanceof Qe&&s instanceof Qe?ln(t,e,n,r.left,s.left)&&ln(t,e,n,r.right,s.right):r instanceof Fe&&s instanceof Fe?ln(t,e,n,r.target,s.target)&&ln(t,e,n,r.base,s.base)&&ln(t,e,n,r.fun,s.fun):r instanceof Ve&&s instanceof Ve?ln(t,e,n,r.equality,s.equality):r instanceof Ge&&s instanceof Ge?ln(t,e,n,r.target,s.target)&&ln(t,e,n,r.motive,s.motive)&&ln(t,e,n,r.base,s.base):r instanceof Xe&&s instanceof Xe?ln(t,e,n,r.type,s.type)&&ln(t,e,n,r.length,s.length):r instanceof Ke&&s instanceof Ke?ln(t,e,n,r.head,s.head)&&ln(t,e,n,r.tail,s.tail):r instanceof Ze&&s instanceof Ze||r instanceof je&&s instanceof je?ln(t,e,n,r.vec,s.vec):r instanceof We&&s instanceof We?ln(t,e,n,r.length,s.length)&&ln(t,e,n,r.target,s.target)&&ln(t,e,n,r.motive,s.motive)&&ln(t,e,n,r.base,s.base)&&ln(t,e,n,r.step,s.step):r instanceof Je&&s instanceof Je?ln(t,e,n,r.left,s.left)&&ln(t,e,n,r.right,s.right):r instanceof tn&&s instanceof tn||r instanceof en&&s instanceof en?ln(t,e,n,r.value,s.value):r instanceof nn&&s instanceof nn?ln(t,e,n,r.target,s.target)&&ln(t,e,n,r.motive,s.motive)&&ln(t,e,n,r.baseLeft,s.baseLeft)&&ln(t,e,n,r.baseRight,s.baseRight):r instanceof rn&&s instanceof rn&&(function(t,e){return t.startLine===e.startLine&&t.startColumn===e.startColumn&&t.endLine===e.endLine&&t.endColumn===e.endColumn}(r.loc,s.loc)&&ln(t,e,n,r.type,s.type))))}function pn(t,e){t.forInfo}function fn(t,e){const n=t.get(e);return n||e}function wn(t,e,n){return new Map([[e,n],...t])}function yn(t,e,n,r){const s=n.readBackType(t),i=r.readBackType(t);return on(s,i)?new S(void 0):new $(e,new _([`Expected ${i} but got ${s}`]))}function dn(t,e,n,r,s){return on(lt(t,n,r),lt(t,n,s))?new S(void 0):new $(e,new _([`The terms ${r} and ${s} are not the same ${n}.`]))}function mn(t){return gn(t.split(""))}function gn(t){return 0===t.length||(e=t[0],!(!/^[a-zA-Z]$/.test(e)&&"-"!==t[0])&&gn(t.slice(1)));var e}function vn(t,e,n){return new Er(t.location,t,e,n)}class En{source;startLine;startColumn;endLine;endColumn;constructor(t,e,n,r,s){this.source=t,this.startLine=e,this.startColumn=n,this.endLine=r,this.endColumn=s}}class Pn{start;end;source;constructor(t,e,n){this.start=t,this.end=e,this.source=n}}let Tn=class{syntax;forInfo;constructor(t,e){this.syntax=t,this.forInfo=e}locationToSrcLoc(){return new En(this.syntax.source,this.syntax.start.line,this.syntax.start.column,this.syntax.end.line,this.syntax.end.column)}toString(){return`${this.syntax.source}:${this.syntax.start.line}:${this.syntax.start.column}`}};function bn(t){return new Tn(t.syntax,!1)}class Nn{static synthNat(t,e){return new S(new we(new ye,new de))}static synthUniverse(t,e,n){return new $(n,new _(["U is a type, but it does not have a type."]))}static synthArrow(t,e,n,r,s,i){if(0===i.length){const n=M(t,s,"x"),i=new O("Aout"),a=new O("Bout");return L([[i,()=>r.check(t,e,new ce)],[a,()=>s.check(W(t,n,D(t,i.value)),e,new ce)]],(()=>new S(new we(new ye,new be(n,i.value,a.value)))))}{const[a,...o]=i,c=M(t,vn(s,a,o),"x"),u=new O("Aout"),h=new O("tout");return L([[u,()=>r.check(t,e,new ce)],[h,()=>new Cn(bn(n),s,a,o).check(W(t,c,D(t,u.value)),e,new ce)]],(()=>new S(new we(new ye,new be(c,u.value,h.value)))))}}static synthPi(t,e,n,r,s){if(1===r.length){const[n,i]=[r[0].binder,r[0].type],a=q(t,n.varName),o=(n.location,new O("Aout")),c=new O("Bout");return L([[o,()=>i.check(t,e,new ce)],[c,()=>s.check(W(t,a,D(t,o.value)),wn(e,n.varName,a),new ce)]],(()=>(o.value,new S(new we(new ye,new be(a,o.value,c.value))))))}if(r.length>1){const[i,...a]=r,[o,c]=[i.binder,i.type],u=(o.location,o.varName),h=q(t,u),l=new O("Aout"),p=new O("Bout");return L([[l,()=>c.check(t,e,new ce)],[p,()=>new Rn(bn(n),a,s).check(W(t,h,D(t,l.value)),wn(e,u,h),new ce)]],(()=>(l.value,new S(new we(new ye,new be(h,l.value,p.value))))))}throw new Error("Invalid number of binders in Pi type")}static synthZero(t,e){return new S(new we(new de,new me))}static synthAdd1(t,e,n){const r=new O("nout");return L([[r,()=>n.check(t,e,new Qt)]],(()=>new S(new we(new de,new ge(r.value)))))}static synthWhichNat(t,e,n,r,s){const i=new O("tgtout"),a=new O("bout"),o=new O("sout");let c=q(t,"n_minus_1");return L([[i,()=>n.check(t,e,new Qt)],[a,()=>r.synth(t,e)],[o,()=>s.check(t,e,new Gt(c,new Qt,new I(V(t),c,a.value.type)))]],(()=>new S(new we(a.value.type,new ve(i.value,new we(a.value.type,a.value.expr),o.value)))))}static synthIterNat(t,e,n,r,s){const i=new O("tgtout"),a=new O("bout"),o=new O("sout");return L([[i,()=>n.check(t,e,new Qt)],[a,()=>r.synth(t,e)],[o,()=>s.check(t,e,(()=>{const e=q(t,"old");return D(t,new be(e,a.value.type,a.value.type))})())]],(()=>new S(new we(a.value.type,new Ee(i.value,new we(a.value.type,a.value.expr),o.value)))))}static synthRecNat(t,e,n,r,s){const i=new O("tgtout"),a=new O("bout"),o=new O("sout");return L([[i,()=>n.check(t,e,new Qt)],[a,()=>r.synth(t,e)],[o,()=>s.check(t,e,(()=>{const e=q(t,"n_minus_1"),n=q(t,"old");return D(t,new be(e,new de,new be(n,a.value.type,a.value.type)))})())]],(()=>new S(new we(a.value.type,new Pe(i.value,new we(a.value.type,a.value.expr),o.value)))))}static synthIndNat(t,e,n,r,s,i){const a=new O("tgtout"),o=new O("motout"),c=new O("motval"),u=new O("bout"),h=new O("sout");return L([[a,()=>n.check(t,e,new Qt)],[o,()=>r.check(t,e,new Gt("n",new Qt,new B((t=>new ce))))],[c,()=>new S(D(t,o.value))],[u,()=>s.check(t,e,J(c.value,new Ft))],[h,()=>i.check(t,e,new Gt("n_minus_1",new Qt,new B((t=>new Gt("ih",J(c.value,t),new B((e=>J(c.value,new Vt(t)))))))))]],(()=>new S(new we(new sn(o.value,a.value),new Te(a.value,o.value,u.value,h.value)))))}static synthAtom(t,e){return new S(new we(new ye,new xe))}static synthPair(t,e,n,r){const s=q(t,"a"),i=new O("Aout"),a=new O("Dout");return L([[i,()=>n.check(t,e,new ce)],[a,()=>r.check(W(t,s,D(t,i.value)),e,new ce)]],(()=>new S(new we(new ye,new ke(s,i.value,a.value)))))}static synthSigma(t,e,n,r,s){if(1===r.length){const[n,i]=[r[0].binder,r[0].type],a=q(t,n.varName),o=(n.location,new O("Aout")),c=new O("Dout");return L([[o,()=>i.check(t,e,new ce)],[c,()=>s.check(W(t,a,D(t,o.value)),wn(e,n.varName,a),new ce)]],(()=>(o.value,new S(new we(new ye,new ke(a,o.value,c.value))))))}if(r.length>1){const[i,...a]=r,[o,c]=[i.binder,i.type],u=(o.location,o.varName),h=q(t,u),l=new O("Aout"),p=new O("Dout");return L([[l,()=>c.check(t,e,new ce)],[p,()=>new Mn(bn(n),a,s).check(W(t,h,D(t,l.value)),wn(e,u,h),new ce)]],(()=>(l.value,new S(new we(new ye,new ke(h,l.value,p.value))))))}throw new Error("Invalid number of binders in Sigma type")}static synthCar(t,e,n,r){const s=new O("p_rst");return L([[s,()=>r.synth(t,e)]],(()=>{const e=D(t,s.value.type);return e instanceof Kt?new S(new we(e.carType.readBackType(t),new $e(s.value.expr))):new $(n,new _([`car requires a Pair type, but was used as a: ${e}.`]))}))}static synthCdr(t,e,n,r){const s=new O("pout");return L([[s,()=>r.synth(t,e)]],(()=>{const e=D(t,s.value.type);if(e instanceof Kt){const[n,r,i]=[e.carName,e.carType,e.cdrType];return new S(new we(i.valOfClosure(rt(D(t,s.value.expr))).readBackType(t),new Oe(s.value.expr)))}return new $(n,new _([`cdr requires a Pair type, but was used as a: ${e}.`]))}))}static synthQuote(t,e,n,r){return mn(r)?new S(new we(new xe,new _e(r))):new $(n,new _([`Invalid atom: ${r}. Atoms consist of letters and hyphens.`]))}static synthTrivial(t,e){return new S(new we(new ye,new Re))}static synthSole(t,e){return new S(new we(new Re,new qe))}static synthIndList(t,e,n,r,s,i,a){const o=new O("tgtout"),c=new O("motout"),u=new O("motval"),h=new O("bout"),l=new O("sout");return L([[o,()=>r.synth(t,e)]],(()=>{const[r,p]=[o.value.type,o.value.expr],f=D(t,r);if(f instanceof Zt){const n=f.entryType;return L([[c,()=>s.check(t,e,new Gt("xs",new Zt(n),new I(V(t),"xs",new ye)))],[u,()=>new S(D(t,c.value))],[h,()=>i.check(t,e,J(u.value,new jt))],[l,()=>a.check(t,e,new Gt("e",n,new B((t=>new Gt("es",new Zt(n),new B((e=>new Gt("ih",J(u.value,e),new B((n=>J(u.value,new Wt(t,e))))))))))))]],(()=>new S(new we(new sn(c.value,p),new Ce(p,c.value,h.value,l.value)))))}return new $(n,new _([`Not a List: ${f.readBackType(t)}.`]))}))}static synthRecList(t,e,n,r,s,i){const a=new O("tgtout");return L([[a,()=>r.synth(t,e)]],(()=>{const[r,o]=[a.value.type,a.value.expr],c=D(t,r);if(c instanceof Zt){const n=c.entryType,r=new O("bout"),a=new O("btval"),u=new O("sout");return L([[r,()=>s.synth(t,e)],[a,()=>new S(D(t,r.value.type))],[u,()=>i.check(t,e,new Gt("e",n,new B((t=>new Gt("es",new Zt(n),new B((t=>new Gt("ih",a.value,new B((t=>a.value))))))))))]],(()=>new S(new we(r.value.type,new Be(o,new we(r.value.type,r.value.expr),u.value)))))}return new $(n,new _([`Not a List: ${c.readBackType(t)}.`]))}))}static synthList(t,e,n){const r=new O("Eout");return L([[r,()=>n.entryType.check(t,e,new ce)]],(()=>new S(new we(new ye,new Ie(r.value)))))}static synthListCons(t,e,n,r){const s=new O("eout"),i=new O("esout");return L([[s,()=>n.synth(t,e)],[i,()=>r.check(t,e,D(t,new Ie(s.value.type)))]],(()=>new S(new we(new Ie(s.value.type),new Le(s.value.expr,i.value)))))}static synthAbsurd(t,e,n){return new S(new we(new ye,new Me))}static synthIndAbsurd(t,e,n){const r=new O("tgtout"),s=new O("motout");return L([[r,()=>n.target.check(t,e,new pe)],[s,()=>n.motive.check(t,e,new ce)]],(()=>new S(new we(s.value,new Ue(r.value,s.value)))))}static synthEqual(t,e,n,r,s){const i=new O("Aout"),a=new O("Av"),o=new O("from_out"),c=new O("to_out");return L([[i,()=>n.check(t,e,new ce)],[a,()=>new S(D(t,i.value))],[o,()=>r.check(t,e,a.value)],[c,()=>s.check(t,e,a.value)]],(()=>new S(new we(new ye,new He(i.value,o.value,c.value)))))}static synthReplace(t,e,n,r,s,i){const a=new O("tgt_rst"),o=new O("motout"),c=new O("bout");return L([[a,()=>r.synth(t,e)]],(()=>{const r=D(t,a.value.type);if(r instanceof Jt){const[n,u,h]=[r.type,r.from,r.to];return L([[o,()=>s.check(t,e,new Gt("x",n,new B((t=>new ce))))],[c,()=>i.check(t,e,J(D(t,o.value),u))]],(()=>new S(new we(J(D(t,o.value),h).readBackType(t),new ze(a.value.expr,o.value,c.value)))))}return new $(n,new _([`Expected an expression with = type, but the type was: ${a.value.type}.`]))}))}static synthTrans(t,e,n,r,s){const i=new O("p1_rst"),a=new O("p2_rst");return L([[i,()=>r.synth(t,e)],[a,()=>s.synth(t,e)]],(()=>{const e=D(t,i.value.type),r=D(t,a.value.type);if(e instanceof Jt&&r instanceof Jt){const[s,o,c]=[e.type,e.from,e.to],[u,h,l]=[r.type,r.from,r.to];return L([[new O("_"),()=>yn(t,n,s,u)],[new O("_"),()=>dn(t,n,s,c,h)]],(()=>new S(new we(new Jt(s,o,l).readBackType(t),new Qe(i.value.expr,a.value.expr)))))}return new $(n,new _([`Expected =, got ${e} and ${r}.`]))}))}static synthCong(t,e,n,r,s){const i=new O("bout"),a=new O("f_rst");return L([[i,()=>r.synth(t,e)],[a,()=>s.synth(t,e)]],(()=>{const e=D(t,i.value.type),r=D(t,a.value.type);if(e instanceof Jt){const[s,o,c]=[e.type,e.from,e.to];if(r instanceof Gt){const[e,u,h]=[r.argName,r.argType,r.resultType],l=new O("ph"),p=new O("Cv"),f=new O("fv");return L([[l,()=>yn(t,n,s,u)],[p,()=>new S(h.valOfClosure(o))],[f,()=>new S(D(t,a.value.expr))]],(()=>new S(new we(new He(p.value.readBackType(t),lt(t,p.value,J(f.value,o)),lt(t,p.value,J(f.value,c))),new Fe(i.value.expr,p.value.readBackType(t),a.value.expr)))))}return new $(n,new _([`Expected a function type, got ${r.readBackType(t)}.`]))}return new $(n,new _([`Expected an = type, got ${e.readBackType(t)}.`]))}))}static synthSymm(t,e,n,r){const s=new O("eout");return L([[s,()=>r.synth(t,e)]],(()=>{const e=D(t,s.value.type);if(e instanceof Jt){const[n,r,i]=[e.type,e.from,e.to];return new S(new we(new Jt(n,i,r).readBackType(t),new Ve(s.value.expr)))}return new $(n,new _([`Expected an = type, got ${e.readBackType(t)}.`]))}))}static synthIndEqual(t,e,n,r,s,i){const a=new O("tgtout"),o=new O("motout"),c=new O("motv"),u=new O("baseout");return L([[a,()=>r.synth(t,e)]],(()=>{const r=D(t,a.value.type);if(r instanceof Jt){const[n,h,l]=[r.type,r.from,r.to];return L([[o,()=>s.check(t,e,new Gt("to",n,new B((t=>new Gt("p",new Jt(n,h,t),new B((t=>new ce)))))))],[c,()=>new S(D(t,o.value))],[u,()=>i.check(t,e,J(J(c.value,h),new te(h)))]],(()=>new S(new we(J(J(c.value,l),D(t,a.value.expr)).readBackType(t),new Ge(a.value.expr,o.value,u.value)))))}return new $(n,new _([`Expected evidence of equality, got ${r.readBackType(t)}.`]))}))}static synthVec(t,e,n,r){const s=new O("tout"),i=new O("lenout");return L([[s,()=>n.check(t,e,new ce)],[i,()=>r.check(t,e,new Qt)]],(()=>new S(new we(new ye,new Xe(s.value,i.value)))))}static synthHead(t,e,n,r){const s=new O("vout");return L([[s,()=>r.synth(t,e)]],(()=>{const e=D(t,s.value.type).now();if(e instanceof ee){const[r,i]=[e.entryType,e.length];return i.now()instanceof Vt?new S(new we(r.readBackType(t),new Ze(s.value.expr))):new $(n,new _([`Expected a Vec with add1 at the top of the length, got ${lt(t,new Qt,i)}.`]))}return new $(n,new _([`Expected a Vec, got ${e.readBackType(t)}.`]))}))}static synthTail(t,e,n,r){const s=new O("vout");return L([[s,()=>r.synth(t,e)]],(()=>{const e=D(t,s.value.type).now();if(e instanceof ee){const[r,i]=[e.entryType,e.length],a=i.now();if(a instanceof Vt){const e=a.smaller;return new S(new we(new Xe(r.readBackType(t),lt(t,new Qt,e)),new je(s.value.expr)))}return new $(n,new _([`Expected a Vec with add1 at the top of the length, got ${lt(t,new Qt,i)}.`]))}return new $(n,new _([`Expected a Vec, got ${e.readBackType(t)}.`]))}))}static synthIndVec(t,e,n,r,s,i,a,o){const c=new O("lenout"),u=new O("lenv"),h=new O("vecout"),l=new O("motout"),p=new O("motval"),f=new O("bout"),w=new O("sout");return L([[c,()=>r.check(t,e,new Qt)],[u,()=>new S(D(t,c.value))],[h,()=>s.synth(t,e)]],(()=>{const r=D(t,h.value.type);if(r instanceof ee){const[s,y]=[r.entryType,r.length];return L([[new O("_"),()=>dn(t,n,new Qt,u.value,y)],[l,()=>i.check(t,e,new Gt("k",new Qt,new B((t=>new Gt("es",new ee(s,t),new B((t=>new ce)))))))],[p,()=>new S(D(t,l.value))],[f,()=>a.check(t,e,J(J(p.value,new Ft),new ne))],[w,()=>o.check(t,e,ct(s,p.value))]],(()=>new S(new we(new sn(new sn(l.value,c.value),h.value.expr),new We(c.value,h.value.expr,l.value,f.value,w.value)))))}return new $(n,new _([`Expected a Vec, got ${r.readBackType(t)}.`]))}))}static synthEither(t,e,n,r){const s=new O("Lout"),i=new O("Rout");return L([[s,()=>n.check(t,e,new ce)],[i,()=>r.check(t,e,new ce)]],(()=>new S(new we(new ye,new Je(s.value,i.value)))))}static synthIndEither(t,e,n,r,s,i,a){const o=new O("tgtout"),c=new O("motout"),u=new O("motval"),h=new O("lout"),l=new O("rout");return L([[o,()=>r.synth(t,e)]],(()=>{const r=D(t,o.value.type);if(r instanceof se){const[n,p]=[r.leftType,r.rightType];return L([[c,()=>s.check(t,e,new Gt("x",new se(n,p),new B((t=>new ce))))],[u,()=>new S(D(t,c.value))],[h,()=>i.check(t,e,new Gt("x",n,new B((t=>J(u.value,new ie(t))))))],[l,()=>a.check(t,e,new Gt("x",p,new B((t=>J(u.value,new ae(t))))))]],(()=>new S(new we(new sn(c.value,o.value.expr),new nn(o.value.expr,c.value,h.value,l.value)))))}return new $(n,new _([`Expected an Either, but got a ${r.readBackType(t)}.`]))}))}static synthThe(t,e,n,r){const s=new O("t_out"),i=new O("e_out");return L([[s,()=>n.isType(t,e)],[i,()=>r.check(t,e,D(t,s.value))]],(()=>new S(new we(s.value,i.value))))}static synthApplication(t,e,n,r,s,i){if(0===i.length){const i=new O("fout");return L([[i,()=>r.synth(t,e)]],(()=>{const r=D(t,i.value.type);if(r instanceof Gt){const[n,a,o]=[r.argName,r.argType,r.resultType],c=new O("argout");return L([[c,()=>s.check(t,e,a)]],(()=>new S(new we(o.valOfClosure(D(t,c.value)).readBackType(t),new sn(i.value.expr,c.value)))))}return new $(n,new _([`Not a function type: ${r.readBackType(t)}.`]))}))}{const a=new O("appout");return L([[a,()=>new Er(bn(n),r,s,i.slice(0,i.length-1)).synth(t,e)]],(()=>{const r=D(t,a.value.type);if(r instanceof Gt){const[n,s,o]=[r.argName,r.argType,r.resultType],c=new O("fout");return L([[c,()=>i[i.length-1].check(t,e,s)]],(()=>new S(new we(o.valOfClosure(D(t,c.value)).readBackType(t),new sn(a.value.expr,c.value)))))}return new $(n,new _([`Not a function type: ${r.readBackType(t)}.`]))}))}}static synthName(t,e,n,r){const s=fn(e,r),i=new O("x_tv");return L([[i,()=>j(t,0,s)]],(()=>(t.get(s),new S(new we(i.value.readBackType(t),new an(s))))))}static synthNumber(t,e,n,r){if(0===r)return new S(new we(new de,new me));if(r>0){const s=new O("n_1_out");return L([[s,()=>new Yn(n,r-1).check(t,e,new Qt)]],(()=>new S(new we(new de,new ge(s.value)))))}return new $(n,new _([`Expected a positive number, got ${r}.`]))}}class xn{location;constructor(t){this.location=t}isType(t,e){const n=new O("ok"),r=this.getType(t,e);return L([[n,()=>r]],(()=>(pn(this.location,n.value),new S(n.value))))}getType(t,e){const n=this.check(t,e,new ce);if(n instanceof S)return n;if(n instanceof $){if(this instanceof Un&&C(this.name)){const e=new O("other-tv");return new L([[e,()=>j(t,this.location,this.name)]],(()=>{new $(this.location,new _([`Expected , but given ${e.value.readBackType(t)}`]))}))}return new $(this.location,new _(["not a type"]))}throw new Error("Invalid checkType")}check(t,e,n){const r=new O("ok"),s=this.checkOut(t,e,n);return L([[r,()=>s]],(()=>new S(r.value)))}synth(t,e){const n=new O("ok");return L([[n,()=>this.synthHelper(t,e)]],(()=>(pn(this.location,n.value.type),new S(n.value))))}checkOut(t,e,n){const r=new O("theT");return L([[r,()=>this.synth(t,e)],[new O("_"),()=>yn(t,this.location,D(t,r.value.type),n)]],(()=>new S(r.value.expr)))}}class _n extends xn{location;type;value;constructor(t,e,n){super(t),this.location=t,this.type=e,this.value=n}synthHelper(t,e){return Nn.synthThe(t,e,this.type,this.value)}findNames(){return this.type.findNames().concat(this.value.findNames())}prettyPrint(){return`(the ${this.type.prettyPrint()} ${this.value.prettyPrint()})`}toString(){return this.prettyPrint()}}class kn extends xn{location;constructor(t){super(t),this.location=t}synthHelper(t,e){return Nn.synthUniverse(t,e,this.location)}findNames(){return[]}getType(t,e){return new S(new ye)}prettyPrint(){return"U"}toString(){return this.prettyPrint()}}class Sn extends xn{location;constructor(t){super(t),this.location=t}synthHelper(t,e){return Nn.synthNat(t,e)}findNames(){return[]}getType(t,e){return new S(new de)}prettyPrint(){return"Nat"}toString(){return this.prettyPrint()}}class $n extends xn{location;constructor(t){super(t),this.location=t}synthHelper(t,e){return Nn.synthZero(t,e)}findNames(){return[]}prettyPrint(){return"zero"}toString(){return this.prettyPrint()}}class On extends xn{location;base;constructor(t,e){super(t),this.location=t,this.base=e}synthHelper(t,e){return Nn.synthAdd1(t,e,this.base)}findNames(){return this.base.findNames()}prettyPrint(){return`(add1 ${this.base.prettyPrint()})`}toString(){return this.prettyPrint()}}class Ln extends xn{location;target;base;step;constructor(t,e,n,r){super(t),this.location=t,this.target=e,this.base=n,this.step=r}synthHelper(t,e){return Nn.synthWhichNat(t,e,this.target,this.base,this.step)}findNames(){return this.target.findNames().concat(this.base.findNames()).concat(this.step.findNames())}prettyPrint(){return`(which-nat ${this.target.prettyPrint()} \n              ${this.base.prettyPrint()} \n              ${this.step.prettyPrint()})`}toString(){return this.prettyPrint()}}class An extends xn{location;target;base;step;constructor(t,e,n,r){super(t),this.location=t,this.target=e,this.base=n,this.step=r}synthHelper(t,e){return Nn.synthIterNat(t,e,this.target,this.base,this.step)}findNames(){return this.target.findNames().concat(this.base.findNames()).concat(this.step.findNames())}prettyPrint(){return`(iter-nat ${this.target.prettyPrint()} \n              ${this.base.prettyPrint()} \n              ${this.step.prettyPrint()})`}toString(){return this.prettyPrint()}}class In extends xn{location;target;base;step;constructor(t,e,n,r){super(t),this.location=t,this.target=e,this.base=n,this.step=r}synthHelper(t,e){return Nn.synthRecNat(t,e,this.target,this.base,this.step)}findNames(){return this.target.findNames().concat(this.base.findNames()).concat(this.step.findNames())}prettyPrint(){return`(rec-nat ${this.target.prettyPrint()} \n              ${this.base.prettyPrint()} \n              ${this.step.prettyPrint()})`}toString(){return this.prettyPrint()}}class Bn extends xn{location;target;motive;base;step;constructor(t,e,n,r,s){super(t),this.location=t,this.target=e,this.motive=n,this.base=r,this.step=s}synthHelper(t,e){return Nn.synthIndNat(t,e,this.target,this.motive,this.base,this.step)}findNames(){return this.target.findNames().concat(this.motive.findNames()).concat(this.base.findNames()).concat(this.step.findNames())}prettyPrint(){return`(ind-nat ${this.target.prettyPrint()} \n              ${this.motive.prettyPrint()} \n              ${this.base.prettyPrint()} \n              ${this.step.prettyPrint()})`}toString(){return this.prettyPrint()}}class Cn extends xn{location;arg1;arg2;args;constructor(t,e,n,r){super(t),this.location=t,this.arg1=e,this.arg2=n,this.args=r}synthHelper(t,e){return Nn.synthArrow(t,e,this.location,this.arg1,this.arg2,this.args)}findNames(){return this.arg1.findNames().concat(this.arg2.findNames()).concat(this.args.flatMap((t=>t.findNames())))}getType(t,e){const[n,r,s]=[this.arg1,this.arg2,this.args];if(0===s.length){const s=M(t,r,"x"),i=new O("Aout"),a=new O("Bout");return L([[i,()=>n.isType(t,e)],[a,()=>r.isType(W(t,s,D(t,i.value)),e)]],(()=>new S(new be(s,i.value,a.value))))}{const[i,...a]=s,o=M(t,vn(r,i,a),"x"),c=new O("Aout"),u=new O("tout");return L([[c,()=>n.isType(t,e)],[u,()=>new Cn(bn(this.location),r,i,a).isType(W(t,o,D(t,c.value)),e)]],(()=>new S(new be(o,c.value,u.value))))}}prettyPrint(){return`(-> ${this.arg1.prettyPrint()} ${this.arg2.prettyPrint()} ${this.args.map((t=>t.prettyPrint())).join(" ")})`}toString(){return this.prettyPrint()}}class Rn extends xn{location;binders;body;constructor(t,e,n){super(t),this.location=t,this.binders=e,this.body=n}synthHelper(t,e){return Nn.synthPi(t,e,this.location,this.binders,this.body)}findNames(){return this.binders.flatMap((t=>U(t))).concat(this.body.findNames())}getType(t,e){const[n,r]=[this.binders,this.body];if(1===n.length){const[s,i]=[n[0].binder,n[0].type],a=q(t,s.varName),o=(s.location,new O("Aout")),c=new O("Aoutv"),u=new O("Bout");return L([[o,()=>i.isType(t,e)],[c,()=>new S(D(t,o.value))],[u,()=>r.isType(W(t,a,c.value),wn(e,s.varName,a))]],(()=>(o.value,new S(new be(a,o.value,u.value)))))}if(n.length>1){const[s,...i]=n,[a,o]=[s.binder.varName,s.type],c=q(t,a),u=(s.binder.location,new O("Aout")),h=new O("Aoutv"),l=new O("Bout");return L([[u,()=>o.isType(t,e)],[h,()=>new S(D(t,u.value))],[l,()=>new Rn(bn(this.location),i,r).isType(W(t,c,h.value),wn(e,s.binder.varName,c))]],(()=>(u.value,new S(new be(c,u.value,l.value)))))}throw new Error("Invalid number of binders in Pi type")}prettyPrint(){return`(Π ${this.binders.map((t=>`(${t.binder.varName} ${t.type.prettyPrint()})`)).join(" ")} \n            ${this.body.prettyPrint()})`}toString(){return this.prettyPrint()}}class qn extends xn{location;binders;body;constructor(t,e,n){super(t),this.location=t,this.binders=e,this.body=n}synthHelper(t,e){throw new Error("Method not implemented.")}findNames(){return this.binders.map((t=>t.varName)).concat(this.body.findNames())}checkOut(t,e,n){if(1===this.binders.length){const r=this.body,s=this.binders[0],i=s.varName,a=s.location,o=n.now();if(o instanceof Gt){const n=o.argType,s=o.resultType,a=fn(e,i),c=new O("bout");return L([[c,()=>r.check(W(t,a,n),wn(e,i,a),s.valOfClosure(new oe(n,new wt(a))))]],(()=>(n.readBackType(t),new S(new Ne(a,c.value)))))}return new $(a,new _([`Not a function type: ${o.readBackType(t)}.`]))}return new qn(this.location,[this.binders[0]],new qn(bn(this.location),this.binders.slice(1),this.body)).check(t,e,n)}prettyPrint(){return`(lambda ${this.binders.map((t=>t.varName)).join(" ")} ${this.body.prettyPrint()})`}toString(){return this.prettyPrint()}}class Mn extends xn{location;binders;body;constructor(t,e,n){super(t),this.location=t,this.binders=e,this.body=n}synthHelper(t,e){return Nn.synthSigma(t,e,this.location,this.binders,this.body)}findNames(){return this.binders.flatMap((t=>U(t))).concat(this.body.findNames())}getType(t,e){const[n,r]=[this.binders,this.body];if(1===n.length){const[s,i]=[n[0].binder,n[0].type],a=s.varName,o=q(t,a),c=(s.location,new O("Aout")),u=new O("Aoutv"),h=new O("Dout");return L([[c,()=>i.isType(t,e)],[u,()=>new S(D(t,c.value))],[h,()=>r.isType(W(t,o,u.value),wn(e,a,o))]],(()=>(c.value,new S(new ke(o,c.value,h.value)))))}if(n.length>1){const[[s,i],...a]=[[n[0].binder,n[0].type],n[1],...n.slice(2)],o=s.varName,c=q(t,o),u=(s.location,new O("Aout")),h=new O("Aoutv"),l=new O("Dout");return L([[u,()=>i.isType(t,e)],[h,()=>new S(D(t,u.value))],[l,()=>new Mn(this.location,a,r).isType(W(t,o,h.value),wn(e,o,c))]],(()=>(u.value,new S(new ke(c,u.value,l.value)))))}throw new Error("Invalid number of binders in Sigma type")}prettyPrint(){return`(Σ ${this.binders.map((t=>`(${t.binder.varName} ${t.type.prettyPrint()})`)).join(" ")} \n            ${this.body.prettyPrint()})`}toString(){return this.prettyPrint()}}class Un extends xn{location;name;constructor(t,e){super(t),this.location=t,this.name=e}synthHelper(t,e){return Nn.synthName(t,e,this.location,this.name)}findNames(){return[this.name]}prettyPrint(){return this.name}toString(){return this.prettyPrint()}}class Hn extends xn{location;constructor(t){super(t),this.location=t}synthHelper(t,e){return Nn.synthAtom(t,e)}findNames(){return[]}getType(t,e){return new S(new xe)}prettyPrint(){return"Atom"}toString(){return this.prettyPrint()}}class Dn extends xn{location;name;constructor(t,e){super(t),this.location=t,this.name=e}synthHelper(t,e){return Nn.synthQuote(t,e,this.location,this.name)}findNames(){return[]}prettyPrint(){return`'${this.name}`}toString(){return this.prettyPrint()}}class zn extends xn{location;first;second;constructor(t,e,n){super(t),this.location=t,this.first=e,this.second=n}synthHelper(t,e){return Nn.synthPair(t,e,this.first,this.second)}findNames(){return this.first.findNames().concat(this.second.findNames())}getType(t,e){const n=new O("Aout"),r=new O("Dout"),s=M(t,this.second,"x");return L([[n,()=>this.first.isType(t,e)],[r,()=>this.second.isType(W(t,s,D(t,n.value)),e)]],(()=>new S(new ke(s,n.value,r.value))))}prettyPrint(){return`(Pair ${this.first.prettyPrint()} ${this.second.prettyPrint()})`}toString(){return this.prettyPrint()}}class Qn extends xn{location;first;second;constructor(t,e,n){super(t),this.location=t,this.first=e,this.second=n}synthHelper(t,e){throw new Error("Method not implemented.")}findNames(){return this.first.findNames().concat(this.second.findNames())}checkOut(t,e,n){const r=n.now();if(r instanceof Kt){const n=r.carType,s=r.cdrType,i=new O("aout"),a=new O("dout");return L([[i,()=>this.first.check(t,e,n)],[a,()=>this.second.check(t,e,s.valOfClosure(D(t,i.value)))]],(()=>new S(new Se(i.value,a.value))))}return new $(this.location,new _([`cons requires a Pair or Σ type, but was used as a: ${r.readBackType(t)}.`]))}prettyPrint(){return`(cons ${this.first.prettyPrint()} ${this.second.prettyPrint()})`}toString(){return this.prettyPrint()}}class Fn extends xn{location;pair;constructor(t,e){super(t),this.location=t,this.pair=e}synthHelper(t,e){return Nn.synthCar(t,e,this.location,this.pair)}findNames(){return this.pair.findNames()}prettyPrint(){return`(car ${this.pair.prettyPrint()})`}toString(){return this.prettyPrint()}}class Vn extends xn{location;pair;constructor(t,e){super(t),this.location=t,this.pair=e}synthHelper(t,e){return Nn.synthCdr(t,e,this.location,this.pair)}findNames(){return this.pair.findNames()}prettyPrint(){return`(cdr ${this.pair.prettyPrint()})`}toString(){return this.prettyPrint()}}class Gn extends xn{location;constructor(t){super(t),this.location=t}synthHelper(t,e){return Nn.synthTrivial(t,e)}findNames(){return[]}getType(t,e){return new S(new Re)}prettyPrint(){return"Trivial"}toString(){return this.prettyPrint()}}class Xn extends xn{location;constructor(t){super(t),this.location=t}synthHelper(t,e){return Nn.synthSole(t,e)}findNames(){return[]}prettyPrint(){return"Sole"}}class Kn extends xn{location;constructor(t){super(t),this.location=t}synthHelper(t,e){throw new Error("Method not implemented.")}findNames(){return[]}checkOut(t,e,n){const r=n.now();return r instanceof Zt?new S(new Ae):new $(this.location,new _([`nil requires a List type, but was used as a: ${r.readBackType(t)}.`]))}prettyPrint(){return"nil"}toString(){return this.prettyPrint()}}let Yn=class extends xn{location;value;constructor(t,e){super(t),this.location=t,this.value=e}synthHelper(t,e){return Nn.synthNumber(t,e,this.location,this.value)}findNames(){return[]}prettyPrint(){return`${this.value}`}toString(){return this.prettyPrint()}};class Zn extends xn{location;entryType;constructor(t,e){super(t),this.location=t,this.entryType=e}synthHelper(t,e){return Nn.synthList(t,e,this)}findNames(){return this.entryType.findNames()}getType(t,e){const n=new O("Eout");return L([[n,()=>this.entryType.isType(t,e)]],(()=>new S(new Ie(n.value))))}prettyPrint(){return`(List ${this.entryType.prettyPrint()})`}toString(){return this.prettyPrint()}}class jn extends xn{location;x;xs;constructor(t,e,n){super(t),this.location=t,this.x=e,this.xs=n}synthHelper(t,e){return Nn.synthListCons(t,e,this.x,this.xs)}findNames(){return this.x.findNames().concat(this.xs.findNames())}prettyPrint(){return`(:: ${this.x.prettyPrint()} ${this.xs.prettyPrint()})`}toString(){return this.prettyPrint()}}class Wn extends xn{location;target;base;step;constructor(t,e,n,r){super(t),this.location=t,this.target=e,this.base=n,this.step=r}synthHelper(t,e){return Nn.synthRecList(t,e,this.location,this.target,this.base,this.step)}findNames(){return this.target.findNames().concat(this.base.findNames()).concat(this.step.findNames())}prettyPrint(){return`(rec-list ${this.target.prettyPrint()} \n              ${this.base.prettyPrint()} \n              ${this.step.prettyPrint()})`}toString(){return this.prettyPrint()}}class Jn extends xn{location;target;motive;base;step;constructor(t,e,n,r,s){super(t),this.location=t,this.target=e,this.motive=n,this.base=r,this.step=s}synthHelper(t,e){return Nn.synthIndList(t,e,this.location,this.target,this.motive,this.base,this.step)}findNames(){return this.target.findNames().concat(this.motive.findNames()).concat(this.base.findNames()).concat(this.step.findNames())}prettyPrint(){return`(ind-list ${this.target.prettyPrint()} \n              ${this.motive.prettyPrint()} \n              ${this.base.prettyPrint()} \n              ${this.step.prettyPrint()})`}toString(){return this.prettyPrint()}}class tr extends xn{location;constructor(t){super(t),this.location=t}synthHelper(t,e){return Nn.synthAbsurd(t,e,this)}findNames(){return[]}getType(t,e){return new S(new Me)}prettyPrint(){return"Absurd"}toString(){return this.prettyPrint()}}class er extends xn{location;target;motive;constructor(t,e,n){super(t),this.location=t,this.target=e,this.motive=n}synthHelper(t,e){return Nn.synthIndAbsurd(t,e,this)}findNames(){return this.target.findNames().concat(this.motive.findNames())}prettyPrint(){return`(ind-Absurd \n              ${this.target.prettyPrint()} \n              ${this.motive.prettyPrint()})`}toString(){return this.prettyPrint()}}class nr extends xn{location;type;left;right;constructor(t,e,n,r){super(t),this.location=t,this.type=e,this.left=n,this.right=r}synthHelper(t,e){return Nn.synthEqual(t,e,this.type,this.left,this.right)}findNames(){return this.type.findNames().concat(this.left.findNames()).concat(this.right.findNames())}getType(t,e){const[n,r,s]=[this.type,this.left,this.right],i=new O("Aout"),a=new O("Av"),o=new O("from_out"),c=new O("to_out");return L([[i,()=>n.isType(t,e)],[a,()=>new S(D(t,i.value))],[o,()=>r.check(t,e,a.value)],[c,()=>s.check(t,e,a.value)]],(()=>new S(new He(i.value,o.value,c.value))))}prettyPrint(){return`(= ${this.type.prettyPrint()} \n              ${this.left.prettyPrint()} \n              ${this.right.prettyPrint()})`}toString(){return this.prettyPrint()}}class rr extends xn{location;type;constructor(t,e){super(t),this.location=t,this.type=e}findNames(){return this.type.findNames()}synthHelper(t,e){throw new Error("Method not implemented.")}checkOut(t,e,n){const r=n.now();if(r instanceof Jt){const n=r.type,s=r.from,i=r.to,a=new O("cout"),o=new O("val");return L([[a,()=>this.type.check(t,e,n)],[o,()=>new S(D(t,a.value))],[new O("_"),()=>dn(t,this.type.location,n,s,o.value)],[new O("_"),()=>dn(t,this.type.location,n,i,o.value)]],(()=>new S(new De(a.value))))}return new $(this.location,new _([`same requires an Equal type, but was used as a: ${r.readBackType(t)}.`]))}prettyPrint(){return`(same ${this.type.prettyPrint()})`}toString(){return this.prettyPrint()}}class sr extends xn{location;target;motive;base;constructor(t,e,n,r){super(t),this.location=t,this.target=e,this.motive=n,this.base=r}synthHelper(t,e){return Nn.synthReplace(t,e,this.location,this.target,this.motive,this.base)}findNames(){return this.target.findNames().concat(this.motive.findNames()).concat(this.base.findNames())}prettyPrint(){return`(replace ${this.target.prettyPrint()} \n              ${this.motive.prettyPrint()} \n              ${this.base.prettyPrint()})`}toString(){return this.prettyPrint()}}class ir extends xn{location;left;right;synthHelper(t,e){return Nn.synthTrans(t,e,this.location,this.left,this.right)}constructor(t,e,n){super(t),this.location=t,this.left=e,this.right=n}findNames(){return this.left.findNames().concat(this.right.findNames())}prettyPrint(){return`(trans ${this.left.prettyPrint()} ${this.right.prettyPrint()})`}toString(){return this.prettyPrint()}}class ar extends xn{location;target;fun;constructor(t,e,n){super(t),this.location=t,this.target=e,this.fun=n}synthHelper(t,e){return Nn.synthCong(t,e,this.location,this.target,this.fun)}findNames(){return this.target.findNames().concat(this.fun.findNames())}prettyPrint(){return`(cong ${this.target.prettyPrint()} ${this.fun.prettyPrint()})`}toString(){return this.prettyPrint()}}class or extends xn{location;equality;constructor(t,e){super(t),this.location=t,this.equality=e}synthHelper(t,e){return Nn.synthSymm(t,e,this.location,this.equality)}findNames(){return this.equality.findNames()}prettyPrint(){return`(symm ${this.equality.prettyPrint()})`}toString(){return this.prettyPrint()}}class cr extends xn{location;target;motive;base;constructor(t,e,n,r){super(t),this.location=t,this.target=e,this.motive=n,this.base=r}synthHelper(t,e){return Nn.synthIndEqual(t,e,this.location,this.target,this.motive,this.base)}findNames(){return this.target.findNames().concat(this.motive.findNames()).concat(this.base.findNames())}prettyPrint(){return`(ind-= ${this.target.prettyPrint()} \n              ${this.motive.prettyPrint()} \n              ${this.base.prettyPrint()})`}toString(){return this.prettyPrint()}}class ur extends xn{location;type;length;constructor(t,e,n){super(t),this.location=t,this.type=e,this.length=n}synthHelper(t,e){return Nn.synthVec(t,e,this.type,this.length)}findNames(){return this.type.findNames().concat(this.length.findNames())}getType(t,e){const n=new O("Eout"),r=new O("lenout");return L([[n,()=>this.type.isType(t,e)],[r,()=>this.length.check(t,e,new Qt)]],(()=>new S(new Xe(n.value,r.value))))}prettyPrint(){return`(Vec ${this.type.prettyPrint()} ${this.length.prettyPrint()})`}toString(){return this.prettyPrint()}}class hr extends xn{location;constructor(t){super(t),this.location=t}synthHelper(t,e){throw new Error("Method not implemented.")}findNames(){return[]}checkOut(t,e,n){const r=n.now();if(r instanceof ee){return r.length.now()instanceof Ft?new S(new Ye):new $(this.location,new _([`vecnil requires a Vec type with length ZERO, but was used as a: \n          ${lt(t,new Qt,r.length)}.`]))}return new $(this.location,new _([`vecnil requires a Vec type, but was used as a: ${r.readBackType(t)}.`]))}prettyPrint(){return"vecnil"}toString(){return this.prettyPrint()}}class lr extends xn{location;x;xs;constructor(t,e,n){super(t),this.location=t,this.x=e,this.xs=n}synthHelper(t,e){throw new Error("Method not implemented.")}findNames(){return this.x.findNames().concat(this.xs.findNames())}checkOut(t,e,n){const r=n.now();if(r instanceof ee){const n=r.length.now();if(n instanceof Vt){const s=new O("hout"),i=new O("tout"),a=n.smaller;return L([[s,()=>this.x.check(t,e,r.entryType)],[i,()=>this.xs.check(t,e,new ee(r.entryType,a))]],(()=>new S(new Ke(s.value,i.value))))}return new $(this.location,new _([`vec:: requires a Vec type with length Add1, but was used with a: \n          ${lt(t,new Qt,r.length)}.`]))}return new $(this.location,new _([`vec:: requires a Vec type, but was used as a: ${r.readBackType(t)}.`]))}prettyPrint(){return`(vec:: ${this.x.prettyPrint()} ${this.xs.prettyPrint()})`}toString(){return this.prettyPrint()}}class pr extends xn{location;vec;constructor(t,e){super(t),this.location=t,this.vec=e}synthHelper(t,e){return Nn.synthHead(t,e,this.location,this.vec)}findNames(){return this.vec.findNames()}prettyPrint(){return`(head ${this.vec.prettyPrint()})`}toString(){return this.prettyPrint()}}class fr extends xn{location;vec;constructor(t,e){super(t),this.location=t,this.vec=e}synthHelper(t,e){return Nn.synthTail(t,e,this.location,this.vec)}findNames(){return this.vec.findNames()}prettyPrint(){return`(tail ${this.vec.prettyPrint()})`}toString(){return this.prettyPrint()}}class wr extends xn{location;length;target;motive;base;step;constructor(t,e,n,r,s,i){super(t),this.location=t,this.length=e,this.target=n,this.motive=r,this.base=s,this.step=i}synthHelper(t,e){return Nn.synthIndVec(t,e,this.location,this.length,this.target,this.motive,this.base,this.step)}findNames(){return this.length.findNames().concat(this.target.findNames()).concat(this.motive.findNames()).concat(this.base.findNames()).concat(this.step.findNames())}prettyPrint(){return`ind-Vec ${this.length.prettyPrint()}\n              ${this.target.prettyPrint()}\n              ${this.motive.prettyPrint()}\n              ${this.base.prettyPrint()}\n              ${this.step.prettyPrint()}`}toString(){return this.prettyPrint()}}class yr extends xn{location;left;right;constructor(t,e,n){super(t),this.location=t,this.left=e,this.right=n}synthHelper(t,e){return Nn.synthEither(t,e,this.left,this.right)}findNames(){return this.left.findNames().concat(this.right.findNames())}getType(t,e){const n=new O("Lout"),r=new O("Rout");return L([[n,()=>this.left.isType(t,e)],[r,()=>this.right.isType(t,e)]],(()=>new S(new Je(n.value,r.value))))}prettyPrint(){return`(Either ${this.left.prettyPrint()} ${this.right.prettyPrint()})`}toString(){return this.prettyPrint()}}class dr extends xn{location;value;constructor(t,e){super(t),this.location=t,this.value=e}synthHelper(t,e){throw new Error("Method not implemented.")}findNames(){return this.value.findNames()}checkOut(t,e,n){const r=n.now();if(r instanceof se){const n=new O("lout");return L([[n,()=>this.value.check(t,e,r.leftType)]],(()=>new S(new tn(n.value))))}return new $(this.location,new _([`left requires an Either type, but was used as a: ${r.readBackType(t)}.`]))}prettyPrint(){return`(left ${this.value.prettyPrint()})`}toString(){return this.prettyPrint()}}class mr extends xn{location;value;constructor(t,e){super(t),this.location=t,this.value=e}synthHelper(t,e){throw new Error("Method not implemented.")}findNames(){return this.value.findNames()}checkOut(t,e,n){const r=n.now();if(r instanceof se){const n=new O("rout");return L([[n,()=>this.value.check(t,e,r.rightType)]],(()=>new S(new en(n.value))))}return new $(this.location,new _([`right requires an Either type, but was used as a: ${r.readBackType(t)}.`]))}prettyPrint(){return`(right ${this.value.prettyPrint()})`}toString(){return this.prettyPrint()}}class gr extends xn{location;target;motive;baseLeft;baseRight;constructor(t,e,n,r,s){super(t),this.location=t,this.target=e,this.motive=n,this.baseLeft=r,this.baseRight=s}synthHelper(t,e){return Nn.synthIndEither(t,e,this.location,this.target,this.motive,this.baseLeft,this.baseRight)}findNames(){return this.target.findNames().concat(this.motive.findNames()).concat(this.baseLeft.findNames()).concat(this.baseRight.findNames())}prettyPrint(){return`(ind-Either ${this.target.prettyPrint()} \n              ${this.motive.prettyPrint()} \n              ${this.baseLeft.prettyPrint()} \n              ${this.baseRight.prettyPrint()})`}toString(){return this.prettyPrint()}}class vr extends xn{location;constructor(t){super(t),this.location=t}synthHelper(t,e){throw new Error("Method not implemented.")}findNames(){return[]}checkOut(t,e,n){const r=n.readBackType(t);return pn(this.location,z(t)),new S(new rn(this.location.locationToSrcLoc(),r))}prettyPrint(){return"TODO"}toString(){return this.prettyPrint()}}class Er extends xn{location;func;arg;args;constructor(t,e,n,r){super(t),this.location=t,this.func=e,this.arg=n,this.args=r}synthHelper(t,e){return Nn.synthApplication(t,e,this.location,this.func,this.arg,this.args)}findNames(){return this.func.findNames().concat(this.arg.findNames()).concat(this.args.flatMap((t=>t.findNames())))}prettyPrint(){return`(${this.func.prettyPrint()} ${this.arg.prettyPrint()} ${this.args.map((t=>t.prettyPrint())).join(" ")})`}toString(){return this.prettyPrint()}}var Pr,Tr;!function(t){t[t.INTEGER=1]="INTEGER",t[t.RATIONAL=2]="RATIONAL",t[t.REAL=3]="REAL",t[t.COMPLEX=4]="COMPLEX"}(Pr||(Pr={}));class br{result;constructor(t){this.result=t}}class Nr extends br{result;value;constructor(t,e){super(t),this.result=t,this.value=e}isSigned(){return!!this.result&&("+"===this.value[0]||"-"===this.value[0])}build(){return Or.build(this.value)}}class xr extends br{result;numerator;denominator;constructor(t,e,n){super(t),this.result=t,this.numerator=e,this.denominator=n}build(){return Lr.build(this.numerator,this.denominator)}}class _r extends br{result;integer;decimal;exponent;constructor(t,e,n,r){super(t),this.result=t,this.integer=e,this.decimal=n,this.exponent=r}build(){if(this.integer?.includes("inf"))return this.integer.includes("-")?Ar.NEG_INFINITY:Ar.INFINITY;if(this.integer?.includes("nan"))return Ar.NAN;let t=(this.exponent?this.exponent.build():Ar.INEXACT_ZERO).coerce(),e=Number((this.integer?this.integer:"0")+"."+(this.decimal?this.decimal:"0"));return e*=Math.pow(10,t),Ar.build(e)}}class kr extends br{result;real;sign;imaginary;constructor(t,e,n,r){super(t),this.result=t,this.real=e,this.sign=n,this.imaginary=r}build(){const t=this.real?this.real.build():Or.EXACT_ZERO,e=this.imaginary.build();return this.sign&&"-"===this.sign?Ir.build(t,e.negate()):Ir.build(t,e)}}function Sr(t){const e=new RegExp("^([+-]?)(\\d+)$").exec(t);return e?new Nr(!0,e[0]):new Nr(!1)}function $r(t,e){const n=Sr(t);if(n.result&&e>=Pr.INTEGER)return n;const r=function(t){if(1!==(t.match(/\//g)||[]).length)return new xr(!1);const e=t.split("/");if(2!==e.length)return new xr(!1);const[n,r]=e,s=Sr(n),i=Sr(r);return s.result&&i.result?new xr(!0,n,r):new xr(!1)}(t);if(r.result&&e>=Pr.RATIONAL)return r;const s=function(t){function e(t){if(function(t){return"+inf.0"===t||"-inf.0"===t||"+nan.0"===t||"-nan.0"===t}(t))return new _r(!0,t);const e=(t.match(/\./g)||[]).length;if(e>1)return new _r(!1);if(0===e){const e=Sr(t);return new _r(e.result,e.value)}const[n,r]=t.split("."),s=Sr(n),i=Sr(r),a=s.result||""===n,o=i.result||""===r;return"+"===n||"-"===n?""===r?new _r(!1):new _r(!0,`${n}0`,t):s.result&&o||a&&i.result?i.result&&i.isSigned()?new _r(!1):new _r(!0,s.value,i.value):new _r(!1)}return 0===(t.match(/[eE]/g)||[]).length?e(t):function(t){const n=t.indexOf("e"),r=t.indexOf("E");if(-1===n&&-1===r)return new _r(!1);const s=-1===n?r:n,i=t.substring(0,s),a=t.substring(s+1);if(""===i||""==a)return new _r(!1);const o=e(i);if(!o.result)return new _r(!1);const c=$r(a,Pr.REAL);return c.result?new _r(!0,o.integer,o.decimal,c):new _r(!1)}(t)}(t);if(s.result&&e>=Pr.REAL)return s;const i=function(t){if((t.match(/i/g)||[]).length<1)return new kr(!1);if("i"!==t[t.length-1])return new kr(!1);const e=t.search(/(?<!^)[+-]/);if(-1===e){const e=$r(t.slice(0,-1),Pr.REAL);return e.result?new kr(!0,void 0,void 0,e):new kr(!1)}const n=t.slice(0,e);let r=t.slice(e+1,-1);"+"!==r[0]&&"-"!==r[0]&&(r="+"+r);const s=$r(n,Pr.REAL),i=$r(r,Pr.REAL);return s.result&&i.result?new kr(!0,s,t[e],i):new kr(!1)}(t);return i.result&&e>=Pr.COMPLEX?i:new Nr(!1)}class Or{numberType=Pr.INTEGER;value;static EXACT_ZERO=new Or(0n);constructor(t){this.value=t}static build(t,e=!1){const n=BigInt(t);return 0n===n?Or.EXACT_ZERO:new Or(n)}promote(t){switch(t){case Pr.INTEGER:return this;case Pr.RATIONAL:return Lr.build(this.value,1n,!0);case Pr.REAL:return Ar.build(this.coerce(),!0);case Pr.COMPLEX:return Ir.build(this,Or.EXACT_ZERO,!0)}}equals(t){return t instanceof Or&&this.value===t.value}greaterThan(t){return this.value>t.value}negate(){return this===Or.EXACT_ZERO?this:Or.build(-this.value)}multiplicativeInverse(){if(this===Or.EXACT_ZERO)throw new Error("Division by zero");return Lr.build(1n,this.value,!1)}add(t){return Or.build(this.value+t.value)}multiply(t){return Or.build(this.value*t.value)}getBigInt(){return this.value}coerce(){return this.value>Number.MAX_SAFE_INTEGER?1/0:this.value<Number.MIN_SAFE_INTEGER?-1/0:Number(this.value)}toString(){return this.value.toString()}}class Lr{numberType=Pr.RATIONAL;numerator;denominator;constructor(t,e){this.numerator=t,this.denominator=e}static build(t,e,n=!1){return Lr.simplify(BigInt(t),BigInt(e),n)}static simplify(t,e,n=!1){const r=(t,e)=>0n===e?t:r(e,t.valueOf()%e.valueOf()),s=r(t,e),i=t<0n?-1n:1n,a=e<0n?-1n:1n,o=i*a;return t*=i,1n!==(e*=a)||n?new Lr(o*t/s,e/s):Or.build(o*t)}getNumerator(){return this.numerator}getDenominator(){return this.denominator}promote(t){switch(t){case Pr.RATIONAL:return this;case Pr.REAL:return Ar.build(this.coerce(),!0);case Pr.COMPLEX:return Ir.build(this,Or.EXACT_ZERO,!0);default:throw new Error("Unable to demote rational")}}equals(t){return t instanceof Lr&&this.numerator===t.numerator&&this.denominator===t.denominator}greaterThan(t){return this.numerator*t.denominator>t.numerator*this.denominator}negate(){return Lr.build(-this.numerator,this.denominator)}multiplicativeInverse(){if(0n===this.numerator)throw new Error("Division by zero");return Lr.build(this.denominator,this.numerator)}add(t){const e=this.numerator*t.denominator+t.numerator*this.denominator,n=this.denominator*t.denominator;return Lr.build(e,n)}multiply(t){const e=this.numerator*t.numerator,n=this.denominator*t.denominator;return Lr.build(e,n)}coerce(){const t=this.numerator<0n?-this.numerator:this.numerator;let e=this.denominator;const n=Number(t/e);if(n>Number.MAX_VALUE)return this.numerator<0n?-1/0:1/0;let r=t%e;for(;r>Number.MAX_SAFE_INTEGER||e>Number.MAX_SAFE_INTEGER;)r/=2n,e/=2n;const s=Number(r)/Number(e);return this.numerator<0n?-(n+s):n+s}toString(){return`${this.numerator}/${this.denominator}`}}class Ar{numberType=Pr.REAL;value;static INEXACT_ZERO=new Ar(0);static INEXACT_NEG_ZERO=new Ar(-0);static INFINITY=new Ar(1/0);static NEG_INFINITY=new Ar(-1/0);static NAN=new Ar(NaN);static build(t,e=!1){return t===1/0?Ar.INFINITY:t===-1/0?Ar.NEG_INFINITY:isNaN(t)?Ar.NAN:0===t?Ar.INEXACT_ZERO:-0===t?Ar.INEXACT_NEG_ZERO:new Ar(t)}constructor(t){this.value=t}promote(t){switch(t){case Pr.REAL:return this;case Pr.COMPLEX:return Ir.build(this,Or.EXACT_ZERO,!0);default:throw new Error("Unable to demote real")}}equals(t){return t instanceof Ar&&this.value===t.value}greaterThan(t){return this.value>t.value}negate(){return Ar.build(-this.value)}multiplicativeInverse(){if(this===Ar.INEXACT_ZERO||this===Ar.INEXACT_NEG_ZERO)throw new Error("Division by zero");return Ar.build(1/this.value)}add(t){return Ar.build(this.value+t.value)}multiply(t){return Ar.build(this.value*t.value)}coerce(){return this.value}toString(){return this===Ar.INFINITY?"+inf.0":this===Ar.NEG_INFINITY?"-inf.0":this===Ar.NAN?"+nan.0":this.value.toString()}}class Ir{numberType=Pr.COMPLEX;real;imaginary;static build(t,e,n=!1){return Ir.simplify(new Ir(t,e),n)}constructor(t,e){this.real=t,this.imaginary=e}static simplify(t,e){return!e&&qr(t.imaginary,Or.EXACT_ZERO)?t.real:t}promote(t){if(t===Pr.COMPLEX)return this;throw new Error("Unable to demote complex")}negate(){return Ir.build(this.real.negate(),this.imaginary.negate())}equals(t){return qr(this.real,t.real)&&qr(this.imaginary,t.imaginary)}greaterThan(t){return Mr(this.real,t.real)&&Mr(this.imaginary,t.imaginary)}multiplicativeInverse(){const t=Ur(Hr(this.real,this.real),Hr(this.imaginary,this.imaginary));return Ir.build(Hr(t.multiplicativeInverse(),this.real),Hr(t.multiplicativeInverse(),this.imaginary.negate()))}add(t){return Ir.build(Ur(this.real,t.real),Ur(this.imaginary,t.imaginary))}multiply(t){const e=(n=Hr(this.real,t.real),r=Hr(this.imaginary,t.imaginary),Ur(n,function(t){return t.negate()}(r)));var n,r;const s=Ur(Hr(this.real,t.imaginary),Hr(this.imaginary,t.real));return Ir.build(e,s)}getReal(){return this.real}getImaginary(){return this.imaginary}coerce(){throw new Error("Cannot coerce a complex number to a javascript number")}toPolar(){const t=this.real.promote(Pr.REAL),e=this.imaginary.promote(Pr.REAL),n=Ar.build(Math.sqrt(t.coerce()*t.coerce()+e.coerce()*e.coerce())),r=Ar.build(Math.atan2(e.coerce(),t.coerce()));return Br.build(n,r)}toString(){return`${this.real}+${this.imaginary}i`}}class Br{magnitude;angle;constructor(t,e){this.magnitude=t,this.angle=e}static build(t,e){return new Br(t,e)}toCartesian(){const t=Ar.build(this.magnitude.coerce()*Math.cos(this.angle.coerce())),e=Ar.build(this.magnitude.coerce()*Math.sin(this.angle.coerce()));return Ir.build(t,e)}}function Cr(t){switch(t.numberType){case Pr.INTEGER:return t;case Pr.RATIONAL:return 1n===t.getDenominator()?Or.build(t.getNumerator()):t;case Pr.REAL:return t;case Pr.COMPLEX:return Ir.build(Cr(t.getReal()),Cr(t.getImaginary()))}}function Rr(t,e){return t.numberType>e.numberType?[t,e.promote(t.numberType)]:t.numberType<e.numberType?[t.promote(e.numberType),e]:[t,e]}function qr(t,e){const[n,r]=Rr(t,e);return n.equals(r)}function Mr(t,e){const[n,r]=Rr(t,e);return n.greaterThan(r)}function Ur(t,e){const[n,r]=Rr(t,e);return Cr(n.add(r))}function Hr(t,e){const[n,r]=Rr(t,e);return Cr(n.multiply(r))}class Dr{start;end;constructor(t,e){this.start=t,this.end=e}merge(t){return new Dr(this.start,t.end)}}class zr{line;column;constructor(t,e){this.line=t,this.column=e}}function Qr(t,e){return t.split("\n")[e.line-1]}function Fr(t){return"^".padStart(t.column," ")}!function(t){t[t.LEFT_PAREN=0]="LEFT_PAREN",t[t.RIGHT_PAREN=1]="RIGHT_PAREN",t[t.LEFT_BRACKET=2]="LEFT_BRACKET",t[t.RIGHT_BRACKET=3]="RIGHT_BRACKET",t[t.DOT=4]="DOT",t[t.HASH_SEMICOLON=5]="HASH_SEMICOLON",t[t.IDENTIFIER=6]="IDENTIFIER",t[t.NUMBER=7]="NUMBER",t[t.BOOLEAN=8]="BOOLEAN",t[t.STRING=9]="STRING",t[t.IF=10]="IF",t[t.LET=11]="LET",t[t.COND=12]="COND",t[t.ELSE=13]="ELSE",t[t.DEFINE=14]="DEFINE",t[t.LAMBDA=15]="LAMBDA",t[t.APOSTROPHE=16]="APOSTROPHE",t[t.BACKTICK=17]="BACKTICK",t[t.COMMA=18]="COMMA",t[t.COMMA_AT=19]="COMMA_AT",t[t.QUOTE=20]="QUOTE",t[t.QUASIQUOTE=21]="QUASIQUOTE",t[t.UNQUOTE=22]="UNQUOTE",t[t.UNQUOTE_SPLICING=23]="UNQUOTE_SPLICING",t[t.SET=24]="SET",t[t.BEGIN=25]="BEGIN",t[t.DELAY=26]="DELAY",t[t.IMPORT=27]="IMPORT",t[t.EXPORT=28]="EXPORT",t[t.DEFINE_SYNTAX=29]="DEFINE_SYNTAX",t[t.SYNTAX_RULES=30]="SYNTAX_RULES",t[t.HASH_VECTOR=31]="HASH_VECTOR",t[t.VECTOR=32]="VECTOR",t[t.EOF=33]="EOF"}(Tr||(Tr={}));class Vr extends SyntaxError{loc;constructor(t,e){super(`Syntax error at (${e.line}:${e.column})\n${t}`),this.loc=e}toString(){return this.message}}let Gr=class extends Vr{constructor(t,e){super(Qr(t,e)+"\nUnexpected EOF",e),this.name="UnexpectedEOFError"}};class Xr extends Vr{form;constructor(t,e,n){super(Qr(t,e)+"\n"+Fr(e)+"\n"+`Unexpected '${n}'`,e),this.form=n,this.name="UnexpectedTokenError"}}class Kr extends Vr{form;expected;constructor(t,e,n,r){super(Qr(t,e)+"\n"+Fr(e)+"\n"+`Expected '${r}' but got '${n}'`,e),this.form=n,this.expected=r,this.name="ExpectedTokenError"}}class Yr extends Vr{token;constructor(t,e,n,r){super(Qr(t,e)+"\n"+Fr(e)+"\n"+`Syntax '${n}' not allowed at Scheme §${r}`,e),this.token=n,this.name="DisallowedTokenError"}}class Zr extends Vr{token;constructor(t,e,n){super(Qr(t,e)+"\n"+Fr(e)+"\n"+`Syntax '${n}' not supported yet`,e),this.token=n,this.name="UnsupportedTokenError"}}class jr{elements;location;constructor(t){this.elements=t,this.location=new Dr(this.firstPos(),this.lastPos())}static build(t){if(0===t.length)throw new Error("Illegal empty group. This should never happen.");if(1===t.length){const n=t[0];if(Jr(n))return n;if((e=n).type!==Tr.IDENTIFIER&&e.type!==Tr.NUMBER&&e.type!==Tr.STRING&&e.type!==Tr.BOOLEAN)throw new Kr("",n.pos,n,"<data>");return new jr(t)}var e;if(2===t.length){const e=t[0];if(Wr(e)&&function(t){return t.type===Tr.APOSTROPHE||t.type===Tr.BACKTICK||t.type===Tr.HASH_VECTOR||t.type===Tr.COMMA||t.type===Tr.COMMA_AT}(e))return new jr(t)}const n=t[0],r=t[t.length-1];if(Wr(n)&&Wr(r)&&(i=r,(s=n).type===Tr.LEFT_PAREN&&i.type===Tr.RIGHT_PAREN||s.type===Tr.LEFT_BRACKET&&i.type===Tr.RIGHT_BRACKET))return new jr(t);var s,i;const a=new jr(t);throw new Kr("",a.location.start,a,"matching parentheses")}first(){return this.elements[0]}firstToken(){const t=this.first();return Wr(t)?t:t.firstToken()}firstPos(){return this.firstToken().pos}last(){return this.elements[this.elements.length-1]}lastToken(){const t=this.last();return Wr(t)?t:t.lastToken()}lastPos(){return this.lastToken().pos}isParenthesized(){const t=this.first();return Wr(t)&&(t.type===Tr.LEFT_PAREN||t.type===Tr.LEFT_BRACKET)}isSingleIdentifier(){return!this.isParenthesized()&&1===this.length()}unwrap(){return this.isParenthesized()?this.elements.slice(1,this.elements.length-1):this.elements}length(){return this.unwrap().length}toString(){return this.elements.map((t=>t.toString())).join(" ")}}function Wr(t){return t instanceof ts}function Jr(t){return t instanceof jr}class ts{type;lexeme;literal;start;end;pos;endPos;constructor(t,e,n,r,s,i,a){this.type=t,this.lexeme=e,this.literal=n,this.start=r,this.end=s,this.pos=new zr(i,a),this.endPos=new zr(i,a+e.length-1)}convertToken(){switch(this.type){case Tr.APOSTROPHE:return new ts(Tr.QUOTE,this.lexeme,this.literal,this.start,this.end,this.pos.line,this.pos.column);case Tr.BACKTICK:return new ts(Tr.QUASIQUOTE,this.lexeme,this.literal,this.start,this.end,this.pos.line,this.pos.column);case Tr.HASH_VECTOR:return new ts(Tr.VECTOR,this.lexeme,this.literal,this.start,this.end,this.pos.line,this.pos.column);case Tr.COMMA:return new ts(Tr.UNQUOTE,this.lexeme,this.literal,this.start,this.end,this.pos.line,this.pos.column);case Tr.COMMA_AT:return new ts(Tr.UNQUOTE_SPLICING,this.lexeme,this.literal,this.start,this.end,this.pos.line,this.pos.column);default:return this}}toString(){return`${this.lexeme}`}}class es extends SyntaxError{loc;constructor(t,e,n){super(t),this.loc={line:e,column:n}}toString(){return this.message}}class ns extends es{char;constructor(t,e,n){super(`Unexpected character '${n}' (${t}:${e})`,t,e),this.char=n,this.name="UnexpectedCharacterError"}}class rs extends es{constructor(t,e){super(`Unexpected EOF (${t}:${e})`,t,e),this.name="UnexpectedEOFError"}}let ss=new Map([[".",Tr.DOT],["if",Tr.IF],["let",Tr.LET],["cond",Tr.COND],["else",Tr.ELSE],["set!",Tr.SET],["begin",Tr.BEGIN],["delay",Tr.DELAY],["quote",Tr.QUOTE],["export",Tr.EXPORT],["import",Tr.IMPORT],["define",Tr.DEFINE],["lambda",Tr.LAMBDA],["define-syntax",Tr.DEFINE_SYNTAX],["syntax-rules",Tr.SYNTAX_RULES]]);class is{source;tokens;start=0;current=0;line=1;col=0;constructor(t){this.source=t,this.tokens=[]}isAtEnd(){return this.current>=this.source.length}advance(){return this.col++,this.source.charAt(this.current++)}jump(){this.start=this.current,this.col++,this.current++}addToken(t,e=null){const n=this.source.substring(this.start,this.current);this.tokens.push(new ts(t,n,e,this.start,this.current,this.line,this.col))}scanTokens(){for(;!this.isAtEnd();)this.start=this.current,this.scanToken();return this.tokens.push(new ts(Tr.EOF,"",null,this.start,this.current,this.line,this.col)),this.tokens}scanToken(){const t=this.advance();switch(t){case"(":this.addToken(Tr.LEFT_PAREN);break;case")":this.addToken(Tr.RIGHT_PAREN);break;case"[":this.addToken(Tr.LEFT_BRACKET);break;case"]":this.addToken(Tr.RIGHT_BRACKET);break;case"'":this.addToken(Tr.APOSTROPHE);break;case"`":this.addToken(Tr.BACKTICK);break;case",":if(this.match("@")){this.addToken(Tr.COMMA_AT);break}this.addToken(Tr.COMMA);break;case"#":if(this.match("t")||this.match("f"))this.booleanToken();else if(this.match("|"))this.comment();else if(this.match(";"))this.addToken(Tr.HASH_SEMICOLON);else{if("("!==this.peek()&&"["!==this.peek())throw new ns(this.line,this.col,t);this.addToken(Tr.HASH_VECTOR)}break;case";":for(;"\n"!=this.peek()&&!this.isAtEnd();)this.advance();break;case" ":case"\r":case"\t":break;case"\n":this.line++,this.col=0;break;case'"':this.stringToken();break;case"|":this.identifierTokenLoose();break;default:if(this.isDigit(t)||"-"===t||"+"===t||"."===t||"i"===t||"n"===t)this.identifierNumberToken();else{if(!this.isValidIdentifier(t))throw new ns(this.line,this.col,t);this.identifierToken()}}}comment(){for(;("|"!=this.peek()||"#"!=this.peekNext())&&!this.isAtEnd();)"\n"===this.peek()&&(this.line++,this.col=0),this.advance();if(this.isAtEnd())throw new rs(this.line,this.col);this.jump(),this.jump()}identifierToken(){for(;this.isValidIdentifier(this.peek());)this.advance();this.addToken(this.checkKeyword())}identifierTokenLoose(){for(this.advance();"|"!=this.peek()&&!this.isAtEnd();)"\n"===this.peek()&&(this.line++,this.col=0),this.advance();if(this.isAtEnd())throw new rs(this.line,this.col);this.advance(),this.addToken(this.checkKeyword())}identifierNumberToken(){for(;this.isValidIdentifier(this.peek());)this.advance();const t=this.source.substring(this.start,this.current);$r(t,Pr.COMPLEX).result?this.addToken(Tr.NUMBER,t):this.addToken(this.checkKeyword())}checkKeyword(){var t=this.source.substring(this.start,this.current);return ss.has(t)?ss.get(t):Tr.IDENTIFIER}stringToken(){for(;'"'!=this.peek()&&!this.isAtEnd();)"\n"===this.peek()&&(this.line++,this.col=0),this.advance();if(this.isAtEnd())throw new rs(this.line,this.col);this.advance();const t=this.source.substring(this.start+1,this.current-1);this.addToken(Tr.STRING,t)}booleanToken(){this.addToken(Tr.BOOLEAN,"t"===this.peekPrev())}match(t){return!this.isAtEnd()&&(this.source.charAt(this.current)==t&&(this.current++,!0))}peek(){return this.isAtEnd()?"\0":this.source.charAt(this.current)}peekNext(){return this.current+1>=this.source.length?"\0":this.source.charAt(this.current+1)}peekPrev(){return this.current-1<0?"\0":this.source.charAt(this.current-1)}isDigit(t){return t>="0"&&t<="9"}isSpecialSyntax(t){return"("===t||")"===t||"["===t||"]"===t||";"===t||"|"===t}isValidIdentifier(t){return!this.isWhitespace(t)&&!this.isSpecialSyntax(t)}isWhitespace(t){return" "===t||"\0"===t||"\n"===t||"\r"===t||"\t"===t}}var as,os;!function(t){class e{location;expressions;constructor(t,e){this.location=t,this.expressions=e}accept(t){return t.visitSequence(this)}equals(t){if(t instanceof e){if(this.expressions.length!==t.expressions.length)return!1;for(let e=0;e<this.expressions.length;e++)if(!this.expressions[e].equals(t.expressions[e]))return!1;return!0}return!1}}t.Sequence=e;class n{location;value;constructor(t,e){this.location=t,this.value=e}accept(t){return t.visitNumericLiteral(this)}equals(t){return t instanceof n&&this.value===t.value}}t.NumericLiteral=n;class r{location;value;constructor(t,e){this.location=t,this.value=e}accept(t){return t.visitBooleanLiteral(this)}equals(t){return t instanceof r&&this.value===t.value}}t.BooleanLiteral=r;class 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Dr(t.pos,t.endPos)}destructureList(t,e=t=>{}){if(0===t.length)return[[],void 0];if(1===t.length)return e(t[0]),[[this.parseExpression(t[0])],void 0];const n=t.at(-2);if(Wr(n)&&n.type===Tr.DOT){const n=t.at(-1),r=t.slice(0,-2);return e(n),r.forEach(e),[r.map(this.parseExpression.bind(this)),this.parseExpression(n)]}const r=t;return r.forEach(e),[r.map(this.parseExpression.bind(this)),void 0]}grouping(t){const e=[];let n=!1;t&&(n=!0,e.push(t));do{let t=this.advance();switch(t.type){case Tr.LEFT_PAREN:case Tr.LEFT_BRACKET:const r=this.grouping(t);e.push(r);break;case Tr.RIGHT_PAREN:case Tr.RIGHT_BRACKET:if(!n)throw new Xr(this.source,t.pos,t);e.push(t),n=!1;break;case Tr.APOSTROPHE:case Tr.BACKTICK:case Tr.COMMA:case Tr.COMMA_AT:case Tr.HASH_VECTOR:let s;do{s=this.grouping()}while(!s);e.push(this.affect(t,s));break;case Tr.QUOTE:case Tr.QUASIQUOTE:case Tr.UNQUOTE:case Tr.UNQUOTE_SPLICING:case Tr.IDENTIFIER:case Tr.NUMBER:case Tr.BOOLEAN:case Tr.STRING:case Tr.DOT:case Tr.DEFINE:case Tr.IF:case Tr.ELSE:case Tr.COND:case Tr.LAMBDA:case Tr.LET:case Tr.SET:case Tr.BEGIN:case Tr.DELAY:case Tr.IMPORT:case Tr.EXPORT:case Tr.DEFINE_SYNTAX:case Tr.SYNTAX_RULES:e.push(t);break;case Tr.HASH_SEMICOLON:for(;!this.grouping(););break;case Tr.EOF:throw new Gr(this.source,t.pos);default:throw new Xr(this.source,t.pos,t)}}while(n);if(0!==e.length)try{return jr.build(e)}catch(t){if(t instanceof Kr)throw new Kr(this.source,t.loc,t.form,t.expected);throw t}}affect(t,e){return jr.build([t,e])}parseExpression(t){return Wr(t)?this.parseToken(t):t.isSingleIdentifier()?this.parseToken(t.unwrap()[0]):this.parseGroup(t)}parseToken(t){switch(t.type){case Tr.IDENTIFIER:return this.quoteMode===cs.NONE?new as.Identifier(this.toLocation(t),t.lexeme):new as.Symbol(this.toLocation(t),t.lexeme);case Tr.NUMBER:return new as.NumericLiteral(this.toLocation(t),t.literal);case Tr.BOOLEAN:return new as.BooleanLiteral(this.toLocation(t),t.literal);case Tr.STRING:return new as.StringLiteral(this.toLocation(t),t.literal);default:if(this.quoteMode!==cs.NONE||this.chapter>=5)return new as.Symbol(this.toLocation(t),t.lexeme);throw new Xr(this.source,t.pos,t)}}parseGroup(t){if(!t.isParenthesized())return this.parseAffectorGroup(t);switch(this.quoteMode){case cs.NONE:return this.parseNormalGroup(t);case cs.QUOTE:case cs.QUASIQUOTE:return this.parseQuotedGroup(t)}}parseAffectorGroup(t){const[e,n]=t.unwrap();switch(e.type){case Tr.APOSTROPHE:case Tr.QUOTE:if(this.validateChapter(e,2),this.quoteMode!==cs.NONE){const t=this.parseExpression(n),r=new as.Symbol(this.toLocation(e),"quote"),s=r.location.merge(t.location);return new os.List(s,[r,t])}this.quoteMode=cs.QUOTE;const r=this.parseExpression(n);return this.quoteMode=cs.NONE,r;case Tr.BACKTICK:case Tr.QUASIQUOTE:if(this.validateChapter(e,2),this.quoteMode!==cs.NONE){const t=this.parseExpression(n),r=new as.Symbol(this.toLocation(e),"quasiquote"),s=r.location.merge(t.location);return new os.List(s,[r,t])}this.quoteMode=cs.QUASIQUOTE;const s=this.parseExpression(n);return this.quoteMode=cs.NONE,s;case Tr.COMMA:case Tr.UNQUOTE:this.validateChapter(e,2);let i=this.quoteMode;if(i===cs.NONE)throw new Zr(this.source,e.pos,e);if(i===cs.QUOTE){const t=this.parseExpression(n),r=new as.Symbol(this.toLocation(e),"unquote"),s=r.location.merge(t.location);return new os.List(s,[r,t])}this.quoteMode=cs.NONE;const a=this.parseExpression(n);return this.quoteMode=i,a;case Tr.COMMA_AT:case Tr.UNQUOTE_SPLICING:this.validateChapter(e,2);let o=this.quoteMode;if(o===cs.NONE)throw new Xr(this.source,e.pos,e);if(o===cs.QUOTE){const t=this.parseExpression(n),r=new as.Symbol(this.toLocation(e),"unquote-splicing"),s=r.location.merge(t.location);return new os.List(s,[r,t])}this.quoteMode=cs.NONE;const c=this.parseExpression(n);this.quoteMode=o;const u=this.toLocation(e).merge(c.location);return new as.SpliceMarker(u,c);case Tr.HASH_VECTOR:this.validateChapter(e,3);let 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this.validateChapter(e,3),this.parseDelay(t);case Tr.SET:return this.validateChapter(e,3),this.parseSet(t);case Tr.DEFINE_SYNTAX:return this.validateChapter(e,5),this.parseDefineSyntax(t);case Tr.SYNTAX_RULES:throw new Xr(this.source,e.pos,e);case Tr.IMPORT:return this.validateChapter(e,1),this.parseImport(t);case Tr.EXPORT:return this.validateChapter(e,1),this.parseExport(t);case Tr.VECTOR:return this.validateChapter(e,3),this.parseAffectorGroup(t);default:return this.parseApplication(t)}return this.parseApplication(t)}parseQuotedGroup(t){if(0===t.length())return new as.Nil(t.location);if(1===t.length()){const e=[this.parseExpression(t.unwrap()[0])];return new os.List(t.location,e)}const e=t.unwrap(),[n,r]=this.destructureList(e);return new os.List(t.location,n,r)}parseLambda(t){if(t.length()<3)throw new Kr(this.source,t.location.start,t,"(lambda (<identifier>* . <rest-identifier>?) <body>+) | (lambda <rest-identifer> <body>+)");const e=t.unwrap(),n=e[1],r=e.slice(2);let 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re&&s instanceof ie){let e;for(const[n,r]of t)if(n===s.name&&r instanceof _){e=r;break}if(!e)throw new Error(`Constructor ${s.name} not found in context`);const n=k(t,e.constructorType),r=[];for(let e=0;e<s.args.length;e++){const i=n.argTypes[e];r.push(tt(t,i,s.args[e]))}const i=[];for(let e=0;e<s.recursive_args.length;e++){const r=n.rec_argTypes[e];i.push(tt(t,r,s.recursive_args[e]))}return new nn(s.name,s.index,s.type,r,i)}if(s instanceof Zt)return s.neutral.readBackNeutral(t);throw new Error(`Cannot read back ${s.prettyPrint()} : ${r.prettyPrint()}`)}class et{type;value;constructor(t,e){this.type=t,this.value=e}}let nt=class{constructor(){}toString(){return this.prettyPrint()}};class rt extends nt{name;constructor(t){super(),this.name=t}readBackNeutral(t){return new Je(this.name)}prettyPrint(){return`N-${this.name}`}}let st=class extends nt{where;type;constructor(t,e){super(),this.where=t,this.type=e}readBackNeutral(t){return new Ze(this.where,this.type.readBackType(t))}prettyPrint(){return"N-TODO"}},it=class extends nt{target;base;step;constructor(t,e,n){super(),this.target=t,this.base=e,this.step=n}readBackNeutral(t){return new fe(this.target.readBackNeutral(t),new ce(this.base.type.readBackType(t),tt(t,this.base.type,this.base.value)),tt(t,this.step.type,this.step.value))}prettyPrint(){return"N-WhichNat"}},at=class extends nt{target;base;step;constructor(t,e,n){super(),this.target=t,this.base=e,this.step=n}readBackNeutral(t){return new ye(this.target.readBackNeutral(t),new ce(this.base.type.readBackType(t),tt(t,this.base.type,this.base.value)),tt(t,this.step.type,this.step.value))}prettyPrint(){return"N-IterNat"}},ot=class extends nt{target;base;step;constructor(t,e,n){super(),this.target=t,this.base=e,this.step=n}readBackNeutral(t){return new we(this.target.readBackNeutral(t),new 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qe(this.target.readBackNeutral(t),tt(t,this.motive.type,this.motive.value),tt(t,this.base.type,this.base.value))}prettyPrint(){return"N-Replace"}};class wt extends nt{target1;target2;constructor(t,e){super(),this.target1=t,this.target2=e}readBackNeutral(t){return new Me(this.target1.readBackNeutral(t),tt(t,this.target2.type,this.target2.value))}prettyPrint(){return"N-Trans1"}}class dt extends nt{target1;target2;constructor(t,e){super(),this.target1=t,this.target2=e}readBackNeutral(t){return new Me(tt(t,this.target1.type,this.target1.value),this.target2.readBackNeutral(t))}prettyPrint(){return"N-Trans2"}}class mt extends nt{target1;target2;constructor(t,e){super(),this.target1=t,this.target2=e}readBackNeutral(t){return new Me(this.target1.readBackNeutral(t),this.target2.readBackNeutral(t))}prettyPrint(){return"N-Trans12"}}let gt=class extends nt{target;func;constructor(t,e){super(),this.target=t,this.func=e}readBackNeutral(t){const e=this.func.type;if(e instanceof qt){const n=e.resultType;return new _e(this.target.readBackNeutral(t),n.valOfClosure(new ne).readBackType(t),tt(t,this.func.type,this.func.value))}throw new Error("Cong applied to non-Pi type.")}prettyPrint(){return"N-Cong"}},vt=class extends nt{target;constructor(t){super(),this.target=t}readBackNeutral(t){return new Ge(this.target.readBackNeutral(t))}prettyPrint(){return"N-Symm"}},Tt=class extends nt{target;motive;base;constructor(t,e,n){super(),this.target=t,this.motive=e,this.base=n}readBackNeutral(t){return new ze(this.target.readBackNeutral(t),tt(t,this.motive.type,this.motive.value),tt(t,this.base.type,this.base.value))}prettyPrint(){return"N-IndEqual"}},Et=class extends nt{target;constructor(t){super(),this.target=t}readBackNeutral(t){return new Fe(this.target.readBackNeutral(t))}prettyPrint(){return"N-Head"}},Nt=class extends nt{target;constructor(t){super(),this.target=t}readBackNeutral(t){return new Ve(this.target.readBackNeutral(t))}prettyPrint(){return"N-Tail"}};class Pt extends nt{length;target;motive;base;step;constructor(t,e,n,r,s){super(),this.length=t,this.target=e,this.motive=n,this.base=r,this.step=s}readBackNeutral(t){return new Qe(tt(t,this.length.type,this.length.value),this.target.readBackNeutral(t),tt(t,this.motive.type,this.motive.value),tt(t,this.base.type,this.base.value),tt(t,this.step.type,this.step.value))}prettyPrint(){return"N-IndVec2"}}class xt extends nt{length;target;motive;base;step;constructor(t,e,n,r,s){super(),this.length=t,this.target=e,this.motive=n,this.base=r,this.step=s}readBackNeutral(t){return new Qe(this.length.readBackNeutral(t),this.target.readBackNeutral(t),tt(t,this.motive.type,this.motive.value),tt(t,this.base.type,this.base.value),tt(t,this.step.type,this.step.value))}prettyPrint(){return"N-IndVec12"}}let bt=class extends nt{target;motive;baseLeft;baseRight;constructor(t,e,n,r){super(),this.target=t,this.motive=e,this.baseLeft=n,this.baseRight=r}readBackNeutral(t){return new Ye(this.target.readBackNeutral(t),tt(t,this.motive.type,this.motive.value),tt(t,this.baseLeft.type,this.baseLeft.value),tt(t,this.baseRight.type,this.baseRight.value))}prettyPrint(){return"N-IndEither"}};class kt extends nt{typeName;target;motive;methods;constructor(t,e,n,r){super(),this.typeName=t,this.target=e,this.motive=n,this.methods=r}readBackNeutral(t){return new sn(this.typeName,this.target.readBackNeutral(t),tt(t,this.motive.type,this.motive.value),this.methods.map((e=>tt(t,e.type,e.value))))}prettyPrint(){return`N-GenericEliminator-${this.typeName}`}}let $t=class extends nt{operator;operand;constructor(t,e){super(),this.operator=t,this.operand=e}readBackNeutral(t){return new We(this.operator.readBackNeutral(t),tt(t,this.operand.type,this.operand.value))}prettyPrint(){return"N-Application"}};class St{now(){return this}}class Lt{env;expr;constructor(t,e){this.env=t,this.expr=e}undelay(){return this.expr.valOf(this.env).now()}toString(){return`DelayClosure(${this.env}, ${this.expr})`}}class Ot{content;constructor(t){this.content=t}get(){return this.content}set(t){this.content=t}}class At extends St{val;constructor(t){super(),this.val=t}now(){const t=this.val.get();if(t instanceof Lt){let e=t.undelay();return this.val.set(e),e}return t}readBackType(t){return this.now().readBackType(t)}prettyPrint(){return this.now().prettyPrint()}toString(){return`Delay(${this.val})`}}let It=class extends St{name;constructor(t){super(),this.name=t}readBackType(t){throw new Error("No readBackType for Quote.")}prettyPrint(){return`'${this.name}`}toString(){return this.prettyPrint()}},Bt=class extends St{constructor(){super()}readBackType(t){return new he}prettyPrint(){return"Nat"}toString(){return this.prettyPrint()}},Ct=class extends St{constructor(){super()}readBackType(t){throw new Error("No readBackType for Zero.")}prettyPrint(){return"zero"}toString(){return this.prettyPrint()}},Rt=class extends St{smaller;constructor(t){super(),this.smaller=t}readBackType(t){throw new Error("No readBackType for Add1.")}prettyPrint(){return`(add1 ${this.smaller.prettyPrint()})`}toString(){return this.prettyPrint()}},qt=class extends St{argName;argType;resultType;constructor(t,e,n){super(),this.argName=t,this.argType=e,this.resultType=n}readBackType(t){const e=this.argType.readBackType(t),n=N(t,this.argName),r=z(t,n,this.argType);return new me(n,e,this.resultType.valOfClosure(new Zt(this.argType,new rt(n))).readBackType(r))}prettyPrint(){return`(Π ${this.argName} ${this.argType.prettyPrint()} ${this.resultType.prettyPrint()})`}toString(){return this.prettyPrint()}},Mt=class extends St{argName;body;constructor(t,e){super(),this.argName=t,this.body=e}readBackType(t){throw new Error("No readBackType for Lambda.")}prettyPrint(){return`(lambda ${this.argName} ${this.body.prettyPrint()})`}toString(){return this.prettyPrint()}},_t=class extends St{carName;carType;cdrType;constructor(t,e,n){super(),this.carName=t,this.carType=e,this.cdrType=n}readBackType(t){const e=this.carType.readBackType(t),n=N(t,this.carName),r=z(t,n,this.carType);return new Ee(n,e,this.cdrType.valOfClosure(new Zt(this.carType,new rt(n))).readBackType(r))}prettyPrint(){return`(Σ ${this.carName} ${this.carType.prettyPrint()} ${this.cdrType.prettyPrint()})`}toString(){return this.prettyPrint()}},Gt=class extends St{car;cdr;constructor(t,e){super(),this.car=t,this.cdr=e}readBackType(t){throw new Error("No readBackType for Cons.")}prettyPrint(){return`(cons ${this.car.prettyPrint()} ${this.cdr.prettyPrint()})`}toString(){return this.prettyPrint()}},zt=class extends St{entryType;constructor(t){super(),this.entryType=t}readBackType(t){return new $e(this.entryType.readBackType(t))}prettyPrint(){return`(List ${this.entryType.prettyPrint()})`}toString(){return this.prettyPrint()}},Ut=class extends St{constructor(){super()}readBackType(t){throw new Error("No readBackType for Nil.")}prettyPrint(){return"nil"}toString(){return this.prettyPrint()}},Ht=class extends St{head;tail;constructor(t,e){super(),this.head=t,this.tail=e}readBackType(t){throw new Error("No readBackType for ListCons.")}prettyPrint(){return`(:: ${this.head.prettyPrint()} ${this.tail.prettyPrint()})`}toString(){return this.prettyPrint()}},Dt=class extends St{type;from;to;constructor(t,e,n){super(),this.type=t,this.from=e,this.to=n}readBackType(t){return new Ce(this.type.readBackType(t),tt(t,this.type,this.from),tt(t,this.type,this.to))}prettyPrint(){return`(= ${this.type.prettyPrint()} ${this.from.prettyPrint()} ${this.to.prettyPrint()})`}toString(){return this.prettyPrint()}},Ft=class extends St{value;constructor(t){super(),this.value=t}readBackType(t){throw new Error("No readBackType for Same.")}prettyPrint(){return`(same ${this.value.prettyPrint()})`}toString(){return this.prettyPrint()}},Vt=class extends St{entryType;length;constructor(t,e){super(),this.entryType=t,this.length=e}readBackType(t){return new Ue(this.entryType.readBackType(t),tt(t,new Bt,this.length))}prettyPrint(){return`(Vec ${this.entryType.prettyPrint()} ${this.length.prettyPrint()})`}},Qt=class extends St{constructor(){super()}readBackType(t){throw new Error("No readBackType for VecNil.")}prettyPrint(){return"vecnil"}toString(){return this.prettyPrint()}},Xt=class extends St{head;tail;constructor(t,e){super(),this.head=t,this.tail=e}readBackType(t){throw new Error("No readBackType for VecCons.")}prettyPrint(){return`(vec:: ${this.head.prettyPrint()} ${this.tail.prettyPrint()})`}toString(){return this.prettyPrint()}},Kt=class extends St{leftType;rightType;constructor(t,e){super(),this.leftType=t,this.rightType=e}readBackType(t){return new Xe(this.leftType.readBackType(t),this.rightType.readBackType(t))}prettyPrint(){return`(Either ${this.leftType.prettyPrint()} ${this.rightType.prettyPrint()})`}toString(){return this.prettyPrint()}},jt=class extends St{value;constructor(t){super(),this.value=t}readBackType(t){throw new Error("No readBackType for Left.")}prettyPrint(){return`(left ${this.value.prettyPrint()})`}toString(){return this.prettyPrint()}},Yt=class extends St{value;constructor(t){super(),this.value=t}readBackType(t){throw new Error("No readBackType for Right.")}prettyPrint(){return`(right ${this.value.prettyPrint()})`}toString(){return this.prettyPrint()}};class Zt extends St{type;neutral;constructor(t,e){super(),this.type=t,this.neutral=e}readBackType(t){return this.neutral.readBackNeutral(t)}prettyPrint(){return`(Neutral ${this.type.prettyPrint()} ${this.neutral.prettyPrint()})`}toString(){return this.prettyPrint()}}let Wt=class extends St{constructor(){super()}readBackType(t){return new ue}prettyPrint(){return"U"}toString(){return this.prettyPrint()}},Jt=class extends St{constructor(){super()}readBackType(t){return new ve}prettyPrint(){return"Atom"}toString(){return this.prettyPrint()}},te=class extends St{constructor(){super()}readBackType(t){return new Oe}prettyPrint(){return"Trivial"}toString(){return this.prettyPrint()}},ee=class extends St{constructor(){super()}readBackType(t){throw new Error("No readBackType for Sole.")}prettyPrint(){return"sole"}toString(){return this.prettyPrint()}},ne=class extends St{constructor(){super()}readBackType(t){return new Ie}prettyPrint(){return"Absurd"}toString(){return this.prettyPrint()}},re=class extends St{name;parameters;indices;constructor(t,e,n){super(),this.name=t,this.parameters=e,this.indices=n}readBackType(t){return new tn(this.name,this.parameters.map((e=>e.readBackType(t))),this.indices.map((e=>{if(!(e instanceof At)){const n=e.now();return n instanceof Zt?n.neutral.readBackNeutral(t):tt(t,new Bt,n)}{const n=e.val.get();if(!(n instanceof Lt)){const e=n;return e instanceof Zt?e.neutral.readBackNeutral(t):tt(t,new Bt,e)}try{const n=e.now();return n instanceof Zt?n.neutral.readBackNeutral(t):tt(t,new Bt,n)}catch(t){return n.expr}}})))}prettyPrint(){return`InductiveType ${this.name}`}toString(){return this.prettyPrint()}},se=class extends St{name;parameterTypes;indexTypes;constructor(t,e,n){super(),this.name=t,this.parameterTypes=e,this.indexTypes=n}readBackType(t){return new en(this.name,this.parameterTypes.map((e=>e.readBackType(t))),this.indexTypes.map((e=>e.readBackType(t))))}prettyPrint(){return`InductiveType ${this.name}`}toString(){return this.prettyPrint()}},ie=class extends St{name;type;args;index;recursive_args;constructor(t,e,n,r,s){super(),this.name=t,this.type=e,this.args=n,this.index=r,this.recursive_args=s}readBackType(t){throw new Error("No readBackType for Constructor.")}prettyPrint(){const t=this.args.map((t=>t.prettyPrint())).join(" ");return`(${this.name}${t.length>0?" "+t:""})`}toString(){return this.prettyPrint()}},ae=class extends St{name;index;type;argTypes;rec_argTypes;resultType;numTypeParams;argNames;constructor(t,e,n,r,s,i,a=0,o=[]){super(),this.name=t,this.index=e,this.type=n,this.argTypes=r,this.rec_argTypes=s,this.resultType=i,this.numTypeParams=a,this.argNames=o}readBackType(t){throw Error("Method not implemented")}prettyPrint(){return`ConstructorType (${this.argTypes.map((t=>t.prettyPrint())).join(" ")})`}};class oe{toLazy(t){return new At(new Ot(new Lt(t,this)))}}let ce=class extends oe{type;expr;constructor(t,e){super(),this.type=t,this.expr=e}valOf(t){return this.expr.valOf(t)}prettyPrint(){return`(the ${this.type.prettyPrint()} ${this.expr.prettyPrint()})`}toString(){return this.prettyPrint()}},ue=class extends oe{valOf(t){return new Wt}prettyPrint(){return"U"}toString(){return this.prettyPrint()}},he=class extends oe{valOf(t){return new Bt}prettyPrint(){return"Nat"}toString(){return this.prettyPrint()}},le=class extends oe{valOf(t){return new Ct}prettyPrint(){return"0"}toString(){return this.prettyPrint()}},pe=class extends oe{n;constructor(t){super(),this.n=t}valOf(t){return new Rt(this.n.toLazy(t))}prettyPrint(){return isNaN(Number(this.n.prettyPrint()))?`(add1 ${this.n.prettyPrint()})`:`${Number(this.n.prettyPrint())+1}`}toString(){return this.prettyPrint()}},fe=class extends oe{target;base;step;constructor(t,e,n){super(),this.target=t,this.base=e,this.step=n}valOf(t){return function(t,e,n,r){const s=t.now();if(s instanceof Ct)return n;if(s instanceof Rt)return U(r,s.smaller);if(s instanceof Zt&&s.type.now()instanceof Bt)return new Zt(e,new it(s.neutral,new et(e,n),new et(new qt("n",new Bt,new v((t=>e))),r)));throw new Error(`invalid input for whichNat ${[t,e,n,r]}`)}(this.target.toLazy(t),this.base.type.toLazy(t),this.base.expr.toLazy(t),this.step.toLazy(t))}prettyPrint(){return`(which-Nat ${this.target.prettyPrint()} \n              ${this.base.prettyPrint()} \n              ${this.step.prettyPrint()})`}toString(){return this.prettyPrint()}},ye=class extends oe{target;base;step;constructor(t,e,n){super(),this.target=t,this.base=e,this.step=n}valOf(t){return H(this.target.toLazy(t),this.base.type.toLazy(t),this.base.expr.toLazy(t),this.step.toLazy(t))}prettyPrint(){return`(iter-Nat ${this.target.prettyPrint()} \n              ${this.base.prettyPrint()} \n              ${this.step.prettyPrint()})`}toString(){return this.prettyPrint()}},we=class extends oe{target;base;step;constructor(t,e,n){super(),this.target=t,this.base=e,this.step=n}valOf(t){return D(this.target.toLazy(t),this.base.type.toLazy(t),this.base.expr.toLazy(t),this.step.toLazy(t))}prettyPrint(){return`(rec-Nat ${this.target.prettyPrint()} \n              ${this.base.prettyPrint()} \n              ${this.step.prettyPrint()})`}toString(){return this.prettyPrint()}},de=class extends oe{target;motive;base;step;constructor(t,e,n,r){super(),this.target=t,this.motive=e,this.base=n,this.step=r}valOf(t){return F(this.target.toLazy(t),this.motive.toLazy(t),this.base.toLazy(t),this.step.toLazy(t))}prettyPrint(){return`(ind-Nat ${this.target.prettyPrint()} \n              ${this.motive.prettyPrint()} \n              ${this.base.prettyPrint()} \n              ${this.step.prettyPrint()})`}toString(){return this.prettyPrint()}},me=class extends oe{name;type;body;constructor(t,e,n){super(),this.name=t,this.type=e,this.body=n}valOf(t){const e=this.type.toLazy(t);return new qt(this.name,e,new g(t,this.name,this.body))}prettyPrint(){return`(Π (${this.name} ${this.type.prettyPrint()}) \n          ${this.body.prettyPrint()})`}toString(){return this.prettyPrint()}},ge=class extends oe{param;body;constructor(t,e){super(),this.param=t,this.body=e}valOf(t){return new Mt(this.param,new g(t,this.param,this.body))}prettyPrint(){return`(λ (${this.param}) ${this.body.prettyPrint()})`}toString(){return this.prettyPrint()}},ve=class extends oe{valOf(t){return new Jt}prettyPrint(){return"Atom"}toString(){return this.prettyPrint()}},Te=class extends oe{sym;constructor(t){super(),this.sym=t}valOf(t){return new It(this.sym)}prettyPrint(){return`'${this.sym}`}toString(){return this.prettyPrint()}},Ee=class extends oe{name;type;body;constructor(t,e,n){super(),this.name=t,this.type=e,this.body=n}valOf(t){const e=this.type.toLazy(t);return new _t(this.name,e,new g(t,this.name,this.body))}prettyPrint(){return`(Σ (${this.name} ${this.type.prettyPrint()}) \n              ${this.body.prettyPrint()})`}toString(){return this.prettyPrint()}},Ne=class extends oe{first;second;constructor(t,e){super(),this.first=t,this.second=e}valOf(t){const e=this.first.toLazy(t),n=this.second.toLazy(t);return new Gt(e,n)}prettyPrint(){return`(cons ${this.first.prettyPrint()} ${this.second.prettyPrint()})`}toString(){return this.prettyPrint()}},Pe=class extends oe{pair;constructor(t){super(),this.pair=t}valOf(t){return V(this.pair.toLazy(t))}prettyPrint(){return`(car ${this.pair.prettyPrint()})`}toString(){return this.prettyPrint()}},xe=class extends oe{pair;constructor(t){super(),this.pair=t}valOf(t){return Q(this.pair.toLazy(t))}prettyPrint(){return`(cdr ${this.pair.prettyPrint()})`}toString(){return this.prettyPrint()}},be=class extends oe{head;tail;constructor(t,e){super(),this.head=t,this.tail=e}valOf(t){const e=this.head.toLazy(t),n=this.tail.toLazy(t);return new Ht(e,n)}prettyPrint(){return`(:: ${this.head.prettyPrint()} ${this.tail.prettyPrint()})`}toString(){return this.prettyPrint()}},ke=class extends oe{valOf(t){return new Ut}prettyPrint(){return"nil"}toString(){return this.prettyPrint()}},$e=class extends oe{elemType;constructor(t){super(),this.elemType=t}valOf(t){return new zt(this.elemType.toLazy(t))}prettyPrint(){return`(List ${this.elemType.prettyPrint()})`}toString(){return this.prettyPrint()}},Se=class extends oe{target;base;step;constructor(t,e,n){super(),this.target=t,this.base=e,this.step=n}valOf(t){return K(this.target.toLazy(t),this.base.type.toLazy(t),this.base.expr.toLazy(t),this.step.toLazy(t))}prettyPrint(){return`(rec-List ${this.target.prettyPrint()} \n              ${this.base.prettyPrint()} \n              ${this.step.prettyPrint()})`}toString(){return this.prettyPrint()}},Le=class extends oe{target;motive;base;step;constructor(t,e,n,r){super(),this.target=t,this.motive=e,this.base=n,this.step=r}valOf(t){return X(this.target.toLazy(t),this.motive.toLazy(t),this.base.toLazy(t),this.step.toLazy(t))}prettyPrint(){return`(ind-List ${this.target.prettyPrint()} \n              ${this.motive.prettyPrint()} \n              ${this.base.prettyPrint()} \n              ${this.step.prettyPrint()})`}toString(){return this.prettyPrint()}},Oe=class extends oe{valOf(t){return new te}prettyPrint(){return"Trivial"}toString(){return this.prettyPrint()}},Ae=class extends oe{valOf(t){return new ee}prettyPrint(){return"sole"}toString(){return this.prettyPrint()}},Ie=class extends oe{valOf(t){return new ne}prettyPrint(){return"Absurd"}toString(){return this.prettyPrint()}},Be=class extends oe{target;motive;constructor(t,e){super(),this.target=t,this.motive=e}valOf(t){return function(t,e){const n=t.now();if(n instanceof Zt&&n.type.now()instanceof ne)return new Zt(e,new ft(n.neutral,new et(new Wt,e)));throw new Error(`invalid input for indAbsurd ${[t,e]}`)}(this.target.toLazy(t),this.motive.toLazy(t))}prettyPrint(){return`(ind-Absurd \n              ${this.target.prettyPrint()} \n              ${this.motive.prettyPrint()})`}toString(){return this.prettyPrint()}},Ce=class extends oe{type;left;right;constructor(t,e,n){super(),this.type=t,this.left=e,this.right=n}valOf(t){return new Dt(this.type.toLazy(t),this.left.toLazy(t),this.right.toLazy(t))}prettyPrint(){return`(= ${this.type.prettyPrint()} \n              ${this.left.prettyPrint()} \n              ${this.right.prettyPrint()})`}toString(){return this.prettyPrint()}},Re=class extends oe{type;constructor(t){super(),this.type=t}valOf(t){return new Ft(this.type.toLazy(t))}prettyPrint(){return`(same ${this.type.prettyPrint()})`}toString(){return this.prettyPrint()}},qe=class extends oe{target;motive;base;constructor(t,e,n){super(),this.target=t,this.motive=e,this.base=n}valOf(t){return function(t,e,n){const r=t.now();if(r instanceof Ft)return n;if(r instanceof Zt){const t=r.type.now();if(t instanceof Dt){const s=r.neutral,i=t.type,a=t.from,o=t.to;return new Zt(U(e,o),new yt(s,new et(new qt("x",i,new v((t=>new Wt))),e),new et(U(e,a),n)))}}throw new Error(`invalid input for replace ${[t,e,n]}`)}(this.target.toLazy(t),this.motive.toLazy(t),this.base.toLazy(t))}prettyPrint(){return`(replace ${this.target.prettyPrint()} \n              ${this.motive.prettyPrint()} \n              ${this.base.prettyPrint()})`}toString(){return this.prettyPrint()}},Me=class extends oe{left;right;constructor(t,e){super(),this.left=t,this.right=e}valOf(t){return function(t,e){const n=t.now(),r=e.now();if(n instanceof Ft&&r instanceof Ft)return new Ft(n.value);if(n instanceof Ft&&r instanceof Zt){const t=r.type.now();if(t instanceof Dt){const e=n.value,s=t.to,i=t.type,a=r.neutral;return new Zt(new Dt(i,e,s),new dt(new et(new Dt(i,e,e),new Ft(e)),a))}}else if(n instanceof Zt&&r instanceof Ft){const t=n.type.now();if(t instanceof Dt){const e=t.from,s=r.value,i=t.type,a=n.neutral;return new Zt(new Dt(i,e,s),new wt(a,new et(new Dt(i,s,s),new Ft(s))))}}else if(n instanceof Zt&&r instanceof Zt){const t=n.type.now(),e=r.type.now();if(t instanceof Dt&&e instanceof Dt){const s=t.from,i=e.to,a=t.type,o=n.neutral,c=r.neutral;return new Zt(new Dt(a,s,i),new mt(o,c))}}throw new Error(`invalid input for do-trans: ${[t,e]}`)}(this.left.toLazy(t),this.right.toLazy(t))}prettyPrint(){return`(trans ${this.left.prettyPrint()} ${this.right.prettyPrint()})`}toString(){return this.prettyPrint()}},_e=class extends oe{target;base;fun;constructor(t,e,n){super(),this.target=t,this.base=e,this.fun=n}valOf(t){return function(t,e,n){const r=t.now();if(r instanceof Ft)return new Ft(U(n,r.value));if(r instanceof Zt){const t=r.type.now();if(t instanceof Dt){const s=t.type,i=t.from,a=t.to,o=r.neutral;return new Zt(new Dt(e,U(n,i),U(n,a)),new gt(o,new et(new qt("x",s,new v((t=>e))),n)))}}throw new Error(`invalid input for cong ${[t,e,n]}`)}(this.target.toLazy(t),this.base.toLazy(t),this.fun.toLazy(t))}prettyPrint(){return`(cong ${this.target.prettyPrint()} ${this.fun.prettyPrint()})`}toString(){return this.prettyPrint()}},Ge=class extends oe{equality;constructor(t){super(),this.equality=t}valOf(t){return function(t){const e=t.now();if(e instanceof Ft)return new Ft(e.value);if(e instanceof Zt){const t=e.type.now();if(t instanceof Dt)return new Zt(new Dt(t.type,t.to,t.from),new vt(e.neutral))}throw new Error(`invalid input for symm 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Vt(this.type.toLazy(t),this.length.toLazy(t))}prettyPrint(){return`(Vec ${this.type.prettyPrint()} ${this.length.prettyPrint()})`}toString(){return this.prettyPrint()}},He=class extends oe{head;tail;constructor(t,e){super(),this.head=t,this.tail=e}valOf(t){return new Xt(this.head.toLazy(t),this.tail.toLazy(t))}prettyPrint(){return`(vec:: ${this.head.prettyPrint()} ${this.tail.prettyPrint()})`}toString(){return this.prettyPrint()}},De=class extends oe{valOf(t){return new Qt}prettyPrint(){return"vecnil"}toString(){return this.prettyPrint()}},Fe=class extends oe{vec;constructor(t){super(),this.vec=t}valOf(t){return function(t){const e=t.now();if(e instanceof Xt)return e.head;if(e instanceof Zt){const t=e.type.now();if(t instanceof Vt&&t.length.now()instanceof Rt)return new Zt(t.entryType,new Et(e.neutral))}throw new Error(`invalid input for head ${t}`)}(this.vec.toLazy(t))}prettyPrint(){return`(head ${this.vec.prettyPrint()})`}toString(){return this.prettyPrint()}},Ve=class extends oe{vec;constructor(t){super(),this.vec=t}valOf(t){return j(this.vec.toLazy(t))}prettyPrint(){return`(tail ${this.vec.prettyPrint()})`}toString(){return this.prettyPrint()}},Qe=class extends oe{length;target;motive;base;step;constructor(t,e,n,r,s){super(),this.length=t,this.target=e,this.motive=n,this.base=r,this.step=s}valOf(t){return Z(this.length.toLazy(t),this.target.toLazy(t),this.motive.toLazy(t),this.base.toLazy(t),this.step.toLazy(t))}prettyPrint(){return`ind-Vec ${this.length.prettyPrint()}\n              ${this.target.prettyPrint()}\n              ${this.motive.prettyPrint()}\n              ${this.base.prettyPrint()}\n              ${this.step.prettyPrint()}`}toString(){return this.prettyPrint()}},Xe=class extends oe{left;right;constructor(t,e){super(),this.left=t,this.right=e}valOf(t){return new Kt(this.left.toLazy(t),this.right.toLazy(t))}prettyPrint(){return`(Either ${this.left.prettyPrint()} ${this.right.prettyPrint()})`}toString(){return this.prettyPrint()}},Ke=class extends oe{value;constructor(t){super(),this.value=t}valOf(t){return new jt(this.value.toLazy(t))}prettyPrint(){return`(left ${this.value.prettyPrint()})`}toString(){return this.prettyPrint()}},je=class extends oe{value;constructor(t){super(),this.value=t}valOf(t){return new Yt(this.value.toLazy(t))}prettyPrint(){return`(right ${this.value.prettyPrint()})`}toString(){return this.prettyPrint()}},Ye=class extends oe{target;motive;baseLeft;baseRight;constructor(t,e,n,r){super(),this.target=t,this.motive=e,this.baseLeft=n,this.baseRight=r}valOf(t){return function(t,e,n,r){const s=t.now();if(s instanceof jt)return U(n,s.value);if(s instanceof Yt)return U(r,s.value);if(s instanceof Zt){const i=s.type.now();if(i instanceof Kt){const a=i.leftType,o=i.rightType,c=new qt("x",new Kt(a,o),new v((t=>new Wt)));return new Zt(U(e,t),new bt(s.neutral,new et(c,e),new et(new qt("x",a,new v((t=>U(e,new jt(t))))),n),new et(new qt("x",o,new v((t=>U(e,new Yt(t))))),r)))}}throw new Error(`invalid input for 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hn(t,e,n,r.target,s.target)&&hn(t,e,n,r.motive,s.motive)&&hn(t,e,n,r.base,s.base)&&hn(t,e,n,r.step,s.step);if(r instanceof Ne&&s instanceof Ne)return hn(t,e,n,r.first,s.first)&&hn(t,e,n,r.second,s.second);if(r instanceof Pe&&s instanceof Pe)return hn(t,e,n,r.pair,s.pair);if(r instanceof xe&&s instanceof xe)return hn(t,e,n,r.pair,s.pair);if(r instanceof be&&s instanceof be)return hn(t,e,n,r.head,s.head)&&hn(t,e,n,r.tail,s.tail);if(r instanceof Se&&s instanceof Se)return hn(t,e,n,r.target,s.target)&&hn(t,e,n,r.base,s.base)&&hn(t,e,n,r.step,s.step);if(r instanceof Le&&s instanceof Le)return hn(t,e,n,r.target,s.target)&&hn(t,e,n,r.motive,s.motive)&&hn(t,e,n,r.base,s.base)&&hn(t,e,n,r.step,s.step);if(r instanceof Be&&s instanceof Be)return hn(t,e,n,r.target,s.target)&&hn(t,e,n,r.motive,s.motive);if(r instanceof Ce&&s instanceof Ce)return hn(t,e,n,r.type,s.type)&&hn(t,e,n,r.left,s.left)&&hn(t,e,n,r.right,s.right);if(r instanceof Re&&s instanceof Re)return hn(t,e,n,r.type,s.type);if(r 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hn(t,e,n,r.length,s.length)&&hn(t,e,n,r.target,s.target)&&hn(t,e,n,r.motive,s.motive)&&hn(t,e,n,r.base,s.base)&&hn(t,e,n,r.step,s.step);if(r instanceof Xe&&s instanceof Xe)return hn(t,e,n,r.left,s.left)&&hn(t,e,n,r.right,s.right);if(r instanceof Ke&&s instanceof Ke)return hn(t,e,n,r.value,s.value);if(r instanceof je&&s instanceof je)return hn(t,e,n,r.value,s.value);if(r instanceof Ye&&s instanceof Ye)return hn(t,e,n,r.target,s.target)&&hn(t,e,n,r.motive,s.motive)&&hn(t,e,n,r.baseLeft,s.baseLeft)&&hn(t,e,n,r.baseRight,s.baseRight);if(r instanceof Ze&&s instanceof Ze)return function(t,e){return t.startLine===e.startLine&&t.startColumn===e.startColumn&&t.endLine===e.endLine&&t.endColumn===e.endColumn}(r.loc,s.loc)&&hn(t,e,n,r.type,s.type);if(r instanceof tn&&s instanceof tn){if(r.typeName!==s.typeName)return!1;if(r.parameters.length!==s.parameters.length)return!1;if(r.indices.length!==s.indices.length)return!1;for(let 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Tn{start;end;source;constructor(t,e,n){this.start=t,this.end=e,this.source=n}}let En=class{syntax;forInfo;constructor(t,e){this.syntax=t,this.forInfo=e}locationToSrcLoc(){return new vn(this.syntax.source,this.syntax.start.line,this.syntax.start.column,this.syntax.end.line,this.syntax.end.column)}toString(){return`${this.syntax.source}:${this.syntax.start.line}:${this.syntax.start.column}`}};function Nn(t){return new En(t.syntax,!1)}class Pn{static synthNat(t,e){return new f(new ce(new ue,new he))}static synthUniverse(t,e,n){return new y(n,new l(["U is a type, but it does not have a type."]))}static synthArrow(t,e,n,r,s,i){if(0===i.length){const n=P(t,s,"x"),i=new w("Aout"),a=new w("Bout");return d([[i,()=>r.check(t,e,new Wt)],[a,()=>s.check(z(t,n,k(t,i.value)),e,new Wt)]],(()=>new f(new ce(new ue,new me(n,i.value,a.value)))))}{const[a,...o]=i,c=P(t,gn(s,a,o),"x"),u=new w("Aout"),h=new w("tout");return d([[u,()=>r.check(t,e,new Wt)],[h,()=>new Cn(Nn(n),s,a,o).check(z(t,c,k(t,u.value)),e,new Wt)]],(()=>new f(new ce(new ue,new me(c,u.value,h.value)))))}}static synthPi(t,e,n,r,s){if(1===r.length){const[n,i]=[r[0].binder,r[0].type],a=N(t,n.varName),o=(n.location,new w("Aout")),c=new w("Bout");return d([[o,()=>i.check(t,e,new Wt)],[c,()=>s.check(z(t,a,k(t,o.value)),fn(e,n.varName,a),new Wt)]],(()=>(o.value,new f(new ce(new ue,new me(a,o.value,c.value))))))}if(r.length>1){const[i,...a]=r,[o,c]=[i.binder,i.type],u=(o.location,o.varName),h=N(t,u),l=new w("Aout"),p=new w("Bout");return d([[l,()=>c.check(t,e,new Wt)],[p,()=>new Rn(Nn(n),a,s).check(z(t,h,k(t,l.value)),fn(e,u,h),new Wt)]],(()=>(l.value,new f(new ce(new ue,new me(h,l.value,p.value))))))}throw new Error("Invalid number of binders in Pi type")}static synthZero(t,e){return new f(new ce(new he,new le))}static synthAdd1(t,e,n){const r=new w("nout");return d([[r,()=>n.check(t,e,new Bt)]],(()=>new f(new ce(new he,new pe(r.value)))))}static synthWhichNat(t,e,n,r,s){const i=new w("tgtout"),a=new w("bout"),o=new w("sout");let c=N(t,"n_minus_1");return d([[i,()=>n.check(t,e,new Bt)],[a,()=>r.synth(t,e)],[o,()=>s.check(t,e,new qt(c,new Bt,new g(O(t),c,a.value.type)))]],(()=>new f(new ce(a.value.type,new fe(i.value,new ce(a.value.type,a.value.expr),o.value)))))}static synthIterNat(t,e,n,r,s){const i=new w("tgtout"),a=new w("bout"),o=new w("sout");return d([[i,()=>n.check(t,e,new Bt)],[a,()=>r.synth(t,e)],[o,()=>s.check(t,e,(()=>{const e=N(t,"old");return k(t,new me(e,a.value.type,a.value.type))})())]],(()=>new f(new ce(a.value.type,new ye(i.value,new ce(a.value.type,a.value.expr),o.value)))))}static synthRecNat(t,e,n,r,s){const i=new w("tgtout"),a=new w("bout"),o=new w("sout");return d([[i,()=>n.check(t,e,new Bt)],[a,()=>r.synth(t,e)],[o,()=>s.check(t,e,(()=>{const e=N(t,"n_minus_1"),n=N(t,"old");return k(t,new me(e,new he,new me(n,a.value.type,a.value.type)))})())]],(()=>new f(new ce(a.value.type,new we(i.value,new ce(a.value.type,a.value.expr),o.value)))))}static synthIndNat(t,e,n,r,s,i){const a=new w("tgtout"),o=new w("motout"),c=new w("motval"),u=new w("bout"),h=new w("sout");return d([[a,()=>n.check(t,e,new Bt)],[o,()=>r.check(t,e,new qt("n",new Bt,new v((t=>new Wt))))],[c,()=>new f(k(t,o.value))],[u,()=>s.check(t,e,U(c.value,new Ct))],[h,()=>i.check(t,e,new qt("n-1",new Bt,new v((t=>new qt("x",U(c.value,t),new v((e=>U(c.value,new Rt(t)))))))))]],(()=>new f(new ce(new We(o.value,a.value),new de(a.value,o.value,u.value,h.value)))))}static synthAtom(t,e){return new f(new ce(new ue,new ve))}static synthPair(t,e,n,r){const s=N(t,"a"),i=new w("Aout"),a=new w("Dout");return d([[i,()=>n.check(t,e,new Wt)],[a,()=>r.check(z(t,s,k(t,i.value)),e,new Wt)]],(()=>new f(new ce(new ue,new Ee(s,i.value,a.value)))))}static synthSigma(t,e,n,r,s){if(1===r.length){const[n,i]=[r[0].binder,r[0].type],a=N(t,n.varName),o=(n.location,new w("Aout")),c=new w("Dout");return d([[o,()=>i.check(t,e,new Wt)],[c,()=>s.check(z(t,a,k(t,o.value)),fn(e,n.varName,a),new Wt)]],(()=>(o.value,new f(new ce(new ue,new Ee(a,o.value,c.value))))))}if(r.length>1){const[i,...a]=r,[o,c]=[i.binder,i.type],u=(o.location,o.varName),h=N(t,u),l=new w("Aout"),p=new w("Dout");return d([[l,()=>c.check(t,e,new Wt)],[p,()=>new Mn(Nn(n),a,s).check(z(t,h,k(t,l.value)),fn(e,u,h),new Wt)]],(()=>(l.value,new f(new ce(new ue,new Ee(h,l.value,p.value))))))}throw new Error("Invalid number of binders in Sigma type")}static synthCar(t,e,n,r){const s=new w("p_rst");return d([[s,()=>r.synth(t,e)]],(()=>{const e=k(t,s.value.type);return e instanceof _t?new f(new ce(e.carType.readBackType(t),new Pe(s.value.expr))):new y(n,new l([`car requires a Pair type, but was used as a: ${e}.`]))}))}static synthCdr(t,e,n,r){const s=new w("pout");return d([[s,()=>r.synth(t,e)]],(()=>{const e=k(t,s.value.type);if(e instanceof _t){const[n,r,i]=[e.carName,e.carType,e.cdrType];return new f(new ce(i.valOfClosure(V(k(t,s.value.expr))).readBackType(t),new xe(s.value.expr)))}return new y(n,new l([`cdr requires a Pair type, but was used as a: ${e}.`]))}))}static synthQuote(t,e,n,r){return dn(r)?new f(new ce(new ve,new Te(r))):new y(n,new l([`Invalid atom: ${r}. Atoms consist of letters and hyphens.`]))}static synthTrivial(t,e){return new f(new ce(new ue,new Oe))}static synthSole(t,e){return new f(new ce(new Oe,new Ae))}static synthIndList(t,e,n,r,s,i,a){const o=new w("tgtout"),c=new w("motout"),u=new w("motval"),h=new w("bout"),p=new w("sout");return d([[o,()=>r.synth(t,e)]],(()=>{const[r,w]=[o.value.type,o.value.expr],m=k(t,r);if(m instanceof zt){const n=m.entryType;return d([[c,()=>s.check(t,e,new qt("xs",new zt(n),new g(O(t),"xs",new ue)))],[u,()=>new f(k(t,c.value))],[h,()=>i.check(t,e,U(u.value,new Ut))],[p,()=>a.check(t,e,new qt("e",n,new v((t=>new qt("es",new zt(n),new v((e=>new qt("ih",U(u.value,e),new v((n=>U(u.value,new Ht(t,e))))))))))))]],(()=>new f(new ce(new We(c.value,w),new Le(w,c.value,h.value,p.value)))))}return new y(n,new l([`Not a List: ${m.readBackType(t)}.`]))}))}static synthRecList(t,e,n,r,s,i){const a=new w("tgtout");return d([[a,()=>r.synth(t,e)]],(()=>{const[r,o]=[a.value.type,a.value.expr],c=k(t,r);if(c instanceof zt){const n=c.entryType,r=new w("bout"),a=new w("btval"),u=new w("sout");return d([[r,()=>s.synth(t,e)],[a,()=>new f(k(t,r.value.type))],[u,()=>i.check(t,e,new qt("e",n,new v((t=>new qt("es",new zt(n),new v((t=>new qt("ih",a.value,new v((t=>a.value))))))))))]],(()=>new f(new ce(r.value.type,new Se(o,new ce(r.value.type,r.value.expr),u.value)))))}return new y(n,new l([`Not a List: ${c.readBackType(t)}.`]))}))}static synthList(t,e,n){const r=new w("Eout");return d([[r,()=>n.entryType.check(t,e,new Wt)]],(()=>new f(new ce(new ue,new $e(r.value)))))}static synthListCons(t,e,n,r){const s=new w("eout"),i=new w("esout");return d([[s,()=>n.synth(t,e)],[i,()=>r.check(t,e,k(t,new $e(s.value.type)))]],(()=>new f(new ce(new $e(s.value.type),new be(s.value.expr,i.value)))))}static synthAbsurd(t,e,n){return new f(new ce(new ue,new Ie))}static synthIndAbsurd(t,e,n){const r=new w("tgtout"),s=new w("motout");return d([[r,()=>n.target.check(t,e,new ne)],[s,()=>n.motive.check(t,e,new Wt)]],(()=>new f(new ce(s.value,new Be(r.value,s.value)))))}static synthEqual(t,e,n,r,s){const i=new w("Aout"),a=new w("Av"),o=new w("from_out"),c=new w("to_out");return d([[i,()=>n.check(t,e,new Wt)],[a,()=>new f(k(t,i.value))],[o,()=>r.check(t,e,a.value)],[c,()=>s.check(t,e,a.value)]],(()=>new f(new ce(new ue,new Ce(i.value,o.value,c.value)))))}static synthReplace(t,e,n,r,s,i){const a=new w("tgt_rst"),o=new w("motout"),c=new w("bout");return d([[a,()=>r.synth(t,e)]],(()=>{const r=k(t,a.value.type);if(r instanceof Dt){const[n,u,h]=[r.type,r.from,r.to];return d([[o,()=>s.check(t,e,new qt("x",n,new v((t=>new Wt))))],[c,()=>i.check(t,e,U(k(t,o.value),u))]],(()=>new f(new ce(U(k(t,o.value),h).readBackType(t),new qe(a.value.expr,o.value,c.value)))))}return new y(n,new l([`Expected an expression with = type, but the type was: ${a.value.type}.`]))}))}static synthTrans(t,e,n,r,s){const i=new w("p1_rst"),a=new w("p2_rst");return d([[i,()=>r.synth(t,e)],[a,()=>s.synth(t,e)]],(()=>{const e=k(t,i.value.type),r=k(t,a.value.type);if(e instanceof Dt&&r instanceof Dt){const[s,o,c]=[e.type,e.from,e.to],[u,h,l]=[r.type,r.from,r.to];return d([[new w("_"),()=>yn(t,n,s,u)],[new w("_"),()=>wn(t,n,s,c,h)]],(()=>new f(new ce(new Dt(s,o,l).readBackType(t),new Me(i.value.expr,a.value.expr)))))}return new y(n,new l([`Expected =, got ${e} and ${r}.`]))}))}static synthCong(t,e,n,r,s){const i=new w("bout"),a=new w("f_rst");return d([[i,()=>r.synth(t,e)],[a,()=>s.synth(t,e)]],(()=>{const e=k(t,i.value.type),r=k(t,a.value.type);if(e instanceof Dt){const[s,o,c]=[e.type,e.from,e.to];if(r instanceof qt){const[e,u,h]=[r.argName,r.argType,r.resultType],l=new w("ph"),p=new w("Cv"),y=new w("fv");return d([[l,()=>yn(t,n,s,u)],[p,()=>new f(h.valOfClosure(o))],[y,()=>new f(k(t,a.value.expr))]],(()=>new f(new ce(new Ce(p.value.readBackType(t),tt(t,p.value,U(y.value,o)),tt(t,p.value,U(y.value,c))),new _e(i.value.expr,p.value.readBackType(t),a.value.expr)))))}return new y(n,new l([`Expected a function type, got ${r.readBackType(t)}.`]))}return new y(n,new l([`Expected an = type, got ${e.readBackType(t)}.`]))}))}static synthSymm(t,e,n,r){const s=new w("eout");return d([[s,()=>r.synth(t,e)]],(()=>{const e=k(t,s.value.type);if(e instanceof Dt){const[n,r,i]=[e.type,e.from,e.to];return new f(new ce(new Dt(n,i,r).readBackType(t),new Ge(s.value.expr)))}return new y(n,new l([`Expected an = type, got ${e.readBackType(t)}.`]))}))}static synthIndEqual(t,e,n,r,s,i){const a=new w("tgtout"),o=new w("motout"),c=new w("motv"),u=new w("baseout");return d([[a,()=>r.synth(t,e)]],(()=>{const r=k(t,a.value.type);if(r instanceof Dt){const[n,h,l]=[r.type,r.from,r.to];return d([[o,()=>s.check(t,e,new qt("to",n,new v((t=>new qt("p",new Dt(n,h,t),new v((t=>new Wt)))))))],[c,()=>new f(k(t,o.value))],[u,()=>i.check(t,e,U(U(c.value,h),new Ft(h)))]],(()=>new f(new ce(U(U(c.value,l),k(t,a.value.expr)).readBackType(t),new ze(a.value.expr,o.value,u.value)))))}return new y(n,new l([`Expected evidence of equality, got ${r.readBackType(t)}.`]))}))}static synthVec(t,e,n,r){const s=new w("tout"),i=new w("lenout");return d([[s,()=>n.check(t,e,new Wt)],[i,()=>r.check(t,e,new Bt)]],(()=>new f(new ce(new ue,new Ue(s.value,i.value)))))}static synthHead(t,e,n,r){const s=new w("vout");return d([[s,()=>r.synth(t,e)]],(()=>{const e=k(t,s.value.type).now();if(e instanceof Vt){const[r,i]=[e.entryType,e.length];return i.now()instanceof Rt?new f(new ce(r.readBackType(t),new Fe(s.value.expr))):new y(n,new l([`Expected a Vec with add1 at the top of the length, got ${tt(t,new Bt,i)}.`]))}return new y(n,new l([`Expected a Vec, got ${e.readBackType(t)}.`]))}))}static synthTail(t,e,n,r){const s=new w("vout");return d([[s,()=>r.synth(t,e)]],(()=>{const e=k(t,s.value.type).now();if(e instanceof Vt){const[r,i]=[e.entryType,e.length],a=i.now();if(a instanceof Rt){const e=a.smaller;return new f(new ce(new Ue(r.readBackType(t),tt(t,new Bt,e)),new Ve(s.value.expr)))}return new y(n,new l([`Expected a Vec with add1 at the top of the length, got ${tt(t,new Bt,i)}.`]))}return new y(n,new l([`Expected a Vec, got ${e.readBackType(t)}.`]))}))}static synthIndVec(t,e,n,r,s,i,a,o){const c=new w("lenout"),u=new w("lenv"),h=new w("vecout"),p=new w("motout"),m=new w("motval"),g=new w("bout"),T=new w("sout");return d([[c,()=>r.check(t,e,new Bt)],[u,()=>new f(k(t,c.value))],[h,()=>s.synth(t,e)]],(()=>{const r=k(t,h.value.type);if(r instanceof Vt){const[s,l]=[r.entryType,r.length];return d([[new w("_"),()=>wn(t,n,new Bt,u.value,l)],[p,()=>i.check(t,e,new qt("k",new Bt,new v((t=>new qt("es",new Vt(s,t),new v((t=>new Wt)))))))],[m,()=>new f(k(t,p.value))],[g,()=>a.check(t,e,U(U(m.value,new Ct),new Qt))],[T,()=>o.check(t,e,Y(s,m.value))]],(()=>new f(new ce(new We(new We(p.value,c.value),h.value.expr),new Qe(c.value,h.value.expr,p.value,g.value,T.value)))))}return new y(n,new l([`Expected a Vec, got ${r.readBackType(t)}.`]))}))}static synthEither(t,e,n,r){const s=new w("Lout"),i=new w("Rout");return d([[s,()=>n.check(t,e,new Wt)],[i,()=>r.check(t,e,new Wt)]],(()=>new f(new ce(new ue,new Xe(s.value,i.value)))))}static synthIndEither(t,e,n,r,s,i,a){const o=new w("tgtout"),c=new w("motout"),u=new w("motval"),h=new w("lout"),p=new w("rout");return d([[o,()=>r.synth(t,e)]],(()=>{const r=k(t,o.value.type);if(r instanceof Kt){const[n,l]=[r.leftType,r.rightType];return d([[c,()=>s.check(t,e,new qt("x",new Kt(n,l),new v((t=>new Wt))))],[u,()=>new f(k(t,c.value))],[h,()=>i.check(t,e,new qt("x",n,new v((t=>U(u.value,new jt(t))))))],[p,()=>a.check(t,e,new qt("x",l,new v((t=>U(u.value,new Yt(t))))))]],(()=>new f(new ce(new We(c.value,o.value.expr),new Ye(o.value.expr,c.value,h.value,p.value)))))}return new y(n,new l([`Expected an Either, but got a ${r.readBackType(t)}.`]))}))}static synthThe(t,e,n,r){const s=new w("t_out"),i=new w("e_out");return d([[s,()=>n.isType(t,e)],[i,()=>r.check(t,e,k(t,s.value))]],(()=>new f(new ce(s.value,i.value))))}static synthApplication(t,e,n,r,s,i){if(0===i.length){const i=new w("fout");return d([[i,()=>r.synth(t,e)]],(()=>{const r=k(t,i.value.type);if(r instanceof qt){const[n,a,o]=[r.argName,r.argType,r.resultType],c=new w("argout");return d([[c,()=>s.check(t,e,a)]],(()=>new f(new ce(o.valOfClosure(k(t,c.value)).readBackType(t),new We(i.value.expr,c.value)))))}return new y(n,new l([`Not a function type: ${r.readBackType(t)}.`]))}))}{const a=new w("appout");return d([[a,()=>new vr(Nn(n),r,s,i.slice(0,i.length-1)).synth(t,e)]],(()=>{const r=k(t,a.value.type);if(r instanceof qt){const[n,s,o]=[r.argName,r.argType,r.resultType],c=new w("fout");return d([[c,()=>i[i.length-1].check(t,e,s)]],(()=>new f(new ce(o.valOfClosure(k(t,c.value)).readBackType(t),new We(a.value.expr,c.value)))))}return new y(n,new l([`Not a function type: ${r.readBackType(t)}.`]))}))}}static synthName(t,e,n,r){const s=pn(e,r),i=new w("x_tv");return d([[i,()=>G(t,0,s)]],(()=>{const e=t.get(s);if(e instanceof M){const n=e.type;return new f(new ce(new ue,new tn(n.name,n.parameterTypes.map((e=>e.readBackType(t))),n.indexTypes.map((e=>e.readBackType(t))))))}return new f(new ce(i.value.readBackType(t),new Je(s)))}))}static synthNumber(t,e,n,r){if(0===r)return new f(new ce(new he,new le));if(r>0){const s=new w("n_1_out");return d([[s,()=>new Kn(n,r-1).check(t,e,new Bt)]],(()=>new f(new ce(new he,new pe(s.value)))))}return new y(n,new l([`Expected a positive number, got ${r}.`]))}static synthConstructorApplication(t,e,n){const r=t.get(n.constructorName);if(!(r&&r instanceof _))throw new Error(`Unknown constructor: ${n.constructorName}`);const s=r.constructorType,i=s.argTypes.concat(s.rec_argTypes);let a=t,o=e;if(i.length!==n.args.length)return new y(n.location,new l([`Expected ${i.length} arguments, got ${n.args.length}`]));const c=[];let u,h=new Map(O(t));for(let e=0;e<s.numTypeParams&&e<n.args.length;e++){const r=n.args[e].check(a,o,new Wt);if(r instanceof y)return r;const s=r.result;c.push(s);const u=k(t,s);for(let t=e+1;t<i.length;t++)i[t]instanceof Je&&h.set(i[t].name,u)}for(let e=s.numTypeParams;e<n.args.length;e++){const r=i[e].valOf(h),u=n.args[e].check(a,o,r);if(u instanceof y)return u;const l=u.result;if(c.push(l),e<s.argNames.length){const n=s.argNames[e],r=k(t,l);h.set(n,r)}}if(s.numTypeParams>0){const e=new Map(O(t)),n=[];for(let e=0;e<s.numTypeParams;e++)n.push(k(t,c[e]));const r=t=>t instanceof Je?[t.name]:t instanceof tn?[...t.parameters.flatMap((t=>r(t))),...t.indices.flatMap((t=>r(t)))]:t instanceof pe?r(t.n):[],a=r(s.resultType);for(let t=0;t<Math.min(a.length,n.length);t++)e.set(a[t],n[t]);for(let t=0;t<i.length;t++){0===r(i[t]).length&&i[t]}for(const[t,n]of h)e.has(t)||e.set(t,n);u=s.resultType.valOf(e)}else u=s.resultType.valOf(h);return new f(new ce(u.readBackType(t),new nn(n.constructorName,s.index,s.type,c.slice(0,s.argTypes.length),c.slice(s.argTypes.length))))}static synthGeneralEliminator(t,e,n){const r=A(t,n.location,n.typeName);if(r instanceof y)return r;const s=r.result.type,i=n.target.synth(t,e);if(i instanceof y)return i;const a=i.result,o=k(t,a.type);if(!(o instanceof re)||o.name!==n.typeName)return new y(n.location,new l([`Expected type ${n.typeName}, got ${o.readBackType(t)}`]));let c=s.indexTypes;const u=(e,n)=>{if(e>=c.length)return new qt("target",new re(o.name,o.parameters,n),new v((t=>new Wt)));const r=c[e];return new qt(N(t,"idx"),r,new v((t=>u(e+1,[...n,t]))))},h=u(0,[]),p=n.motive.check(t,e,h);if(p instanceof y)return p;const w=p.result,d=k(t,w),m=this.getConstructorTypesForDatatype(t,n.typeName);if(n.methods.length!==m.length)return new y(n.location,new l([`Expected ${m.length} methods, got ${n.methods.length}`]));const g=[];for(let r=0;r<n.methods.length;r++){const s=this.generateMethodTypeForConstructor(t,m[r],d,o.parameters),i=n.methods[r].check(t,e,s);if(i instanceof y)return i;g.push(i.result)}let T=d;for(const t of o.indices)T=U(T,t);T=U(T,k(t,a.expr));const E=new sn(n.typeName,a.expr,w,g);return new f(new ce(T.readBackType(t),E))}static getConstructorTypesForDatatype(t,e){const n=[];for(const[r,s]of t)if(s instanceof _){s.constructorType.type===e&&n.push(s.constructorType)}return n.sort(((t,e)=>t.index-e.index))}static generateMethodTypeForConstructor(t,e,n,r){let s=new Map(O(t));const i=new Set;[...e.argTypes,...e.rec_argTypes].forEach((t=>{t instanceof Je&&i.add(t.name)}));const a=Array.from(i);for(let t=0;t<a.length&&t<r.length;t++)s.set(a[t],r[t]);const o=[...e.argTypes.map((t=>t.valOf(s))),...e.rec_argTypes.map((t=>t.valOf(s)))],c=(r,s)=>{if(r>=o.length){let r;const i=new ie(e.name,e.type,s,e.index,[]),a=function(t){if(t instanceof re)return t.indices;return[]}(k(t,e.resultType));r=n;for(const t of a)r=U(r,t);r=U(r,i);const c=e.argTypes.length;for(let t=e.rec_argTypes.length-1;t>=0;t--){const e=c+t,i=s[e],a=o[e];let u=n;if(a instanceof re)for(const t of a.indices)u=U(u,t);u=U(u,i);const h=r;r=new qt(`ih${t}`,u,new v((t=>h)))}return r}return new qt(`arg${r}`,o[r],new v((t=>c(r+1,[...s,t]))))};return c(0,[])}}class xn{location;constructor(t){this.location=t}isType(t,e){const n=new w("ok"),r=this.getType(t,e);return d([[n,()=>r]],(()=>(ln(this.location,n.value),new f(n.value))))}getType(t,e){const n=this.check(t,e,new Wt);if(n instanceof f)return n;if(n instanceof y){if(this instanceof _n&&T(this.name)){const e=new w("other-tv");return new d([[e,()=>G(t,this.location,this.name)]],(()=>{new y(this.location,new l([`Expected U, but given ${e.value.readBackType(t)}`]))}))}return new y(this.location,new l(["not a type"]))}throw new Error("Invalid checkType")}check(t,e,n){const r=new w("ok"),s=this.checkOut(t,e,n);return d([[r,()=>s]],(()=>new f(r.value)))}synth(t,e){const n=new w("ok");return d([[n,()=>this.synthHelper(t,e)]],(()=>(ln(this.location,n.value.type),new f(n.value))))}checkOut(t,e,n){const r=new w("theT");return d([[r,()=>this.synth(t,e)],[new w("_"),()=>yn(t,this.location,k(t,r.value.type),n)]],(()=>new f(r.value.expr)))}}class bn extends xn{location;type;value;constructor(t,e,n){super(t),this.location=t,this.type=e,this.value=n}synthHelper(t,e){return Pn.synthThe(t,e,this.type,this.value)}findNames(){return this.type.findNames().concat(this.value.findNames())}prettyPrint(){return`(the ${this.type.prettyPrint()} ${this.value.prettyPrint()})`}toString(){return this.prettyPrint()}}class kn extends xn{location;constructor(t){super(t),this.location=t}synthHelper(t,e){return Pn.synthUniverse(t,e,this.location)}findNames(){return[]}getType(t,e){return new f(new ue)}prettyPrint(){return"U"}toString(){return this.prettyPrint()}}class $n extends xn{location;constructor(t){super(t),this.location=t}synthHelper(t,e){return Pn.synthNat(t,e)}findNames(){return[]}getType(t,e){return new f(new he)}prettyPrint(){return"Nat"}toString(){return this.prettyPrint()}}class Sn extends xn{location;constructor(t){super(t),this.location=t}synthHelper(t,e){return Pn.synthZero(t,e)}findNames(){return[]}prettyPrint(){return"zero"}toString(){return this.prettyPrint()}}class Ln extends xn{location;base;constructor(t,e){super(t),this.location=t,this.base=e}synthHelper(t,e){return Pn.synthAdd1(t,e,this.base)}findNames(){return this.base.findNames()}prettyPrint(){return`(add1 ${this.base.prettyPrint()})`}toString(){return this.prettyPrint()}}class On extends xn{location;target;base;step;constructor(t,e,n,r){super(t),this.location=t,this.target=e,this.base=n,this.step=r}synthHelper(t,e){return Pn.synthWhichNat(t,e,this.target,this.base,this.step)}findNames(){return this.target.findNames().concat(this.base.findNames()).concat(this.step.findNames())}prettyPrint(){return`(which-nat ${this.target.prettyPrint()} \n              ${this.base.prettyPrint()} \n              ${this.step.prettyPrint()})`}toString(){return this.prettyPrint()}}class An extends xn{location;target;base;step;constructor(t,e,n,r){super(t),this.location=t,this.target=e,this.base=n,this.step=r}synthHelper(t,e){return Pn.synthIterNat(t,e,this.target,this.base,this.step)}findNames(){return this.target.findNames().concat(this.base.findNames()).concat(this.step.findNames())}prettyPrint(){return`(iter-nat ${this.target.prettyPrint()} \n              ${this.base.prettyPrint()} \n              ${this.step.prettyPrint()})`}toString(){return this.prettyPrint()}}class In extends xn{location;target;base;step;constructor(t,e,n,r){super(t),this.location=t,this.target=e,this.base=n,this.step=r}synthHelper(t,e){return Pn.synthRecNat(t,e,this.target,this.base,this.step)}findNames(){return this.target.findNames().concat(this.base.findNames()).concat(this.step.findNames())}prettyPrint(){return`(rec-nat ${this.target.prettyPrint()} \n              ${this.base.prettyPrint()} \n              ${this.step.prettyPrint()})`}toString(){return this.prettyPrint()}}class Bn extends xn{location;target;motive;base;step;constructor(t,e,n,r,s){super(t),this.location=t,this.target=e,this.motive=n,this.base=r,this.step=s}synthHelper(t,e){return Pn.synthIndNat(t,e,this.target,this.motive,this.base,this.step)}findNames(){return this.target.findNames().concat(this.motive.findNames()).concat(this.base.findNames()).concat(this.step.findNames())}prettyPrint(){return`(ind-nat ${this.target.prettyPrint()} \n              ${this.motive.prettyPrint()} \n              ${this.base.prettyPrint()} \n              ${this.step.prettyPrint()})`}toString(){return this.prettyPrint()}}class Cn extends xn{location;arg1;arg2;args;constructor(t,e,n,r){super(t),this.location=t,this.arg1=e,this.arg2=n,this.args=r}synthHelper(t,e){return Pn.synthArrow(t,e,this.location,this.arg1,this.arg2,this.args)}findNames(){return this.arg1.findNames().concat(this.arg2.findNames()).concat(this.args.flatMap((t=>t.findNames())))}getType(t,e){const[n,r,s]=[this.arg1,this.arg2,this.args];if(0===s.length){const s=P(t,r,"x"),i=new w("Aout"),a=new w("Bout");return d([[i,()=>n.isType(t,e)],[a,()=>r.isType(z(t,s,k(t,i.value)),e)]],(()=>new f(new me(s,i.value,a.value))))}{const[i,...a]=s,o=P(t,gn(r,i,a),"x"),c=new w("Aout"),u=new w("tout");return d([[c,()=>n.isType(t,e)],[u,()=>new Cn(Nn(this.location),r,i,a).isType(z(t,o,k(t,c.value)),e)]],(()=>new f(new me(o,c.value,u.value))))}}prettyPrint(){return`(-> ${this.arg1.prettyPrint()} ${this.arg2.prettyPrint()} ${this.args.map((t=>t.prettyPrint())).join(" ")})`}toString(){return this.prettyPrint()}}class Rn extends xn{location;binders;body;constructor(t,e,n){super(t),this.location=t,this.binders=e,this.body=n}synthHelper(t,e){return Pn.synthPi(t,e,this.location,this.binders,this.body)}findNames(){return this.binders.flatMap((t=>x(t))).concat(this.body.findNames())}getType(t,e){const[n,r]=[this.binders,this.body];if(1===n.length){const[s,i]=[n[0].binder,n[0].type],a=N(t,s.varName),o=(s.location,new w("Aout")),c=new w("Aoutv"),u=new w("Bout");return d([[o,()=>i.isType(t,e)],[c,()=>new f(k(t,o.value))],[u,()=>r.isType(z(t,a,c.value),fn(e,s.varName,a))]],(()=>(o.value,new f(new me(a,o.value,u.value)))))}if(n.length>1){const[s,...i]=n,[a,o]=[s.binder.varName,s.type],c=N(t,a),u=(s.binder.location,new w("Aout")),h=new w("Aoutv"),l=new w("Bout");return d([[u,()=>o.isType(t,e)],[h,()=>new f(k(t,u.value))],[l,()=>new Rn(Nn(this.location),i,r).isType(z(t,c,h.value),fn(e,s.binder.varName,c))]],(()=>(u.value,new f(new me(c,u.value,l.value)))))}throw new Error("Invalid number of binders in Pi type")}prettyPrint(){return`(Π ${this.binders.map((t=>`(${t.binder.varName} ${t.type.prettyPrint()})`)).join(" ")} \n            ${this.body.prettyPrint()})`}toString(){return this.prettyPrint()}}class qn extends xn{location;binders;body;constructor(t,e,n){super(t),this.location=t,this.binders=e,this.body=n}synthHelper(t,e){throw new Error("Method not implemented.")}findNames(){return this.binders.map((t=>t.varName)).concat(this.body.findNames())}checkOut(t,e,n){if(1===this.binders.length){const r=this.body,s=this.binders[0],i=s.varName,a=s.location,o=n.now();if(o instanceof qt){const n=o.argType,s=o.resultType,a=pn(e,i),c=new w("bout");return d([[c,()=>r.check(z(t,a,n),fn(e,i,a),s.valOfClosure(new Zt(n,new rt(a))))]],(()=>(n.readBackType(t),new f(new ge(a,c.value)))))}return new y(a,new l([`Not a function type: ${o.readBackType(t)}.`]))}return new qn(this.location,[this.binders[0]],new qn(Nn(this.location),this.binders.slice(1),this.body)).check(t,e,n)}prettyPrint(){return`(lambda ${this.binders.map((t=>t.varName)).join(" ")} ${this.body.prettyPrint()})`}toString(){return this.prettyPrint()}}class Mn extends xn{location;binders;body;constructor(t,e,n){super(t),this.location=t,this.binders=e,this.body=n}synthHelper(t,e){return Pn.synthSigma(t,e,this.location,this.binders,this.body)}findNames(){return this.binders.flatMap((t=>x(t))).concat(this.body.findNames())}getType(t,e){const[n,r]=[this.binders,this.body];if(1===n.length){const[s,i]=[n[0].binder,n[0].type],a=s.varName,o=N(t,a),c=(s.location,new w("Aout")),u=new w("Aoutv"),h=new w("Dout");return d([[c,()=>i.isType(t,e)],[u,()=>new f(k(t,c.value))],[h,()=>r.isType(z(t,o,u.value),fn(e,a,o))]],(()=>(c.value,new f(new Ee(o,c.value,h.value)))))}if(n.length>1){const[[s,i],...a]=[[n[0].binder,n[0].type],n[1],...n.slice(2)],o=s.varName,c=N(t,o),u=(s.location,new w("Aout")),h=new w("Aoutv"),l=new w("Dout");return d([[u,()=>i.isType(t,e)],[h,()=>new f(k(t,u.value))],[l,()=>new Mn(this.location,a,r).isType(z(t,o,h.value),fn(e,o,c))]],(()=>(u.value,new f(new Ee(c,u.value,l.value)))))}throw new Error("Invalid number of binders in Sigma type")}prettyPrint(){return`(Σ ${this.binders.map((t=>`(${t.binder.varName} ${t.type.prettyPrint()})`)).join(" ")} \n            ${this.body.prettyPrint()})`}toString(){return this.prettyPrint()}}class _n extends xn{location;name;constructor(t,e){super(t),this.location=t,this.name=e}synthHelper(t,e){return Pn.synthName(t,e,this.location,this.name)}findNames(){return[this.name]}prettyPrint(){return this.name}toString(){return this.prettyPrint()}}class Gn extends xn{location;constructor(t){super(t),this.location=t}synthHelper(t,e){return Pn.synthAtom(t,e)}findNames(){return[]}getType(t,e){return new f(new ve)}prettyPrint(){return"Atom"}toString(){return this.prettyPrint()}}class zn extends xn{location;name;constructor(t,e){super(t),this.location=t,this.name=e}synthHelper(t,e){return Pn.synthQuote(t,e,this.location,this.name)}findNames(){return[]}prettyPrint(){return`'${this.name}`}toString(){return this.prettyPrint()}}class Un extends xn{location;first;second;constructor(t,e,n){super(t),this.location=t,this.first=e,this.second=n}synthHelper(t,e){return Pn.synthPair(t,e,this.first,this.second)}findNames(){return this.first.findNames().concat(this.second.findNames())}getType(t,e){const n=new w("Aout"),r=new w("Dout"),s=P(t,this.second,"x");return d([[n,()=>this.first.isType(t,e)],[r,()=>this.second.isType(z(t,s,k(t,n.value)),e)]],(()=>new f(new Ee(s,n.value,r.value))))}prettyPrint(){return`(Pair ${this.first.prettyPrint()} ${this.second.prettyPrint()})`}toString(){return this.prettyPrint()}}class Hn extends xn{location;first;second;constructor(t,e,n){super(t),this.location=t,this.first=e,this.second=n}synthHelper(t,e){throw new Error("Method not implemented.")}findNames(){return this.first.findNames().concat(this.second.findNames())}checkOut(t,e,n){const r=n.now();if(r instanceof _t){const n=r.carType,s=r.cdrType,i=new w("aout"),a=new w("dout");return d([[i,()=>this.first.check(t,e,n)],[a,()=>this.second.check(t,e,s.valOfClosure(k(t,i.value)))]],(()=>new f(new Ne(i.value,a.value))))}return new y(this.location,new l([`cons requires a Pair or Σ type, but was used as a: ${r.readBackType(t)}.`]))}prettyPrint(){return`(cons ${this.first.prettyPrint()} ${this.second.prettyPrint()})`}toString(){return this.prettyPrint()}}class Dn extends xn{location;pair;constructor(t,e){super(t),this.location=t,this.pair=e}synthHelper(t,e){return Pn.synthCar(t,e,this.location,this.pair)}findNames(){return this.pair.findNames()}prettyPrint(){return`(car ${this.pair.prettyPrint()})`}toString(){return this.prettyPrint()}}class Fn extends xn{location;pair;constructor(t,e){super(t),this.location=t,this.pair=e}synthHelper(t,e){return Pn.synthCdr(t,e,this.location,this.pair)}findNames(){return this.pair.findNames()}prettyPrint(){return`(cdr ${this.pair.prettyPrint()})`}toString(){return this.prettyPrint()}}class Vn extends xn{location;constructor(t){super(t),this.location=t}synthHelper(t,e){return Pn.synthTrivial(t,e)}findNames(){return[]}getType(t,e){return new f(new Oe)}prettyPrint(){return"Trivial"}toString(){return this.prettyPrint()}}class Qn extends xn{location;constructor(t){super(t),this.location=t}synthHelper(t,e){return Pn.synthSole(t,e)}findNames(){return[]}prettyPrint(){return"Sole"}}class Xn extends xn{location;constructor(t){super(t),this.location=t}synthHelper(t,e){throw new Error("Method not implemented.")}findNames(){return[]}checkOut(t,e,n){const r=n.now();return r instanceof zt?new f(new ke):new y(this.location,new l([`nil requires a List type, but was used as a: ${r.readBackType(t)}.`]))}prettyPrint(){return"nil"}toString(){return this.prettyPrint()}}let Kn=class extends xn{location;value;constructor(t,e){super(t),this.location=t,this.value=e}synthHelper(t,e){return Pn.synthNumber(t,e,this.location,this.value)}findNames(){return[]}prettyPrint(){return`${this.value}`}toString(){return this.prettyPrint()}};class jn extends xn{location;entryType;constructor(t,e){super(t),this.location=t,this.entryType=e}synthHelper(t,e){return Pn.synthList(t,e,this)}findNames(){return this.entryType.findNames()}getType(t,e){const n=new w("Eout");return d([[n,()=>this.entryType.isType(t,e)]],(()=>new f(new $e(n.value))))}prettyPrint(){return`(List ${this.entryType.prettyPrint()})`}toString(){return this.prettyPrint()}}class Yn extends xn{location;x;xs;constructor(t,e,n){super(t),this.location=t,this.x=e,this.xs=n}synthHelper(t,e){return Pn.synthListCons(t,e,this.x,this.xs)}findNames(){return this.x.findNames().concat(this.xs.findNames())}prettyPrint(){return`(:: ${this.x.prettyPrint()} ${this.xs.prettyPrint()})`}toString(){return this.prettyPrint()}}class Zn extends xn{location;target;base;step;constructor(t,e,n,r){super(t),this.location=t,this.target=e,this.base=n,this.step=r}synthHelper(t,e){return Pn.synthRecList(t,e,this.location,this.target,this.base,this.step)}findNames(){return this.target.findNames().concat(this.base.findNames()).concat(this.step.findNames())}prettyPrint(){return`(rec-list ${this.target.prettyPrint()} \n              ${this.base.prettyPrint()} \n              ${this.step.prettyPrint()})`}toString(){return this.prettyPrint()}}class Wn extends xn{location;target;motive;base;step;constructor(t,e,n,r,s){super(t),this.location=t,this.target=e,this.motive=n,this.base=r,this.step=s}synthHelper(t,e){return Pn.synthIndList(t,e,this.location,this.target,this.motive,this.base,this.step)}findNames(){return this.target.findNames().concat(this.motive.findNames()).concat(this.base.findNames()).concat(this.step.findNames())}prettyPrint(){return`(ind-list ${this.target.prettyPrint()} \n              ${this.motive.prettyPrint()} \n              ${this.base.prettyPrint()} \n              ${this.step.prettyPrint()})`}toString(){return this.prettyPrint()}}class Jn extends xn{location;constructor(t){super(t),this.location=t}synthHelper(t,e){return Pn.synthAbsurd(t,e,this)}findNames(){return[]}getType(t,e){return new f(new Ie)}prettyPrint(){return"Absurd"}toString(){return this.prettyPrint()}}class tr extends xn{location;target;motive;constructor(t,e,n){super(t),this.location=t,this.target=e,this.motive=n}synthHelper(t,e){return Pn.synthIndAbsurd(t,e,this)}findNames(){return this.target.findNames().concat(this.motive.findNames())}prettyPrint(){return`(ind-Absurd \n              ${this.target.prettyPrint()} \n              ${this.motive.prettyPrint()})`}toString(){return this.prettyPrint()}}class er extends xn{location;type;left;right;constructor(t,e,n,r){super(t),this.location=t,this.type=e,this.left=n,this.right=r}synthHelper(t,e){return Pn.synthEqual(t,e,this.type,this.left,this.right)}findNames(){return this.type.findNames().concat(this.left.findNames()).concat(this.right.findNames())}getType(t,e){const[n,r,s]=[this.type,this.left,this.right],i=new w("Aout"),a=new w("Av"),o=new w("from_out"),c=new w("to_out");return d([[i,()=>n.isType(t,e)],[a,()=>new f(k(t,i.value))],[o,()=>r.check(t,e,a.value)],[c,()=>s.check(t,e,a.value)]],(()=>new f(new Ce(i.value,o.value,c.value))))}prettyPrint(){return`(= ${this.type.prettyPrint()} \n              ${this.left.prettyPrint()} \n              ${this.right.prettyPrint()})`}toString(){return this.prettyPrint()}}class nr extends xn{location;type;constructor(t,e){super(t),this.location=t,this.type=e}findNames(){return this.type.findNames()}synthHelper(t,e){throw new Error("Method not implemented.")}checkOut(t,e,n){const r=n.now();if(r instanceof Dt){const n=r.type,s=r.from,i=r.to,a=new w("cout"),o=new w("val");return d([[a,()=>this.type.check(t,e,n)],[o,()=>new f(k(t,a.value))],[new w("_"),()=>wn(t,this.type.location,n,s,o.value)],[new w("_"),()=>wn(t,this.type.location,n,i,o.value)]],(()=>new f(new Re(a.value))))}return new y(this.location,new l([`same requires an Equal type, but encounter: ${r.readBackType(t)}.`]))}prettyPrint(){return`(same ${this.type.prettyPrint()})`}toString(){return this.prettyPrint()}}class rr extends xn{location;target;motive;base;constructor(t,e,n,r){super(t),this.location=t,this.target=e,this.motive=n,this.base=r}synthHelper(t,e){return Pn.synthReplace(t,e,this.location,this.target,this.motive,this.base)}findNames(){return this.target.findNames().concat(this.motive.findNames()).concat(this.base.findNames())}prettyPrint(){return`(replace ${this.target.prettyPrint()} \n              ${this.motive.prettyPrint()} \n              ${this.base.prettyPrint()})`}toString(){return this.prettyPrint()}}class sr extends xn{location;left;right;synthHelper(t,e){return Pn.synthTrans(t,e,this.location,this.left,this.right)}constructor(t,e,n){super(t),this.location=t,this.left=e,this.right=n}findNames(){return this.left.findNames().concat(this.right.findNames())}prettyPrint(){return`(trans ${this.left.prettyPrint()} ${this.right.prettyPrint()})`}toString(){return this.prettyPrint()}}class ir extends xn{location;target;fun;constructor(t,e,n){super(t),this.location=t,this.target=e,this.fun=n}synthHelper(t,e){return Pn.synthCong(t,e,this.location,this.target,this.fun)}findNames(){return this.target.findNames().concat(this.fun.findNames())}prettyPrint(){return`(cong ${this.target.prettyPrint()} ${this.fun.prettyPrint()})`}toString(){return this.prettyPrint()}}class ar extends xn{location;equality;constructor(t,e){super(t),this.location=t,this.equality=e}synthHelper(t,e){return Pn.synthSymm(t,e,this.location,this.equality)}findNames(){return this.equality.findNames()}prettyPrint(){return`(symm ${this.equality.prettyPrint()})`}toString(){return this.prettyPrint()}}class or extends xn{location;target;motive;base;constructor(t,e,n,r){super(t),this.location=t,this.target=e,this.motive=n,this.base=r}synthHelper(t,e){return Pn.synthIndEqual(t,e,this.location,this.target,this.motive,this.base)}findNames(){return this.target.findNames().concat(this.motive.findNames()).concat(this.base.findNames())}prettyPrint(){return`(ind-= ${this.target.prettyPrint()} \n              ${this.motive.prettyPrint()} \n              ${this.base.prettyPrint()})`}toString(){return this.prettyPrint()}}class cr extends xn{location;type;length;constructor(t,e,n){super(t),this.location=t,this.type=e,this.length=n}synthHelper(t,e){return Pn.synthVec(t,e,this.type,this.length)}findNames(){return this.type.findNames().concat(this.length.findNames())}getType(t,e){const n=new w("Eout"),r=new w("lenout");return d([[n,()=>this.type.isType(t,e)],[r,()=>this.length.check(t,e,new Bt)]],(()=>new f(new Ue(n.value,r.value))))}prettyPrint(){return`(Vec ${this.type.prettyPrint()} ${this.length.prettyPrint()})`}toString(){return this.prettyPrint()}}class ur extends xn{location;constructor(t){super(t),this.location=t}synthHelper(t,e){throw new Error("Method not implemented.")}findNames(){return[]}checkOut(t,e,n){const r=n.now();if(r instanceof Vt){return r.length.now()instanceof Ct?new f(new De):new y(this.location,new l([`vecnil requires a Vec type with length ZERO, but was used as a: \n          ${tt(t,new Bt,r.length)}.`]))}return new y(this.location,new l([`vecnil requires a Vec type, but was used as a: ${r.readBackType(t)}.`]))}prettyPrint(){return"vecnil"}toString(){return this.prettyPrint()}}class hr extends xn{location;x;xs;constructor(t,e,n){super(t),this.location=t,this.x=e,this.xs=n}synthHelper(t,e){throw new Error("Method not implemented.")}findNames(){return this.x.findNames().concat(this.xs.findNames())}checkOut(t,e,n){const r=n.now();if(r instanceof Vt){const n=r.length.now();if(n instanceof Rt){const s=new w("hout"),i=new w("tout"),a=n.smaller;return d([[s,()=>this.x.check(t,e,r.entryType)],[i,()=>this.xs.check(t,e,new Vt(r.entryType,a))]],(()=>new f(new He(s.value,i.value))))}return new y(this.location,new l([`vec:: requires a Vec type with length Add1, but was used with a: \n          ${tt(t,new Bt,r.length)}.`]))}return new y(this.location,new l([`vec:: requires a Vec type, but was used as a: ${r.readBackType(t)}.`]))}prettyPrint(){return`(vec:: ${this.x.prettyPrint()} ${this.xs.prettyPrint()})`}toString(){return this.prettyPrint()}}class lr extends xn{location;vec;constructor(t,e){super(t),this.location=t,this.vec=e}synthHelper(t,e){return Pn.synthHead(t,e,this.location,this.vec)}findNames(){return this.vec.findNames()}prettyPrint(){return`(head ${this.vec.prettyPrint()})`}toString(){return this.prettyPrint()}}class pr extends xn{location;vec;constructor(t,e){super(t),this.location=t,this.vec=e}synthHelper(t,e){return Pn.synthTail(t,e,this.location,this.vec)}findNames(){return this.vec.findNames()}prettyPrint(){return`(tail ${this.vec.prettyPrint()})`}toString(){return this.prettyPrint()}}class fr extends xn{location;length;target;motive;base;step;constructor(t,e,n,r,s,i){super(t),this.location=t,this.length=e,this.target=n,this.motive=r,this.base=s,this.step=i}synthHelper(t,e){return Pn.synthIndVec(t,e,this.location,this.length,this.target,this.motive,this.base,this.step)}findNames(){return this.length.findNames().concat(this.target.findNames()).concat(this.motive.findNames()).concat(this.base.findNames()).concat(this.step.findNames())}prettyPrint(){return`ind-Vec ${this.length.prettyPrint()}\n              ${this.target.prettyPrint()}\n              ${this.motive.prettyPrint()}\n              ${this.base.prettyPrint()}\n              ${this.step.prettyPrint()}`}toString(){return this.prettyPrint()}}class yr extends xn{location;left;right;constructor(t,e,n){super(t),this.location=t,this.left=e,this.right=n}synthHelper(t,e){return Pn.synthEither(t,e,this.left,this.right)}findNames(){return this.left.findNames().concat(this.right.findNames())}getType(t,e){const n=new w("Lout"),r=new w("Rout");return d([[n,()=>this.left.isType(t,e)],[r,()=>this.right.isType(t,e)]],(()=>new f(new Xe(n.value,r.value))))}prettyPrint(){return`(Either ${this.left.prettyPrint()} ${this.right.prettyPrint()})`}toString(){return this.prettyPrint()}}class wr extends xn{location;value;constructor(t,e){super(t),this.location=t,this.value=e}synthHelper(t,e){throw new Error("Method not implemented.")}findNames(){return this.value.findNames()}checkOut(t,e,n){const r=n.now();if(r instanceof Kt){const n=new w("lout");return d([[n,()=>this.value.check(t,e,r.leftType)]],(()=>new f(new Ke(n.value))))}return new y(this.location,new l([`left requires an Either type, but was used as a: ${r.readBackType(t)}.`]))}prettyPrint(){return`(left ${this.value.prettyPrint()})`}toString(){return this.prettyPrint()}}class dr extends xn{location;value;constructor(t,e){super(t),this.location=t,this.value=e}synthHelper(t,e){throw new Error("Method not implemented.")}findNames(){return this.value.findNames()}checkOut(t,e,n){const r=n.now();if(r instanceof Kt){const n=new w("rout");return d([[n,()=>this.value.check(t,e,r.rightType)]],(()=>new f(new je(n.value))))}return new y(this.location,new l([`right requires an Either type, but was used as a: ${r.readBackType(t)}.`]))}prettyPrint(){return`(right ${this.value.prettyPrint()})`}toString(){return this.prettyPrint()}}class mr extends xn{location;target;motive;baseLeft;baseRight;constructor(t,e,n,r,s){super(t),this.location=t,this.target=e,this.motive=n,this.baseLeft=r,this.baseRight=s}synthHelper(t,e){return Pn.synthIndEither(t,e,this.location,this.target,this.motive,this.baseLeft,this.baseRight)}findNames(){return this.target.findNames().concat(this.motive.findNames()).concat(this.baseLeft.findNames()).concat(this.baseRight.findNames())}prettyPrint(){return`(ind-Either ${this.target.prettyPrint()} \n              ${this.motive.prettyPrint()} \n              ${this.baseLeft.prettyPrint()} \n              ${this.baseRight.prettyPrint()})`}toString(){return this.prettyPrint()}}class gr extends xn{location;constructor(t){super(t),this.location=t}synthHelper(t,e){throw new Error("Method not implemented.")}findNames(){return[]}checkOut(t,e,n){const r=n.readBackType(t);return ln(this.location,$(t)),new f(new Ze(this.location.locationToSrcLoc(),r))}prettyPrint(){return"TODO"}toString(){return this.prettyPrint()}}class vr extends xn{location;func;arg;args;constructor(t,e,n,r){super(t),this.location=t,this.func=e,this.arg=n,this.args=r}synthHelper(t,e){return Pn.synthApplication(t,e,this.location,this.func,this.arg,this.args)}findNames(){return this.func.findNames().concat(this.arg.findNames()).concat(this.args.flatMap((t=>t.findNames())))}prettyPrint(){return`(${this.func.prettyPrint()} ${this.arg.prettyPrint()} ${this.args.map((t=>t.prettyPrint())).join(" ")})`}toString(){return this.prettyPrint()}}class Tr extends xn{location;name;paramType;indicesType;constructor(t,e,n,r){super(t),this.location=t,this.name=e,this.paramType=n,this.indicesType=r}findNames(){throw new Error("Method not implemented.")}prettyPrint(){throw new Error("Method not implemented.")}synthHelper(t,e){throw new Error("Method not implemented.")}getType(t,e){let n=t,r=e,s=[],i=[];for(let t=0;t<this.paramType.length;t++){const e=N(n,this.paramType[t].binder.varName),i=this.paramType[t].type.isType(n,r);if(r=fn(r,this.paramType[t].binder.varName,e),i instanceof y)return i;n=z(n,e,k(n,i.result)),s.push(i.result)}for(let t=0;t<this.indicesType.length;t++){const e=N(n,this.indicesType[t].binder.varName),s=this.indicesType[t].type.isType(n,r);if(r=fn(r,this.indicesType[t].binder.varName,e),s instanceof y)return s;n=z(n,e,k(n,s.result)),i.push(s.result)}return new f(new en(this.name,s,i))}}class Er extends xn{location;name;params;indices;findNames(){throw new Error("Method not implemented.")}prettyPrint(){throw new Error("Method not implemented.")}synthHelper(t,e){throw new Error("Method not implemented.")}constructor(t,e,n,r){super(t),this.location=t,this.name=e,this.params=n,this.indices=r}getType(t,e){const n=A(t,this.location,this.name);if(n instanceof y)return n;const r=n.result.type;if(this.params.length!==r.parameterTypes.length||this.indices.length!==r.indexTypes.length)return new y(this.location,new l(["Parameter/index count mismatch for type "+this.name]));const s=[];for(let n=0;n<this.params.length;n++){const i=this.params[n].check(t,e,r.parameterTypes[n].now());if(i instanceof y)return i;s.push(i.result)}const i=[];for(let n=0;n<this.indices.length;n++){const s=this.indices[n].check(t,e,r.indexTypes[n].now());if(s instanceof y)return s;i.push(s.result)}return new f(new tn(this.name,s,i))}checkOut(t,e,n){let r=n.now(),s=[],i=[];if(!(r instanceof se))return new y(this.location,new l(["target type is not user defined inductive type, or use the wrong type"]));const a=r;let o=a.parameterTypes,c=a.indexTypes;if(this.params.length!=o.length||this.indices.length!=c.length)return new y(this.location,new l(["the number of parameters/indices is inconsistent in constructor"]));for(let n=0;n<this.params.length;n++){const r=this.params[n].check(t,e,o[n].now());if(r instanceof y)return y;s.push(r.result)}for(let n=0;n<this.indices.length;n++){const r=this.indices[n].check(t,e,c[n].now());if(r instanceof y)return y;i.push(r.result)}return new f(new tn(this.name,s,i))}}class Nr extends xn{location;typeName;target;motive;methods;constructor(t,e,n,r,s){super(t),this.location=t,this.typeName=e,this.target=n,this.motive=r,this.methods=s}findNames(){return[this.typeName].concat(this.target.findNames()).concat(this.motive.findNames()).concat(this.methods.flatMap((t=>t.findNames())))}prettyPrint(){const t=this.methods.map((t=>t.prettyPrint())).join(" ");return`(elim-${this.typeName} ${this.target.prettyPrint()} ${this.motive.prettyPrint()} ${t})`}synthHelper(t,e){return Pn.synthGeneralEliminator(t,e,this)}}class Pr extends xn{location;constructorName;args;constructor(t,e,n){super(t),this.location=t,this.constructorName=e,this.args=n}findNames(){return[this.constructorName].concat(this.args.flatMap((t=>t.findNames())))}prettyPrint(){const t=this.args.map((t=>t.prettyPrint())).join(" ");return`(${this.constructorName}${t.length>0?" "+t:""})`}synthHelper(t,e){return Pn.synthConstructorApplication(t,e,this)}}var xr,br;!function(t){t[t.INTEGER=1]="INTEGER",t[t.RATIONAL=2]="RATIONAL",t[t.REAL=3]="REAL",t[t.COMPLEX=4]="COMPLEX"}(xr||(xr={}));class kr{result;constructor(t){this.result=t}}class $r extends kr{result;value;constructor(t,e){super(t),this.result=t,this.value=e}isSigned(){return!!this.result&&("+"===this.value[0]||"-"===this.value[0])}build(){return Br.build(this.value)}}class Sr extends kr{result;numerator;denominator;constructor(t,e,n){super(t),this.result=t,this.numerator=e,this.denominator=n}build(){return Cr.build(this.numerator,this.denominator)}}class Lr extends kr{result;integer;decimal;exponent;constructor(t,e,n,r){super(t),this.result=t,this.integer=e,this.decimal=n,this.exponent=r}build(){if(this.integer?.includes("inf"))return this.integer.includes("-")?Rr.NEG_INFINITY:Rr.INFINITY;if(this.integer?.includes("nan"))return Rr.NAN;let t=(this.exponent?this.exponent.build():Rr.INEXACT_ZERO).coerce(),e=Number((this.integer?this.integer:"0")+"."+(this.decimal?this.decimal:"0"));return e*=Math.pow(10,t),Rr.build(e)}}class Or extends kr{result;real;sign;imaginary;constructor(t,e,n,r){super(t),this.result=t,this.real=e,this.sign=n,this.imaginary=r}build(){const t=this.real?this.real.build():Br.EXACT_ZERO,e=this.imaginary.build();return this.sign&&"-"===this.sign?qr.build(t,e.negate()):qr.build(t,e)}}function Ar(t){const e=new RegExp("^([+-]?)(\\d+)$").exec(t);return e?new $r(!0,e[0]):new $r(!1)}function Ir(t,e){const n=Ar(t);if(n.result&&e>=xr.INTEGER)return n;const r=function(t){if(1!==(t.match(/\//g)||[]).length)return new Sr(!1);const e=t.split("/");if(2!==e.length)return new Sr(!1);const[n,r]=e,s=Ar(n),i=Ar(r);return s.result&&i.result?new Sr(!0,n,r):new Sr(!1)}(t);if(r.result&&e>=xr.RATIONAL)return r;const s=function(t){function e(t){if(function(t){return"+inf.0"===t||"-inf.0"===t||"+nan.0"===t||"-nan.0"===t}(t))return new Lr(!0,t);const e=(t.match(/\./g)||[]).length;if(e>1)return new Lr(!1);if(0===e){const e=Ar(t);return new Lr(e.result,e.value)}const[n,r]=t.split("."),s=Ar(n),i=Ar(r),a=s.result||""===n,o=i.result||""===r;return"+"===n||"-"===n?""===r?new Lr(!1):new Lr(!0,`${n}0`,t):s.result&&o||a&&i.result?i.result&&i.isSigned()?new Lr(!1):new Lr(!0,s.value,i.value):new Lr(!1)}return 0===(t.match(/[eE]/g)||[]).length?e(t):function(t){const n=t.indexOf("e"),r=t.indexOf("E");if(-1===n&&-1===r)return new Lr(!1);const s=-1===n?r:n,i=t.substring(0,s),a=t.substring(s+1);if(""===i||""==a)return new Lr(!1);const o=e(i);if(!o.result)return new Lr(!1);const c=Ir(a,xr.REAL);return c.result?new Lr(!0,o.integer,o.decimal,c):new Lr(!1)}(t)}(t);if(s.result&&e>=xr.REAL)return s;const i=function(t){if((t.match(/i/g)||[]).length<1)return new Or(!1);if("i"!==t[t.length-1])return new Or(!1);const e=t.search(/(?<!^)[+-]/);if(-1===e){const e=Ir(t.slice(0,-1),xr.REAL);return e.result?new Or(!0,void 0,void 0,e):new Or(!1)}const n=t.slice(0,e);let r=t.slice(e+1,-1);"+"!==r[0]&&"-"!==r[0]&&(r="+"+r);const s=Ir(n,xr.REAL),i=Ir(r,xr.REAL);return s.result&&i.result?new Or(!0,s,t[e],i):new Or(!1)}(t);return i.result&&e>=xr.COMPLEX?i:new $r(!1)}class Br{numberType=xr.INTEGER;value;static EXACT_ZERO=new Br(0n);constructor(t){this.value=t}static build(t,e=!1){const n=BigInt(t);return 0n===n?Br.EXACT_ZERO:new Br(n)}promote(t){switch(t){case xr.INTEGER:return this;case xr.RATIONAL:return Cr.build(this.value,1n,!0);case xr.REAL:return Rr.build(this.coerce(),!0);case xr.COMPLEX:return qr.build(this,Br.EXACT_ZERO,!0)}}equals(t){return t instanceof Br&&this.value===t.value}greaterThan(t){return this.value>t.value}negate(){return this===Br.EXACT_ZERO?this:Br.build(-this.value)}multiplicativeInverse(){if(this===Br.EXACT_ZERO)throw new Error("Division by zero");return Cr.build(1n,this.value,!1)}add(t){return Br.build(this.value+t.value)}multiply(t){return Br.build(this.value*t.value)}getBigInt(){return this.value}coerce(){return this.value>Number.MAX_SAFE_INTEGER?1/0:this.value<Number.MIN_SAFE_INTEGER?-1/0:Number(this.value)}toString(){return this.value.toString()}}class Cr{numberType=xr.RATIONAL;numerator;denominator;constructor(t,e){this.numerator=t,this.denominator=e}static build(t,e,n=!1){return Cr.simplify(BigInt(t),BigInt(e),n)}static simplify(t,e,n=!1){const r=(t,e)=>0n===e?t:r(e,t.valueOf()%e.valueOf()),s=r(t,e),i=t<0n?-1n:1n,a=e<0n?-1n:1n,o=i*a;return t*=i,1n!==(e*=a)||n?new Cr(o*t/s,e/s):Br.build(o*t)}getNumerator(){return this.numerator}getDenominator(){return this.denominator}promote(t){switch(t){case xr.RATIONAL:return this;case xr.REAL:return Rr.build(this.coerce(),!0);case xr.COMPLEX:return qr.build(this,Br.EXACT_ZERO,!0);default:throw new Error("Unable to demote rational")}}equals(t){return t instanceof Cr&&this.numerator===t.numerator&&this.denominator===t.denominator}greaterThan(t){return this.numerator*t.denominator>t.numerator*this.denominator}negate(){return Cr.build(-this.numerator,this.denominator)}multiplicativeInverse(){if(0n===this.numerator)throw new Error("Division by zero");return Cr.build(this.denominator,this.numerator)}add(t){const e=this.numerator*t.denominator+t.numerator*this.denominator,n=this.denominator*t.denominator;return Cr.build(e,n)}multiply(t){const e=this.numerator*t.numerator,n=this.denominator*t.denominator;return Cr.build(e,n)}coerce(){const t=this.numerator<0n?-this.numerator:this.numerator;let e=this.denominator;const n=Number(t/e);if(n>Number.MAX_VALUE)return this.numerator<0n?-1/0:1/0;let r=t%e;for(;r>Number.MAX_SAFE_INTEGER||e>Number.MAX_SAFE_INTEGER;)r/=2n,e/=2n;const s=Number(r)/Number(e);return this.numerator<0n?-(n+s):n+s}toString(){return`${this.numerator}/${this.denominator}`}}class Rr{numberType=xr.REAL;value;static INEXACT_ZERO=new Rr(0);static INEXACT_NEG_ZERO=new Rr(-0);static INFINITY=new Rr(1/0);static NEG_INFINITY=new Rr(-1/0);static NAN=new Rr(NaN);static build(t,e=!1){return t===1/0?Rr.INFINITY:t===-1/0?Rr.NEG_INFINITY:isNaN(t)?Rr.NAN:0===t?Rr.INEXACT_ZERO:-0===t?Rr.INEXACT_NEG_ZERO:new Rr(t)}constructor(t){this.value=t}promote(t){switch(t){case xr.REAL:return this;case xr.COMPLEX:return qr.build(this,Br.EXACT_ZERO,!0);default:throw new Error("Unable to demote real")}}equals(t){return t instanceof Rr&&this.value===t.value}greaterThan(t){return this.value>t.value}negate(){return Rr.build(-this.value)}multiplicativeInverse(){if(this===Rr.INEXACT_ZERO||this===Rr.INEXACT_NEG_ZERO)throw new Error("Division by zero");return Rr.build(1/this.value)}add(t){return Rr.build(this.value+t.value)}multiply(t){return Rr.build(this.value*t.value)}coerce(){return this.value}toString(){return this===Rr.INFINITY?"+inf.0":this===Rr.NEG_INFINITY?"-inf.0":this===Rr.NAN?"+nan.0":this.value.toString()}}class qr{numberType=xr.COMPLEX;real;imaginary;static build(t,e,n=!1){return qr.simplify(new qr(t,e),n)}constructor(t,e){this.real=t,this.imaginary=e}static simplify(t,e){return!e&&zr(t.imaginary,Br.EXACT_ZERO)?t.real:t}promote(t){if(t===xr.COMPLEX)return this;throw new Error("Unable to demote complex")}negate(){return qr.build(this.real.negate(),this.imaginary.negate())}equals(t){return zr(this.real,t.real)&&zr(this.imaginary,t.imaginary)}greaterThan(t){return Ur(this.real,t.real)&&Ur(this.imaginary,t.imaginary)}multiplicativeInverse(){const t=Hr(Dr(this.real,this.real),Dr(this.imaginary,this.imaginary));return qr.build(Dr(t.multiplicativeInverse(),this.real),Dr(t.multiplicativeInverse(),this.imaginary.negate()))}add(t){return qr.build(Hr(this.real,t.real),Hr(this.imaginary,t.imaginary))}multiply(t){const e=(n=Dr(this.real,t.real),r=Dr(this.imaginary,t.imaginary),Hr(n,function(t){return t.negate()}(r)));var n,r;const s=Hr(Dr(this.real,t.imaginary),Dr(this.imaginary,t.real));return qr.build(e,s)}getReal(){return this.real}getImaginary(){return this.imaginary}coerce(){throw new Error("Cannot coerce a complex number to a javascript number")}toPolar(){const t=this.real.promote(xr.REAL),e=this.imaginary.promote(xr.REAL),n=Rr.build(Math.sqrt(t.coerce()*t.coerce()+e.coerce()*e.coerce())),r=Rr.build(Math.atan2(e.coerce(),t.coerce()));return Mr.build(n,r)}toString(){return`${this.real}+${this.imaginary}i`}}class Mr{magnitude;angle;constructor(t,e){this.magnitude=t,this.angle=e}static build(t,e){return new Mr(t,e)}toCartesian(){const t=Rr.build(this.magnitude.coerce()*Math.cos(this.angle.coerce())),e=Rr.build(this.magnitude.coerce()*Math.sin(this.angle.coerce()));return qr.build(t,e)}}function _r(t){switch(t.numberType){case xr.INTEGER:return t;case xr.RATIONAL:return 1n===t.getDenominator()?Br.build(t.getNumerator()):t;case xr.REAL:return t;case xr.COMPLEX:return qr.build(_r(t.getReal()),_r(t.getImaginary()))}}function Gr(t,e){return t.numberType>e.numberType?[t,e.promote(t.numberType)]:t.numberType<e.numberType?[t.promote(e.numberType),e]:[t,e]}function zr(t,e){const[n,r]=Gr(t,e);return n.equals(r)}function Ur(t,e){const[n,r]=Gr(t,e);return n.greaterThan(r)}function Hr(t,e){const[n,r]=Gr(t,e);return _r(n.add(r))}function Dr(t,e){const[n,r]=Gr(t,e);return _r(n.multiply(r))}class Fr{start;end;constructor(t,e){this.start=t,this.end=e}merge(t){return new Fr(this.start,t.end)}}class Vr{line;column;constructor(t,e){this.line=t,this.column=e}}function Qr(t,e){return t.split("\n")[e.line-1]}function Xr(t){return"^".padStart(t.column," ")}!function(t){t[t.LEFT_PAREN=0]="LEFT_PAREN",t[t.RIGHT_PAREN=1]="RIGHT_PAREN",t[t.LEFT_BRACKET=2]="LEFT_BRACKET",t[t.RIGHT_BRACKET=3]="RIGHT_BRACKET",t[t.DOT=4]="DOT",t[t.HASH_SEMICOLON=5]="HASH_SEMICOLON",t[t.IDENTIFIER=6]="IDENTIFIER",t[t.NUMBER=7]="NUMBER",t[t.BOOLEAN=8]="BOOLEAN",t[t.STRING=9]="STRING",t[t.IF=10]="IF",t[t.LET=11]="LET",t[t.COND=12]="COND",t[t.ELSE=13]="ELSE",t[t.DEFINE=14]="DEFINE",t[t.LAMBDA=15]="LAMBDA",t[t.APOSTROPHE=16]="APOSTROPHE",t[t.BACKTICK=17]="BACKTICK",t[t.COMMA=18]="COMMA",t[t.COMMA_AT=19]="COMMA_AT",t[t.QUOTE=20]="QUOTE",t[t.QUASIQUOTE=21]="QUASIQUOTE",t[t.UNQUOTE=22]="UNQUOTE",t[t.UNQUOTE_SPLICING=23]="UNQUOTE_SPLICING",t[t.SET=24]="SET",t[t.BEGIN=25]="BEGIN",t[t.DELAY=26]="DELAY",t[t.IMPORT=27]="IMPORT",t[t.EXPORT=28]="EXPORT",t[t.DEFINE_SYNTAX=29]="DEFINE_SYNTAX",t[t.SYNTAX_RULES=30]="SYNTAX_RULES",t[t.HASH_VECTOR=31]="HASH_VECTOR",t[t.VECTOR=32]="VECTOR",t[t.EOF=33]="EOF"}(br||(br={}));class Kr extends SyntaxError{loc;constructor(t,e){super(`Syntax error at (${e.line}:${e.column})\n${t}`),this.loc=e}toString(){return this.message}}let jr=class extends Kr{constructor(t,e){super(Qr(t,e)+"\nUnexpected EOF",e),this.name="UnexpectedEOFError"}};class Yr extends Kr{form;constructor(t,e,n){super(Qr(t,e)+"\n"+Xr(e)+"\n"+`Unexpected '${n}'`,e),this.form=n,this.name="UnexpectedTokenError"}}class Zr extends Kr{form;expected;constructor(t,e,n,r){super(Qr(t,e)+"\n"+Xr(e)+"\n"+`Expected '${r}' but got '${n}'`,e),this.form=n,this.expected=r,this.name="ExpectedTokenError"}}class Wr extends Kr{token;constructor(t,e,n,r){super(Qr(t,e)+"\n"+Xr(e)+"\n"+`Syntax '${n}' not allowed at Scheme §${r}`,e),this.token=n,this.name="DisallowedTokenError"}}class Jr extends Kr{token;constructor(t,e,n){super(Qr(t,e)+"\n"+Xr(e)+"\n"+`Syntax '${n}' not supported yet`,e),this.token=n,this.name="UnsupportedTokenError"}}class ts{elements;location;constructor(t){this.elements=t,this.location=new Fr(this.firstPos(),this.lastPos())}static build(t){if(0===t.length)throw new Error("Illegal empty group. This should never happen.");if(1===t.length){const n=t[0];if(ns(n))return n;if((e=n).type!==br.IDENTIFIER&&e.type!==br.NUMBER&&e.type!==br.STRING&&e.type!==br.BOOLEAN)throw new Zr("",n.pos,n,"<data>");return new ts(t)}var e;if(2===t.length){const e=t[0];if(es(e)&&function(t){return t.type===br.APOSTROPHE||t.type===br.BACKTICK||t.type===br.HASH_VECTOR||t.type===br.COMMA||t.type===br.COMMA_AT}(e))return new ts(t)}const n=t[0],r=t[t.length-1];if(es(n)&&es(r)&&(i=r,(s=n).type===br.LEFT_PAREN&&i.type===br.RIGHT_PAREN||s.type===br.LEFT_BRACKET&&i.type===br.RIGHT_BRACKET))return new ts(t);var s,i;const a=new ts(t);throw new Zr("",a.location.start,a,"matching parentheses")}first(){return this.elements[0]}firstToken(){const t=this.first();return es(t)?t:t.firstToken()}firstPos(){return this.firstToken().pos}last(){return this.elements[this.elements.length-1]}lastToken(){const t=this.last();return es(t)?t:t.lastToken()}lastPos(){return this.lastToken().pos}isParenthesized(){const t=this.first();return es(t)&&(t.type===br.LEFT_PAREN||t.type===br.LEFT_BRACKET)}isSingleIdentifier(){return!this.isParenthesized()&&1===this.length()}unwrap(){return this.isParenthesized()?this.elements.slice(1,this.elements.length-1):this.elements}length(){return this.unwrap().length}toString(){return this.elements.map((t=>t.toString())).join(" ")}}function es(t){return t instanceof rs}function ns(t){return t instanceof ts}class rs{type;lexeme;literal;start;end;pos;endPos;constructor(t,e,n,r,s,i,a){this.type=t,this.lexeme=e,this.literal=n,this.start=r,this.end=s,this.pos=new Vr(i,a),this.endPos=new Vr(i,a+e.length-1)}convertToken(){switch(this.type){case br.APOSTROPHE:return new rs(br.QUOTE,this.lexeme,this.literal,this.start,this.end,this.pos.line,this.pos.column);case br.BACKTICK:return new rs(br.QUASIQUOTE,this.lexeme,this.literal,this.start,this.end,this.pos.line,this.pos.column);case br.HASH_VECTOR:return new rs(br.VECTOR,this.lexeme,this.literal,this.start,this.end,this.pos.line,this.pos.column);case br.COMMA:return new rs(br.UNQUOTE,this.lexeme,this.literal,this.start,this.end,this.pos.line,this.pos.column);case br.COMMA_AT:return new rs(br.UNQUOTE_SPLICING,this.lexeme,this.literal,this.start,this.end,this.pos.line,this.pos.column);default:return this}}toString(){return`${this.lexeme}`}}class ss extends SyntaxError{loc;constructor(t,e,n){super(t),this.loc={line:e,column:n}}toString(){return this.message}}class is extends ss{char;constructor(t,e,n){super(`Unexpected character '${n}' (${t}:${e})`,t,e),this.char=n,this.name="UnexpectedCharacterError"}}class as extends ss{constructor(t,e){super(`Unexpected EOF (${t}:${e})`,t,e),this.name="UnexpectedEOFError"}}let os=new Map([[".",br.DOT],["if",br.IF],["let",br.LET],["cond",br.COND],["else",br.ELSE],["set!",br.SET],["begin",br.BEGIN],["delay",br.DELAY],["quote",br.QUOTE],["export",br.EXPORT],["import",br.IMPORT],["define",br.DEFINE],["lambda",br.LAMBDA],["define-syntax",br.DEFINE_SYNTAX],["syntax-rules",br.SYNTAX_RULES]]);class cs{source;tokens;start=0;current=0;line=1;col=0;constructor(t){this.source=t,this.tokens=[]}isAtEnd(){return this.current>=this.source.length}advance(){return this.col++,this.source.charAt(this.current++)}jump(){this.start=this.current,this.col++,this.current++}addToken(t,e=null){const n=this.source.substring(this.start,this.current);this.tokens.push(new rs(t,n,e,this.start,this.current,this.line,this.col))}scanTokens(){for(;!this.isAtEnd();)this.start=this.current,this.scanToken();return this.tokens.push(new rs(br.EOF,"",null,this.start,this.current,this.line,this.col)),this.tokens}scanToken(){const t=this.advance();switch(t){case"(":this.addToken(br.LEFT_PAREN);break;case")":this.addToken(br.RIGHT_PAREN);break;case"[":this.addToken(br.LEFT_BRACKET);break;case"]":this.addToken(br.RIGHT_BRACKET);break;case"'":this.addToken(br.APOSTROPHE);break;case"`":this.addToken(br.BACKTICK);break;case",":if(this.match("@")){this.addToken(br.COMMA_AT);break}this.addToken(br.COMMA);break;case"#":if(this.match("t")||this.match("f"))this.booleanToken();else if(this.match("|"))this.comment();else if(this.match(";"))this.addToken(br.HASH_SEMICOLON);else{if("("!==this.peek()&&"["!==this.peek())throw new is(this.line,this.col,t);this.addToken(br.HASH_VECTOR)}break;case";":for(;"\n"!=this.peek()&&!this.isAtEnd();)this.advance();break;case" ":case"\r":case"\t":break;case"\n":this.line++,this.col=0;break;case'"':this.stringToken();break;case"|":this.identifierTokenLoose();break;default:if(this.isDigit(t)||"-"===t||"+"===t||"."===t||"i"===t||"n"===t)this.identifierNumberToken();else{if(!this.isValidIdentifier(t))throw new is(this.line,this.col,t);this.identifierToken()}}}comment(){for(;("|"!=this.peek()||"#"!=this.peekNext())&&!this.isAtEnd();)"\n"===this.peek()&&(this.line++,this.col=0),this.advance();if(this.isAtEnd())throw new as(this.line,this.col);this.jump(),this.jump()}identifierToken(){for(;this.isValidIdentifier(this.peek());)this.advance();this.addToken(this.checkKeyword())}identifierTokenLoose(){for(this.advance();"|"!=this.peek()&&!this.isAtEnd();)"\n"===this.peek()&&(this.line++,this.col=0),this.advance();if(this.isAtEnd())throw new as(this.line,this.col);this.advance(),this.addToken(this.checkKeyword())}identifierNumberToken(){for(;this.isValidIdentifier(this.peek());)this.advance();const t=this.source.substring(this.start,this.current);Ir(t,xr.COMPLEX).result?this.addToken(br.NUMBER,t):this.addToken(this.checkKeyword())}checkKeyword(){var t=this.source.substring(this.start,this.current);return os.has(t)?os.get(t):br.IDENTIFIER}stringToken(){for(;'"'!=this.peek()&&!this.isAtEnd();)"\n"===this.peek()&&(this.line++,this.col=0),this.advance();if(this.isAtEnd())throw new as(this.line,this.col);this.advance();const t=this.source.substring(this.start+1,this.current-1);this.addToken(br.STRING,t)}booleanToken(){this.addToken(br.BOOLEAN,"t"===this.peekPrev())}match(t){return!this.isAtEnd()&&(this.source.charAt(this.current)==t&&(this.current++,!0))}peek(){return this.isAtEnd()?"\0":this.source.charAt(this.current)}peekNext(){return this.current+1>=this.source.length?"\0":this.source.charAt(this.current+1)}peekPrev(){return this.current-1<0?"\0":this.source.charAt(this.current-1)}isDigit(t){return t>="0"&&t<="9"}isSpecialSyntax(t){return"("===t||")"===t||"["===t||"]"===t||";"===t||"|"===t}isValidIdentifier(t){return!this.isWhitespace(t)&&!this.isSpecialSyntax(t)}isWhitespace(t){return" "===t||"\0"===t||"\n"===t||"\r"===t||"\t"===t}}var us,hs;!function(t){class e{location;expressions;constructor(t,e){this.location=t,this.expressions=e}accept(t){return t.visitSequence(this)}equals(t){if(t instanceof e){if(this.expressions.length!==t.expressions.length)return!1;for(let e=0;e<this.expressions.length;e++)if(!this.expressions[e].equals(t.expressions[e]))return!1;return!0}return!1}}t.Sequence=e;class n{location;value;constructor(t,e){this.location=t,this.value=e}accept(t){return t.visitNumericLiteral(this)}equals(t){return t instanceof n&&this.value===t.value}}t.NumericLiteral=n;class r{location;value;constructor(t,e){this.location=t,this.value=e}accept(t){return t.visitBooleanLiteral(this)}equals(t){return t instanceof r&&this.value===t.value}}t.BooleanLiteral=r;class s{location;value;constructor(t,e){this.location=t,this.value=e}accept(t){return t.visitStringLiteral(this)}equals(t){return t instanceof s&&this.value===t.value}}t.StringLiteral=s;class i{location;params;rest;body;constructor(t,e,n,r=void 0){this.location=t,this.params=n,this.rest=r,this.body=e}accept(t){return t.visitLambda(this)}equals(t){if(t instanceof i){if(this.params.length!==t.params.length)return!1;for(let e=0;e<this.params.length;e++)if(!this.params[e].equals(t.params[e]))return!1;if(this.rest&&t.rest){if(!this.rest.equals(t.rest))return!1}else if(this.rest||t.rest)return!1;return this.body.equals(t.body)}return!1}}t.Lambda=i;class a{location;name;constructor(t,e){this.location=t,this.name=e}accept(t){return t.visitIdentifier(this)}equals(t){return t instanceof a&&this.name===t.name}}t.Identifier=a;class o{location;name;value;constructor(t,e,n){this.location=t,this.name=e,this.value=n}accept(t){return t.visitDefinition(this)}equals(t){return t instanceof o&&(this.name.equals(t.name)&&this.value.equals(t.value))}}t.Definition=o;class c{location;operator;operands;constructor(t,e,n){this.location=t,this.operator=e,this.operands=n}accept(t){return t.visitApplication(this)}equals(t){if(t instanceof c){if(!this.operator.equals(t.operator))return!1;if(this.operands.length!==t.operands.length)return!1;for(let e=0;e<this.operands.length;e++)if(!this.operands[e].equals(t.operands[e]))return!1;return!0}return!1}}t.Application=c;class u{location;test;consequent;alternate;constructor(t,e,n,r){this.location=t,this.test=e,this.consequent=n,this.alternate=r}accept(t){return t.visitConditional(this)}equals(t){return t instanceof u&&(this.test.equals(t.test)&&this.consequent.equals(t.consequent)&&this.alternate.equals(t.alternate))}}t.Conditional=u;class h{location;car;cdr;constructor(t,e,n){this.location=t,this.car=e,this.cdr=n}accept(t){return t.visitPair(this)}equals(t){return t instanceof h&&(this.car.equals(t.car)&&this.cdr.equals(t.cdr))}}t.Pair=h;class l{location;constructor(t){this.location=t}accept(t){return t.visitNil(this)}equals(t){return t instanceof l}}t.Nil=l;class p{location;value;constructor(t,e){this.location=t,this.value=e}accept(t){return t.visitSymbol(this)}equals(t){return t instanceof p&&this.value===t.value}}t.Symbol=p;class f{location;value;constructor(t,e){this.location=t,this.value=e}accept(t){return t.visitSpliceMarker(this)}equals(t){return t instanceof f&&this.value.equals(t.value)}}t.SpliceMarker=f;class y{location;name;value;constructor(t,e,n){this.location=t,this.name=e,this.value=n}accept(t){return t.visitReassignment(this)}equals(t){return t instanceof y&&(this.name.equals(t.name)&&this.value.equals(t.value))}}t.Reassignment=y;class w{location;source;identifiers;constructor(t,e,n){this.location=t,this.source=e,this.identifiers=n}accept(t){return t.visitImport(this)}equals(t){if(t instanceof w){if(!this.source.equals(t.source))return!1;if(this.identifiers.length!==t.identifiers.length)return!1;for(let e=0;e<this.identifiers.length;e++)if(!this.identifiers[e].equals(t.identifiers[e]))return!1;return!0}return!1}}t.Import=w;class d{location;definition;constructor(t,e){this.location=t,this.definition=e}accept(t){return t.visitExport(this)}equals(t){return t instanceof d&&this.definition.equals(t.definition)}}t.Export=d;class m{location;elements;constructor(t,e){this.location=t,this.elements=e}accept(t){return t.visitVector(this)}equals(t){if(t instanceof m){if(this.elements.length!==t.elements.length)return!1;for(let e=0;e<this.elements.length;e++)if(!this.elements[e].equals(t.elements[e]))return!1;return!0}return!1}}t.Vector=m;class g{location;name;transformer;constructor(t,e,n){this.location=t,this.name=e,this.transformer=n}accept(t){return t.visitDefineSyntax(this)}equals(t){return t instanceof g&&(this.name.equals(t.name)&&this.transformer.equals(t.transformer))}}t.DefineSyntax=g;class v{location;literals;rules;constructor(t,e,n){this.location=t,this.literals=e,this.rules=n}accept(t){return t.visitSyntaxRules(this)}equals(t){if(t instanceof v){if(this.literals.length!==t.literals.length)return!1;for(let e=0;e<this.literals.length;e++)if(!this.literals[e].equals(t.literals[e]))return!1;if(this.rules.length!==t.rules.length)return!1;for(let e=0;e<this.rules.length;e++)if(!this.rules[e][0].equals(t.rules[e][0])||!this.rules[e][1].equals(t.rules[e][1]))return!1;return!0}return!1}}t.SyntaxRules=v}(us||(us={})),function(t){class e{location;name;params;rest;body;constructor(t,e,n,r,s=void 0){this.location=t,this.name=e,this.body=n,this.params=r,this.rest=s}accept(t){return t.visitFunctionDefinition(this)}equals(t){if(t instanceof e){if(this.params.length!==t.params.length)return!1;for(let e=0;e<this.params.length;e++)if(!this.params[e].equals(t.params[e]))return!1;if(this.rest&&t.rest){if(!this.rest.equals(t.rest))return!1}else if(this.rest||t.rest)return!1;return this.body.equals(t.body)}return!1}}t.FunctionDefinition=e;class n{location;identifiers;values;body;constructor(t,e,n,r){this.location=t,this.identifiers=e,this.values=n,this.body=r}accept(t){return t.visitLet(this)}equals(t){if(t instanceof n){if(this.identifiers.length!==t.identifiers.length)return!1;for(let e=0;e<this.identifiers.length;e++)if(!this.identifiers[e].equals(t.identifiers[e]))return!1;if(this.values.length!==t.values.length)return!1;for(let e=0;e<this.values.length;e++)if(!this.values[e].equals(t.values[e]))return!1;return this.body.equals(t.body)}return!1}}t.Let=n;class r{location;predicates;consequents;catchall;constructor(t,e,n,r){this.location=t,this.predicates=e,this.consequents=n,this.catchall=r}accept(t){return t.visitCond(this)}equals(t){if(t instanceof r){if(this.predicates.length!==t.predicates.length)return!1;for(let e=0;e<this.predicates.length;e++)if(!this.predicates[e].equals(t.predicates[e]))return!1;if(this.consequents.length!==t.consequents.length)return!1;for(let e=0;e<this.consequents.length;e++)if(!this.consequents[e].equals(t.consequents[e]))return!1;return this.catchall&&t.catchall?this.catchall.equals(t.catchall):!this.catchall&&!t.catchall}return!1}}t.Cond=r;class s{location;elements;terminator;constructor(t,e,n=void 0){this.location=t,this.elements=e,this.terminator=n}accept(t){return t.visitList(this)}equals(t){if(t instanceof s){if(this.elements.length!==t.elements.length)return!1;for(let e=0;e<this.elements.length;e++)if(!this.elements[e].equals(t.elements[e]))return!1;return this.terminator&&t.terminator?this.terminator.equals(t.terminator):!this.terminator&&!t.terminator}return!1}}t.List=s;class i{location;expressions;constructor(t,e){this.location=t,this.expressions=e}accept(t){return t.visitBegin(this)}equals(t){if(t instanceof i){if(this.expressions.length!==t.expressions.length)return!1;for(let e=0;e<this.expressions.length;e++)if(!this.expressions[e].equals(t.expressions[e]))return!1;return!0}return!1}}t.Begin=i;class a{location;expression;constructor(t,e){this.location=t,this.expression=e}accept(t){return t.visitDelay(this)}equals(t){return t instanceof a&&this.expression.equals(t.expression)}}t.Delay=a}(hs||(hs={}));var ls;!function(t){t[t.NONE=0]="NONE",t[t.QUOTE=1]="QUOTE",t[t.QUASIQUOTE=2]="QUASIQUOTE"}(ls||(ls={}));class ps{source;tokens;chapter;current=0;quoteMode=ls.NONE;constructor(t,e,n=1/0){this.source=t,this.tokens=e,this.chapter=n}advance(){return this.isAtEnd()||this.current++,this.previous()}isAtEnd(){return this.current>=this.tokens.length}previous(){return this.tokens[this.current-1]}peek(){return this.tokens[this.current]}validateChapter(t,e){if(this.chapter<e)throw new Wr(this.source,t.pos,t,this.chapter)}toLocation(t){return new Fr(t.pos,t.endPos)}destructureList(t,e=t=>{}){if(0===t.length)return[[],void 0];if(1===t.length)return e(t[0]),[[this.parseExpression(t[0])],void 0];const n=t.at(-2);if(es(n)&&n.type===br.DOT){const n=t.at(-1),r=t.slice(0,-2);return e(n),r.forEach(e),[r.map(this.parseExpression.bind(this)),this.parseExpression(n)]}const r=t;return r.forEach(e),[r.map(this.parseExpression.bind(this)),void 0]}grouping(t){const e=[];let n=!1;t&&(n=!0,e.push(t));do{let t=this.advance();switch(t.type){case br.LEFT_PAREN:case br.LEFT_BRACKET:const r=this.grouping(t);e.push(r);break;case br.RIGHT_PAREN:case br.RIGHT_BRACKET:if(!n)throw new Yr(this.source,t.pos,t);e.push(t),n=!1;break;case br.APOSTROPHE:case br.BACKTICK:case br.COMMA:case br.COMMA_AT:case br.HASH_VECTOR:let s;do{s=this.grouping()}while(!s);e.push(this.affect(t,s));break;case br.QUOTE:case br.QUASIQUOTE:case br.UNQUOTE:case br.UNQUOTE_SPLICING:case br.IDENTIFIER:case br.NUMBER:case br.BOOLEAN:case br.STRING:case br.DOT:case br.DEFINE:case br.IF:case br.ELSE:case br.COND:case br.LAMBDA:case br.LET:case br.SET:case br.BEGIN:case br.DELAY:case br.IMPORT:case br.EXPORT:case br.DEFINE_SYNTAX:case br.SYNTAX_RULES:e.push(t);break;case br.HASH_SEMICOLON:for(;!this.grouping(););break;case br.EOF:throw new jr(this.source,t.pos);default:throw new Yr(this.source,t.pos,t)}}while(n);if(0!==e.length)try{return ts.build(e)}catch(t){if(t instanceof Zr)throw new Zr(this.source,t.loc,t.form,t.expected);throw t}}affect(t,e){return ts.build([t,e])}parseExpression(t){return es(t)?this.parseToken(t):t.isSingleIdentifier()?this.parseToken(t.unwrap()[0]):this.parseGroup(t)}parseToken(t){switch(t.type){case br.IDENTIFIER:return this.quoteMode===ls.NONE?new us.Identifier(this.toLocation(t),t.lexeme):new us.Symbol(this.toLocation(t),t.lexeme);case br.NUMBER:return new us.NumericLiteral(this.toLocation(t),t.literal);case br.BOOLEAN:return new us.BooleanLiteral(this.toLocation(t),t.literal);case br.STRING:return new us.StringLiteral(this.toLocation(t),t.literal);default:if(this.quoteMode!==ls.NONE||this.chapter>=5)return new us.Symbol(this.toLocation(t),t.lexeme);throw new Yr(this.source,t.pos,t)}}parseGroup(t){if(!t.isParenthesized())return this.parseAffectorGroup(t);switch(this.quoteMode){case ls.NONE:return this.parseNormalGroup(t);case ls.QUOTE:case ls.QUASIQUOTE:return this.parseQuotedGroup(t)}}parseAffectorGroup(t){const[e,n]=t.unwrap();switch(e.type){case br.APOSTROPHE:case br.QUOTE:if(this.validateChapter(e,2),this.quoteMode!==ls.NONE){const t=this.parseExpression(n),r=new us.Symbol(this.toLocation(e),"quote"),s=r.location.merge(t.location);return new hs.List(s,[r,t])}this.quoteMode=ls.QUOTE;const r=this.parseExpression(n);return this.quoteMode=ls.NONE,r;case br.BACKTICK:case br.QUASIQUOTE:if(this.validateChapter(e,2),this.quoteMode!==ls.NONE){const t=this.parseExpression(n),r=new us.Symbol(this.toLocation(e),"quasiquote"),s=r.location.merge(t.location);return new hs.List(s,[r,t])}this.quoteMode=ls.QUASIQUOTE;const s=this.parseExpression(n);return this.quoteMode=ls.NONE,s;case br.COMMA:case br.UNQUOTE:this.validateChapter(e,2);let i=this.quoteMode;if(i===ls.NONE)throw new Jr(this.source,e.pos,e);if(i===ls.QUOTE){const t=this.parseExpression(n),r=new us.Symbol(this.toLocation(e),"unquote"),s=r.location.merge(t.location);return new hs.List(s,[r,t])}this.quoteMode=ls.NONE;const a=this.parseExpression(n);return this.quoteMode=i,a;case br.COMMA_AT:case br.UNQUOTE_SPLICING:this.validateChapter(e,2);let o=this.quoteMode;if(o===ls.NONE)throw new Yr(this.source,e.pos,e);if(o===ls.QUOTE){const t=this.parseExpression(n),r=new us.Symbol(this.toLocation(e),"unquote-splicing"),s=r.location.merge(t.location);return new hs.List(s,[r,t])}this.quoteMode=ls.NONE;const c=this.parseExpression(n);this.quoteMode=o;const u=this.toLocation(e).merge(c.location);return new us.SpliceMarker(u,c);case br.HASH_VECTOR:this.validateChapter(e,3);let h=this.quoteMode;this.quoteMode=ls.QUOTE;const l=this.parseVector(t);return this.quoteMode=h,l;default:throw new Yr(this.source,e.pos,e)}}parseNormalGroup(t){if(0===t.length()){if(this.chapter>=5)return new us.Nil(t.location);throw new Zr(this.source,t.location.start,t,"non-empty group")}const e=t.unwrap()[0];if(es(e))switch(e.type){case br.LAMBDA:return this.validateChapter(e,1),this.parseLambda(t);case br.DEFINE:return this.validateChapter(e,1),this.parseDefinition(t);case br.IF:return this.validateChapter(e,1),this.parseConditional(t);case br.LET:return this.validateChapter(e,1),this.parseLet(t);case br.COND:return this.validateChapter(e,1),this.parseExtendedCond(t);case br.QUOTE:case br.APOSTROPHE:case br.QUASIQUOTE:case br.BACKTICK:case br.UNQUOTE:case br.COMMA:case br.UNQUOTE_SPLICING:case br.COMMA_AT:return this.validateChapter(e,2),this.parseAffectorGroup(t);case br.BEGIN:return this.validateChapter(e,3),this.parseBegin(t);case br.DELAY:return this.validateChapter(e,3),this.parseDelay(t);case br.SET:return this.validateChapter(e,3),this.parseSet(t);case br.DEFINE_SYNTAX:return this.validateChapter(e,5),this.parseDefineSyntax(t);case br.SYNTAX_RULES:throw new Yr(this.source,e.pos,e);case br.IMPORT:return this.validateChapter(e,1),this.parseImport(t);case br.EXPORT:return this.validateChapter(e,1),this.parseExport(t);case br.VECTOR:return this.validateChapter(e,3),this.parseAffectorGroup(t);default:return this.parseApplication(t)}return this.parseApplication(t)}parseQuotedGroup(t){if(0===t.length())return new us.Nil(t.location);if(1===t.length()){const e=[this.parseExpression(t.unwrap()[0])];return new hs.List(t.location,e)}const e=t.unwrap(),[n,r]=this.destructureList(e);return new hs.List(t.location,n,r)}parseLambda(t){if(t.length()<3)throw new Zr(this.source,t.location.start,t,"(lambda (<identifier>* . <rest-identifier>?) <body>+) | (lambda <rest-identifer> <body>+)");const e=t.unwrap(),n=e[1],r=e.slice(2);let s,i=[];if(es(n)){if(n.type!==br.IDENTIFIER)throw new Zr(this.source,n.pos,n,"<rest-identifier>");s=new us.Identifier(this.toLocation(n),n.lexeme)}else{const t=n.unwrap();[i,s]=this.destructureList(t,(t=>{if(!es(t))throw new Zr(this.source,t.pos,t,"<identifier>");if(t.type!==br.IDENTIFIER)throw new Zr(this.source,t.pos,t,"<identifier>")}))}const a=r.map(this.parseExpression.bind(this));if(a.length<1)throw new Zr(this.source,t.location.start,t,"(lambda ... <body>+)");if(1===a.length)return new us.Lambda(t.location,a[0],i,s);const o=a.at(0).location.merge(a.at(-1).location),c=new us.Sequence(o,a);return new us.Lambda(t.location,c,i,s)}parseDefinition(t){if(t.length()<3)throw new Zr(this.source,t.location.start,t,"(define <identifier> <expr>) | (define (<identifier> <formals>) <body>+)");const e=t.unwrap(),n=e[1],r=e.slice(2);let s,i,a=[],o=!1;if(ns(n)){o=!0;const t=n.unwrap(),e=t[0],r=t.splice(1);if(!es(e))throw new 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us.Definition(t.location,s,c)}parseConditional(t){if(t.length()<3||t.length()>4)throw new Zr(this.source,t.location.start,t,"(if <pred> <cons> <alt>?)");const e=t.unwrap(),n=e[1],r=e[2],s=t.length()>3?e[3]:void 0,i=this.parseExpression(n),a=this.parseExpression(r),o=s?this.parseExpression(s):new us.Identifier(t.location,"undefined");return new us.Conditional(t.location,i,a,o)}parseApplication(t){if(t.length()<1)throw new Zr(this.source,t.location.start,t,"(<func> <args>*)");const e=t.unwrap(),n=e[0],r=e.splice(1),s=this.parseExpression(n),i=[];for(const t of r)i.push(this.parseExpression(t));return new us.Application(t.location,s,i)}parseLet(t){if(this.chapter>=5){return t.unwrap().slice(1).forEach((t=>{this.parseExpression(t)})),new hs.Let(t.location,[],[],new us.Identifier(t.location,"undefined"))}if(t.length()<3)throw new Zr(this.source,t.location.start,t,"(let ((<identifier> <value>)*) <body>+)");const e=t.unwrap(),n=e[1],r=e.slice(2);if(!ns(n))throw new Zr(this.source,n.pos,n,"((<identifier> <value>)*)");const s=[],i=[],a=n.unwrap();for(const t of a){if(!ns(t))throw new Zr(this.source,t.pos,t,"(<identifier> <value>)");if(2!==t.length())throw new Zr(this.source,t.location.start,t,"(<identifier> <value>)");const[e,n]=t.unwrap();if(!es(e))throw new Zr(this.source,e.location.start,e,"<identifier>");if(e.type!==br.IDENTIFIER)throw new Zr(this.source,e.pos,e,"<identifier>");s.push(new us.Identifier(this.toLocation(e),e.lexeme)),i.push(this.parseExpression(n))}const o=r.map(this.parseExpression.bind(this));if(o.length<1)throw new Zr(this.source,t.location.start,t,"(let ... <body>+)");if(1===o.length)return new hs.Let(t.location,s,i,o[0]);const c=o.at(0).location.merge(o.at(-1).location),u=new us.Sequence(c,o);return new hs.Let(t.location,s,i,u)}parseExtendedCond(t){if(this.chapter>=5){return t.unwrap().slice(1).forEach((t=>{this.parseExpression(t)})),new hs.Cond(t.location,[],[],new us.Identifier(t.location,"undefined"))}if(t.length()<2)throw new Zr(this.source,t.location.start,t,"(cond (<pred> <body>*)* (else <val>)?)");const e=t.unwrap().splice(1),n=e.pop(),r=[],s=[];for(const t of e){if(!ns(t))throw new Zr(this.source,t.pos,t,"(<pred> <body>*)");if(t.length()<1)throw new Zr(this.source,t.firstToken().pos,t.firstToken(),"(<pred> <body>*)");const[e,...n]=t.unwrap();if(es(e)&&e.type===br.ELSE)throw new Zr(this.source,e.pos,e,"<predicate>");const i=this.parseExpression(e),a=n.map(this.parseExpression.bind(this)),o=n.length<1?i.location:a.at(0).location.merge(a.at(-1).location),c=n.length<1?i:n.length<2?a[0]:new us.Sequence(o,a);r.push(i),s.push(c)}if(!ns(n))throw new Zr(this.source,n.pos,n,"(<pred> <body>+) | (else <val>)");if(n.length()<2)throw new Zr(this.source,n.firstToken().pos,n.firstToken(),"(<pred> <body>+) | (else <val>)");const[i,...a]=n.unwrap();let o=!1;if(es(i)&&i.type===br.ELSE&&(o=!0,1!==a.length))throw new Zr(this.source,n.location.start,n,"(else <val>)");if(a.length<1)throw new Zr(this.source,n.location.start,n,"(<pred> <body>+)");const c=a.map(this.parseExpression.bind(this)),u=c.at(0).location.merge(c.at(-1).location),h=1===a.length?c[0]:new us.Sequence(u,c);if(o)return new hs.Cond(t.location,r,s,h);const l=this.parseExpression(i);return r.push(l),s.push(h),new hs.Cond(t.location,r,s)}parseSet(t){if(3!==t.length())throw new Zr(this.source,t.location.start,t,"(set! <identifier> <expr>)");const e=t.unwrap(),n=e[1],r=e[2];if(ns(n))throw new Zr(this.source,n.location.start,n,"<identifier>");if(n.type!==br.IDENTIFIER)throw new Zr(this.source,n.pos,n,"<identifier>");const s=new us.Identifier(this.toLocation(n),n.lexeme),i=this.parseExpression(r);return new us.Reassignment(t.location,s,i)}parseBegin(t){if(t.length()<2)throw new Zr(this.source,t.location.start,t,"(begin <body>+)");const e=t.unwrap().slice(1),n=[];for(const t of e)n.push(this.parseExpression(t));return new hs.Begin(t.location,n)}parseDelay(t){if(this.chapter>=5){return t.unwrap().slice(1).forEach((t=>{this.parseExpression(t)})),new hs.Delay(t.location,new us.Identifier(t.location,"undefined"))}if(2!==t.length())throw new Zr(this.source,t.location.start,t,"(delay <expr>)");const e=t.unwrap()[1],n=this.parseExpression(e);return new hs.Delay(t.location,n)}parseDefineSyntax(t){if(3!==t.length())throw new Zr(this.source,t.location.start,t,"(define-syntax <identifier> <transformer>)");const e=t.unwrap(),n=e[1],r=e[2];this.quoteMode=ls.QUOTE;const s=this.parseExpression(n);if(this.quoteMode=ls.NONE,!(s instanceof us.Symbol))throw new Zr(this.source,s.location.start,n,"<identifier>");if(!ns(r))throw new Zr(this.source,r.pos,r,"<transformer>");if(r.length()<2)throw new Zr(this.source,r.firstToken().pos,r,"(syntax-rules ...)");const i=r.unwrap()[0];if(!es(r.unwrap()[0]))throw new Zr(this.source,r.firstToken().pos,i,"syntax-rules");if(i.type!==br.SYNTAX_RULES)throw new Zr(this.source,i.pos,i,"syntax-rules");const a=this.parseSyntaxRules(r);return new us.DefineSyntax(t.location,s,a)}isValidPattern(t){if(t instanceof hs.List){if(void 0===t.terminator){if(t.elements.filter((t=>t instanceof us.Symbol&&"..."===t.value)).length>1)return!1;const e=t.elements.findIndex((t=>t instanceof us.Symbol&&"..."===t.value));if(-1!=e&&0===e)return!1;for(const e of t.elements)if(!this.isValidPattern(e))return!1;return!0}{if(t.elements.filter((t=>t instanceof us.Symbol&&"..."===t.value)).length>1)return!1;const e=t.elements.findIndex((t=>t instanceof us.Symbol&&"..."===t.value));if(-1!=e){if(0===e)return!1;if(e===t.elements.length-1)return!1}for(const e of t.elements)if(!this.isValidPattern(e))return!1;return this.isValidPattern(t.terminator)}}return t instanceof us.Symbol||t instanceof us.BooleanLiteral||t instanceof us.NumericLiteral||t instanceof us.StringLiteral||t instanceof us.Nil}isValidTemplate(t){if(t instanceof hs.List){if(void 0===t.terminator){if(0===t.elements.length)return!1;if(2===t.elements.length&&t.elements[0]instanceof us.Symbol&&"..."===t.elements[0].value)return this.isValidTemplate(t.elements[1]);let e=!1;for(let n=0;n<t.elements.length;n++){const r=t.elements[n];if(r instanceof us.Symbol&&"..."===r.value){if(e){e=!1;continue}return!1}if(!this.isValidTemplate(r))return!1;e=!0}return!0}{if(0===t.elements.length)return!1;let e=!1;for(let n=0;n<t.elements.length;n++){const r=t.elements[n];if(r instanceof us.Symbol&&"..."===r.value){if(e){e=!1;continue}return!1}if(!this.isValidTemplate(r))return!1;e=!0}return this.isValidTemplate(t.terminator)}}return t instanceof us.Symbol||t instanceof us.BooleanLiteral||t instanceof us.NumericLiteral||t instanceof us.StringLiteral||t instanceof us.Nil}parseSyntaxRules(t){if(t.length()<3)throw new Zr(this.source,t.location.start,t,"(syntax-rules (<literal>*) <syntax-rule>+)");const e=t.unwrap(),n=e[1],r=e.slice(2),s=[];if(!ns(n))throw new Zr(this.source,n.pos,n,"(<literal>*)");this.quoteMode=ls.QUOTE;for(const t of n.unwrap()){if(!es(t))throw new Zr(this.source,t.location.start,t,"<literal>");const e=this.parseExpression(t);if(!(e instanceof us.Symbol))throw new Zr(this.source,t.pos,t,"<literal>");s.push(e)}const i=[];for(const t of r){if(!ns(t))throw new Zr(this.source,t.pos,t,"(<pattern> <template>)");if(2!==t.length())throw new Zr(this.source,t.location.start,t,"(<pattern> <template>)");const[e,n]=t.unwrap(),r=this.parseExpression(e),s=this.parseExpression(n);if(!this.isValidPattern(r))throw new Zr(this.source,r.location.start,e,"<symbol> | <literal> | (<pattern>+) | (<pattern>+ ... <pattern>*) | (<pattern>+ ... <pattern>+ . <pattern>)");if(!this.isValidTemplate(s))throw new Zr(this.source,s.location.start,n,"<symbol> | <literal> | (<element>+) | (<element>+ . <template>) | (... <template>)");i.push([r,s])}return this.quoteMode=ls.NONE,new us.SyntaxRules(t.location,s,i)}parseImport(t){if(3!==t.length())throw new Zr(this.source,t.firstToken().pos,t.firstToken(),'(import "<source>" (<identifier>*))');const e=t.unwrap(),n=e[1],r=e[2];if(!es(n))throw new Zr(this.source,n.location.start,n,'"<source>"');if(n.type!==br.STRING)throw new Zr(this.source,n.pos,n,'"<source>"');if(!ns(r))throw new Zr(this.source,r.pos,r,"(<identifier>*)");const s=r.unwrap(),i=[];for(const t of s){if(!es(t))throw new Zr(this.source,t.location.start,t,"<identifier>");if(t.type!==br.IDENTIFIER)throw new Zr(this.source,t.pos,t,"<identifier>");i.push(new us.Identifier(this.toLocation(t),t.lexeme))}const a=new us.StringLiteral(this.toLocation(n),n.literal);return new us.Import(t.location,a,i)}parseExport(t){if(2!==t.length())throw new Zr(this.source,t.firstToken().pos,t.firstToken(),"(export (<definition>))");const e=t.unwrap()[1];if(!ns(e))throw new Zr(this.source,e.pos,e,"(<definition>)");const n=this.parseExpression(e);if(!(n instanceof us.Definition||n instanceof hs.FunctionDefinition))throw new Zr(this.source,e.location.start,e,"(<definition>)");return new us.Export(t.location,n)}parseVector(t){const e=t.unwrap()[1].unwrap().map(this.parseExpression.bind(this));return new us.Vector(t.location,e)}parse(t=!1){t&&(this.quoteMode=ls.QUOTE,this.current=0);const e=[];for(;!this.isAtEnd()&&this.peek().type!==br.EOF;){const t=this.grouping();if(!t)continue;const n=this.parseExpression(t);e.push(n)}if(this.chapter>=5&&!t){return[...e.filter((t=>t instanceof us.Import)),...this.parse(!0).filter((t=>!(t instanceof hs.List&&t.elements&&t.elements[0]instanceof us.Symbol&&"import"===t.elements[0].value)))]}return e}}class fs{location;name;parameters;indices;constructors;eliminatorName;constructor(t,e,n,r,s,i){this.location=t,this.name=e,this.parameters=n,this.indices=r,this.constructors=s,this.eliminatorName=i}normalize_constructor(t,e){const n=new Tr(this.location,this.name,this.parameters,this.indices).isType(t,e);if(n instanceof y)throw new Error(n.message.toString());const r=n.result;let s=t,i=e;for(const t of this.parameters){const e=t.binder.varName,n=t.type.isType(s,i);if(n instanceof y)throw new Error(n.message.toString());const r=n.result,a=N(s,e);s=z(s,a,k(s,r)),i=fn(i,e,a)}const a=k(s,r);s=b(s,this.name,new M(this.name,a));let o=[];for(let t=0;t<this.constructors.length;t++)o.push(this.constructors[t].checkValid(s,i,a,t));let c=t,u=e;return c=b(c,this.name,new M(this.name,a)),o.forEach((e=>{const n=N(c,e.name);let r;r=e.numTypeParams>0?k(s,e.resultType):k(t,e.resultType),c=b(c,n,new _(n,e,r)),u=fn(u,e.name,n)})),[c,u]}generateMethodType(t,e,n,r,s){let i=new Map(O(t));const a=new Set;[...n.argTypes,...n.rec_argTypes].forEach((t=>{t instanceof Je&&a.add(t.name)}));const o=Array.from(a);for(let t=0;t<o.length&&t<s.length;t++)i.set(o[t],s[t]);const c=[...n.argTypes.map((t=>t.valOf(i))),...n.rec_argTypes.map((t=>t.valOf(i)))],u=(e,s)=>{if(e>=c.length){let e;const i=new ie(n.name,n.type,s,n.index,[]),a=function(t){if(t instanceof re)return t.indices;return[]}(k(t,n.resultType));e=r;for(const t of a)e=U(e,t);e=U(e,i);const o=n.argTypes.length;for(let t=n.rec_argTypes.length-1;t>=0;t--){const n=o+t,i=s[n],a=c[n];let u=r;if(a instanceof re)for(const t of a.indices)u=U(u,t);u=U(u,i);const h=e;e=new qt(`ih${t}`,u,new v((t=>h)))}return e}return new qt(`arg${e}`,c[e],new v((t=>u(e+1,[...s,t]))))};return u(0,[])}}class ys{location;name;args;returnType;constructor(t,e,n,r){this.location=t,this.name=e,this.args=n,this.returnType=r}checkValid(t,e,n,r){let s=t,i=e,a=[],o=[],c=0,u=[];for(let t=0;t<this.args.length;t++){const e=this.args[t].binder.varName,n=N(s,e);u.push(e);const r=this.args[t].type.isType(s,i);if(r instanceof y)throw new Error(r.message.toString());const p=r.result;this.args[t].type instanceof kn&&c++,h=this.args[t].type,l=this.returnType.name,h instanceof _n&&h.name===l||h instanceof Er&&h.name===l?o.push(p):a.push(p),s=z(s,n,k(s,p)),i=fn(i,e,n)}var h,l;const p=this.returnType.check(s,i,n);if(p instanceof y)throw new Error(p.message.toString());const f=p.result;return new rn(this.name,r,this.returnType.name,a,o,f,c,u)}}class ws{id;type;context;renaming;term;constructor(t,e,n,r,s){this.id=t,this.type=e,this.context=n,this.renaming=r,this.term=s}clone(t={}){return new ws(t.id??this.id,t.type??this.type,t.context??new Map(this.context),t.renaming??new Map(this.renaming),t.term??this.term)}addHypothesis(t,e){const n=N(this.context,t);b(this.context,n,new C(e))}getVariableType(t){const e=this.context.get(t);return e?.type}prettyPrintWithContext(){const t=Array.from(this.context.entries()).map((([t,e])=>`${t} : ${e.type.readBackType(this.context).prettyPrint()}`)).join("\n  "),e=this.type.readBackType(this.context).prettyPrint();return t?`Context:\n  ${t}\n────────────────\nGoal: ${e}`:`Goal: ${e}`}}class ds{goal;children=[];parent=null;isComplete=!1;childFocusIndex=-1;constructor(t){this.goal=t}addChildren(t){t.forEach((t=>{t.parent=this})),this.children=t}findById(t){if(this.goal.id===t)return this;for(const e of this.children){const n=e.findById(t);if(n)return n}return null}}class ms{location;goalTree;currentGoal;proofHistory=[];goalIdCounter=0;constructor(t,e){this.location=t,this.goalTree=e,this.currentGoal=this.goalTree}static initialize(t,e,n){const r=new ws("goal_0",e,new Map(t),new Map),s=new ms(n,new ds(r));return s.currentGoal=s.goalTree,s}generateGoalId(){return"goal_"+ ++this.goalIdCounter}isComplete(){return this.goalTree.isComplete}getCurrentGoal(){if(null===this.currentGoal)throw new Error("No current goal available.");return new f(this.currentGoal.goal)}visualizeTree(){return this.visualizeNode(this.goalTree,"",!0)}visualizeNode(t,e,n){let r=e+(n?"└── ":"├── ")+`${t.isComplete?"✓":t===this.currentGoal?"→":"○"} ${t.goal.id}`+"\n";const s=e+(n?"    ":"│   ");for(let e=0;e<t.children.length;e++){const n=e===t.children.length-1;r+=this.visualizeNode(t.children[e],s,n)}return r}addGoal(t){this.currentGoal.addChildren(t),this.currentGoal.childFocusIndex=0,this.currentGoal=t[0]}nextGoal(){if(null===this.currentGoal.parent)return!0;let t=this.currentGoal.parent;const e=this.nextGoalAux(t);return null===e||(this.currentGoal=e,!1)}nextGoalAux(t){return-1===t.childFocusIndex||t.childFocusIndex>=t.children.length-1?(t.isComplete=!0,null===t.parent?null:this.nextGoalAux(t.parent)):(t.childFocusIndex+=1,t.children[t.childFocusIndex])}previousGoal(){if(null===this.currentGoal.parent)throw new Error("No previous goal available at the root level.");const t=this.PreviousGoalAux(this.currentGoal);if(null===t)throw new Error("No previous goal found.");this.currentGoal=t}PreviousGoalAux(t){if(0===t.childFocusIndex)return t;{let e=!1,n=t.children[t.childFocusIndex-1];for(;!e;){if(-1===n.childFocusINdex)return e=!0,n;n=n.children[n.childFocusIndex]}}}}class gs{location;constructor(t){this.location=t}}class vs extends gs{location;varName;constructor(t,e){super(t),this.location=t,this.varName=e}getName(){return"intro"}toString(){return`intro ${this.varName||""}`}apply(t){const e=t.currentGoal.goal,n=e.type;if(!(n instanceof qt))return new y(t.location,new l([`Cannot introduce a variable for non-function type: ${n.prettyPrint()}`]));const r=this.varName||n.argName||N(e.context,"x");let s=e.renaming;r!==n.argName&&fn(s,n.argName,r);const i=b(e.context,r,new q(n.argType)),a=n.resultType.valOfClosure(new Zt(n.argType,new rt(r))),o=new ds(new ws(t.generateGoalId(),a,i,s));return t.addGoal([o]),new f(t)}}class Ts extends gs{location;term;constructor(t,e){super(t),this.location=t,this.term=e}toString(){return`exact ${this.term.prettyPrint()}`}apply(t){const e=t.getCurrentGoal().result,n=e.type;console.log("goalType:",n.prettyPrint()),console.log("term:",this.term.prettyPrint());const r=this.term.check(e.context,e.renaming,n);return r instanceof y?r:(t.currentGoal.isComplete=!0,t.nextGoal(),new f(t))}}class Es extends gs{location;value;varName;constructor(t,e,n){super(t),this.location=t,this.value=e,this.varName=n}toString(){return`exists ${this.varName||""}`}apply(t){const e=t.getCurrentGoal().result,n=e.type;if(!(n instanceof _t))return new y(t.location,new l([`Cannot use exists on non-product type: ${n.prettyPrint()}`]));const r=this.varName||n.carName||N(e.context,"x");let s=e.renaming;r!==n.carName&&fn(s,n.carName,r);const i=this.value.check(e.context,e.renaming,n.carType);if(i instanceof y)return i;const a=i.result.valOf(O(e.context)),o=b(e.context,r,new R(n.carType,a)),c=n.cdrType.valOfClosure(a),u=new ds(new ws(t.generateGoalId(),c,o,s));return t.addGoal([u]),new f(t)}}class Ns extends gs{location;target;motive;constructor(t,e,n){super(t),this.location=t,this.target=e,this.motive=n}toString(){return`elim-nat ${this.target} to prove ${this.motive.prettyPrint()}`}apply(t){const e=t.getCurrentGoal().result,n=e.context.get(this.target);if(!n)return new y(t.location,new l([`target not found in current context: ${this.target}`]));let r;if(!(n instanceof q))throw new Error("Expected target to be a free variable");if(r=n.type.now(),!(r instanceof Bt))return new y(t.location,new l([`Cannot eliminate non-Nat type: ${r.prettyPrint()}`]));const s=N(e.context,"n"),i=this.motive.check(e.context,e.renaming,new qt(s,new Bt,new v((t=>new Wt))));if(i instanceof y)return i;{const n=this.eliminateNat(e.context,e.renaming,i.result.valOf(O(e.context)));return t.addGoal(n.map((n=>new ds(new ws(t.generateGoalId(),n,e.context,e.renaming))))),new f(t)}}eliminateNat(t,e,n){return[U(n,new Ct),new qt(N(t,"n-1"),new Bt,new v((e=>new qt(N(t,"ih"),U(n,e),new v((t=>U(n,new Rt(e))))))))]}}class Ps extends gs{location;target;motive;constructor(t,e,n){super(t),this.location=t,this.target=e,this.motive=n}toString(){return`elim-list ${this.target} to prove ${this.motive.prettyPrint()}`}apply(t){const e=t.getCurrentGoal().result,r=e.context.get(this.target);if(!r)return new y(t.location,new l([`target not found in current context: ${this.target}`]));let s;if(!(r instanceof q))throw new Error("Expected target to be a free variable");if(s=r.type.now(),!(s instanceof zt))return new y(t.location,new l([`Cannot eliminate non-List type: ${s.prettyPrint()}`]));N(e.context,"motive");const i=s.entryType,a=this.motive.check(e.context,e.renaming,new qt("xs",new zt(i),new g(O(e.context),"xs",new ue)));if(a instanceof y)return a;{const r=a.result.valOf(O(e.context)),s=this.eliminateList(e.context,e.renaming,r,i);return console.log("Eliminating List with motive:",n.inspect(s,!0,null,!0)),t.addGoal(s.map((n=>new ds(new ws(t.generateGoalId(),n,e.context,e.renaming))))),new f(t)}}eliminateList(t,e,n,r){return[U(n,new Ut),new qt(N(t,"x"),r,new v((e=>new qt(N(t,"xs"),new zt(r),new v((r=>new qt(N(t,"ih"),U(n,r),new v((t=>U(n,new Ht(e,r)))))))))))]}}class xs extends gs{location;target;motive;length;constructor(t,e,n,r){super(t),this.location=t,this.target=e,this.motive=n,this.length=r}toString(){return`elim-list ${this.target} to prove ${this.motive.prettyPrint()}`}apply(t){const e=t.getCurrentGoal().result,n=e.context.get(this.target);if(!n)return new y(t.location,new l([`target not found in current context: ${this.target}`]));let r;if(!(n instanceof q))throw new Error("Expected target to be a free variable");if(r=n.type.now(),!(r instanceof Vt))return new y(t.location,new l([`Cannot eliminate non-Vec type: ${r.prettyPrint()}`]));const s=this.length.check(e.context,e.renaming,new Bt);if(s instanceof y)return s;const[i,a]=[r.entryType,r.length];wn(e.context,this.location,new Bt,k(e.context,s.result),a),N(e.context,"motive");const o=this.motive.check(e.context,e.renaming,new qt("k",new Bt,new v((t=>new qt("es",new Vt(i,t),new v((t=>new Wt)))))));if(o instanceof y)return o;{const n=o.result.valOf(O(e.context)),r=this.eliminateVec(e.context,e.renaming,n,i);return t.addGoal(r.map((n=>new ds(new ws(t.generateGoalId(),n,e.context,e.renaming))))),new f(t)}}eliminateVec(t,e,n,r){return[U(U(n,new Ct),new Qt),Y(r,n)]}}class bs extends gs{location;target;motive;constructor(t,e,n){super(t),this.location=t,this.target=e,this.motive=n}toString(){return`elim-equal ${this.target} with motive ${this.motive.prettyPrint()}`}apply(t){const e=t.getCurrentGoal().result,n=e.context.get(this.target);if(!n)return new y(t.location,new l([`target not found in current context: ${this.target}`]));let r;if(!(n instanceof q))throw new Error("Expected target to be a free variable");if(r=n.type.now(),!(r instanceof Dt))return new y(t.location,new l([`Cannot eliminate non-Equal type: ${r.prettyPrint()}`]));const[s,i,a]=[r.type,r.from,r.to],o=this.motive.check(e.context,e.renaming,new qt("to",s,new v((t=>new qt("p",new Dt(s,i,t),new v((t=>new Wt)))))));if(o instanceof y)return o;{const n=[U(U(o.result.valOf(O(e.context)),i),new Ft(i))];return t.addGoal(n.map((n=>new ds(new ws(t.generateGoalId(),n,e.context,e.renaming))))),new f(t)}}}class ks extends gs{location;constructor(t){super(t),this.location=t}toString(){return"left"}apply(t){const e=t.getCurrentGoal().result;if(!(e.type.now()instanceof Kt))return new y(t.location,new l([`"left" expected goal type to be Either, but got: ${e.type.prettyPrint()}`]));const n=e.type.leftType.now();return t.addGoal([new ds(new ws(t.generateGoalId(),n,e.context,e.renaming))]),new f(t)}}class $s extends gs{location;constructor(t){super(t),this.location=t}toString(){return"right"}apply(t){const e=t.getCurrentGoal().result;if(!(e.type.now()instanceof Kt))return new y(t.location,new l([`"right" expected goal type to be Either, but got: ${e.type.prettyPrint()}`]));const n=e.type.rightType.now();return t.addGoal([new ds(new ws(t.generateGoalId(),n,e.context,e.renaming))]),new f(t)}}class Ss extends gs{location;target;motive;constructor(t,e,n){super(t),this.location=t,this.target=e,this.motive=n}toString(){return`elim-either ${this.target} with motive ${this.motive.prettyPrint()}`}apply(t){const e=t.getCurrentGoal().result,n=e.context.get(this.target);if(!n)return new y(t.location,new l([`target not found in current context: ${this.target}`]));let r;if(!(n instanceof q))throw new Error("Expected target to be a free variable");if(r=n.type.now(),!(r instanceof Kt))return new y(t.location,new l([`Cannot eliminate non-Either type: ${r.prettyPrint()}`]));const[s,i]=[r.leftType,r.rightType],a=this.motive.check(e.context,e.renaming,new qt("x",new Kt(s,i),new v((t=>new Wt))));if(a instanceof y)return a;{const n=a.result.valOf(O(e.context)),r=new qt("x",s,new v((t=>U(n,new jt(t))))),o=new qt("x",i,new v((t=>U(n,new Yt(t)))));return t.addGoal([new ds(new ws(t.generateGoalId(),r,e.context,e.renaming)),new ds(new ws(t.generateGoalId(),o,e.context,e.renaming))]),new f(t)}}}class Ls extends gs{constructor(t){super(t)}toString(){return"split"}apply(t){const e=t.getCurrentGoal().result;if(!(e.type.now()instanceof _t))return new y(t.location,new l([`"split" expected goal type to be Sigma, but got: ${e.type.prettyPrint()}`]));const n=e.type.now(),r=n.carType.now(),s=n.cdrType.valOfClosure(n);return t.addGoal([new ds(new ws(t.generateGoalId(),r,e.context,e.renaming)),new ds(new ws(t.generateGoalId(),s,e.context,e.renaming))]),new f(t)}}class Os extends gs{location;target;motive;constructor(t,e,n){super(t),this.location=t,this.target=e,this.motive=n}toString(){return`elim-absurd ${this.target} with motive ${this.motive.prettyPrint()}`}apply(t){const e=t.getCurrentGoal().result,n=e.context.get(this.target);if(!n)return new y(t.location,new l([`target not found in current context: ${this.target}`]));let r;if(!(n instanceof q))throw new Error("Expected target to be a free variable");if(r=n.type.now(),!(r instanceof ne))return new y(t.location,new l([`Cannot eliminate non-Absurd type: ${r.prettyPrint()}`]));const s=this.motive.check(e.context,e.renaming,new Wt);return s instanceof y?s:(t.currentGoal.isComplete=!0,t.nextGoal(),new f(t))}}function As(t,e){return[t,...e]}function Is(t){return new En(t,!0)}function Bs(t){return new u(Is(t),t.source)}function Cs(t){if(t instanceof us.Symbol)return t.value;if(t instanceof us.NumericLiteral)return t.value;if(t instanceof hs.List)return Cs(t.elements[0]);throw new Error("Expected a Element, but got: "+t)}function Rs(t,e){return new Tn(e.start,e.end,t)}function qs(t,e){return Rs(Cs(t),e)}function Ms(t){const e=new cs(t);return new ps("",e.scanTokens()).parse()}class _s{static parsePie(t){return _s.parseElements(Ms(t)[0])}static parseElements(t){const e=Cs(t);if("U"===e)return n=Rs("U",t.location),new kn(Is(n));if("the"===e){let e=t.elements;return function(t,e,n){return new bn(Is(t),e,n)}(Rs("the",t.location),this.parseElements(e[1]),this.parseElements(e[2]))}if("Nat"===e)return function(t){return new $n(Is(t))}(Rs("Nat",t.location));if("zero"===e)return function(t){return new Sn(Is(t))}(Rs("zero",t.location));if("add1"===e)return function(t,e){return new Ln(Is(t),e)}(Rs("add1",t.location),this.parseElements(t.elements[1]));if("->"===e||"→"===e){let e=t.elements;return function(t,e){return new Cn(Is(t),e[0],e[1],e[2])}(Rs("->",t.location),[this.parseElements(e[1]),this.parseElements(e[2]),e.slice(3).map((t=>this.parseElements(t)))])}if("lambda"===e||"λ"===e){let e=t.elements,n=t.location,r=e[1],s=e[2];return function(t,e,n){return new qn(Is(t),e,n)}(Rs("λ",n),r.elements.map((e=>Bs(qs(e,t.location)))),this.parseElements(s))}if("Pi"===e||"Π"===e){let e=t.elements,n=e[1],r=e[2],s=n.elements[0],i=s.elements[0],a=s.elements[1],o=n.elements.slice(1).map((t=>{let e=t.elements[0],n=t.elements[1];return new h(Bs(qs(e,t.location)),this.parseElements(n))}));return function(t,e,n){return new Rn(Is(t),e,n)}(Rs("Π",t.location),As(new h(Bs(qs(i,s.location)),this.parseElements(a)),o),this.parseElements(r))}if("Sigma"===e||"Σ"===e){let e=t.elements,n=e[1],r=e[2],s=n.elements[0],i=s.elements[0],a=s.elements[1],o=n.elements.slice(1).map((t=>{let e=t.elements[0],n=t.elements[1];return new h(Bs(qs(e,t.location)),this.parseElements(n))}));return function(t,e,n){return new Mn(Is(t),e,n)}(Rs("Π",t.location),As(new h(Bs(qs(i,s.location)),this.parseElements(a)),o),this.parseElements(r))}if("Pair"===e){let e=t.elements;return function(t,e,n){return new Un(Is(t),e,n)}(Rs("Pair",t.location),this.parseElements(e[1]),this.parseElements(e[2]))}if("cons"===e){let e=t.elements;return function(t,e,n){return new Hn(Is(t),e,n)}(Rs("Cons",t.location),this.parseElements(e[1]),this.parseElements(e[2]))}if("car"===e)return function(t,e){return new Dn(Is(t),e)}(Rs("car",t.location),this.parseElements(t.elements[1]));if("cdr"===e)return function(t,e){return new Fn(Is(t),e)}(Rs("cdr",t.location),this.parseElements(t.elements[1]));if("which-Nat"===e){let e=t.elements;return function(t,e,n,r){return new On(Is(t),e,n,r)}(Rs("which-Nat",t.location),this.parseElements(e[1]),this.parseElements(e[2]),this.parseElements(e[3]))}if("iter-Nat"===e){let e=t.elements;return function(t,e,n,r){return new An(Is(t),e,n,r)}(Rs("iter-Nat",t.location),this.parseElements(e[1]),this.parseElements(e[2]),this.parseElements(e[3]))}if("rec-Nat"===e){let e=t.elements;return function(t,e,n,r){return new In(Is(t),e,n,r)}(Rs("rec-Nat",t.location),this.parseElements(e[1]),this.parseElements(e[2]),this.parseElements(e[3]))}if("ind-Nat"===e){let e=t.elements;return function(t,e,n,r,s){return new Bn(Is(t),e,n,r,s)}(Rs("ind-Nat",t.location),this.parseElements(e[1]),this.parseElements(e[2]),this.parseElements(e[3]),this.parseElements(e[4]))}if("Atom"===e)return function(t){return new Gn(Is(t))}(Rs("Atom",t.location));if("quote"===e)return function(t,e){return new 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Ts(Is(n),r);if("intro"===e)return function(t,e){return new vs(Is(t),e)}(Rs("intro",t.location),t.elements[1].value);if("exists"===e)return function(t,e,n){return new Es(Is(t),e,n)}(Rs("exists",t.location),this.parseElements(t.elements[1]),t.elements[2].value);if("elimNat"===e)return function(t,e,n){return new Ns(Is(t),e,n)}(Rs("elimNat",t.location),t.elements[1].value,this.parseElements(t.elements[2]));if("elimList"===e)return function(t,e,n){return new Ps(Is(t),e,n)}(Rs("elimList",t.location),t.elements[1].value,this.parseElements(t.elements[2]));if("elimVec"===e)return function(t,e,n,r){return new xs(Is(t),e,n,r)}(Rs("elimVec",t.location),t.elements[1].value,this.parseElements(t.elements[2]),this.parseElements(t.elements[3]));if("elimEqual"===e)return function(t,e,n){return new bs(Is(t),e,n)}(Rs("elimEqual",t.location),t.elements[1].value,this.parseElements(t.elements[2]));if("left"===e)return function(t){return new ks(Is(t))}(Rs("left",t.location));if("right"===e)return 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Map,a.value)],[c,()=>s.check(t,new Map,a.value)],[u,()=>k(t,o.value)],[h,()=>k(t,c.value)]],(()=>wn(t,e,a.value,u.value,h.value)))}function Qs(t){return t.prettyPrint()}class Xs{currentState=null;startProof(t,e,n){const r=e.get(t);return r instanceof C?(this.currentState=ms.initialize(e,r.type,n),new f(`Started proof of ${t}\nCurrent goal: \n${r.type.readBackType(e).prettyPrint()}`)):new y(n,new l([`${t} is not a valid type or has already been proved`]))}applyTactic(t){if(!this.currentState)return new y(t.location,new l(["No proof has been initialized"]));const e=t.apply(this.currentState);if(e instanceof y)return e;this.currentState=e.result;let n=`\nApplied tactic: ${t}`;const r=this.currentState.getCurrentGoal();if(this.currentState.isComplete())n+="\nAll goals have been solved!";else{const t=r.result;n+="\nCurrent goal: \n"+t.type.readBackType(t.context).prettyPrint()}return new f(n)}}class Ks extends e.BasicEvaluator{executionCount;constructor(t){super(t),this.executionCount=0}async evaluateChunk(t){this.executionCount++;try{let e=function(t){const e=Ms(t);let n=I,r=new Map,s="";for(const t of e){const e=Ds.parseDeclaration(t);if(e instanceof Gs){const t=S(n,e.name,e.location,e.type);if(t instanceof f)n=t.result;else if(t instanceof y)throw new Error(""+t.where+t.message)}else if(e instanceof zs){const t=L(n,e.name,e.location,e.expr);if(t instanceof f)n=t.result;else if(t instanceof y)throw new Error(""+t.where+t.message)}else if(e instanceof Us){const t=Vs(n,e.location,e.type,e.left,e.right);if(t instanceof f)n=t.result;else if(t instanceof y)throw new Error(""+t.where+t.message)}else if(e instanceof fs){const[t,s]=e.normalize_constructor(n,r);n=t,r=s}else{if(e instanceof Hs){const t=new Xs;let r="";const s=t.startProof(e.name,n,e.location);if(s instanceof f)r+=s.result+"\n";else if(s instanceof y)throw new Error(""+s.where+s.message);for(const n of e.tactics){const e=t.applyTactic(n);if(e instanceof f)r+=e.result;else if(e instanceof y)throw new Error(""+e.where+e.message)}return r}{const t=Fs(n,e);if(t instanceof f){const e=t.result;s+=`${Qs(e.expr)}: ${Qs(e.type)}\n`}else if(t instanceof y)throw new Error(`${t.message} at ${t.where}`)}}}for(const[t,e]of n)e instanceof R?(s+=t+" : "+Qs(e.type.readBackType(n))+"\n",s+=t+" = "+Qs(tt(n,e.type,e.value))+"\n"):s+=t+" : "+Qs(e.type.readBackType(n))+"\n";return s}(t);this.conductor.sendOutput(`Result of expression: execution ${e}`)}catch(t){t instanceof Error?this.conductor.sendOutput(`Error: ${t.message}`):this.conductor.sendOutput(`Error: ${String(t)}`)}}}const{runnerPlugin:js,conduit:Ys}=t.initialise(Ks)}(_,runner,util);
 //# sourceMappingURL=index.js.map
diff --git a/dist/index.js.map b/dist/index.js.map
index 96314ed5..3b49644f 100644
--- a/dist/index.js.map
+++ b/dist/index.js.map
@@ -1 +1 @@
-{"version":3,"file":"index.js","sources":["../node_modules/conductor/src/common/errors/ConductorError.ts","../node_modules/conductor/src/common/errors/ConductorInternalError.ts","../node_modules/conductor/src/conductor/runner/BasicEvaluator.ts","../node_modules/conductor/src/common/util/importExternalPlugin.ts","../node_modules/tslib/tslib.es6.js","../node_modules/conductor/src/conduit/Channel.ts","../node_modules/conductor/src/common/ds/Queue.ts","../node_modules/conductor/src/common/ds/MessageQueue.ts","../node_modules/conductor/src/conduit/ChannelQueue.ts","../node_modules/conductor/src/conduit/Conduit.ts","../node_modules/conductor/src/conduit/rpc/types/RpcCallMessage.ts","../node_modules/conductor/src/conduit/rpc/types/RpcErrorMessage.ts","../node_modules/conductor/src/conduit/rpc/types/RpcReturnMessage.ts","../node_modules/conductor/src/conduit/util/checkIsPluginClass.ts","../node_modules/conductor/src/conductor/types/moduleInterface/DataType.ts","../node_modules/conductor/src/conductor/types/serviceMessages/AbortServiceMessage.ts","../node_modules/conductor/src/conductor/types/serviceMessages/HelloServiceMessage.ts","../node_modules/conductor/src/conductor/types/serviceMessages/PluginServiceMessage.ts","../node_modules/conductor/src/conductor/runner/RunnerPlugin.ts","../node_modules/conductor/src/common/util/importExternalModule.ts","../node_modules/conductor/src/conduit/rpc/makeRpc.ts","../src/pie_interpreter/utils/fresh.ts","../src/pie_interpreter/types/utils.ts","../src/pie_interpreter/utils/environment.ts","../src/pie_interpreter/utils/context.ts","../src/pie_interpreter/evaluator/evaluator.ts","../src/pie_interpreter/evaluator/utils.ts","../src/pie_interpreter/types/neutral.ts","../src/pie_interpreter/types/value.ts","../src/pie_interpreter/types/core.ts","../src/pie_interpreter/utils/alphaeqv.ts","../src/pie_interpreter/typechecker/utils.ts","../src/pie_interpreter/utils/locations.ts","../src/pie_interpreter/typechecker/synthesizer.ts","../src/pie_interpreter/types/source.ts","../src/scheme_parser/core-math.ts","../src/scheme_parser/transpiler/types/tokens/token-type.ts","../src/scheme_parser/transpiler/types/location.ts","../src/scheme_parser/transpiler/parser/parser-error.ts","../src/scheme_parser/transpiler/types/tokens/group.ts","../src/scheme_parser/transpiler/types/tokens/index.ts","../src/scheme_parser/transpiler/types/tokens/token.ts","../src/scheme_parser/transpiler/lexer/lexer-error.ts","../src/scheme_parser/transpiler/lexer/scheme-lexer.ts","../src/scheme_parser/transpiler/types/nodes/scheme-node-types.ts","../src/scheme_parser/transpiler/parser/scheme-parser.ts","../src/scheme_parser/transpiler/types/constants.ts","../src/pie_interpreter/parser/parser.ts","../src/pie_interpreter/typechecker/represent.ts","../src/pie_interpreter/unparser/pretty.ts","../node_modules/conductor/src/conductor/runner/util/initialise.ts","../src/pie_interpreter/index.ts","../src/pie_interpreter/PieEvaluator.ts","../src/pie_interpreter/main.ts"],"sourcesContent":[null,null,null,null,"/******************************************************************************\r\nCopyright (c) Microsoft Corporation.\r\n\r\nPermission to use, copy, modify, and/or distribute this software for any\r\npurpose with or without fee is hereby granted.\r\n\r\nTHE SOFTWARE IS PROVIDED \"AS IS\" AND THE AUTHOR DISCLAIMS ALL WARRANTIES WITH\r\nREGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY\r\nAND FITNESS. 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--- /dev/null
+++ b/docs/pie_language/pie_examples.md
@@ -0,0 +1,408 @@
+# Pie Code Examples
+
+Real working examples extracted from the test suite.
+
+---
+
+## Basic Types
+
+### Nat Examples
+```
+zero
+(add1 zero)
+(add1 (add1 zero))
+1
+2
+3
+```
+
+### Atom Examples
+```
+'foo
+'bar
+'pea
+'olive
+'oil
+```
+
+### Trivial Example
+```
+sole
+```
+
+---
+
+## Function Examples
+
+### Identity Function
+```
+(the (→ Nat Nat)
+  (λ (x) x))
+```
+
+### Constant Function
+```
+(the (→ Nat Nat)
+  (λ (x) zero))
+```
+
+### Two-Argument Function
+```
+(the (→ (→ Nat Nat) Nat Nat)
+  (λ (f x) (f x)))
+```
+
+### Addition Using ind-Nat
+```
+(the (→ Nat Nat Nat)
+  (λ (x y)
+    (ind-Nat x
+      (λ (k) Nat)
+      y
+      (λ (n-1 ih) (add1 ih)))))
+```
+
+### Addition Using iter-Nat
+```
+(the (→ Nat Nat Nat)
+  (λ (x y)
+    (iter-Nat x
+      y
+      (λ (prev) (add1 prev)))))
+```
+
+---
+
+## Pair Examples
+
+### Simple Pair
+```
+(the (Pair Atom Atom)
+  (cons 'olive 'oil))
+```
+
+### Pair Projections
+```
+(car (the (Pair Atom Atom) (cons 'olive 'oil)))  ; Returns 'olive
+(cdr (the (Pair Atom Atom) (cons 'olive 'oil)))  ; Returns 'oil
+```
+
+### Function with Pair
+```
+(the (→ Trivial (Pair Trivial Trivial))
+  (λ (x) (cons x x)))
+```
+
+### Nested Pairs
+```
+(the (Pair Nat (Pair Atom Trivial))
+  (cons zero (cons 'foo sole)))
+```
+
+---
+
+## List Examples
+
+### Empty List
+```
+(the (List Nat) nil)
+```
+
+### Single Element
+```
+(:: (add1 zero)
+  (the (List Nat) nil))
+```
+
+### Multiple Elements
+```
+(:: (add1 (add1 (add1 zero)))
+  (:: (add1 (add1 zero))
+    (the (List Nat) nil)))
+```
+
+### List Recursion - Sum
+```
+(the (→ (List Nat) Nat)
+  (λ (ns)
+    (ind-List ns
+      (λ (_) Nat)
+      zero
+      (λ (x y z)
+        (ind-Nat x
+          (λ (n) Nat)
+          z
+          (λ (_ q) (add1 q)))))))
+```
+
+---
+
+## Vec Examples
+
+### Empty Vector
+```
+(the (Vec Nat zero) vecnil)
+```
+
+### Vector Length 1
+```
+(vec:: zero (the (Vec Nat zero) vecnil))
+```
+
+### Vector Length 3
+```
+(vec:: zero
+  (vec:: (add1 zero)
+    (vec:: (add1 (add1 zero))
+      (the (Vec Nat zero) vecnil))))
+```
+
+### First of Vector
+```
+(claim first
+  (Π ((E U) (l Nat))
+    (→ (Vec E (add1 l)) E)))
+
+(define first
+  (λ (E l es) (head es)))
+```
+
+### Rest of Vector
+```
+(claim rest
+  (Π ((E U) (l Nat))
+    (→ (Vec E (add1 l)) (Vec E l))))
+
+(define rest
+  (λ (E l es) (tail es)))
+```
+
+### Build Vector Using ind-Nat
+```
+(claim peas
+  (Π ((how-many-peas Nat))
+    (Vec Atom how-many-peas)))
+
+(define peas
+  (λ (how-many-peas)
+    (ind-Nat how-many-peas
+      (λ (k) (Vec Atom k))
+      (the (Vec Atom zero) vecnil)
+      (λ (l-1 peas-l-1)
+        (vec:: 'pea peas-l-1)))))
+```
+
+---
+
+## Either Examples
+
+### Left Injection
+```
+(left zero)          ; Type: (Either Nat Atom)
+```
+
+### Right Injection
+```
+(right 'foo)         ; Type: (Either Nat Atom)
+```
+
+### Case Analysis
+```
+(λ (e)
+  (ind-Either e
+    (λ (_) Nat)
+    (λ (n) n)
+    (λ (a) zero)))
+```
+
+---
+
+## Equality Examples
+
+### Reflexivity
+```
+(the (= Nat zero zero)
+  (same zero))
+```
+
+### Symmetry with replace
+```
+(the (Π ((n Nat) (m Nat))
+       (→ (= Nat n m)
+          (= Nat m n)))
+  (λ (n m n=m)
+    (replace n=m
+      (λ (k) (= Nat k n))
+      (same n))))
+```
+
+### Using replace
+```
+(replace (the (= Nat 4 4) (same 4))
+  (λ (k) (= Nat k 4))
+  (same 4))
+```
+
+### Congruence with ind-=
+```
+(λ (n-1 incr=add1n-1)
+  (ind-= incr=add1n-1
+    (λ (x proof-incr-n-1=x)
+      (= Nat (add1 (incr n-1)) (add1 x)))
+    (same (add1 (incr n-1)))))
+```
+
+---
+
+## Dependent Type Examples
+
+### Pi Type (Dependent Function)
+```
+(the (Π ((A U)) U)
+  (λ (B) B))
+```
+
+### Multiple Dependent Parameters
+```
+(the (Π ((A U) (a A)) A)
+  (λ (B b) b))
+```
+
+### Complex Dependent Function with Pair
+```
+(the (Π ((f (→ Nat U))
+         (p (Σ ((n Nat)) (f n))))
+       (f (car p)))
+  (λ (f p) (cdr p)))
+```
+
+---
+
+## User-Defined Inductive Types
+
+### Bool Definition
+```
+(data Bool () ()
+  (true () (Bool))
+  (false () (Bool))
+  ind-Bool)
+```
+
+### Bool Usage
+```
+(data-true)
+(data-false)
+
+(data-ind-Bool (data-true)
+  (λ (b) Nat)
+  (add1 zero)
+  zero)
+```
+
+### Less-Than Definition (Indexed Type)
+```
+(data Less-Than () ((j Nat) (k Nat))
+  (zero-smallest ((n Nat))
+    (Less-Than zero (add1 n)))
+  (add1-smaller ((j Nat) (k Nat) (j<k (Less-Than j k)))
+    (Less-Than (add1 j) (add1 k)))
+  ind-Less-Than)
+```
+
+### Less-Than Usage
+```
+(claim proof-0<1 (Less-Than zero (add1 zero)))
+(define proof-0<1 (data-zero-smallest zero))
+
+(claim proof-1<2 (Less-Than (add1 zero) (add1 (add1 zero))))
+(define proof-1<2
+  (data-add1-smaller zero (add1 zero)
+    (data-zero-smallest zero)))
+
+(data-ind-Less-Than proof-0<1
+  (λ (j k p) Nat)
+  (λ (n) zero)
+  (λ (j k j<k ih) (add1 ih)))
+```
+
+---
+
+## Complete Programs
+
+### Addition Function
+```
+(claim +
+  (→ Nat Nat Nat))
+
+(claim step-plus
+  (→ Nat Nat))
+
+(define step-plus
+  (λ (n-1) (add1 n-1)))
+
+(define +
+  (λ (n j)
+    (iter-Nat n j step-plus)))
+```
+
+### Increment Function
+```
+(claim incr
+  (→ Nat Nat))
+
+(define incr
+  (λ (n)
+    (iter-Nat n 1 (+ 1))))
+```
+
+### Proof: incr n = add1 n
+```
+(claim incr=add1
+  (Π ((n Nat))
+    (= Nat (incr n) (add1 n))))
+
+(claim base-incr=add1
+  (= Nat (incr zero) (add1 zero)))
+
+(define base-incr=add1
+  (same (add1 zero)))
+
+(claim step-incr=add1
+  (Π ((n-1 Nat))
+    (→ (= Nat (incr n-1) (add1 n-1))
+       (= Nat (add1 (incr n-1)) (add1 (add1 n-1))))))
+
+(define step-incr=add1
+  (λ (n-1 incr=add1n-1)
+    (ind-= incr=add1n-1
+      (λ (x proof-incr-n-1=x)
+        (= Nat (add1 (incr n-1)) (add1 x)))
+      (same (add1 (incr n-1))))))
+```
+
+---
+
+## Key Observations from Examples
+
+1. **Empty collections always need `(the Type value)`**:
+   - `(the (List Nat) nil)` not `nil`
+   - `(the (Vec Atom zero) vecnil)` not `vecnil`
+
+2. **User-defined constructors/eliminators get `data-` prefix**:
+   - `(data-true)` not `(true)`
+   - `(data-ind-Bool ...)` not `(ind-Bool ...)`
+
+3. **Numeric literals are shorthand**:
+   - `0` = `zero`
+   - `1` = `(add1 zero)`
+   - `2` = `(add1 (add1 zero))`
+
+4. **Lambda can take multiple arguments**:
+   - `(λ (x y) body)` is curried as `(λ (x) (λ (y) body))`
+
+5. **Eliminators have fixed structure**:
+   - `ind-Nat`: target, motive, base, step
+   - `ind-List`: target, motive, base, step
+   - `ind-Vec`: length, target, motive, base, step
+   - `ind-Either`: target, motive, left-case, right-case
+   - `ind-=`: proof, motive, base
diff --git a/docs/pie_language/pie_language_spec.md b/docs/pie_language/pie_language_spec.md
new file mode 100644
index 00000000..4adee4d7
--- /dev/null
+++ b/docs/pie_language/pie_language_spec.md
@@ -0,0 +1,210 @@
+# Pie Language Specification
+
+Pie is a dependently-typed programming language based on "The Little Typer" book. This document describes the syntax and semantics for generating valid Pie expressions.
+
+## Basic Syntax
+
+### Numbers (Literals)
+- Numeric literals: `0`, `1`, `2`, `3`, `4`, `5`, etc. are shorthand for Nat constructors
+- `0` is equivalent to `zero`
+- `1` is equivalent to `(add1 zero)`
+- `2` is equivalent to `(add1 (add1 zero))`
+
+### Variables
+- Variable names: alphanumeric identifiers, can include hyphens: `x`, `my-var`, `n-1`, `vec-length`
+- Variables are introduced by lambda parameters, Pi parameters, or definitions
+
+### Type Annotations
+When explicit type annotation is needed, use `(the Type value)`:
+```
+(the Nat zero)
+(the Atom 'foo)
+(the (List Nat) nil)
+```
+
+## Core Types
+
+### Nat (Natural Numbers)
+- The type of natural numbers
+- Syntax: `Nat`
+
+### Atom
+- The type of quoted symbols
+- Syntax: `Atom`
+
+### Trivial
+- The unit type with only one value
+- Syntax: `Trivial`
+
+### Absurd
+- The empty type with no values
+- Syntax: `Absurd`
+
+### U (Universe)
+- The type of types
+- Syntax: `U`
+
+### → (Arrow/Function Type)
+Non-dependent function type shorthand:
+```
+(-> A B)           ; A → B
+(-> A B C)         ; A → B → C (curried)
+```
+
+### Π (Pi Type)
+Dependent function type with explicit parameter names:
+```
+(Π ((x A)) B)                    ; Π(x:A). B
+(Π ((x A) (y B)) C)             ; Π(x:A)(y:B). C
+```
+
+### Pair (Sigma Type)
+Non-dependent pair type shorthand:
+```
+(Pair A D)         ; Σ(a:A). D
+```
+
+### Σ (Sigma Type)
+Dependent pair type with explicit parameter names:
+```
+(Σ ((x A)) B)                    ; Σ(x:A). B
+(Σ ((x A) (y B)) C)             ; Σ(x:A)(y:B). C
+```
+
+### List
+Polymorphic list type:
+```
+(List A)           ; List of elements of type A
+```
+
+### Vec
+Length-indexed vector type:
+```
+(Vec E n)          ; Vector of elements of type E with length n (where n is a Nat)
+```
+
+### Either
+Sum type (disjoint union):
+```
+(Either L R)       ; Either left (type L) or right (type R)
+```
+
+### = (Equality Type)
+Propositional equality:
+```
+(= T from to)      ; Proof that from equals to, both of type T
+```
+
+## Constructors
+
+### Nat Constructors
+- `zero`: The number 0
+- `(add1 n)`: The successor of n
+
+### Atom Constructors
+- `'symbol`: A quoted symbol, e.g., `'foo`, `'bar`, `'pea`, `'olive`
+
+### Trivial Constructor
+- `sole`: The only value of type Trivial
+
+### Pair/Sigma Constructors
+- `(cons a d)`: Construct a pair with car `a` and cdr `d`
+
+### List Constructors
+- `nil`: Empty list (requires type annotation: `(the (List T) nil)`)
+- `(:: head tail)`: Cons cell with head and tail
+
+### Vec Constructors
+- `vecnil`: Empty vector (requires type annotation: `(the (Vec E zero) vecnil)`)
+- `(vec:: head tail)`: Vector cons with head element and tail vector
+
+### Either Constructors
+- `(left x)`: Left injection into Either type
+- `(right y)`: Right injection into Either type
+
+### Equality Constructor
+- `same`: Reflexivity proof for equality (when both sides are definitionally equal)
+- `(same x)`: Explicit reflexivity proof at value x
+
+### Function Constructor
+- `(λ (x) body)`: Lambda function (can also write as `lambda`)
+- `(λ (x y) body)`: Multi-parameter lambda (curried: `(λ (x) (λ (y) body))`)
+
+## Eliminators
+
+### Nat Eliminators
+- `(ind-Nat target motive base step)`: Induction on natural numbers
+  - `target`: The Nat being analyzed
+  - `motive`: `(λ (k) T)` - function from Nat to type
+  - `base`: Value for zero case
+  - `step`: `(λ (n-1 ih) ...)` - function taking predecessor and inductive hypothesis
+
+- `(rec-Nat target base step)`: Recursion (simpler than ind-Nat)
+  - Similar to ind-Nat but motive is implicit (always returns same type)
+
+- `(iter-Nat target base step)`: Iteration (simplest)
+  - `step`: `(λ (x) ...)` - function taking only result of previous iteration
+
+- `(which-Nat target base step)`: Case analysis (if zero then base, else step)
+  - `step`: `(λ (n-1) ...)` - function taking predecessor only
+
+### List Eliminators
+- `(ind-List target motive base step)`: Induction on lists
+  - `target`: The list being analyzed
+  - `motive`: `(λ (xs) T)` - function from list to type
+  - `base`: Value for nil case
+  - `step`: `(λ (head tail ih) ...)` - head, tail, and inductive hypothesis
+
+- `(rec-List target base step)`: Recursion on lists
+  - Similar structure to ind-List
+
+### Vec Eliminators
+- `(ind-Vec length target motive base step)`: Induction on vectors
+  - `length`: The length (Nat) of the vector
+  - `target`: The vector being analyzed
+  - `motive`: Function taking length and vector to type
+  - `base`: Value for vecnil case
+  - `step`: Function for vec:: case
+
+- `head`: Get first element of non-empty vector
+- `tail`: Get rest of non-empty vector (one element shorter)
+
+### Pair/Sigma Eliminators
+- `(car p)`: First projection (get first element of pair)
+- `(cdr p)`: Second projection (get second element of pair)
+
+### Either Eliminators
+- `(ind-Either target motive on-left on-right)`: Case analysis on Either
+  - `target`: The Either value
+  - `motive`: `(λ (e) T)` - function from Either to type
+  - `on-left`: `(λ (x) ...)` - handler for left case
+  - `on-right`: `(λ (y) ...)` - handler for right case
+
+### Absurd Eliminator
+- `(ind-Absurd target motive)`: Ex falso quodlibet (from false, anything follows)
+
+### Equality Eliminators
+- `(replace proof motive base)`: Use equality proof to convert types
+  - `proof`: A proof of `(= T from to)`
+  - `motive`: `(λ (x) T)` - how the type depends on the value
+  - `base`: Value of type `(motive from)`, returns value of type `(motive to)`
+
+## Function Application
+- `(f x)`: Apply function f to argument x
+- `(f x y)`: Apply f to x and y (curried: `((f x) y)`)
+
+## Top-Level Definitions
+- `(claim name type)`: Declare a name with a type
+- `(define name value)`: Define the value for a previously claimed name
+- `(define-tactically name tactics)`: Define using tactics (for proof mode)
+
+## Comments
+Lines can be omitted or preceded with `;` for comments (though not used in generation).
+
+## Key Rules
+
+1. **Empty collections need type annotations**: `(the (List Nat) nil)`, `(the (Vec Atom zero) vecnil)`
+2. **Variables must be in scope**: Use only variables from the context or introduced by lambdas
+3. **Type consistency**: The generated expression must match the expected type
+4. **Constructor arity**: Each constructor takes a specific number of arguments
+5. **Eliminator structure**: Eliminators have fixed parameter patterns (target, motive, cases)
diff --git a/docs/pie_language/pie_type_reference.md b/docs/pie_language/pie_type_reference.md
new file mode 100644
index 00000000..954ca713
--- /dev/null
+++ b/docs/pie_language/pie_type_reference.md
@@ -0,0 +1,582 @@
+# Pie Type Reference
+
+Quick reference for all Pie types with their constructors and eliminators.
+
+## Summary Table
+
+| Type | Constructors | Eliminators | Notes |
+|------|--------------|-------------|-------|
+| Nat | `zero`, `(add1 n)` | `ind-Nat`, `rec-Nat`, `iter-Nat`, `which-Nat` | Natural numbers |
+| Atom | `'symbol` | None (atoms are compared by name) | Quoted symbols |
+| Trivial | `sole` | None (only one value) | Unit type |
+| Absurd | None | `ind-Absurd` | Empty type |
+| U | Type expressions | None | Universe of types |
+| → | `(λ (x) body)` | Application `(f x)` | Non-dependent function |
+| Π | `(λ (x) body)` | Application `(f x)` | Dependent function |
+| Pair/Σ | `(cons a d)` | `car`, `cdr` | Pairs/dependent pairs |
+| List | `nil`, `(:: h t)` | `ind-List`, `rec-List` | Polymorphic lists |
+| Vec | `vecnil`, `(vec:: h t)` | `ind-Vec`, `head`, `tail` | Length-indexed vectors |
+| Either | `(left x)`, `(right y)` | `ind-Either` | Sum type |
+| = | `same`, `(same x)` | `replace`, `ind-=` | Equality proofs |
+| **User-defined** | Defined by `data` | Generated eliminator | Custom inductive types |
+
+---
+
+## Nat (Natural Numbers)
+
+**Type syntax:** `Nat`
+
+### Constructors
+```
+zero                    ; 0
+(add1 n)               ; n + 1
+
+; Shorthand: numeric literals
+0    ≡ zero
+1    ≡ (add1 zero)
+2    ≡ (add1 (add1 zero))
+```
+
+### Eliminators
+
+#### ind-Nat (Induction)
+Most powerful, allows dependent motives:
+```
+(ind-Nat target motive base step)
+
+target : Nat                           ; The number to analyze
+motive : (→ Nat U)                    ; (λ (k) TypeDependingOnK)
+base   : (motive zero)                ; Value for zero case
+step   : (Π ((n-1 Nat))              ; (λ (n-1 ih) ...)
+          (→ (motive n-1)
+              (motive (add1 n-1))))
+```
+
+**Example - Addition:**
+```
+(λ (x y)
+  (ind-Nat x
+    (λ (k) Nat)
+    y
+    (λ (n-1 ih) (add1 ih))))
+```
+
+#### rec-Nat (Recursion)
+Similar to ind-Nat but simpler (non-dependent result type):
+```
+(rec-Nat target base step)
+
+target : Nat
+base   : T                            ; Value for zero case
+step   : (→ Nat T T)                 ; (λ (n-1 ih) ...)
+```
+
+**Example - Addition:**
+```
+(λ (x y)
+  (rec-Nat x
+    y
+    (λ (n-1 ih) (add1 ih))))
+```
+
+#### iter-Nat (Iteration)
+Simplest, step only gets previous result:
+```
+(iter-Nat target base step)
+
+target : Nat
+base   : T
+step   : (→ T T)                      ; (λ (prev) ...)
+```
+
+**Example - Add constant:**
+```
+(iter-Nat 3
+  5
+  (λ (prev) (add1 prev)))   ; Result: 8
+```
+
+#### which-Nat (Case analysis)
+Check if zero or successor:
+```
+(which-Nat target base step)
+
+target : Nat
+base   : T                            ; If target is zero
+step   : (→ Nat T)                   ; (λ (n-1) ...) if target is (add1 n-1)
+```
+
+---
+
+## Atom
+
+**Type syntax:** `Atom`
+
+### Constructors
+```
+'symbol              ; Examples: 'foo, 'bar, 'pea, 'olive, 'oil
+```
+
+### Eliminators
+None directly. Atoms are primitive values.
+
+---
+
+## Trivial (Unit Type)
+
+**Type syntax:** `Trivial`
+
+### Constructors
+```
+sole                 ; The only value of type Trivial
+```
+
+### Eliminators
+None needed (only one possible value).
+
+---
+
+## Absurd (Empty Type)
+
+**Type syntax:** `Absurd`
+
+### Constructors
+None (uninhabited type).
+
+### Eliminators
+
+#### ind-Absurd
+From contradiction, derive anything:
+```
+(ind-Absurd target motive)
+
+target : Absurd                       ; The impossible value
+motive : U                           ; Any type you want to prove
+```
+
+---
+
+## U (Universe)
+
+**Type syntax:** `U`
+
+The type of types. Type expressions evaluate to values of type U.
+
+**Examples:**
+```
+Nat : U
+Atom : U
+(→ Nat Nat) : U
+(List Atom) : U
+```
+
+---
+
+## → (Function Type / Pi with non-dependent result)
+
+**Type syntax:**
+```
+(→ A B)              ; A → B
+(→ A B C)            ; A → B → C (curried)
+```
+
+### Constructors
+```
+(λ (x) body)                         ; Lambda abstraction
+(λ (x y) body)                       ; Multi-argument (curried)
+```
+
+### Eliminators
+```
+(f x)                                ; Function application
+```
+
+**Example:**
+```
+(the (→ Nat Nat)
+  (λ (x) x))                         ; Identity function
+```
+
+---
+
+## Π (Dependent Function Type / Pi Type)
+
+**Type syntax:**
+```
+(Π ((x A)) B)                        ; Π(x:A). B where B can depend on x
+(Π ((x A) (y B)) C)                 ; Multiple dependent parameters
+```
+
+### Constructors
+```
+(λ (x) body)                         ; Lambda (same as →)
+```
+
+### Eliminators
+```
+(f x)                                ; Application (same as →)
+```
+
+**Example:**
+```
+(the (Π ((n Nat)) (Vec Atom n))
+  (λ (n) (peas n)))                 ; Returns vector of length n
+```
+
+---
+
+## Pair (Non-dependent Pair) / Σ (Dependent Pair / Sigma Type)
+
+**Type syntax:**
+```
+(Pair A D)                           ; Σ(a:A). D (non-dependent)
+(Σ ((x A)) B)                        ; Σ(x:A). B where B can depend on x
+(Σ ((x A) (y B)) C)                 ; Multiple dependent fields
+```
+
+### Constructors
+```
+(cons a d)                           ; Construct pair with car=a, cdr=d
+```
+
+### Eliminators
+```
+(car p)                              ; First projection
+(cdr p)                              ; Second projection
+```
+
+**Examples:**
+```
+; Non-dependent pair
+(the (Pair Atom Atom)
+  (cons 'olive 'oil))
+
+; Dependent pair
+(the (Σ ((n Nat)) (Vec Atom n))
+  (cons 3 (vec:: 'a (vec:: 'b (vec:: 'c vecnil)))))
+```
+
+---
+
+## List (Polymorphic Lists)
+
+**Type syntax:** `(List E)` where E is the element type
+
+### Constructors
+```
+nil                                  ; Empty list (needs annotation!)
+(:: head tail)                       ; Cons cell
+
+; IMPORTANT: nil requires type annotation
+(the (List Nat) nil)                 ; Correct
+nil                                  ; ERROR!
+```
+
+### Eliminators
+
+#### ind-List (Induction)
+```
+(ind-List target motive base step)
+
+target : (List E)
+motive : (→ (List E) U)              ; (λ (xs) TypeDependingOnXs)
+base   : (motive nil)                ; Value for nil case
+step   : (Π ((head E)                ; (λ (h t ih) ...)
+             (tail (List E)))
+          (→ (motive tail)
+             (motive (:: head tail))))
+```
+
+#### rec-List (Recursion)
+Similar to ind-List but simpler.
+
+**Example - Sum of list:**
+```
+(ind-List ns
+  (λ (_) Nat)
+  zero
+  (λ (x y z)
+    (ind-Nat x
+      (λ (n) Nat)
+      z
+      (λ (_ q) (add1 q)))))
+```
+
+**Example - Build list:**
+```
+(:: (add1 zero)
+  (:: (add1 (add1 zero))
+    (the (List Nat) nil)))           ; List [1, 2]
+```
+
+---
+
+## Vec (Length-Indexed Vectors)
+
+**Type syntax:** `(Vec E n)` where E is element type, n is length (a Nat)
+
+### Constructors
+```
+vecnil                               ; Empty vector (needs annotation!)
+(vec:: head tail)                    ; Vector cons
+
+; IMPORTANT: vecnil requires type annotation
+(the (Vec Nat zero) vecnil)          ; Correct
+vecnil                               ; ERROR!
+```
+
+### Eliminators
+
+#### ind-Vec (Induction)
+```
+(ind-Vec length target motive base step)
+
+length : Nat                         ; Length of the vector
+target : (Vec E length)             ; The vector
+motive : (Π ((k Nat))               ; Type depends on length and vector
+          (→ (Vec E k) U))
+base   : (motive zero vecnil)       ; Value for vecnil case
+step   : (Π ((len Nat)              ; (λ (len e es ih) ...)
+             (e E)
+             (es (Vec E len)))
+          (→ (motive len es)
+             (motive (add1 len) (vec:: e es))))
+```
+
+#### head
+```
+(head v)                             ; Get first element (v must be non-empty)
+; Type: (Π ((E U) (n Nat)) (→ (Vec E (add1 n)) E))
+```
+
+#### tail
+```
+(tail v)                             ; Get rest of vector (one shorter)
+; Type: (Π ((E U) (n Nat)) (→ (Vec E (add1 n)) (Vec E n)))
+```
+
+**Example - Build vector of length 3:**
+```
+(vec:: zero
+  (vec:: (add1 zero)
+    (vec:: (add1 (add1 zero))
+      (the (Vec Nat zero) vecnil))))  ; Vec [0, 1, 2] : (Vec Nat 3)
+```
+
+---
+
+## Either (Sum Type)
+
+**Type syntax:** `(Either L R)` where L is left type, R is right type
+
+### Constructors
+```
+(left x)                             ; Inject x into left side
+(right y)                            ; Inject y into right side
+```
+
+### Eliminators
+
+#### ind-Either (Case analysis)
+```
+(ind-Either target motive on-left on-right)
+
+target   : (Either L R)
+motive   : (→ (Either L R) U)        ; (λ (e) TypeDependingOnE)
+on-left  : (Π ((x L)) (motive (left x)))   ; (λ (x) ...)
+on-right : (Π ((y R)) (motive (right y)))  ; (λ (y) ...)
+```
+
+**Example - Swap Either:**
+```
+(λ (e)
+  (ind-Either e
+    (λ (_) (Either Atom Nat))
+    (λ (x) (right x))                ; Swap: Nat goes right
+    (λ (y) (left y))))               ; Swap: Atom goes left
+```
+
+**Example - Simple construction:**
+```
+(left zero)          ; : (Either Nat Atom)
+(right 'foo)         ; : (Either Nat Atom)
+```
+
+---
+
+## = (Equality Type)
+
+**Type syntax:** `(= T from to)` - proof that `from` equals `to`, both of type `T`
+
+### Constructors
+```
+same                                 ; Reflexivity (when from ≡ to definitionally)
+(same x)                             ; Explicit reflexivity at x
+```
+
+### Eliminators
+
+#### replace (Transport across equality)
+```
+(replace proof motive base)
+
+proof  : (= T from to)              ; Equality proof
+motive : (→ T U)                    ; (λ (x) TypeDependingOnX)
+base   : (motive from)              ; Value at 'from'
+; Returns: (motive to)              ; Value transported to 'to'
+```
+
+**Example - Reflexivity proof:**
+```
+(the (= Nat zero zero)
+  (same zero))
+```
+
+**Example - Symmetry using replace:**
+```
+(λ (n m n=m)
+  (replace n=m
+    (λ (k) (= Nat k n))
+    (same n)))                       ; Proves m = n from n = m
+```
+
+#### ind-= (Equality induction / J rule)
+More powerful eliminator for equality:
+```
+(ind-= proof motive base)
+
+proof  : (= T from to)              ; Equality proof
+motive : (Π ((x T))                 ; Two-argument motive
+          (→ (= T from x) U))       ; Depends on x AND proof
+base   : (motive from (same from))  ; Base case for reflexivity
+; Returns: (motive to proof)        ; Result for actual proof
+```
+
+**Example - Congruence for add1:**
+```
+(λ (n-1 incr=add1n-1)
+  (ind-= incr=add1n-1
+    (λ (x proof-incr-n-1=x)
+      (= Nat (add1 (incr n-1)) (add1 x)))
+    (same (add1 (incr n-1)))))
+```
+
+**Difference between `replace` and `ind-=`:**
+- `replace`: Motive takes one argument `(λ (x) T)`
+- `ind-=`: Motive takes two arguments `(λ (x proof) T)` - can use the proof itself!
+
+---
+
+## User-Defined Inductive Types (data)
+
+You can define your own inductive types with parameters and indices.
+
+### Syntax
+```
+(data TypeName
+  (parameters)                       ; Type parameters
+  (indices)                          ; Type indices
+  (constructor1 (args) result-type)
+  (constructor2 (args) result-type)
+  ...
+  eliminator-name)
+```
+
+### Example 1: Simple Bool
+```
+(data Bool () ()                     ; No parameters, no indices
+  (true () (Bool))                   ; Constructor 'true' with no args
+  (false () (Bool))                  ; Constructor 'false' with no args
+  ind-Bool)                          ; Eliminator name
+```
+
+**Using Bool:**
+```
+; Constructors get prefix data-
+(data-true)                          ; : Bool
+(data-false)                         ; : Bool
+
+; Eliminator also gets prefix data-
+(data-ind-Bool (data-true)
+  (lambda (b) Nat)                   ; Motive
+  (add1 zero)                        ; Case for true
+  zero)                              ; Case for false
+```
+
+### Example 2: Indexed Type (Less-Than)
+```
+(data Less-Than () ((j Nat) (k Nat))  ; Indexed by two Nats
+  (zero-smallest ((n Nat))
+    (Less-Than zero (add1 n)))        ; 0 < n+1
+  (add1-smaller ((j Nat) (k Nat) (j<k (Less-Than j k)))
+    (Less-Than (add1 j) (add1 k)))    ; j < k → j+1 < k+1
+  ind-Less-Than)
+```
+
+**Using Less-Than:**
+```
+; Constructors
+(data-zero-smallest zero)             ; : (Less-Than 0 1)
+(data-add1-smaller zero (add1 zero)
+  (data-zero-smallest zero))          ; : (Less-Than 1 2)
+
+; Eliminator
+(data-ind-Less-Than proof
+  (lambda (j k p) Nat)                ; Motive depends on indices and proof
+  (lambda (n) zero)                   ; Case for zero-smallest
+  (lambda (j k j<k ih) (add1 ih)))    ; Case for add1-smaller
+```
+
+### General Constructor Pattern
+```
+(constructor-name
+  ((param1 Type1) (param2 Type2) ... (arg ArgType))
+  (TypeName index1 index2 ...))
+```
+
+- Constructor names get `data-` prefix when used
+- Parameters before the colon
+- Result type must be the datatype with indices
+
+### General Eliminator Pattern
+```
+(data-ind-TypeName target motive method1 method2 ...)
+
+target  : (TypeName idx1 idx2 ...)   ; The value to eliminate
+motive  : Depends on indices + target
+methodN : One method per constructor
+```
+
+Each method gets:
+- Constructor's parameters as arguments
+- Inductive hypotheses for recursive arguments
+- Must return `(motive applied to constructor)`
+
+---
+
+## Type Annotation Reminders
+
+### Always annotate empty collections:
+```
+✓ (the (List Nat) nil)
+✗ nil
+
+✓ (the (Vec Atom zero) vecnil)
+✗ vecnil
+```
+
+### Sometimes need explicit types:
+```
+✓ (the Nat zero)
+✓ (the Atom 'foo)
+✓ (the (= Nat 0 0) (same 0))
+```
+
+### User-defined constructors need prefix:
+```
+✗ (true)                             ; ERROR
+✓ (data-true)                        ; Correct
+
+✗ (ind-Bool ...)                     ; ERROR
+✓ (data-ind-Bool ...)                ; Correct
+```
diff --git a/package-lock.json b/package-lock.json
index a6fc20d4..f820e215 100644
--- a/package-lock.json
+++ b/package-lock.json
@@ -9,7 +9,10 @@
       "version": "1.0.0",
       "license": "ISC",
       "dependencies": {
-        "conductor": "https://github.com/source-academy/conductor.git#0.2.1"
+        "@google/genai": "^1.25.0",
+        "@google/generative-ai": "^0.24.1",
+        "conductor": "https://github.com/source-academy/conductor.git#0.2.1",
+        "dotenv": "^17.2.3"
       },
       "devDependencies": {
         "@babel/core": "^7.26.0",
@@ -2026,6 +2029,36 @@
         "node": "^18.18.0 || ^20.9.0 || >=21.1.0"
       }
     },
+    "node_modules/@google/genai": {
+      "version": "1.25.0",
+      "resolved": "https://registry.npmjs.org/@google/genai/-/genai-1.25.0.tgz",
+      "integrity": "sha512-IBNyel/umavam98SQUfvQSvh/Rp6Ql2fysQLqPyWZr5K8d768X9AO+JZU4o+3qvFDUBA0dVYUSkxyYonVcICvA==",
+      "license": "Apache-2.0",
+      "dependencies": {
+        "google-auth-library": "^9.14.2",
+        "ws": "^8.18.0"
+      },
+      "engines": {
+        "node": ">=20.0.0"
+      },
+      "peerDependencies": {
+        "@modelcontextprotocol/sdk": "^1.11.4"
+      },
+      "peerDependenciesMeta": {
+        "@modelcontextprotocol/sdk": {
+          "optional": true
+        }
+      }
+    },
+    "node_modules/@google/generative-ai": {
+      "version": "0.24.1",
+      "resolved": "https://registry.npmjs.org/@google/generative-ai/-/generative-ai-0.24.1.tgz",
+      "integrity": "sha512-MqO+MLfM6kjxcKoy0p1wRzG3b4ZZXtPI+z2IE26UogS2Cm/XHO+7gGRBh6gcJsOiIVoH93UwKvW4HdgiOZCy9Q==",
+      "license": "Apache-2.0",
+      "engines": {
+        "node": ">=18.0.0"
+      }
+    },
     "node_modules/@humanfs/core": {
       "version": "0.19.1",
       "resolved": "https://registry.npmjs.org/@humanfs/core/-/core-0.19.1.tgz",
@@ -2923,29 +2956,6 @@
         "node": ">= 8"
       }
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-    "node_modules/@rollup/plugin-inject": {
-      "version": "5.0.5",
-      "resolved": "https://registry.npmjs.org/@rollup/plugin-inject/-/plugin-inject-5.0.5.tgz",
-      "integrity": "sha512-2+DEJbNBoPROPkgTDNe8/1YXWcqxbN5DTjASVIOx8HS+pITXushyNiBV56RB08zuptzz8gT3YfkqriTBVycepg==",
-      "dev": true,
-      "license": "MIT",
-      "dependencies": {
-        "@rollup/pluginutils": "^5.0.1",
-        "estree-walker": "^2.0.2",
-        "magic-string": "^0.30.3"
-      },
-      "engines": {
-        "node": ">=14.0.0"
-      },
-      "peerDependencies": {
-        "rollup": "^1.20.0||^2.0.0||^3.0.0||^4.0.0"
-      },
-      "peerDependenciesMeta": {
-        "rollup": {
-          "optional": true
-        }
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-    },
     "node_modules/@rollup/plugin-node-resolve": {
       "version": "16.0.1",
       "resolved": "https://registry.npmjs.org/@rollup/plugin-node-resolve/-/plugin-node-resolve-16.0.1.tgz",
@@ -3761,6 +3771,15 @@
         "acorn": "^6.0.0 || ^7.0.0 || ^8.0.0"
       }
     },
+    "node_modules/agent-base": {
+      "version": "7.1.4",
+      "resolved": "https://registry.npmjs.org/agent-base/-/agent-base-7.1.4.tgz",
+      "integrity": "sha512-MnA+YT8fwfJPgBx3m60MNqakm30XOkyIoH1y6huTQvC0PwZG7ki8NacLBcrPbNoo8vEZy7Jpuk7+jMO+CUovTQ==",
+      "license": "MIT",
+      "engines": {
+        "node": ">= 14"
+      }
+    },
     "node_modules/ajv": {
       "version": "6.12.6",
       "resolved": "https://registry.npmjs.org/ajv/-/ajv-6.12.6.tgz",
@@ -4234,6 +4253,35 @@
       "dev": true,
       "license": "MIT"
     },
+    "node_modules/base64-js": {
+      "version": "1.5.1",
+      "resolved": "https://registry.npmjs.org/base64-js/-/base64-js-1.5.1.tgz",
+      "integrity": "sha512-AKpaYlHn8t4SVbOHCy+b5+KKgvR4vrsD8vbvrbiQJps7fKDTkjkDry6ji0rUJjC0kzbNePLwzxq8iypo41qeWA==",
+      "funding": [
+        {
+          "type": "github",
+          "url": "https://github.com/sponsors/feross"
+        },
+        {
+          "type": "patreon",
+          "url": "https://www.patreon.com/feross"
+        },
+        {
+          "type": "consulting",
+          "url": "https://feross.org/support"
+        }
+      ],
+      "license": "MIT"
+    },
+    "node_modules/bignumber.js": {
+      "version": "9.3.1",
+      "resolved": "https://registry.npmjs.org/bignumber.js/-/bignumber.js-9.3.1.tgz",
+      "integrity": "sha512-Ko0uX15oIUS7wJ3Rb30Fs6SkVbLmPBAKdlm7q9+ak9bbIeFf0MwuBsQV6z7+X768/cHsfg+WlysDWJcmthjsjQ==",
+      "license": "MIT",
+      "engines": {
+        "node": "*"
+      }
+    },
     "node_modules/brace-expansion": {
       "version": "1.1.11",
       "resolved": "https://registry.npmjs.org/brace-expansion/-/brace-expansion-1.1.11.tgz",
@@ -4314,6 +4362,12 @@
         "node-int64": "^0.4.0"
       }
     },
+    "node_modules/buffer-equal-constant-time": {
+      "version": "1.0.1",
+      "resolved": "https://registry.npmjs.org/buffer-equal-constant-time/-/buffer-equal-constant-time-1.0.1.tgz",
+      "integrity": "sha512-zRpUiDwd/xk6ADqPMATG8vc9VPrkck7T07OIx0gnjmJAnHnTVXNQG3vfvWNuiZIkwu9KrKdA1iJKfsfTVxE6NA==",
+      "license": "BSD-3-Clause"
+    },
     "node_modules/buffer-from": {
       "version": "1.1.2",
       "resolved": "https://registry.npmjs.org/buffer-from/-/buffer-from-1.1.2.tgz",
@@ -4721,7 +4775,6 @@
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       "integrity": "sha512-6WTZ/IxCY/T6BALoZHaE4ctp9xm+Z5kY/pzYaCHRFeyVhojxlrm+46y68HA6hr0TcwEssoxNiDEUJQjfPZ/RYA==",
-      "dev": true,
       "license": "MIT",
       "dependencies": {
         "ms": "^2.1.3"
@@ -4836,6 +4889,18 @@
         "node": ">=0.10.0"
       }
     },
+    "node_modules/dotenv": {
+      "version": "17.2.3",
+      "resolved": "https://registry.npmjs.org/dotenv/-/dotenv-17.2.3.tgz",
+      "integrity": "sha512-JVUnt+DUIzu87TABbhPmNfVdBDt18BLOWjMUFJMSi/Qqg7NTYtabbvSNJGOJ7afbRuv9D/lngizHtP7QyLQ+9w==",
+      "license": "BSD-2-Clause",
+      "engines": {
+        "node": ">=12"
+      },
+      "funding": {
+        "url": "https://dotenvx.com"
+      }
+    },
     "node_modules/dunder-proto": {
       "version": "1.0.1",
       "resolved": "https://registry.npmjs.org/dunder-proto/-/dunder-proto-1.0.1.tgz",
@@ -4851,6 +4916,15 @@
         "node": ">= 0.4"
       }
     },
+    "node_modules/ecdsa-sig-formatter": {
+      "version": "1.0.11",
+      "resolved": "https://registry.npmjs.org/ecdsa-sig-formatter/-/ecdsa-sig-formatter-1.0.11.tgz",
+      "integrity": "sha512-nagl3RYrbNv6kQkeJIpt6NJZy8twLB/2vtz6yN9Z4vRKHN4/QZJIEbqohALSgwKdnksuY3k5Addp5lg8sVoVcQ==",
+      "license": "Apache-2.0",
+      "dependencies": {
+        "safe-buffer": "^5.0.1"
+      }
+    },
     "node_modules/ejs": {
       "version": "3.1.10",
       "resolved": "https://registry.npmjs.org/ejs/-/ejs-3.1.10.tgz",
@@ -5513,6 +5587,12 @@
         "node": "^14.15.0 || ^16.10.0 || >=18.0.0"
       }
     },
+    "node_modules/extend": {
+      "version": "3.0.2",
+      "resolved": "https://registry.npmjs.org/extend/-/extend-3.0.2.tgz",
+      "integrity": "sha512-fjquC59cD7CyW6urNXK0FBufkZcoiGG80wTuPujX590cB5Ttln20E2UB4S/WARVqhXffZl2LNgS+gQdPIIim/g==",
+      "license": "MIT"
+    },
     "node_modules/fast-deep-equal": {
       "version": "3.1.3",
       "resolved": "https://registry.npmjs.org/fast-deep-equal/-/fast-deep-equal-3.1.3.tgz",
@@ -5757,6 +5837,36 @@
         "url": "https://github.com/sponsors/ljharb"
       }
     },
+    "node_modules/gaxios": {
+      "version": "6.7.1",
+      "resolved": "https://registry.npmjs.org/gaxios/-/gaxios-6.7.1.tgz",
+      "integrity": "sha512-LDODD4TMYx7XXdpwxAVRAIAuB0bzv0s+ywFonY46k126qzQHT9ygyoa9tncmOiQmmDrik65UYsEkv3lbfqQ3yQ==",
+      "license": "Apache-2.0",
+      "dependencies": {
+        "extend": "^3.0.2",
+        "https-proxy-agent": "^7.0.1",
+        "is-stream": "^2.0.0",
+        "node-fetch": "^2.6.9",
+        "uuid": "^9.0.1"
+      },
+      "engines": {
+        "node": ">=14"
+      }
+    },
+    "node_modules/gcp-metadata": {
+      "version": "6.1.1",
+      "resolved": "https://registry.npmjs.org/gcp-metadata/-/gcp-metadata-6.1.1.tgz",
+      "integrity": "sha512-a4tiq7E0/5fTjxPAaH4jpjkSv/uCaU2p5KC6HVGrvl0cDjA8iBZv4vv1gyzlmK0ZUKqwpOyQMKzZQe3lTit77A==",
+      "license": "Apache-2.0",
+      "dependencies": {
+        "gaxios": "^6.1.1",
+        "google-logging-utils": "^0.0.2",
+        "json-bigint": "^1.0.0"
+      },
+      "engines": {
+        "node": ">=14"
+      }
+    },
     "node_modules/gensync": {
       "version": "1.0.0-beta.2",
       "resolved": "https://registry.npmjs.org/gensync/-/gensync-1.0.0-beta.2.tgz",
@@ -5922,6 +6032,32 @@
         "url": "https://github.com/sponsors/ljharb"
       }
     },
+    "node_modules/google-auth-library": {
+      "version": "9.15.1",
+      "resolved": "https://registry.npmjs.org/google-auth-library/-/google-auth-library-9.15.1.tgz",
+      "integrity": "sha512-Jb6Z0+nvECVz+2lzSMt9u98UsoakXxA2HGHMCxh+so3n90XgYWkq5dur19JAJV7ONiJY22yBTyJB1TSkvPq9Ng==",
+      "license": "Apache-2.0",
+      "dependencies": {
+        "base64-js": "^1.3.0",
+        "ecdsa-sig-formatter": "^1.0.11",
+        "gaxios": "^6.1.1",
+        "gcp-metadata": "^6.1.0",
+        "gtoken": "^7.0.0",
+        "jws": "^4.0.0"
+      },
+      "engines": {
+        "node": ">=14"
+      }
+    },
+    "node_modules/google-logging-utils": {
+      "version": "0.0.2",
+      "resolved": "https://registry.npmjs.org/google-logging-utils/-/google-logging-utils-0.0.2.tgz",
+      "integrity": "sha512-NEgUnEcBiP5HrPzufUkBzJOD/Sxsco3rLNo1F1TNf7ieU8ryUzBhqba8r756CjLX7rn3fHl6iLEwPYuqpoKgQQ==",
+      "license": "Apache-2.0",
+      "engines": {
+        "node": ">=14"
+      }
+    },
     "node_modules/gopd": {
       "version": "1.2.0",
       "resolved": "https://registry.npmjs.org/gopd/-/gopd-1.2.0.tgz",
@@ -5949,6 +6085,19 @@
       "dev": true,
       "license": "MIT"
     },
+    "node_modules/gtoken": {
+      "version": "7.1.0",
+      "resolved": "https://registry.npmjs.org/gtoken/-/gtoken-7.1.0.tgz",
+      "integrity": "sha512-pCcEwRi+TKpMlxAQObHDQ56KawURgyAf6jtIY046fJ5tIv3zDe/LEIubckAO8fj6JnAxLdmWkUfNyulQ2iKdEw==",
+      "license": "MIT",
+      "dependencies": {
+        "gaxios": "^6.0.0",
+        "jws": "^4.0.0"
+      },
+      "engines": {
+        "node": ">=14.0.0"
+      }
+    },
     "node_modules/has-bigints": {
       "version": "1.1.0",
       "resolved": "https://registry.npmjs.org/has-bigints/-/has-bigints-1.1.0.tgz",
@@ -6050,6 +6199,19 @@
       "dev": true,
       "license": "MIT"
     },
+    "node_modules/https-proxy-agent": {
+      "version": "7.0.6",
+      "resolved": "https://registry.npmjs.org/https-proxy-agent/-/https-proxy-agent-7.0.6.tgz",
+      "integrity": "sha512-vK9P5/iUfdl95AI+JVyUuIcVtd4ofvtrOr3HNtM2yxC9bnMbEdp3x01OhQNnjb8IJYi38VlTE3mBXwcfvywuSw==",
+      "license": "MIT",
+      "dependencies": {
+        "agent-base": "^7.1.2",
+        "debug": "4"
+      },
+      "engines": {
+        "node": ">= 14"
+      }
+    },
     "node_modules/human-signals": {
       "version": "2.1.0",
       "resolved": "https://registry.npmjs.org/human-signals/-/human-signals-2.1.0.tgz",
@@ -6480,7 +6642,6 @@
       "version": "2.0.1",
       "resolved": "https://registry.npmjs.org/is-stream/-/is-stream-2.0.1.tgz",
       "integrity": "sha512-hFoiJiTl63nn+kstHGBtewWSKnQLpyb155KHheA1l39uvtO9nWIop1p3udqPcUd/xbF1VLMO4n7OI6p7RbngDg==",
-      "dev": true,
       "license": "MIT",
       "engines": {
         "node": ">=8"
@@ -8511,6 +8672,15 @@
         "node": ">=6"
       }
     },
+    "node_modules/json-bigint": {
+      "version": "1.0.0",
+      "resolved": "https://registry.npmjs.org/json-bigint/-/json-bigint-1.0.0.tgz",
+      "integrity": "sha512-SiPv/8VpZuWbvLSMtTDU8hEfrZWg/mH/nV/b4o0CYbSxu1UIQPLdwKOCIyLQX+VIPO5vrLX3i8qtqFyhdPSUSQ==",
+      "license": "MIT",
+      "dependencies": {
+        "bignumber.js": "^9.0.0"
+      }
+    },
     "node_modules/json-buffer": {
       "version": "3.0.1",
       "resolved": "https://registry.npmjs.org/json-buffer/-/json-buffer-3.0.1.tgz",
@@ -8568,6 +8738,27 @@
         "node": ">=4.0"
       }
     },
+    "node_modules/jwa": {
+      "version": "2.0.1",
+      "resolved": "https://registry.npmjs.org/jwa/-/jwa-2.0.1.tgz",
+      "integrity": "sha512-hRF04fqJIP8Abbkq5NKGN0Bbr3JxlQ+qhZufXVr0DvujKy93ZCbXZMHDL4EOtodSbCWxOqR8MS1tXA5hwqCXDg==",
+      "license": "MIT",
+      "dependencies": {
+        "buffer-equal-constant-time": "^1.0.1",
+        "ecdsa-sig-formatter": "1.0.11",
+        "safe-buffer": "^5.0.1"
+      }
+    },
+    "node_modules/jws": {
+      "version": "4.0.0",
+      "resolved": "https://registry.npmjs.org/jws/-/jws-4.0.0.tgz",
+      "integrity": "sha512-KDncfTmOZoOMTFG4mBlG0qUIOlc03fmzH+ru6RgYVZhPkyiy/92Owlt/8UEN+a4TXR1FQetfIpJE8ApdvdVxTg==",
+      "license": "MIT",
+      "dependencies": {
+        "jwa": "^2.0.0",
+        "safe-buffer": "^5.0.1"
+      }
+    },
     "node_modules/keyv": {
       "version": "4.5.4",
       "resolved": "https://registry.npmjs.org/keyv/-/keyv-4.5.4.tgz",
@@ -8676,16 +8867,6 @@
         "yallist": "^3.0.2"
       }
     },
-    "node_modules/magic-string": {
-      "version": "0.30.17",
-      "resolved": "https://registry.npmjs.org/magic-string/-/magic-string-0.30.17.tgz",
-      "integrity": "sha512-sNPKHvyjVf7gyjwS4xGTaW/mCnF8wnjtifKBEhxfZ7E/S8tQ0rssrwGNn6q8JH/ohItJfSQp9mBtQYuTlH5QnA==",
-      "dev": true,
-      "license": "MIT",
-      "dependencies": {
-        "@jridgewell/sourcemap-codec": "^1.5.0"
-      }
-    },
     "node_modules/make-dir": {
       "version": "4.0.0",
       "resolved": "https://registry.npmjs.org/make-dir/-/make-dir-4.0.0.tgz",
@@ -8800,7 +8981,6 @@
       "version": "2.1.3",
       "resolved": "https://registry.npmjs.org/ms/-/ms-2.1.3.tgz",
       "integrity": "sha512-6FlzubTLZG3J2a/NVCAleEhjzq5oxgHyaCU9yYXvcLsvoVaHJq/s5xXI6/XXP6tz7R9xAOtHnSO/tXtF3WRTlA==",
-      "dev": true,
       "license": "MIT"
     },
     "node_modules/natural-compare": {
@@ -8810,6 +8990,26 @@
       "dev": true,
       "license": "MIT"
     },
+    "node_modules/node-fetch": {
+      "version": "2.7.0",
+      "resolved": "https://registry.npmjs.org/node-fetch/-/node-fetch-2.7.0.tgz",
+      "integrity": "sha512-c4FRfUm/dbcWZ7U+1Wq0AwCyFL+3nt2bEw05wfxSz+DWpWsitgmSgYmy2dQdWyKC1694ELPqMs/YzUSNozLt8A==",
+      "license": "MIT",
+      "dependencies": {
+        "whatwg-url": "^5.0.0"
+      },
+      "engines": {
+        "node": "4.x || >=6.0.0"
+      },
+      "peerDependencies": {
+        "encoding": "^0.1.0"
+      },
+      "peerDependenciesMeta": {
+        "encoding": {
+          "optional": true
+        }
+      }
+    },
     "node_modules/node-int64": {
       "version": "0.4.0",
       "resolved": "https://registry.npmjs.org/node-int64/-/node-int64-0.4.0.tgz",
@@ -9577,19 +9777,6 @@
         "fsevents": "~2.3.2"
       }
     },
-    "node_modules/rollup-plugin-polyfill-node": {
-      "version": "0.13.0",
-      "resolved": "https://registry.npmjs.org/rollup-plugin-polyfill-node/-/rollup-plugin-polyfill-node-0.13.0.tgz",
-      "integrity": "sha512-FYEvpCaD5jGtyBuBFcQImEGmTxDTPbiHjJdrYIp+mFIwgXiXabxvKUK7ZT9P31ozu2Tqm9llYQMRWsfvTMTAOw==",
-      "dev": true,
-      "license": "MIT",
-      "dependencies": {
-        "@rollup/plugin-inject": "^5.0.4"
-      },
-      "peerDependencies": {
-        "rollup": "^1.20.0 || ^2.0.0 || ^3.0.0 || ^4.0.0"
-      }
-    },
     "node_modules/run-parallel": {
       "version": "1.2.0",
       "resolved": "https://registry.npmjs.org/run-parallel/-/run-parallel-1.2.0.tgz",
@@ -9638,7 +9825,6 @@
       "version": "5.2.1",
       "resolved": "https://registry.npmjs.org/safe-buffer/-/safe-buffer-5.2.1.tgz",
       "integrity": "sha512-rp3So07KcdmmKbGvgaNxQSJr7bGVSVk5S9Eq1F+ppbRo70+YeaDxkw5Dd8NPN+GD6bjnYm2VuPuCXmpuYvmCXQ==",
-      "dev": true,
       "funding": [
         {
           "type": "github",
@@ -10217,6 +10403,12 @@
         "node": ">=8.0"
       }
     },
+    "node_modules/tr46": {
+      "version": "0.0.3",
+      "resolved": "https://registry.npmjs.org/tr46/-/tr46-0.0.3.tgz",
+      "integrity": "sha512-N3WMsuqV66lT30CrXNbEjx4GEwlow3v6rr4mCcv6prnfwhS01rkgyFdjPNBYd9br7LpXV1+Emh01fHnq2Gdgrw==",
+      "license": "MIT"
+    },
     "node_modules/ts-api-utils": {
       "version": "2.0.1",
       "resolved": "https://registry.npmjs.org/ts-api-utils/-/ts-api-utils-2.0.1.tgz",
@@ -10561,6 +10753,19 @@
         "punycode": "^2.1.0"
       }
     },
+    "node_modules/uuid": {
+      "version": "9.0.1",
+      "resolved": "https://registry.npmjs.org/uuid/-/uuid-9.0.1.tgz",
+      "integrity": "sha512-b+1eJOlsR9K8HJpow9Ok3fiWOWSIcIzXodvv0rQjVoOVNpWMpxf1wZNpt4y9h10odCNrqnYp1OBzRktckBe3sA==",
+      "funding": [
+        "https://github.com/sponsors/broofa",
+        "https://github.com/sponsors/ctavan"
+      ],
+      "license": "MIT",
+      "bin": {
+        "uuid": "dist/bin/uuid"
+      }
+    },
     "node_modules/v8-to-istanbul": {
       "version": "9.3.0",
       "resolved": "https://registry.npmjs.org/v8-to-istanbul/-/v8-to-istanbul-9.3.0.tgz",
@@ -10586,6 +10791,22 @@
         "makeerror": "1.0.12"
       }
     },
+    "node_modules/webidl-conversions": {
+      "version": "3.0.1",
+      "resolved": "https://registry.npmjs.org/webidl-conversions/-/webidl-conversions-3.0.1.tgz",
+      "integrity": "sha512-2JAn3z8AR6rjK8Sm8orRC0h/bcl/DqL7tRPdGZ4I1CjdF+EaMLmYxBHyXuKL849eucPFhvBoxMsflfOb8kxaeQ==",
+      "license": "BSD-2-Clause"
+    },
+    "node_modules/whatwg-url": {
+      "version": "5.0.0",
+      "resolved": "https://registry.npmjs.org/whatwg-url/-/whatwg-url-5.0.0.tgz",
+      "integrity": "sha512-saE57nupxk6v3HY35+jzBwYa0rKSy0XR8JSxZPwgLr7ys0IBzhGviA1/TUGJLmSVqs8pb9AnvICXEuOHLprYTw==",
+      "license": "MIT",
+      "dependencies": {
+        "tr46": "~0.0.3",
+        "webidl-conversions": "^3.0.0"
+      }
+    },
     "node_modules/which": {
       "version": "2.0.2",
       "resolved": "https://registry.npmjs.org/which/-/which-2.0.2.tgz",
@@ -10776,6 +10997,27 @@
         "node": "^12.13.0 || ^14.15.0 || >=16.0.0"
       }
     },
+    "node_modules/ws": {
+      "version": "8.18.3",
+      "resolved": "https://registry.npmjs.org/ws/-/ws-8.18.3.tgz",
+      "integrity": "sha512-PEIGCY5tSlUt50cqyMXfCzX+oOPqN0vuGqWzbcJ2xvnkzkq46oOpz7dQaTDBdfICb4N14+GARUDw2XV2N4tvzg==",
+      "license": "MIT",
+      "engines": {
+        "node": ">=10.0.0"
+      },
+      "peerDependencies": {
+        "bufferutil": "^4.0.1",
+        "utf-8-validate": ">=5.0.2"
+      },
+      "peerDependenciesMeta": {
+        "bufferutil": {
+          "optional": true
+        },
+        "utf-8-validate": {
+          "optional": true
+        }
+      }
+    },
     "node_modules/y18n": {
       "version": "5.0.8",
       "resolved": "https://registry.npmjs.org/y18n/-/y18n-5.0.8.tgz",
diff --git a/package.json b/package.json
index 583c3547..e8cc2db4 100644
--- a/package.json
+++ b/package.json
@@ -36,7 +36,10 @@
     "typescript-eslint": "^8.15.0"
   },
   "dependencies": {
-    "conductor": "https://github.com/source-academy/conductor.git#0.2.1"
+    "@google/genai": "^1.25.0",
+    "@google/generative-ai": "^0.24.1",
+    "conductor": "https://github.com/source-academy/conductor.git#0.2.1",
+    "dotenv": "^17.2.3"
   },
   "scripts": {
     "build": "rollup -c",
diff --git a/src/language_server/package.json b/src/language_server/package.json
new file mode 100644
index 00000000..95739536
--- /dev/null
+++ b/src/language_server/package.json
@@ -0,0 +1,130 @@
+{
+  "name": "pie-lsp",
+  "description": "A language server for Pie",
+  "author": "Ding Feng, Li Daoxin, Zhang Qixiang",
+  "publisher": "source-academy",
+  "version": "1.0.0",
+  "repository": {
+    "type": "git"
+  },
+  "categories": [],
+  "keywords": [
+    "multi-root ready"
+  ],
+  "engines": {
+    "vscode": "^1.103.0"
+  },
+  "activationEvents": [
+    "onLanguage:pie"
+  ],
+  "main": "./out/src/language_server/client/src/extension",
+  "contributes": {
+    "languages": [
+      {
+        "id": "pie",
+        "aliases": [
+          "Pie",
+          "pie"
+        ],
+        "extensions": [
+          ".pie"
+        ],
+        "configuration": "./language-configuration.json"
+      }
+    ],
+    "grammars": [
+      {
+        "language": "pie",
+        "scopeName": "source.pie",
+        "path": "./syntaxes/pie.tmLanguage.json"
+      }
+    ],
+    "views": {
+      "explorer": [
+        {
+          "id": "pieOutput",
+          "name": "Pie Output"
+        }
+      ]
+    },
+    "commands": [
+      {
+        "command": "pie.runCode",
+        "title": "Run Pie Code",
+        "icon": "$(play)"
+      },
+      {
+        "command": "pie.refreshOutput",
+        "title": "Refresh",
+        "icon": "$(refresh)"
+      }
+    ],
+    "menus": {
+      "editor/title": [
+        {
+          "command": "pie.runCode",
+          "when": "resourceExtname == .pie",
+          "group": "navigation"
+        }
+      ],
+      "view/title": [
+        {
+          "command": "pie.refreshOutput",
+          "when": "view == pieOutput",
+          "group": "navigation"
+        }
+      ]
+    },
+    "configuration": {
+      "type": "object",
+      "title": "Example configuration",
+      "properties": {
+        "languageServerExample.maxNumberOfProblems": {
+          "scope": "resource",
+          "type": "number",
+          "default": 100,
+          "description": "Controls the maximum number of problems produced by the server."
+        },
+        "languageServerExample.trace.server": {
+          "scope": "window",
+          "type": "string",
+          "enum": [
+            "off",
+            "messages",
+            "verbose"
+          ],
+          "default": "off",
+          "description": "Traces the communication between VS Code and the language server."
+        }
+      }
+    }
+  },
+  "scripts": {
+    "vscode:prepublish": "npm run compile",
+    "compile": "tsc || true",
+    "watch": "tsc -w",
+    "lint": "eslint",
+    "test": "jest",
+    "clean": "rimraf out"
+  },
+  "dependencies": {
+    "@types/estree": "^1.0.8",
+    "js-base64": "^3.7.8",
+    "vscode-languageclient": "^9.0.1",
+    "vscode-languageserver": "^9.0.1",
+    "vscode-languageserver-textdocument": "^1.0.11"
+  },
+  "devDependencies": {
+    "@eslint/js": "^9.13.0",
+    "@stylistic/eslint-plugin": "^2.9.0",
+    "@types/jest": "^29.5.14",
+    "@types/node": "^22",
+    "@types/vscode": "^1.103.0",
+    "eslint": "^9.13.0",
+    "jest": "^29.7.0",
+    "rimraf": "^3.0.2",
+    "ts-jest": "^29.4.1",
+    "typescript": "^5.9.2",
+    "typescript-eslint": "^8.39.0"
+  }
+}
\ No newline at end of file
diff --git a/src/pie_interpreter/__tests__/test_ai_debug.ts b/src/pie_interpreter/__tests__/test_ai_debug.ts
new file mode 100644
index 00000000..0af6ec78
--- /dev/null
+++ b/src/pie_interpreter/__tests__/test_ai_debug.ts
@@ -0,0 +1,140 @@
+import { GoogleGenAI } from "@google/genai";
+import 'jest'
+import { solveTodo, TodoInfo } from '../try_llm/todo_solver';
+import { inspect } from 'util';
+import { Parser } from '../parser/parser';
+import { Location, Syntax } from '../utils/locations';
+import * as V from '../types/value';
+import * as C from '../types/core';
+import { FirstOrderClosure } from '../types/utils';
+import { readBackContext } from '../utils/context';
+
+
+describe('LLM TODO solver - Debug Complex Cases', () => {
+
+  // Helper function to create a test Location
+  function createTestLocation(source: string): Location {
+    const syntax = new Syntax(
+      { line: 1, column: 1 },
+      { line: 1, column: 1 },
+      source
+    );
+    return new Location(syntax, false);
+  }
+
+  it('should handle Vec type with length 3 - with detailed logging', async () => {
+    const todo: TodoInfo = {
+      location: createTestLocation('test.pie:18:1'),
+      context: new Map(),
+      expectedType: new V.Vec(new V.Nat(), new V.Add1(new V.Add1(new V.Add1(new V.Zero())))),
+      renaming: new Map()
+    };
+
+    console.log('\n========== VEC TYPE TEST ==========');
+    console.log('Expected Type:', inspect(todo.expectedType, { depth: 5, colors: true }));
+    console.log('Expected Type (pretty):', todo.expectedType.prettyPrint());
+    console.log('Expected Type (readBack):', todo.expectedType.readBackType(todo.context).prettyPrint());
+    console.log('Context:', inspect(readBackContext(todo.context), { depth: 3, colors: true }));
+    console.log('Starting LLM solve...\n');
+
+    try {
+      const solution = await solveTodo(todo);
+      console.log('\n✅ SUCCESS!');
+      console.log('Solution:', solution);
+      console.log('Solution (inspect):', inspect(solution, { colors: true }));
+
+      // Try to parse and verify the solution
+      console.log('\nVerifying solution...');
+      const parsed = Parser.parsePie(solution);
+      console.log('Parsed:', inspect(parsed, { depth: 3, colors: true }));
+
+      const checkResult = parsed.check(todo.context, todo.renaming, todo.expectedType);
+      console.log('Type check result:', inspect(checkResult, { depth: 2, colors: true }));
+    } catch (error: any) {
+      console.log('\n❌ FAILED!');
+      console.log('Error:', error.message);
+      console.log('Full error:', inspect(error, { depth: 3, colors: true }));
+    }
+  }, 120000);
+
+  it('should handle List of Pairs (nested types) - with detailed logging', async () => {
+    const todo: TodoInfo = {
+      location: createTestLocation('test.pie:38:1'),
+      context: new Map(),
+      expectedType: new V.List(new V.Sigma('fst', new V.Nat(), new FirstOrderClosure(new Map(), 'snd', new C.Atom()))),
+      renaming: new Map()
+    };
+
+    console.log('\n========== LIST OF PAIRS TEST ==========');
+    console.log('Expected Type:', inspect(todo.expectedType, { depth: 5, colors: true }));
+    console.log('Expected Type (pretty):', todo.expectedType.prettyPrint());
+    console.log('Expected Type (readBack):', todo.expectedType.readBackType(todo.context).prettyPrint());
+    console.log('Context:', inspect(readBackContext(todo.context), { depth: 3, colors: true }));
+    console.log('Starting LLM solve...\n');
+
+    try {
+      const solution = await solveTodo(todo);
+      console.log('\n✅ SUCCESS!');
+      console.log('Solution:', solution);
+      console.log('Solution (inspect):', inspect(solution, { colors: true }));
+
+      // Try to parse and verify the solution
+      console.log('\nVerifying solution...');
+      const parsed = Parser.parsePie(solution);
+      console.log('Parsed:', inspect(parsed, { depth: 3, colors: true }));
+
+      const checkResult = parsed.check(todo.context, todo.renaming, todo.expectedType);
+      console.log('Type check result:', inspect(checkResult, { depth: 2, colors: true }));
+    } catch (error: any) {
+      console.log('\n❌ FAILED!');
+      console.log('Error:', error.message);
+      console.log('Full error:', inspect(error, { depth: 3, colors: true }));
+    }
+  }, 120000);
+
+  it('should handle simpler Vec - length 1', async () => {
+    const todo: TodoInfo = {
+      location: createTestLocation('test.pie:simple-vec:1'),
+      context: new Map(),
+      expectedType: new V.Vec(new V.Nat(), new V.Add1(new V.Zero())),
+      renaming: new Map()
+    };
+
+    console.log('\n========== SIMPLE VEC (LENGTH 1) TEST ==========');
+    console.log('Expected Type (pretty):', todo.expectedType.prettyPrint());
+    console.log('Expected Type (readBack):', todo.expectedType.readBackType(todo.context).prettyPrint());
+    console.log('Starting LLM solve...\n');
+
+    try {
+      const solution = await solveTodo(todo);
+      console.log('\n✅ SUCCESS!');
+      console.log('Solution:', solution);
+    } catch (error: any) {
+      console.log('\n❌ FAILED!');
+      console.log('Error:', error.message);
+    }
+  }, 120000);
+
+  it('should handle simple List (without nested complexity)', async () => {
+    const todo: TodoInfo = {
+      location: createTestLocation('test.pie:simple-list:1'),
+      context: new Map(),
+      expectedType: new V.List(new V.Nat()),
+      renaming: new Map()
+    };
+
+    console.log('\n========== SIMPLE LIST TEST ==========');
+    console.log('Expected Type (pretty):', todo.expectedType.prettyPrint());
+    console.log('Expected Type (readBack):', todo.expectedType.readBackType(todo.context).prettyPrint());
+    console.log('Starting LLM solve...\n');
+
+    try {
+      const solution = await solveTodo(todo);
+      console.log('\n✅ SUCCESS!');
+      console.log('Solution:', solution);
+    } catch (error: any) {
+      console.log('\n❌ FAILED!');
+      console.log('Error:', error.message);
+    }
+  }, 120000);
+});
diff --git a/src/pie_interpreter/__tests__/test_ai_queue.ts b/src/pie_interpreter/__tests__/test_ai_queue.ts
new file mode 100644
index 00000000..37c4b359
--- /dev/null
+++ b/src/pie_interpreter/__tests__/test_ai_queue.ts
@@ -0,0 +1,101 @@
+import 'jest';
+import { todoQueue, addTodo, clearQueue, solveTodo, TodoInfo } from '../try_llm/todo_solver';
+import { inspect } from 'util';
+import { Location, Syntax } from '../utils/locations';
+import * as V from '../types/value';
+
+describe('LLM TODO Queue Sequential Solving', () => {
+
+  // Helper function to create a test Location
+  function createTestLocation(source: string): Location {
+    const syntax = new Syntax(
+      { line: 1, column: 1 },
+      { line: 1, column: 1 },
+      source
+    );
+    return new Location(syntax, false);
+  }
+
+  beforeEach(() => {
+    clearQueue();
+  });
+
+  it('should solve two TODOs sequentially from queue', async () => {
+    // Add two TODOs to the queue
+    const todo1: TodoInfo = {
+      location: createTestLocation('test.pie:1:1'),
+      context: new Map(),
+      expectedType: new V.Nat(),
+      renaming: new Map()
+    };
+
+    const todo2: TodoInfo = {
+      location: createTestLocation('test.pie:2:1'),
+      context: new Map(),
+      expectedType: new V.Trivial(),
+      renaming: new Map()
+    };
+
+    addTodo(todo1);
+    addTodo(todo2);
+
+    console.log('Initial queue length:', todoQueue.length);
+    console.log('TODOs in queue:');
+    todoQueue.forEach((todo, i) => {
+      console.log(`  [${i}] ${todo.location.toString()} - Expected type: ${todo.expectedType.constructor.name}`);
+    });
+
+    // Solve each TODO sequentially
+    console.log('\n=== Solving TODOs sequentially ===\n');
+
+    for (let i = 0; i < todoQueue.length; i++) {
+      const todo = todoQueue[i];
+      console.log(`\n--- Solving TODO ${i + 1}/${todoQueue.length} ---`);
+      console.log(`Location: ${todo.location.toString()}`);
+      console.log(`Expected type: ${todo.expectedType.constructor.name}`);
+
+      const solution = await solveTodo(todo);
+
+      console.log(`Solution: ${inspect(solution, true, null, true)}`);
+    }
+
+    console.log('\n=== All TODOs solved ===');
+  }, 120000);
+
+  it('should solve three different type TODOs sequentially', async () => {
+    const todos: TodoInfo[] = [
+      {
+        location: createTestLocation('test.pie:1:1'),
+        context: new Map(),
+        expectedType: new V.Nat(),
+        renaming: new Map()
+      },
+      {
+        location: createTestLocation('test.pie:2:1'),
+        context: new Map(),
+        expectedType: new V.Atom(),
+        renaming: new Map()
+      },
+      {
+        location: createTestLocation('test.pie:3:1'),
+        context: new Map(),
+        expectedType: new V.List(new V.Nat()),
+        renaming: new Map()
+      }
+    ];
+
+    todos.forEach(todo => addTodo(todo));
+
+    console.log('Queue size:', todoQueue.length);
+
+    for (let i = 0; i < todoQueue.length; i++) {
+      const todo = todoQueue[i];
+      console.log(`\n[${i + 1}/${todoQueue.length}] ${todo.location.toString()}`);
+
+      const solution = await solveTodo(todo);
+
+      console.log('Solution:', inspect(solution, true, null, true));
+    }
+  }, 180000);
+
+});
diff --git a/src/pie_interpreter/__tests__/test_definedatatype.ts b/src/pie_interpreter/__tests__/test_definedatatype.ts
new file mode 100644
index 00000000..e45b37ad
--- /dev/null
+++ b/src/pie_interpreter/__tests__/test_definedatatype.ts
@@ -0,0 +1,761 @@
+import 'jest'
+import { DefineDatatypeSource, GeneralConstructor } from '../typechecker/definedatatype'
+import { Location, Syntax } from '../utils/locations';
+import { Position } from '../../scheme_parser/transpiler/types/location';
+import * as S from '../types/source';
+import { Context, initCtx, valInContext } from '../utils/context';
+import { inspect } from 'util';
+import { Renaming } from '../typechecker/utils';
+import * as C from '../types/core';
+import { go, SiteBinder, TypedBinder } from '../types/utils';
+
+
+const testLoc = new Location(new Syntax(new Position(1, 1), new Position(1, 1), 'test'), false);
+
+
+describe('boolean', () => {
+  let define_boolean = new DefineDatatypeSource(
+    testLoc,
+    'Bool',
+    [],
+    [],
+    [
+      new GeneralConstructor(testLoc, 'true', [], new S.GeneralTypeConstructor(testLoc, 'Bool', [], [])),
+      new GeneralConstructor(testLoc, 'false', [], new S.GeneralTypeConstructor(testLoc, 'Bool', [], []))
+    ]
+  )
+  let ctx = initCtx
+  let renameing = new Map<string, string>()
+  it('test generate type and constructor', () => {
+    let result = define_boolean.normalize_constructor(ctx, renameing)
+    console.log(inspect(result, true, null, true))
+  })
+  let [new_ctx, new_renaming] = define_boolean.normalize_constructor(ctx, renameing)
+  let Mytrue = new S.ConstructorApplication(
+    testLoc,
+    'true',
+    []
+  )
+  let Myfalse = new S.ConstructorApplication(
+    testLoc,
+    'false',
+    []
+  )
+  it('test type check constructors', () => {
+    let result0 = Mytrue.synth(new_ctx as Context, new_renaming as Renaming)
+    let result1 = Myfalse.synth(new_ctx as Context, new_renaming as Renaming)
+    console.log(inspect([result0, result1], true, null, true))
+  })
+  let result0 = (Mytrue.synth(new_ctx as Context, new_renaming as Renaming) as go<C.The>).result
+  let result1 = (Myfalse.synth(new_ctx as Context, new_renaming as Renaming) as go<C.The>).result
+  let eliminateTrue = new S.EliminatorApplication(
+    testLoc,
+    'Bool',
+    Mytrue,
+    new S.Lambda(
+      testLoc,
+      [new SiteBinder(testLoc, 't')],
+      new S.Nat(testLoc)
+    )
+    ,[
+      new S.Add1(testLoc, new S.Zero(testLoc)),
+      new S.Zero(testLoc)
+    ]
+  )
+
+  let eliminateFalse = new S.EliminatorApplication(
+    testLoc,
+    'Bool',
+    Myfalse,
+    new S.Lambda(
+      testLoc,
+      [new SiteBinder(testLoc, 't')],
+      new S.Nat(testLoc)
+    )
+    ,[
+      new S.Add1(testLoc, new S.Zero(testLoc)),
+      new S.Zero(testLoc)
+    ]
+  )
+  it('test eliminate true and false', () => {
+    let resultTrue = eliminateTrue.synth(new_ctx as Context, new_renaming as Renaming)
+    let resultFalse = eliminateFalse.synth(new_ctx as Context, new_renaming as Renaming)
+    console.log(inspect([resultTrue, resultFalse], true, null, true))
+  })
+
+  it('test evaluate eliminators', () => {
+    let resultTrue = (eliminateTrue.synth(new_ctx as Context, new_renaming as Renaming) as go<C.The>).result
+    let resultFalse = (eliminateFalse.synth(new_ctx as Context, new_renaming as Renaming) as go<C.The>).result
+
+    // Evaluate the core expressions
+    let evalTrue = valInContext(new_ctx as Context, resultTrue.expr).now()
+    let evalFalse = valInContext(new_ctx as Context, resultFalse.expr).now()
+
+    console.log(inspect([evalTrue, evalFalse], true, null, true))
+  })
+
+})
+
+describe('mynat', () => {
+  // define-datatype MyNat
+  //   myzero : MyNat
+  //   mysucc : (MyNat -> MyNat)
+  let define_mynat = new DefineDatatypeSource(
+    testLoc,
+    'MyNat',
+    [],
+    [],
+    [
+      new GeneralConstructor(testLoc, 'myzero', [], new S.GeneralTypeConstructor(testLoc, 'MyNat', [], [])),
+      new GeneralConstructor(
+        testLoc,
+        'mysucc',
+        [new TypedBinder(new SiteBinder(testLoc, 'n'), new S.Name(testLoc, 'MyNat'))],
+        new S.GeneralTypeConstructor(testLoc, 'MyNat', [], [])
+      )
+    ]
+  )
+  let ctx = initCtx
+  let renaming = new Map<string, string>()
+
+  it('test generate type and constructors', () => {
+    let result = define_mynat.normalize_constructor(ctx, renaming)
+    console.log(inspect(result, true, null, true))
+  })
+
+  let [new_ctx, new_renaming] = define_mynat.normalize_constructor(ctx, renaming)
+
+  it('test type check constructors', () => {
+    let Myzero = new S.ConstructorApplication(testLoc, 'myzero', [])
+    let Myone = new S.ConstructorApplication(testLoc, 'mysucc', [new S.ConstructorApplication(testLoc, 'myzero', [])])
+    let Mytwo = new S.ConstructorApplication(testLoc, 'mysucc', [new S.ConstructorApplication(testLoc, 'mysucc', [new S.ConstructorApplication(testLoc, 'myzero', [])])])
+
+    let result0 = Myzero.synth(new_ctx as Context, new_renaming as Renaming)
+    let result1 = Myone.synth(new_ctx as Context, new_renaming as Renaming)
+    let result2 = Mytwo.synth(new_ctx as Context, new_renaming as Renaming)
+    console.log(inspect([result0, result1, result2], true, null, true))
+  })
+
+  let Myzero = new S.ConstructorApplication(testLoc, 'myzero', [])
+  let Myone = new S.ConstructorApplication(testLoc, 'mysucc', [new S.ConstructorApplication(testLoc, 'myzero', [])])
+
+  // Eliminator: convert MyNat to Nat
+  let eliminateMyzero = new S.EliminatorApplication(
+    testLoc,
+    'MyNat',
+    Myzero,
+    new S.Lambda(
+      testLoc,
+      [new SiteBinder(testLoc, 'n')],
+      new S.Nat(testLoc)
+    ),
+    [
+      new S.Zero(testLoc),  // myzero case: return 0
+      new S.Lambda(         // mysucc case: λ(pred : MyNat) → λ(ih : Nat) → (add1 ih)
+        testLoc,
+        [new SiteBinder(testLoc, 'pred')],
+        new S.Lambda(
+          testLoc,
+          [new SiteBinder(testLoc, 'ih')],
+          new S.Add1(testLoc, new S.Name(testLoc, 'ih'))
+        )
+      )
+    ]
+  )
+
+  let eliminateMyone = new S.EliminatorApplication(
+    testLoc,
+    'MyNat',
+    Myone,
+    new S.Lambda(
+      testLoc,
+      [new SiteBinder(testLoc, 'n')],
+      new S.Nat(testLoc)
+    ),
+    [
+      new S.Zero(testLoc),  // myzero case: return 0
+      new S.Lambda(         // mysucc case: λ(pred : MyNat) → λ(ih : Nat) → (add1 ih)
+        testLoc,
+        [new SiteBinder(testLoc, 'pred')],
+        new S.Lambda(
+          testLoc,
+          [new SiteBinder(testLoc, 'ih')],
+          new S.Add1(testLoc, new S.Name(testLoc, 'ih'))
+        )
+      )
+    ]
+  )
+
+  it('test eliminate zero and one', () => {
+    let resultZero = eliminateMyzero.synth(new_ctx as Context, new_renaming as Renaming)
+    let resultOne = eliminateMyone.synth(new_ctx as Context, new_renaming as Renaming)
+    console.log(inspect([resultZero, resultOne], true, null, true))
+  })
+
+  it('test evaluate eliminators', () => {
+    let resultZero = (eliminateMyzero.synth(new_ctx as Context, new_renaming as Renaming) as go<C.The>).result
+    let resultOne = (eliminateMyone.synth(new_ctx as Context, new_renaming as Renaming) as go<C.The>).result
+
+    let evalZero = valInContext(new_ctx as Context, resultZero.expr).now()
+    let evalOne = valInContext(new_ctx as Context, resultOne.expr).now()
+
+    console.log(inspect([evalZero, evalOne], true, null, true))
+  })
+})
+
+describe('mylist', () => {
+  // define-datatype MyList (E : U)
+  //   mynil : (E : U) -> MyList E
+  //   mycons : (E : U) -> E -> MyList E -> MyList E
+  // Constructors explicitly take the type parameter E as an argument
+  let define_mylist = new DefineDatatypeSource(
+    testLoc,
+    'MyList',
+    [new TypedBinder(new SiteBinder(testLoc, 'E'), new S.Universe(testLoc))],
+    [],
+    [
+      new GeneralConstructor(
+        testLoc,
+        'mynil',
+        [new TypedBinder(new SiteBinder(testLoc, 'E'), new S.Universe(testLoc))],
+        new S.GeneralTypeConstructor(testLoc, 'MyList', [new S.Name(testLoc, 'E')], [])
+      ),
+      new GeneralConstructor(
+        testLoc,
+        'mycons',
+        [
+          new TypedBinder(new SiteBinder(testLoc, 'E'), new S.Universe(testLoc)),
+          new TypedBinder(new SiteBinder(testLoc, 'head'), new S.Name(testLoc, 'E')),
+          new TypedBinder(new SiteBinder(testLoc, 'tail'), new S.GeneralTypeConstructor(testLoc, 'MyList', [new S.Name(testLoc, 'E')], []))
+        ],
+        new S.GeneralTypeConstructor(testLoc, 'MyList', [new S.Name(testLoc, 'E')], [])
+      )
+    ]
+  )
+  let ctx = initCtx
+  let renaming = new Map<string, string>()
+
+  it('test generate type and constructors', () => {
+    let result = define_mylist.normalize_constructor(ctx, renaming)
+    console.log(inspect(result, true, null, true))
+  })
+
+  let [new_ctx, new_renaming] = define_mylist.normalize_constructor(ctx, renaming)
+
+  it('test type check constructors', () => {
+    // MyList Nat: (mynil Nat)
+    let Mynil = new S.ConstructorApplication(testLoc, 'mynil', [new S.Nat(testLoc)])
+    // MyList Nat: (mycons Nat 1 (mynil Nat))
+    let Myone = new S.ConstructorApplication(
+      testLoc,
+      'mycons',
+      [
+        new S.Nat(testLoc),
+        new S.Add1(testLoc, new S.Zero(testLoc)),
+        new S.ConstructorApplication(testLoc, 'mynil', [new S.Nat(testLoc)])
+      ]
+    )
+
+    let result0 = Mynil.synth(new_ctx as Context, new_renaming as Renaming)
+    let result1 = Myone.synth(new_ctx as Context, new_renaming as Renaming)
+    console.log(inspect([result0, result1], true, null, true))
+  })
+
+  // Construct test lists for elimination
+  let Mynil = new S.ConstructorApplication(testLoc, 'mynil', [new S.Nat(testLoc)])
+  let Myone = new S.ConstructorApplication(
+    testLoc,
+    'mycons',
+    [
+      new S.Nat(testLoc),
+      new S.Add1(testLoc, new S.Zero(testLoc)),
+      new S.ConstructorApplication(testLoc, 'mynil', [new S.Nat(testLoc)])
+    ]
+  )
+
+  // Eliminator: compute length of MyList Nat
+  let eliminateMynil = new S.EliminatorApplication(
+    testLoc,
+    'MyList',
+    Mynil,
+    new S.Lambda(
+      testLoc,
+      [new SiteBinder(testLoc, 'lst')],
+      new S.Nat(testLoc)
+    ),
+    [
+      new S.Lambda(         // mynil case: λ(E : U) → 0
+        testLoc,
+        [new SiteBinder(testLoc, 'E')],
+        new S.Zero(testLoc)
+      ),
+      new S.Lambda(         // mycons case: λ(E : U) → λ(head : E) → λ(tail : MyList E) → λ(ih : Nat) → (add1 ih)
+        testLoc,
+        [new SiteBinder(testLoc, 'E')],
+        new S.Lambda(
+          testLoc,
+          [new SiteBinder(testLoc, 'head')],
+          new S.Lambda(
+            testLoc,
+            [new SiteBinder(testLoc, 'tail')],
+            new S.Lambda(
+              testLoc,
+              [new SiteBinder(testLoc, 'ih')],
+              new S.Add1(testLoc, new S.Name(testLoc, 'ih'))
+            )
+          )
+        )
+      )
+    ]
+  )
+
+  let eliminateMyone = new S.EliminatorApplication(
+    testLoc,
+    'MyList',
+    Myone,
+    new S.Lambda(
+      testLoc,
+      [new SiteBinder(testLoc, 'lst')],
+      new S.Nat(testLoc)
+    ),
+    [
+      new S.Lambda(         // mynil case: λ(E : U) → 0
+        testLoc,
+        [new SiteBinder(testLoc, 'E')],
+        new S.Zero(testLoc)
+      ),
+      new S.Lambda(         // mycons case: λ(E : U) → λ(head : E) → λ(tail : MyList E) → λ(ih : Nat) → (add1 ih)
+        testLoc,
+        [new SiteBinder(testLoc, 'E')],
+        new S.Lambda(
+          testLoc,
+          [new SiteBinder(testLoc, 'head')],
+          new S.Lambda(
+            testLoc,
+            [new SiteBinder(testLoc, 'tail')],
+            new S.Lambda(
+              testLoc,
+              [new SiteBinder(testLoc, 'ih')],
+              new S.Add1(testLoc, new S.Name(testLoc, 'ih'))
+            )
+          )
+        )
+      )
+    ]
+  )
+
+  it('test eliminate nil and cons', () => {
+    let resultNil = eliminateMynil.synth(new_ctx as Context, new_renaming as Renaming)
+    let resultCons = eliminateMyone.synth(new_ctx as Context, new_renaming as Renaming)
+    console.log(inspect([resultNil, resultCons], true, null, true))
+  })
+
+  it('test evaluate eliminators', () => {
+    let resultNil = (eliminateMynil.synth(new_ctx as Context, new_renaming as Renaming) as go<C.The>).result
+    let resultCons = (eliminateMyone.synth(new_ctx as Context, new_renaming as Renaming) as go<C.The>).result
+
+    let evalNil = valInContext(new_ctx as Context, resultNil.expr).now()
+    let evalCons = valInContext(new_ctx as Context, resultCons.expr).now()
+
+    console.log(inspect([evalNil, evalCons], true, null, true))
+  })
+})
+
+describe('myvec', () => {
+  // define-datatype MyVec (E : U) : Nat -> U
+  //   myvecnil : (E : U) -> MyVec E zero
+  //   myveccons : (E : U) -> (k : Nat) -> E -> MyVec E k -> MyVec E (add1 k)
+  let define_myvec = new DefineDatatypeSource(
+    testLoc,
+    'MyVec',
+    [new TypedBinder(new SiteBinder(testLoc, 'E'), new S.Universe(testLoc))],
+    [new TypedBinder(new SiteBinder(testLoc, 'len'), new S.Nat(testLoc))],
+    [
+      new GeneralConstructor(
+        testLoc,
+        'myvecnil',
+        [new TypedBinder(new SiteBinder(testLoc, 'E'), new S.Universe(testLoc))],
+        new S.GeneralTypeConstructor(testLoc, 'MyVec', [new S.Name(testLoc, 'E')], [new S.Zero(testLoc)])
+      ),
+      new GeneralConstructor(
+        testLoc,
+        'myveccons',
+        [
+          new TypedBinder(new SiteBinder(testLoc, 'E'), new S.Universe(testLoc)),
+          new TypedBinder(new SiteBinder(testLoc, 'k'), new S.Nat(testLoc)),
+          new TypedBinder(new SiteBinder(testLoc, 'head'), new S.Name(testLoc, 'E')),
+          new TypedBinder(new SiteBinder(testLoc, 'tail'), new S.GeneralTypeConstructor(testLoc, 'MyVec', [new S.Name(testLoc, 'E')], [new S.Name(testLoc, 'k')]))
+        ],
+        new S.GeneralTypeConstructor(testLoc, 'MyVec', [new S.Name(testLoc, 'E')], [new S.Add1(testLoc, new S.Name(testLoc, 'k'))])
+      )
+    ]
+  )
+  let ctx = initCtx
+  let renaming = new Map<string, string>()
+
+  it('test generate type and constructors', () => {
+    let result = define_myvec.normalize_constructor(ctx, renaming)
+    console.log(inspect(result, true, null, true))
+  })
+
+  let [new_ctx, new_renaming] = define_myvec.normalize_constructor(ctx, renaming)
+
+  it('test type check constructors', () => {
+    // MyVec Nat 0: (myvecnil Nat)
+    let Myvecnil = new S.ConstructorApplication(testLoc, 'myvecnil', [new S.Nat(testLoc)])
+    // MyVec Nat 1: (myveccons Nat 0 1 (myvecnil Nat))
+    let Myvecone = new S.ConstructorApplication(
+      testLoc,
+      'myveccons',
+      [
+        new S.Nat(testLoc),
+        new S.Zero(testLoc),
+        new S.Add1(testLoc, new S.Zero(testLoc)),
+        new S.ConstructorApplication(testLoc, 'myvecnil', [new S.Nat(testLoc)])
+      ]
+    )
+    // MyVec Nat 2: (myveccons Nat 1 2 (myveccons Nat 0 1 (myvecnil Nat)))
+    let Myvectwo = new S.ConstructorApplication(
+      testLoc,
+      'myveccons',
+      [
+        new S.Nat(testLoc),
+        new S.Add1(testLoc, new S.Zero(testLoc)),
+        new S.Add1(testLoc, new S.Add1(testLoc, new S.Zero(testLoc))),
+        new S.ConstructorApplication(
+          testLoc,
+          'myveccons',
+          [
+            new S.Nat(testLoc),
+            new S.Zero(testLoc),
+            new S.Add1(testLoc, new S.Zero(testLoc)),
+            new S.ConstructorApplication(testLoc, 'myvecnil', [new S.Nat(testLoc)])
+          ]
+        )
+      ]
+    )
+
+    let result0 = Myvecnil.synth(new_ctx as Context, new_renaming as Renaming)
+    let result1 = Myvecone.synth(new_ctx as Context, new_renaming as Renaming)
+    let result2 = Myvectwo.synth(new_ctx as Context, new_renaming as Renaming)
+    console.log(inspect([result0, result1, result2], true, null, true))
+  })
+
+  // Construct test vectors for elimination
+  let Myvecnil = new S.ConstructorApplication(testLoc, 'myvecnil', [new S.Nat(testLoc)])
+  let Myvecone = new S.ConstructorApplication(
+    testLoc,
+    'myveccons',
+    [
+      new S.Nat(testLoc),
+      new S.Zero(testLoc),
+      new S.Add1(testLoc, new S.Zero(testLoc)),
+      new S.ConstructorApplication(testLoc, 'myvecnil', [new S.Nat(testLoc)])
+    ]
+  )
+
+  // Eliminator: sum all elements of MyVec Nat k
+  let eliminateMyvecnil = new S.EliminatorApplication(
+    testLoc,
+    'MyVec',
+    Myvecnil,
+    new S.Lambda(
+      testLoc,
+      [new SiteBinder(testLoc, 'len'), new SiteBinder(testLoc, 'vec')],
+      new S.Nat(testLoc)
+    ),
+    [
+      new S.Lambda(         // myvecnil case: λ(E : U) → 0
+        testLoc,
+        [new SiteBinder(testLoc, 'E')],
+        new S.Zero(testLoc)
+      ),
+      new S.Lambda(         // myveccons case: λ(E : U) → λ(k : Nat) → λ(head : E) → λ(tail : MyVec E k) → λ(ih : Nat) → (+ head ih)
+        testLoc,
+        [new SiteBinder(testLoc, 'E')],
+        new S.Lambda(
+          testLoc,
+          [new SiteBinder(testLoc, 'k')],
+          new S.Lambda(
+            testLoc,
+            [new SiteBinder(testLoc, 'head')],
+            new S.Lambda(
+              testLoc,
+              [new SiteBinder(testLoc, 'tail')],
+              new S.Lambda(
+                testLoc,
+                [new SiteBinder(testLoc, 'ih')],
+                new S.IterNat(
+                  testLoc,
+                  new S.Name(testLoc, 'head'),
+                  new S.Name(testLoc, 'ih'),
+                  new S.Lambda(
+                    testLoc,
+                    [new SiteBinder(testLoc, 'n')],
+                    new S.Add1(testLoc, new S.Name(testLoc, 'n'))
+                  )
+                )
+              )
+            )
+          )
+        )
+      )
+    ]
+  )
+
+  let eliminateMyvecone = new S.EliminatorApplication(
+    testLoc,
+    'MyVec',
+    Myvecone,
+    new S.Lambda(
+      testLoc,
+      [new SiteBinder(testLoc, 'len'), new SiteBinder(testLoc, 'vec')],
+      new S.Nat(testLoc)
+    ),
+    [
+      new S.Lambda(         // myvecnil case: λ(E : U) → 0
+        testLoc,
+        [new SiteBinder(testLoc, 'E')],
+        new S.Zero(testLoc)
+      ),
+      new S.Lambda(         // myveccons case: λ(E : U) → λ(k : Nat) → λ(head : E) → λ(tail : MyVec E k) → λ(ih : Nat) → (+ head ih)
+        testLoc,
+        [new SiteBinder(testLoc, 'E')],
+        new S.Lambda(
+          testLoc,
+          [new SiteBinder(testLoc, 'k')],
+          new S.Lambda(
+            testLoc,
+            [new SiteBinder(testLoc, 'head')],
+            new S.Lambda(
+              testLoc,
+              [new SiteBinder(testLoc, 'tail')],
+              new S.Lambda(
+                testLoc,
+                [new SiteBinder(testLoc, 'ih')],
+                new S.IterNat(
+                  testLoc,
+                  new S.Name(testLoc, 'head'),
+                  new S.Name(testLoc, 'ih'),
+                  new S.Lambda(
+                    testLoc,
+                    [new SiteBinder(testLoc, 'n')],
+                    new S.Add1(testLoc, new S.Name(testLoc, 'n'))
+                  )
+                )
+              )
+            )
+          )
+        )
+      )
+    ]
+  )
+
+  it('test eliminate myvecnil and myveccons', () => {
+    let resultNil = eliminateMyvecnil.synth(new_ctx as Context, new_renaming as Renaming)
+    let resultOne = eliminateMyvecone.synth(new_ctx as Context, new_renaming as Renaming)
+    console.log(inspect([resultNil, resultOne], true, null, true))
+  })
+
+  it('test evaluate eliminators', () => {
+    let resultNil = (eliminateMyvecnil.synth(new_ctx as Context, new_renaming as Renaming) as go<C.The>).result
+    let resultOne = (eliminateMyvecone.synth(new_ctx as Context, new_renaming as Renaming) as go<C.The>).result
+
+    let evalNil = valInContext(new_ctx as Context, resultNil.expr).now()
+    let evalOne = valInContext(new_ctx as Context, resultOne.expr).now()
+
+    console.log(inspect([evalNil, evalOne], true, null, true))
+  })
+})
+
+describe('less-than', () => {
+  // define-datatype Less-Than () ((j Nat) (k Nat))
+  //   zero-smallest : (n : Nat) -> Less-Than zero (add1 n)
+  //   add1-smaller : (j : Nat) -> (k : Nat) -> Less-Than j k -> Less-Than (add1 j) (add1 k)
+  let define_less_than = new DefineDatatypeSource(
+    testLoc,
+    'Less-Than',
+    [],  // No parameters
+    [
+      new TypedBinder(new SiteBinder(testLoc, 'j'), new S.Nat(testLoc)),
+      new TypedBinder(new SiteBinder(testLoc, 'k'), new S.Nat(testLoc))
+    ],  // Two indices: j and k
+    [
+      new GeneralConstructor(
+        testLoc,
+        'zero-smallest',
+        [new TypedBinder(new SiteBinder(testLoc, 'n'), new S.Nat(testLoc))],
+        new S.GeneralTypeConstructor(
+          testLoc,
+          'Less-Than',
+          [],
+          [new S.Zero(testLoc), new S.Add1(testLoc, new S.Name(testLoc, 'n'))]
+        )
+      ),
+      new GeneralConstructor(
+        testLoc,
+        'add1-smaller',
+        [
+          new TypedBinder(new SiteBinder(testLoc, 'j'), new S.Nat(testLoc)),
+          new TypedBinder(new SiteBinder(testLoc, 'k'), new S.Nat(testLoc)),
+          new TypedBinder(
+            new SiteBinder(testLoc, 'j<k'),
+            new S.GeneralTypeConstructor(testLoc, 'Less-Than', [], [new S.Name(testLoc, 'j'), new S.Name(testLoc, 'k')])
+          )
+        ],
+        new S.GeneralTypeConstructor(
+          testLoc,
+          'Less-Than',
+          [],
+          [new S.Add1(testLoc, new S.Name(testLoc, 'j')), new S.Add1(testLoc, new S.Name(testLoc, 'k'))]
+        )
+      )
+    ]
+  )
+  let ctx = initCtx
+  let renaming = new Map<string, string>()
+
+  it('test generate type and constructors', () => {
+    let result = define_less_than.normalize_constructor(ctx, renaming)
+    console.log(inspect(result, true, null, true))
+  })
+
+  let [new_ctx, new_renaming] = define_less_than.normalize_constructor(ctx, renaming)
+
+  it('test type check constructors', () => {
+    // Proof of 0 < 1: (zero-smallest 0)
+    let proof_0_lt_1 = new S.ConstructorApplication(testLoc, 'zero-smallest', [new S.Zero(testLoc)])
+
+    // Proof of 0 < 2: (zero-smallest 1)
+    let proof_0_lt_2 = new S.ConstructorApplication(testLoc, 'zero-smallest', [new S.Add1(testLoc, new S.Zero(testLoc))])
+
+    // Proof of 1 < 2: (add1-smaller 0 1 (zero-smallest 0))
+    let proof_1_lt_2 = new S.ConstructorApplication(
+      testLoc,
+      'add1-smaller',
+      [
+        new S.Zero(testLoc),
+        new S.Add1(testLoc, new S.Zero(testLoc)),
+        new S.ConstructorApplication(testLoc, 'zero-smallest', [new S.Zero(testLoc)])
+      ]
+    )
+
+    // Proof of 1 < 3: (add1-smaller 0 2 (zero-smallest 1))
+    let proof_1_lt_3 = new S.ConstructorApplication(
+      testLoc,
+      'add1-smaller',
+      [
+        new S.Zero(testLoc),
+        new S.Add1(testLoc, new S.Add1(testLoc, new S.Zero(testLoc))),
+        new S.ConstructorApplication(testLoc, 'zero-smallest', [new S.Add1(testLoc, new S.Zero(testLoc))])
+      ]
+    )
+
+    let result0 = proof_0_lt_1.synth(new_ctx as Context, new_renaming as Renaming)
+    let result1 = proof_0_lt_2.synth(new_ctx as Context, new_renaming as Renaming)
+    let result2 = proof_1_lt_2.synth(new_ctx as Context, new_renaming as Renaming)
+    let result3 = proof_1_lt_3.synth(new_ctx as Context, new_renaming as Renaming)
+    console.log(inspect([result0, result1, result2, result3], true, null, true))
+  })
+
+  // Test eliminator: extract the smaller number (j)
+  let proof_0_lt_1 = new S.ConstructorApplication(testLoc, 'zero-smallest', [new S.Zero(testLoc)])
+  let proof_1_lt_2 = new S.ConstructorApplication(
+    testLoc,
+    'add1-smaller',
+    [
+      new S.Zero(testLoc),
+      new S.Add1(testLoc, new S.Zero(testLoc)),
+      new S.ConstructorApplication(testLoc, 'zero-smallest', [new S.Zero(testLoc)])
+    ]
+  )
+
+  // Eliminator: return the smaller number (first index j)
+  let eliminate_0_lt_1 = new S.EliminatorApplication(
+    testLoc,
+    'Less-Than',
+    proof_0_lt_1,
+    new S.Lambda(
+      testLoc,
+      [new SiteBinder(testLoc, 'j'), new SiteBinder(testLoc, 'k'), new SiteBinder(testLoc, 'proof')],
+      new S.Nat(testLoc)
+    ),
+    [
+      new S.Lambda(         // zero-smallest case: λ(n : Nat) → 0
+        testLoc,
+        [new SiteBinder(testLoc, 'n')],
+        new S.Zero(testLoc)
+      ),
+      new S.Lambda(         // add1-smaller case: λ(j : Nat) → λ(k : Nat) → λ(j<k : Less-Than j k) → λ(ih : Nat) → (add1 ih)
+        testLoc,
+        [new SiteBinder(testLoc, 'j')],
+        new S.Lambda(
+          testLoc,
+          [new SiteBinder(testLoc, 'k')],
+          new S.Lambda(
+            testLoc,
+            [new SiteBinder(testLoc, 'j<k')],
+            new S.Lambda(
+              testLoc,
+              [new SiteBinder(testLoc, 'ih')],
+              new S.Add1(testLoc, new S.Name(testLoc, 'ih'))
+            )
+          )
+        )
+      )
+    ]
+  )
+
+  let eliminate_1_lt_2 = new S.EliminatorApplication(
+    testLoc,
+    'Less-Than',
+    proof_1_lt_2,
+    new S.Lambda(
+      testLoc,
+      [new SiteBinder(testLoc, 'j'), new SiteBinder(testLoc, 'k'), new SiteBinder(testLoc, 'proof')],
+      new S.Nat(testLoc)
+    ),
+    [
+      new S.Lambda(         // zero-smallest case: λ(n : Nat) → 0
+        testLoc,
+        [new SiteBinder(testLoc, 'n')],
+        new S.Zero(testLoc)
+      ),
+      new S.Lambda(         // add1-smaller case: λ(j : Nat) → λ(k : Nat) → λ(j<k : Less-Than j k) → λ(ih : Nat) → (add1 ih)
+        testLoc,
+        [new SiteBinder(testLoc, 'j')],
+        new S.Lambda(
+          testLoc,
+          [new SiteBinder(testLoc, 'k')],
+          new S.Lambda(
+            testLoc,
+            [new SiteBinder(testLoc, 'j<k')],
+            new S.Lambda(
+              testLoc,
+              [new SiteBinder(testLoc, 'ih')],
+              new S.Add1(testLoc, new S.Name(testLoc, 'ih'))
+            )
+          )
+        )
+      )
+    ]
+  )
+
+  it('test eliminate less-than proofs', () => {
+    let result0 = eliminate_0_lt_1.synth(new_ctx as Context, new_renaming as Renaming)
+    let result1 = eliminate_1_lt_2.synth(new_ctx as Context, new_renaming as Renaming)
+    console.log(inspect([result0, result1], true, null, true))
+  })
+
+  it('test evaluate eliminators', () => {
+    let result0 = (eliminate_0_lt_1.synth(new_ctx as Context, new_renaming as Renaming) as go<C.The>).result
+    let result1 = (eliminate_1_lt_2.synth(new_ctx as Context, new_renaming as Renaming) as go<C.The>).result
+
+    let eval0 = valInContext(new_ctx as Context, result0.expr).now()
+    let eval1 = valInContext(new_ctx as Context, result1.expr).now()
+
+    console.log(inspect([eval0, eval1], true, null, true))
+  })
+})
+
+
diff --git a/src/pie_interpreter/__tests__/test_doEliminator_core.ts b/src/pie_interpreter/__tests__/test_doEliminator_core.ts
new file mode 100644
index 00000000..3999b473
--- /dev/null
+++ b/src/pie_interpreter/__tests__/test_doEliminator_core.ts
@@ -0,0 +1,290 @@
+import 'jest';
+import * as C from '../types/core';
+import * as V from '../types/value';
+import * as Evaluator from '../evaluator/evaluator';
+import { Environment } from '../utils/environment';
+import { inspect } from 'util';
+import { readBack } from '../evaluator/utils';
+import { Context } from '../utils/context';
+
+// Test examples for doEliminator function using Core data structures
+
+// Example 1: List elimination test
+export function createListExample(): {
+  listType: C.InductiveTypeConstructor,
+  sampleList: C.Core,
+  eliminator: C.Eliminator
+} {
+
+  const listType = new C.InductiveTypeConstructor(
+    "List",
+    [new C.Nat()], // parameters
+    [],                   // no indices
+  );
+
+  // Create List constructors
+  const nilConstructor = new C.Constructor(
+    "nil",   // name
+    0,       // constructor index
+    "List",  // type: List A
+    [],      // no arguments
+    []       // no recursive arguments
+  );
+
+  // Create a sample list: cons 1 (cons 2 (cons 3 nil))
+  // Create cons 3 nil
+  const cons3Nil = new C.Constructor(
+    "cons",  // name
+    1,       // constructor index
+    "List",  // type
+    [
+      new C.Add1(new C.Add1(new C.Add1(new C.Zero()))),
+      nilConstructor
+    ],       // arguments
+    [nilConstructor]  // recursive arguments
+  );
+
+  // Create cons 2 (cons 3 nil)
+  const cons2 = new C.Constructor(
+    "cons",  // name
+    1,       // constructor index
+    "List",  // type
+    [new C.Add1(new C.Add1(new C.Zero())), cons3Nil], // 2, (cons 3 nil)
+    [cons3Nil]  // recursive arguments
+  );
+
+
+  // Create eliminator for summing the list with proper lambda expressions
+  const sumEliminator = new C.Eliminator(
+    "List",
+    cons2,
+    new C.Lambda("xs", new C.Nat()), // motive: List A -> Nat
+    [
+      new C.Zero(), // base case: nil -> 0
+      new C.Lambda("head",
+        new C.Lambda("tail",
+          new C.Lambda(
+            'n',
+            new C.Add1(new C.VarName('n'))
+          )
+        )
+      ) // step case: head -> tail -> sum_tail -> add1 sum_tail
+    ]
+  );
+
+  return {
+    listType,
+    sampleList: cons2,
+    eliminator: sumEliminator
+  };
+}
+
+// // Example 2: Binary Tree elimination test  
+// export function createBinaryTreeExample(): {
+//   treeType: C.InductiveType,
+//   sampleTree: C.Core,
+//   eliminator: C.Eliminator
+// } {
+
+//   // Create Tree constructors
+//   const leafConstructor = new C.Constructor(
+//     "leaf",
+//     new C.VarName("Tree"), // type: Tree A
+//     [],  // no arguments
+//     0,   // constructor index
+//     false // not recursive
+//   );
+
+//   const nodeConstructor = new C.Constructor(
+//     "node",
+//     new C.Pi("value", new C.VarName("A"),
+//       new C.Pi("left", new C.VarName("Tree"),
+//         new C.Pi("right", new C.VarName("Tree"), 
+//           new C.VarName("Tree")))), // type: A -> Tree A -> Tree A -> Tree A
+//     [], // no arguments for constructor schema
+//     1,   // constructor index
+//     true // recursive (contains Tree A)
+//   );
+
+//   // Create the Tree inductive type
+//   const treeType = new C.InductiveType(
+//     "Tree", 
+//     [new C.VarName("A")], // parameters
+//     [],                   // no indices
+//     [leafConstructor, nodeConstructor],
+//     new C.Eliminator("Tree",
+//       new C.VarName("tree"), // target
+//       new C.VarName("P"),    // motive
+//       [
+//         new C.VarName("base_leaf"),     // method for leaf
+//         new C.VarName("step_node")     // method for node
+//       ]
+//     )
+//   );
+
+//   // Create a sample tree: node 5 (node 3 leaf (node 4 leaf leaf)) (node 7 leaf leaf)
+
+//   // Create leaf instances
+//   const leaf1 = new C.Constructor("leaf", new C.VarName("Tree"), [], 0, false);
+//   const leaf2 = new C.Constructor("leaf", new C.VarName("Tree"), [], 0, false);
+//   const leaf3 = new C.Constructor("leaf", new C.VarName("Tree"), [], 0, false);
+//   const leaf4 = new C.Constructor("leaf", new C.VarName("Tree"), [], 0, false);
+
+//   // Create node 4 leaf leaf
+//   const node4 = new C.Constructor(
+//     "node",
+//     new C.VarName("Tree"),
+//     [
+//       new C.Add1(new C.Add1(new C.Add1(new C.Add1(new C.Zero())))), // 4
+//       leaf1,
+//       leaf2
+//     ],
+//     1,
+//     true
+//   );
+
+//   // Create node 3 leaf (node 4 leaf leaf)
+//   const node3 = new C.Constructor(
+//     "node", 
+//     new C.VarName("Tree"),
+//     [
+//       new C.Add1(new C.Add1(new C.Add1(new C.Zero()))), // 3
+//       leaf3,
+//       node4
+//     ],
+//     1,
+//     true
+//   );
+
+//   // Create node 7 leaf leaf
+//   const node7 = new C.Constructor(
+//     "node",
+//     new C.VarName("Tree"),
+//     [
+//       new C.Add1(new C.Add1(new C.Add1(new C.Add1(new C.Add1(new C.Add1(new C.Add1(new C.Zero()))))))), // 7
+//       leaf4,
+//       new C.Constructor("leaf", new C.VarName("Tree"), [], 0, false)
+//     ],
+//     1,
+//     true
+//   );
+
+//   // Create root node 5 (node 3 ...) (node 7 ...)
+//   const sampleTree = new C.Constructor(
+//     "node",
+//     new C.VarName("Tree"),
+//     [
+//       new C.Add1(new C.Add1(new C.Add1(new C.Add1(new C.Add1(new C.Zero()))))), // 5
+//       node3,
+//       node7
+//     ],
+//     1,
+//     true
+//   );
+
+//   // Create eliminator for summing tree values
+//   const sumEliminator = new C.Eliminator(
+//     "Tree",
+//     sampleTree,
+//     new C.Lambda("tree", new C.Nat()), // motive: always Nat
+//     [
+//       new C.Zero(), // base case: leaf -> 0
+//       new C.Lambda("value",
+//         new C.Lambda("left",
+//           new C.Lambda("right", 
+//             new C.Lambda("left_sum",
+//               new C.Lambda("right_sum",
+//                 new C.Application( // value + (left_sum + right_sum)
+//                   new C.Application(
+//                     new C.VarName("+"),
+//                     new C.VarName("value")
+//                   ),
+//                   new C.Application(
+//                     new C.Application(
+//                       new C.VarName("+"),
+//                       new C.VarName("left_sum")
+//                     ),
+//                     new C.VarName("right_sum")
+//                   )
+//                 )
+//               )
+//             )
+//           )
+//         )
+//       ) // step case: value -> left -> right -> left_sum -> right_sum -> value + left_sum + right_sum
+//     ]
+//   );
+
+//   return {
+//     treeType,
+//     sampleTree,
+//     eliminator: sumEliminator
+//   };
+// }
+
+// Jest test cases
+describe("doEliminator tests", () => {
+
+  it("should handle list elimination", () => {
+    const env: Environment = new Map();
+    const listExample = createListExample();
+
+    expect(() => {
+      const listResult = Evaluator.doEliminator(
+        "List",
+        listExample.sampleList.toLazy(env),
+        listExample.eliminator.motive.toLazy(env),
+        listExample.eliminator.methods.map(m => m.toLazy(env))
+      );
+      const context: Context = new Map();
+      const normalizedResult = readBack(context, new V.Nat(), listResult);
+      console.log("List elimination result (normalized):", inspect(normalizedResult, true, null, true));
+    }).not.toThrow();
+  });
+
+  // it("should handle binary tree elimination", () => {
+  
+  //   const env: Environment = new Map();
+  //   const treeExample = createBinaryTreeExample();
+
+  //   expect(() => {
+  //     const treeResult = Evaluator.doEliminator(
+  //       "Tree", 
+  //       treeExample.sampleTree.toLazy(env),
+  //       treeExample.eliminator.motive.toLazy(env),
+  //       treeExample.eliminator.methods.map(m => m.toLazy(env))
+  //     );
+  //     console.log("Tree elimination result:", treeResult);
+  //   }).not.toThrow();
+  // });
+
+  it("should test list elimination with specific values", () => {
+    const env: Environment = new Map();
+    const listExample = createListExample();
+
+    const listResult = Evaluator.doEliminator(
+      "List",
+      listExample.sampleList.toLazy(env),
+      listExample.eliminator.motive.toLazy(env),
+      listExample.eliminator.methods.map(m => m.toLazy(env))
+    );
+
+    // Add specific assertions based on expected behavior
+    expect(listResult).toBeDefined();
+  });
+
+  // it("should test tree elimination with specific values", () => {
+  //   const env: Environment = new Map();
+  //   const treeExample = createBinaryTreeExample();
+
+  //   const treeResult = Evaluator.doEliminator(
+  //     "Tree",
+  //     treeExample.sampleTree.toLazy(env),
+  //     treeExample.eliminator.motive.toLazy(env),
+  //     treeExample.eliminator.methods.map(m => m.toLazy(env))
+  //   );
+
+  //   // Add specific assertions based on expected behavior
+  //   expect(treeResult).toBeDefined();
+  //   });
+});
\ No newline at end of file
diff --git a/src/pie_interpreter/__tests__/test_inductive_types.ts b/src/pie_interpreter/__tests__/test_inductive_types.ts
new file mode 100644
index 00000000..c3b7fa7a
--- /dev/null
+++ b/src/pie_interpreter/__tests__/test_inductive_types.ts
@@ -0,0 +1,197 @@
+import 'jest';
+
+import { evaluatePie } from '../main'
+
+describe("Bool_datatype", () => {
+  it("Define Bool datatype", () => {
+    const src = `
+(data Bool () ()
+  (true () (Bool))
+  (false () (Bool))
+  ind-Bool)
+`;
+    console.log(evaluatePie(src));
+  });
+
+  it("Use Bool constructors", () => {
+    const src = `
+(data Bool () ()
+  (true () (Bool))
+  (false () (Bool))
+  ind-Bool)
+
+(data-true)
+(data-false)
+`;
+    console.log(evaluatePie(src));
+  });
+
+  it("Use Bool eliminator", () => {
+    const src = `
+(data Bool () ()
+  (true () (Bool))
+  (false () (Bool))
+  ind-Bool)
+
+(data-ind-Bool (data-true)
+  (lambda (b) Nat)
+  (add1 zero)
+  zero)
+
+(data-ind-Bool (data-false)
+  (lambda (b) Nat)
+  (add1 zero)
+  zero)
+`;
+    console.log(evaluatePie(src));
+  });
+
+  it("Use Bool eliminator with wrapper function", () => {
+    const src = `
+(data Bool () ()
+  (true () (Bool))
+  (false () (Bool))
+  ind-Bool)
+
+(claim bool-to-nat (-> Bool Nat))
+(define bool-to-nat
+  (lambda (b)
+    (data-ind-Bool b
+      (lambda (x) Nat)
+      (add1 zero)
+      zero)))
+
+(bool-to-nat (data-true))
+(bool-to-nat (data-false))
+`;
+    console.log(evaluatePie(src));
+  });
+});
+
+describe("LessThan_datatype", () => {
+  it("Define Less-Than datatype with indices", () => {
+    const src = `
+(data Less-Than () ((j Nat) (k Nat))
+  (zero-smallest ((n Nat))
+    (Less-Than zero (add1 n)))
+  (add1-smaller ((j Nat) (k Nat) (j<k (Less-Than j k)))
+    (Less-Than (add1 j) (add1 k)))
+  ind-Less-Than)
+`;
+    console.log(evaluatePie(src));
+  });
+
+  it("Use Less-Than constructors", () => {
+    const src = `
+(data Less-Than () ((j Nat) (k Nat))
+  (zero-smallest ((n Nat))
+    (Less-Than zero (add1 n)))
+  (add1-smaller ((j Nat) (k Nat) (j<k (Less-Than j k)))
+    (Less-Than (add1 j) (add1 k)))
+  ind-Less-Than)
+
+(data-zero-smallest zero)
+(data-zero-smallest (add1 zero))
+(data-add1-smaller zero (add1 zero) (data-zero-smallest zero))
+`;
+    console.log(evaluatePie(src));
+  });
+
+  it("Debug add1-smaller constructor", () => {
+    const src = `
+(data Less-Than () ((j Nat) (k Nat))
+  (zero-smallest ((n Nat))
+    (Less-Than zero (add1 n)))
+  (add1-smaller ((j Nat) (k Nat) (j<k (Less-Than j k)))
+    (Less-Than (add1 j) (add1 k)))
+  ind-Less-Than)
+
+(data-add1-smaller zero (add1 zero) (data-zero-smallest zero))
+`;
+    console.log(evaluatePie(src));
+  });
+
+  it("Use Less-Than with claim/define", () => {
+    const src = `
+(data Less-Than () ((j Nat) (k Nat))
+  (zero-smallest ((n Nat))
+    (Less-Than zero (add1 n)))
+  (add1-smaller ((j Nat) (k Nat) (j<k (Less-Than j k)))
+    (Less-Than (add1 j) (add1 k)))
+  ind-Less-Than)
+
+(claim proof-0<1 (Less-Than zero (add1 zero)))
+(define proof-0<1 (data-zero-smallest zero))
+
+(claim proof-1<2 (Less-Than (add1 zero) (add1 (add1 zero))))
+(define proof-1<2
+  (data-add1-smaller zero (add1 zero) (data-zero-smallest zero)))
+`;
+    console.log(evaluatePie(src));
+  });
+
+  it("Use Less-Than eliminator with wrapper function", () => {
+    const src = `
+(data Less-Than () ((j Nat) (k Nat))
+  (zero-smallest ((n Nat))
+    (Less-Than zero (add1 n)))
+  (add1-smaller ((j Nat) (k Nat) (j<k (Less-Than j k)))
+    (Less-Than (add1 j) (add1 k)))
+  ind-Less-Than)
+
+(claim proof-0<1 (Less-Than zero (add1 zero)))
+(define proof-0<1 (data-zero-smallest zero))
+
+(claim extract-smaller
+  (Pi ((j Nat) (k Nat))
+    (-> (Less-Than j k) Nat)))
+
+(define extract-smaller
+  (lambda (j k proof)
+    (data-ind-Less-Than proof
+      (lambda (j-idx k-idx p) Nat)
+      (lambda (n) zero)
+      (lambda (j-arg k-arg j<k-arg ih) (add1 ih)))))
+
+(claim result-0 Nat)
+(define result-0 (extract-smaller zero (add1 zero) proof-0<1))
+`;
+    console.log(evaluatePie(src));
+  });
+
+  it("Use extract-smaller on larger proof (returns non-zero)", () => {
+    const src = `
+(data Less-Than () ((j Nat) (k Nat))
+  (zero-smallest ((n Nat))
+    (Less-Than zero (add1 n)))
+  (add1-smaller ((j Nat) (k Nat) (j<k (Less-Than j k)))
+    (Less-Than (add1 j) (add1 k)))
+  ind-Less-Than)
+
+(claim extract-smaller
+  (Pi ((j Nat) (k Nat))
+    (-> (Less-Than j k) Nat)))
+
+(define extract-smaller
+  (lambda (j k proof)
+    (data-ind-Less-Than proof
+      (lambda (j-idx k-idx p) Nat)
+      (lambda (n) zero)
+      (lambda (j-arg k-arg j<k-arg ih) (add1 ih)))))
+
+(claim proof-2<4 (Less-Than (add1 (add1 zero)) (add1 (add1 (add1 (add1 zero))))))
+(define proof-2<4
+  (data-add1-smaller
+    (add1 zero)
+    (add1 (add1 (add1 zero)))
+    (data-add1-smaller
+      zero
+      (add1 (add1 zero))
+      (data-zero-smallest (add1 zero)))))
+
+(claim result-2 Nat)
+(define result-2 (extract-smaller (add1 (add1 zero)) (add1 (add1 (add1 (add1 zero)))) proof-2<4))
+`;
+    console.log(evaluatePie(src));
+  });
+});
diff --git a/src/pie_interpreter/__tests__/test_llm.ts b/src/pie_interpreter/__tests__/test_llm.ts
new file mode 100644
index 00000000..78d42c5e
--- /dev/null
+++ b/src/pie_interpreter/__tests__/test_llm.ts
@@ -0,0 +1,266 @@
+import { GoogleGenAI } from "@google/genai";
+import 'jest'
+import { solveTodo, TodoInfo } from '../try_llm/todo_solver';
+import { inspect } from 'util';
+import { Parser } from '../parser/parser';
+import { Location, Syntax } from '../utils/locations';
+import * as V from '../types/value';
+import * as C from '../types/core';
+import { FirstOrderClosure, go, stop } from '../types/utils';
+import { readBackContext, valInContext } from '../utils/context';
+
+describe('LLM TODO solver with typechecking', () => {
+
+  // Helper function to parse Pie code into a Value (for types)
+  function parseExpectedType(pieCode: string): V.Value {
+    const parsed = Parser.parsePie(pieCode);
+    const typeResult = parsed.isType(new Map(), new Map());
+    if (typeResult instanceof go) {
+      return valInContext(new Map(), typeResult.result);
+    } else if (typeResult instanceof stop) {
+      throw new Error(`Invalid type: ${pieCode} - ${typeResult.message}`);
+    } else {
+      throw new Error(`Invalid type result: ${pieCode}`);
+    }
+  }
+
+  // Helper function to create a test Location
+  function createTestLocation(source: string): Location {
+    const syntax = new Syntax(
+      { line: 1, column: 1 },
+      { line: 1, column: 1 },
+      source
+    );
+    return new Location(syntax, false);
+  }
+
+  // Helper function to log test results in a clear format (4 lines only)
+  function logTestResult(todo: TodoInfo, solution: string) {
+    // Format context
+    let contextStr = 'empty';
+    if (todo.context.size > 0) {
+      const ctxEntries: string[] = [];
+      for (const [name, binder] of todo.context.entries()) {
+        let typeStr: string;
+        if ('type' in binder && binder.type) {
+          typeStr = (binder.type as any).prettyPrint();
+        } else if ('prettyPrint' in binder) {
+          typeStr = (binder as any).prettyPrint();
+        } else {
+          typeStr = String(binder);
+        }
+        ctxEntries.push(`${name}: ${typeStr}`);
+      }
+      contextStr = ctxEntries.join(', ');
+    }
+
+    // Format renaming
+    const renamingStr = todo.renaming.size === 0 ? 'empty' :
+      Array.from(todo.renaming.entries()).map(([k, v]) => `${k}→${v}`).join(', ');
+
+    // 4-line output only
+    console.log(
+      `Expected: ${todo.expectedType.readBackType(todo.context).prettyPrint()}\n` +
+      `Context: ${contextStr}\n` +
+      `Renaming: ${renamingStr}\n` +
+      `Result: ${solution}`
+    );
+  }
+
+  it('should solve simple Nat TODO', async () => {
+    const todo: TodoInfo = {
+      location: createTestLocation('test.pie:2:1'),
+      context: new Map(),
+      expectedType: parseExpectedType("Nat"),
+      renaming: new Map()
+    };
+
+    const solution = await solveTodo(todo);
+    logTestResult(todo, solution);
+  }, 60000);
+
+  it('should handle List type TODO', async () => {
+    const todo: TodoInfo = {
+      location: createTestLocation('test.pie:6:1'),
+      context: new Map(),
+      expectedType: parseExpectedType("(List Nat)"),
+      renaming: new Map()
+    };
+
+    const solution = await solveTodo(todo);
+    logTestResult(todo, solution);
+  }, 60000);
+
+  it('it should solve identity function TODO', async () => {
+    const todo: TodoInfo = {
+      location: createTestLocation('test.pie:10:1'),
+      context: new Map(),
+      expectedType: parseExpectedType("(-> Nat Nat)"),
+      renaming: new Map()
+    };
+    const solution = await solveTodo(todo);
+    logTestResult(todo, solution);
+  }, 60000);
+
+  it('should handle Sigma type (dependent pair)', async () => {
+    const todo: TodoInfo = {
+      location: createTestLocation('test.pie:14:1'),
+      context: new Map(),
+      expectedType: parseExpectedType("(Pair Nat Nat)"),
+      renaming: new Map()
+    };
+
+    const solution = await solveTodo(todo);
+    logTestResult(todo, solution);
+  }, 60000);
+
+  it('should handle Vec type with length 3', async () => {
+    const todo: TodoInfo = {
+      location: createTestLocation('test.pie:18:1'),
+      context: new Map(),
+      expectedType: parseExpectedType("(Vec Nat (add1 (add1 (add1 zero))))"),
+      renaming: new Map()
+    };
+
+    const solution = await solveTodo(todo);
+    logTestResult(todo, solution);
+  }, 60000);
+
+  it('should handle Either type', async () => {
+    const todo: TodoInfo = {
+      location: createTestLocation('test.pie:22:1'),
+      context: new Map(),
+      expectedType: parseExpectedType("(Either Nat Atom)"),
+      renaming: new Map()
+    };
+
+    const solution = await solveTodo(todo);
+    logTestResult(todo, solution);
+  }, 60000);
+
+  it('should handle Equal type (equality proof)', async () => {
+    const todo: TodoInfo = {
+      location: createTestLocation('test.pie:26:1'),
+      context: new Map(),
+      expectedType: parseExpectedType("(= Nat zero zero)"),
+      renaming: new Map()
+    };
+
+    const solution = await solveTodo(todo);
+    logTestResult(todo, solution);
+  }, 60000);
+
+  it('should handle Trivial type', async () => {
+    const todo: TodoInfo = {
+      location: createTestLocation('test.pie:30:1'),
+      context: new Map(),
+      expectedType: parseExpectedType("Trivial"),
+      renaming: new Map()
+    };
+
+    const solution = await solveTodo(todo);
+    logTestResult(todo, solution);
+  }, 60000);
+
+  it('should handle multi-argument Pi type (Nat -> Nat -> Nat)', async () => {
+    const todo: TodoInfo = {
+      location: createTestLocation('test.pie:34:1'),
+      context: new Map(),
+      expectedType: parseExpectedType("(-> Nat Nat Nat)"),
+      renaming: new Map()
+    };
+
+    const solution = await solveTodo(todo);
+    logTestResult(todo, solution);
+  }, 60000);
+
+  it('should handle List of Pairs (nested types)', async () => {
+    const todo: TodoInfo = {
+      location: createTestLocation('test.pie:38:1'),
+      context: new Map(),
+      expectedType: parseExpectedType("(List (Pair Nat Atom))"),
+      renaming: new Map()
+    };
+
+    const solution = await solveTodo(todo);
+    logTestResult(todo, solution);
+  }, 60000);
+
+  it('should use variable from context - simple case', async () => {
+    const ctx = new Map();
+    ctx.set('n', parseExpectedType("A"));
+
+    const todo: TodoInfo = {
+      location: createTestLocation('test.pie:42:1'),
+      context: ctx,
+      expectedType: parseExpectedType("A"),
+      renaming: new Map()
+    };
+
+    const solution = await solveTodo(todo);
+    logTestResult(todo, solution);
+  }, 60000);
+
+  it('should use multiple variables from context', async () => {
+    const ctx = new Map();
+    ctx.set('x', parseExpectedType("A"));
+    ctx.set('y', parseExpectedType("B"));
+
+    const todo: TodoInfo = {
+      location: createTestLocation('test.pie:46:1'),
+      context: ctx,
+      expectedType: parseExpectedType("B"),
+      renaming: new Map()
+    };
+
+    const solution = await solveTodo(todo);
+    logTestResult(todo, solution);
+  }, 60000);
+
+  it('should construct function using context variable', async () => {
+    const ctx = new Map();
+    ctx.set('m', parseExpectedType("A"));
+
+    const todo: TodoInfo = {
+      location: createTestLocation('test.pie:50:1'),
+      context: ctx,
+      expectedType: parseExpectedType("(-> Nat A)"),
+      renaming: new Map()
+    };
+
+    const solution = await solveTodo(todo);
+    logTestResult(todo, solution);
+  }, 60000);
+
+  it('should handle renaming map', async () => {
+    const ctx = new Map();
+    ctx.set('n', parseExpectedType("A"));
+
+    const renaming = new Map();
+    renaming.set('n', 'n-renamed');
+
+    const todo: TodoInfo = {
+      location: createTestLocation('test.pie:66:1'),
+      context: ctx,
+      expectedType: parseExpectedType("A"),
+      renaming: renaming
+    };
+
+    const solution = await solveTodo(todo);
+    logTestResult(todo, solution);
+  }, 60000);
+
+  it('should handle Vec of Either types', async () => {
+    const todo: TodoInfo = {
+      location: createTestLocation('test.pie:70:1'),
+      context: new Map(),
+      expectedType: parseExpectedType("(Vec (Either Nat Trivial) (add1 (add1 zero)))"),
+      renaming: new Map()
+    };
+
+    const solution = await solveTodo(todo);
+    logTestResult(todo, solution);
+  }, 60000);
+
+  
+});
diff --git a/src/pie_interpreter/__tests__/test_lsp.pie b/src/pie_interpreter/__tests__/test_lsp.pie
new file mode 100644
index 00000000..1a89e72d
--- /dev/null
+++ b/src/pie_interpreter/__tests__/test_lsp.pie
@@ -0,0 +1,9 @@
+(claim identity (-> Nat Nat))
+(define-tactically identity 
+  ((intro n)
+   (TODO)))
+
+
+
+
+
diff --git a/src/pie_interpreter/__tests__/test_main.ts b/src/pie_interpreter/__tests__/test_main.ts
index 45fbba39..42c26025 100644
--- a/src/pie_interpreter/__tests__/test_main.ts
+++ b/src/pie_interpreter/__tests__/test_main.ts
@@ -496,28 +496,4 @@ describe("Or_demo", () => {
     console.log(evaluatePie(src));
   });
 
-  it("list length", () => {
-    const src =  
-    `
-    (claim step-replicate 
-      (Pi ((E U) (e E) (l-1 Nat)) 
-        (-> (mot-replicate E l-1) (mot-replicate E (add1 l-1)))))
-    (define step-replicate 
-      (lambda (E e l-1)
-        (lambda (step-l-1)
-          (vec:: e step-l-1))))
-    (claim replicate
-      (Pi ((E U) (len Nat)) 
-          (-> E (Vec E len))))
-    (define replicate
-      (lambda (E l)
-          (lambda (e) 
-            (ind-Nat l
-            (mot-replicate E)
-            vecnil
-            (step-replicate E e)))))
-    (replicate Atom 3 'caonima)`;
-    console.log(evaluatePie(src));
-  });
-  
 });
\ No newline at end of file
diff --git a/src/pie_interpreter/__tests__/test_method_type.ts b/src/pie_interpreter/__tests__/test_method_type.ts
new file mode 100644
index 00000000..d0c9a8ea
--- /dev/null
+++ b/src/pie_interpreter/__tests__/test_method_type.ts
@@ -0,0 +1,148 @@
+import 'jest';
+import * as S from '../types/source';
+import * as C from '../types/core';
+import * as V from '../types/value';
+import { Location, Syntax } from '../utils/locations';
+import { Position } from '../../scheme_parser/transpiler/types/location';
+import { DefineDatatypeSource, GeneralConstructor } from '../typechecker/definedatatype';
+import { Context, valInContext } from '../utils/context';
+import { SiteBinder, TypedBinder, HigherOrderClosure } from '../types/utils';
+
+const testLoc = new Location(new Syntax(new Position(1, 1), new Position(1, 1), 'test'), false);
+
+describe("generateMethodType implementation", () => {
+
+  it("should generate method type structure for Bool true constructor (no args)", () => {
+    const ctx: Context = new Map();
+    const indicesBody = new S.Universe(testLoc) as any;
+
+    const boolDatatype = new DefineDatatypeSource(
+      testLoc,
+      "Bool",
+      [],
+      indicesBody,
+      [
+        new GeneralConstructor(testLoc, "true", [], new S.GeneralTypeConstructor(testLoc, "Bool", [], [])),
+        new GeneralConstructor(testLoc, "false", [], new S.GeneralTypeConstructor(testLoc, "Bool", [], []))
+      ]
+    );
+
+    // First normalize constructors to get C.ConstructorType
+    const normalizedCtors = boolDatatype.normalize_constructor(ctx, new Map());
+    const trueCtorType = normalizedCtors[0];
+
+    // Create a dummy motive value (Lambda) for testing
+    // In real usage, this would be a checked motive expression
+    const dummyMotive = new V.Lambda(
+      'x',
+      new HigherOrderClosure(_ => new V.Universe())
+    );
+
+    const methodType = boolDatatype.generateMethodType(ctx, new Map(), trueCtorType, dummyMotive, []);
+
+    // For true constructor with no args, method type should be: P(true)
+    // Since there are no arguments, it should directly be the result type
+    console.log("✅ True method type:", methodType.prettyPrint());
+
+    expect(methodType).toBeDefined();
+  });
+
+  it("should generate method type for Nat succ constructor (one recursive arg)", () => {
+    const ctx: Context = new Map();
+    const indicesBody = new S.Universe(testLoc) as any;
+
+    const natDatatype = new DefineDatatypeSource(
+      testLoc,
+      "MyNat",
+      [],
+      indicesBody,
+      [
+        new GeneralConstructor(testLoc, "zero", [],
+          new S.GeneralTypeConstructor(testLoc, "MyNat", [], [])),
+        new GeneralConstructor(testLoc, "succ",
+          [new TypedBinder(new SiteBinder(testLoc, "n"),
+            new S.GeneralTypeConstructor(testLoc, "MyNat", [], []))],
+          new S.GeneralTypeConstructor(testLoc, "MyNat", [], []))
+      ]
+    );
+
+    const normalizedCtors = natDatatype.normalize_constructor(ctx, new Map());
+    const succCtorType = normalizedCtors[1];
+
+    // Create a dummy motive value (Lambda)
+    const dummyMotive = new V.Lambda(
+      'x',
+      new HigherOrderClosure(_ => new V.Universe())
+    );
+
+    // Method type for succ should be: (Π [n : MyNat] (Π [ih : P(n)] P(succ n)))
+    const methodType = natDatatype.generateMethodType(ctx, new Map(), succCtorType, dummyMotive, []);
+
+    console.log("✅ Succ method type:", methodType.prettyPrint());
+
+    // Should be a Pi type
+    expect(methodType).toBeInstanceOf(V.Pi);
+
+    if (methodType instanceof V.Pi) {
+      // Outer Pi should be for the argument
+      expect(methodType.argName).toBe('arg0');
+
+      // Inner should contain IH and result
+      const innerType = methodType.resultType.valOfClosure(new V.Zero());
+      expect(innerType).toBeInstanceOf(V.Pi);
+
+      if (innerType instanceof V.Pi) {
+        // Should be IH
+        expect(innerType.argName).toBe('ih0');
+        console.log("  - IH type:", innerType.argType.prettyPrint());
+      }
+    }
+  });
+
+  it("should demonstrate method type structure for List cons", () => {
+    const ctx: Context = new Map();
+    const indicesBody = new S.Universe(testLoc) as any;
+
+    const listDatatype = new DefineDatatypeSource(
+      testLoc,
+      "MyList",
+      [],
+      indicesBody,
+      [
+        new GeneralConstructor(testLoc, "nil", [],
+          new S.GeneralTypeConstructor(testLoc, "MyList", [], [])),
+        new GeneralConstructor(testLoc, "cons", [
+          new TypedBinder(new SiteBinder(testLoc, "head"), new S.Nat(testLoc)),
+          new TypedBinder(new SiteBinder(testLoc, "tail"),
+            new S.GeneralTypeConstructor(testLoc, "MyList", [], []))
+        ],
+          new S.GeneralTypeConstructor(testLoc, "MyList", [], []))
+      ]
+    );
+
+    const normalizedCtors = listDatatype.normalize_constructor(ctx, new Map());
+    const consCtorType = normalizedCtors[1];
+
+    // Create a dummy motive value (Lambda)
+    const dummyMotive = new V.Lambda(
+      'x',
+      new HigherOrderClosure(_ => new V.Universe())
+    );
+
+    // Method type for cons should be:
+    // (Π [head : Nat] (Π [tail : MyList] (Π [ih : P(tail)] P(cons head tail))))
+    const methodType = listDatatype.generateMethodType(ctx, new Map(), consCtorType, dummyMotive, []);
+
+    console.log("\n=== Method Type for cons ===");
+    console.log("Type:", methodType.prettyPrint());
+    console.log("\nStructure:");
+    console.log("- Takes head : Nat (non-recursive)");
+    console.log("- Takes tail : MyList (recursive)");
+    console.log("- Takes ih : P(tail) (inductive hypothesis)");
+    console.log("- Returns P(cons head tail)");
+    console.log("============================\n");
+
+    expect(methodType).toBeDefined();
+    expect(methodType).toBeInstanceOf(V.Pi);
+  });
+});
diff --git a/src/pie_interpreter/__tests__/test_motive_type.ts b/src/pie_interpreter/__tests__/test_motive_type.ts
new file mode 100644
index 00000000..4e3ffd4c
--- /dev/null
+++ b/src/pie_interpreter/__tests__/test_motive_type.ts
@@ -0,0 +1,126 @@
+import 'jest';
+import * as S from '../types/source';
+import * as V from '../types/value';
+import { Location, Syntax } from '../utils/locations';
+import { Position } from '../../scheme_parser/transpiler/types/location';
+import { DefineDatatypeSource, GeneralConstructor } from '../typechecker/definedatatype';
+import { Context } from '../utils/context';
+import { HigherOrderClosure, SiteBinder, TypedBinder } from '../types/utils';
+import { inspect } from 'util';
+
+const testLoc = new Location(new Syntax(new Position(1, 1), new Position(1, 1), 'test'), false);
+
+describe("generateMotiveType implementation", () => {
+
+  it("should generate motive type for Bool (no indices, no parameters)", () => {
+    const ctx: Context = new Map();
+    const indicesBody = new S.Universe(testLoc) as any;
+
+    const boolDatatype = new DefineDatatypeSource(
+      testLoc,
+      "Bool",
+      [],
+      indicesBody,
+      [
+        new GeneralConstructor(testLoc, "true", [], new S.GeneralTypeConstructor(testLoc, "Bool", [], [])),
+        new GeneralConstructor(testLoc, "false", [], new S.GeneralTypeConstructor(testLoc, "Bool", [], []))
+      ]
+    );
+
+    const motiveType = boolDatatype.generateMotiveType(ctx, new Map(), []);
+    console.log(inspect(motiveType, true, null, true))
+    // Should be: (Π [target : InductiveType("Bool", [], [])] U)
+    expect(motiveType).toBeInstanceOf(V.Pi);
+
+    if (motiveType instanceof V.Pi) {
+      expect(motiveType.argName).toBe('target');
+      expect(motiveType.argType).toBeInstanceOf(V.InductiveTypeConstructor);
+
+      const argType = motiveType.argType as V.InductiveTypeConstructor;
+      expect(argType.name).toBe("Bool");
+      expect(argType.parameters).toHaveLength(0);
+      expect(argType.indices).toHaveLength(0);
+
+      // Result type should be Universe
+      const resultType = motiveType.resultType.valOfClosure(new V.Zero()); // dummy arg
+      expect(resultType).toBeInstanceOf(V.Universe);
+    }
+
+    console.log("✅ Bool motive type:", motiveType.prettyPrint());
+  });
+
+  it("should generate motive type for Vec-like type (one index)", () => {
+    const ctx: Context = new Map();
+
+    // Vec E with index (n : Nat)
+    const indicesPi = new S.Pi(
+      testLoc,
+      [new TypedBinder(new SiteBinder(testLoc, "n"), new S.Nat(testLoc))],
+      new S.Universe(testLoc)
+    );
+
+    const vecDatatype = new DefineDatatypeSource(
+      testLoc,
+      "MyVec",
+      [new TypedBinder(new SiteBinder(testLoc, "E"), new S.Universe(testLoc))],
+      indicesPi,
+      [
+        new GeneralConstructor(testLoc, "vnil", [],
+          new S.GeneralTypeConstructor(testLoc, "MyVec", [], [new S.Zero(testLoc)]))
+      ]
+    );
+
+    // For simplicity, pass empty params (should be E value in real usage)
+    const motiveType = vecDatatype.generateMotiveType(ctx, new Map(), []);
+    console.log(inspect(motiveType, true, null, true))
+
+    // Should be: (Π [n : Nat] (Π [target : InductiveType("MyVec", [], [n])] U))
+    expect(motiveType).toBeInstanceOf(V.Pi);
+
+    if (motiveType instanceof V.Pi) {
+      expect(motiveType.argName).toBe('n');
+      expect(motiveType.argType).toBeInstanceOf(V.Nat);
+
+      // Apply the closure to get inner Pi
+      const innerType = motiveType.resultType.valOfClosure(new V.Zero());
+      expect(innerType).toBeInstanceOf(V.Pi);
+
+      if (innerType instanceof V.Pi) {
+        expect(innerType.argName).toBe('target');
+        expect(innerType.argType).toBeInstanceOf(V.InductiveTypeConstructor);
+
+        const argType = innerType.argType as V.InductiveTypeConstructor;
+        expect(argType.name).toBe("MyVec");
+        // The index should be the captured value from the outer closure
+        expect(argType.indices).toHaveLength(1);
+      }
+    }
+
+    console.log("✅ MyVec motive type:", motiveType.prettyPrint());
+  });
+
+  it("should demonstrate closure capturing for indices", () => {
+    const ctx: Context = new Map();
+    const indicesBody = new S.Universe(testLoc) as any;
+
+    const boolDatatype = new DefineDatatypeSource(
+      testLoc,
+      "Bool",
+      [],
+      indicesBody,
+      []
+    );
+
+    const motiveType = boolDatatype.generateMotiveType(ctx, new Map(), []);
+
+    console.log("\n=== Motive Type Structure ===");
+    console.log("Generated:", motiveType.prettyPrint());
+    console.log("\nThis motive type:");
+    console.log("- Is a function from target values to Types");
+    console.log("- Can be applied with doApp(motive, targetValue)");
+    console.log("- Returns Universe (a Type)");
+    console.log("================================\n");
+
+    expect(motiveType).toBeDefined();
+  });
+});
diff --git a/src/pie_interpreter/__tests__/test_normalize_constructor.ts b/src/pie_interpreter/__tests__/test_normalize_constructor.ts
new file mode 100644
index 00000000..a02e63e5
--- /dev/null
+++ b/src/pie_interpreter/__tests__/test_normalize_constructor.ts
@@ -0,0 +1,391 @@
+import 'jest';
+import * as S from '../types/source';
+import * as C from '../types/core';
+import * as V from '../types/value';
+import { Location, Syntax } from '../utils/locations';
+import { Position } from '../../scheme_parser/transpiler/types/location';
+import { DefineDatatypeSource, GeneralConstructor } from '../typechecker/definedatatype';
+import { Context, bindFree } from '../utils/context';
+import { TypedBinder, SiteBinder, fresh } from '../types/utils';
+import { inspect } from 'util';
+
+// Test location
+const testLoc = new Location(new Syntax(new Position(1, 1), new Position(1, 1), 'test'), false);
+
+describe("normalize_constructor tests", () => {
+  it("should normalize constructors for Bool datatype", () => {
+    const ctx: Context = new Map();
+
+    // Create Bool datatype with two simple constructors
+    // For simple types with no parameters/indices, the "indices" is just Universe
+    // (the type signature says S.Pi but it's used as the body of a Pi)
+    const indicesBody = new S.Universe(testLoc) as any;
+
+    const boolDatatype = new DefineDatatypeSource(
+      testLoc,
+      "Bool",
+      [], // no parameters
+      indicesBody, // indices body: U
+      [
+        new GeneralConstructor(
+          testLoc,
+          "true",
+          [], // no args
+          new S.GeneralTypeConstructor(testLoc, "Bool", [], [])
+        ),
+        new GeneralConstructor(
+          testLoc,
+          "false",
+          [], // no args
+          new S.GeneralTypeConstructor(testLoc, "Bool", [], [])
+        )
+      ]
+    );
+
+    // Call normalize_constructor
+    const normalizedConstructors = boolDatatype.normalize_constructor(ctx, new Map());
+    console.log(inspect(normalizedConstructors, true, null, true))
+
+    // Verify we got 2 normalized constructors
+    expect(normalizedConstructors).toHaveLength(2);
+
+    // Check first constructor (true)
+    const trueConstructor = normalizedConstructors[0];
+    expect(trueConstructor).toBeInstanceOf(C.ConstructorType);
+    expect(trueConstructor.name).toBe("true");
+    expect(trueConstructor.index).toBe(0);
+    expect(trueConstructor.type).toBe("Bool");
+    expect(trueConstructor.argTypes).toHaveLength(0); // no arguments
+    expect(trueConstructor.rec_argTypes).toHaveLength(0); // no recursive arguments
+
+    // Check second constructor (false)
+    const falseConstructor = normalizedConstructors[1];
+    expect(falseConstructor).toBeInstanceOf(C.ConstructorType);
+    expect(falseConstructor.name).toBe("false");
+    expect(falseConstructor.index).toBe(1);
+    expect(falseConstructor.type).toBe("Bool");
+    expect(falseConstructor.argTypes).toHaveLength(0);
+    expect(falseConstructor.rec_argTypes).toHaveLength(0);
+
+    console.log("✅ Bool constructors normalized successfully!");
+  });
+
+  it("should normalize constructors with arguments for Nat-like datatype", () => {
+    const ctx: Context = new Map();
+
+    // Create MyNat datatype with constructors that have arguments
+    const indicesBody = new S.Universe(testLoc) as any;
+
+    const myNatDatatype = new DefineDatatypeSource(
+      testLoc,
+      "MyNat",
+      [], // no parameters
+      indicesBody, // indices body: U
+      [
+        new GeneralConstructor(
+          testLoc,
+          "myZero",
+          [], // no args
+          new S.GeneralTypeConstructor(testLoc, "MyNat", [], [])
+        ),
+        new GeneralConstructor(
+          testLoc,
+          "mySucc",
+          [
+            new TypedBinder(
+              new SiteBinder(testLoc, "pred"),
+              new S.GeneralTypeConstructor(testLoc, "MyNat", [], [])
+            )
+          ],
+          new S.GeneralTypeConstructor(testLoc, "MyNat", [], [])
+        )
+      ]
+    );
+
+    // Call normalize_constructor
+    const normalizedConstructors = myNatDatatype.normalize_constructor(ctx, new Map());
+    console.log(inspect(normalizedConstructors, true, null, true))
+
+
+    // Verify we got 2 normalized constructors
+    expect(normalizedConstructors).toHaveLength(2);
+
+    // Check myZero constructor
+    const zeroConstructor = normalizedConstructors[0];
+    expect(zeroConstructor.name).toBe("myZero");
+    expect(zeroConstructor.index).toBe(0);
+    expect(zeroConstructor.argTypes).toHaveLength(0);
+    expect(zeroConstructor.rec_argTypes).toHaveLength(0);
+
+    // Check mySucc constructor - should have one recursive argument
+    const succConstructor = normalizedConstructors[1];
+    expect(succConstructor.name).toBe("mySucc");
+    expect(succConstructor.index).toBe(1);
+    expect(succConstructor.type).toBe("MyNat");
+    // The recursive argument should be detected
+    expect(succConstructor.rec_argTypes).toHaveLength(1);
+    expect(succConstructor.argTypes).toHaveLength(0); // non-recursive args
+
+    console.log("✅ MyNat constructors with recursive arguments normalized successfully!");
+  });
+
+  it("should normalize constructors with both recursive and non-recursive arguments", () => {
+    const ctx: Context = new Map();
+
+    // Create a Pair-like datatype that mixes recursive and non-recursive arguments
+    const indicesBody = new S.Universe(testLoc) as any;
+
+    const pairDatatype = new DefineDatatypeSource(
+      testLoc,
+      "MyList",
+      [], // no parameters
+      indicesBody,
+      [
+        new GeneralConstructor(
+          testLoc,
+          "nil",
+          [],
+          new S.GeneralTypeConstructor(testLoc, "MyList", [], [])
+        ),
+        new GeneralConstructor(
+          testLoc,
+          "cons",
+          [
+            new TypedBinder(
+              new SiteBinder(testLoc, "head"),
+              new S.Nat(testLoc) // non-recursive: Nat
+            ),
+            new TypedBinder(
+              new SiteBinder(testLoc, "tail"),
+              new S.GeneralTypeConstructor(testLoc, "MyList", [], []) // recursive
+            )
+          ],
+          new S.GeneralTypeConstructor(testLoc, "MyList", [], [])
+        )
+      ]
+    );
+
+    const normalizedConstructors = pairDatatype.normalize_constructor(ctx, new Map());
+
+    console.log(inspect(normalizedConstructors, true, null, true))
+
+
+    expect(normalizedConstructors).toHaveLength(2);
+
+    // Check cons constructor
+    const consConstructor = normalizedConstructors[1];
+    expect(consConstructor.name).toBe("cons");
+    expect(consConstructor.index).toBe(1);
+
+    // Should have 1 non-recursive arg (head: Nat) and 1 recursive arg (tail: MyList)
+    expect(consConstructor.argTypes).toHaveLength(1); // head (Nat)
+    expect(consConstructor.rec_argTypes).toHaveLength(1); // tail (MyList)
+
+    // Verify the non-recursive argument is Nat
+    expect(consConstructor.argTypes[0]).toBeInstanceOf(C.Nat);
+
+    console.log("✅ MyList constructors with mixed argument types normalized successfully!");
+  });
+
+  it("should throw error for invalid constructor types", () => {
+    const ctx: Context = new Map();
+
+    // Create a datatype with an invalid constructor return type
+    const indicesBody = new S.Universe(testLoc) as any;
+
+    const invalidDatatype = new DefineDatatypeSource(
+      testLoc,
+      "Invalid",
+      [],
+      indicesBody,
+      [
+        new GeneralConstructor(
+          testLoc,
+          "bad",
+          [
+            new TypedBinder(
+              new SiteBinder(testLoc, "x"),
+              new S.Name(testLoc, "UndefinedType") // This type doesn't exist
+            )
+          ],
+          new S.GeneralTypeConstructor(testLoc, "Invalid", [], [])
+        )
+      ]
+    );
+
+    // Should throw an error during normalization
+    expect(() => {
+      invalidDatatype.normalize_constructor(ctx, new Map());
+    }).toThrow();
+
+    console.log("✅ Invalid constructor properly throws error!");
+  });
+
+  it("should normalize constructors for List with generic type parameter", () => {
+    const ctx: Context = new Map();
+
+    // Create List datatype with generic type parameter E : U
+    // List has type: (E : U) -> U
+    const indicesBody = new S.Universe(testLoc) as any;
+
+    const listDatatype = new DefineDatatypeSource(
+      testLoc,
+      "List",
+      [
+        new TypedBinder(
+          new SiteBinder(testLoc, "E"),
+          new S.Universe(testLoc)
+        )
+      ], // parameter E : U
+      indicesBody,
+      [
+        new GeneralConstructor(
+          testLoc,
+          "nil",
+          [], // no args
+          new S.GeneralTypeConstructor(testLoc, "List", [new S.Name(testLoc, "E")], [])
+        ),
+        new GeneralConstructor(
+          testLoc,
+          "cons",
+          [
+            new TypedBinder(
+              new SiteBinder(testLoc, "head"),
+              new S.Name(testLoc, "E") // head : E
+            ),
+            new TypedBinder(
+              new SiteBinder(testLoc, "tail"),
+              new S.GeneralTypeConstructor(testLoc, "List", [new S.Name(testLoc, "E")], []) // tail : List E
+            )
+          ],
+          new S.GeneralTypeConstructor(testLoc, "List", [new S.Name(testLoc, "E")], [])
+        )
+      ]
+    );
+
+    const normalizedConstructors = listDatatype.normalize_constructor(ctx, new Map());
+    console.log(inspect(normalizedConstructors, true, null, true))
+
+    expect(normalizedConstructors).toHaveLength(2);
+
+    // Check nil constructor
+    const nilConstructor = normalizedConstructors[0];
+    expect(nilConstructor.name).toBe("nil");
+    expect(nilConstructor.index).toBe(0);
+    expect(nilConstructor.type).toBe("List");
+    expect(nilConstructor.argTypes).toHaveLength(0);
+    expect(nilConstructor.rec_argTypes).toHaveLength(0);
+
+    // Check cons constructor
+    const consConstructor = normalizedConstructors[1];
+    expect(consConstructor.name).toBe("cons");
+    expect(consConstructor.index).toBe(1);
+    expect(consConstructor.type).toBe("List");
+
+    // cons should have 1 non-recursive arg (head : E) and 1 recursive arg (tail : List E)
+    expect(consConstructor.argTypes).toHaveLength(1); // head
+    expect(consConstructor.rec_argTypes).toHaveLength(1); // tail
+
+    console.log("✅ List with generic type parameter normalized successfully!");
+  });
+
+  it("should normalize constructors for Vec with generic type parameter and index", () => {
+    const ctx: Context = new Map();
+
+    // Create Vec datatype with generic type parameter E : U and index n : Nat
+    // Vec has type: (E : U) -> (n : Nat) -> U
+    const indicesBody = new S.Pi(
+      testLoc,
+      [
+        new TypedBinder(
+          new SiteBinder(testLoc, "n"),
+          new S.Nat(testLoc)
+        )
+      ],
+      new S.Universe(testLoc)
+    );
+
+    const vecDatatype = new DefineDatatypeSource(
+      testLoc,
+      "Vec",
+      [
+        new TypedBinder(
+          new SiteBinder(testLoc, "E"),
+          new S.Universe(testLoc)
+        )
+      ], // parameter E : U
+      indicesBody, // index n : Nat
+      [
+        new GeneralConstructor(
+          testLoc,
+          "vecnil",
+          [], // no args
+          new S.GeneralTypeConstructor(
+            testLoc,
+            "Vec",
+            [new S.Name(testLoc, "E")],
+            [new S.Zero(testLoc)] // Vec E zero
+          )
+        ),
+        new GeneralConstructor(
+          testLoc,
+          "veccons",
+          [
+            new TypedBinder(
+              new SiteBinder(testLoc, "k"),
+              new S.Nat(testLoc) // k : Nat
+            ),
+            new TypedBinder(
+              new SiteBinder(testLoc, "head"),
+              new S.Name(testLoc, "E") // head : E
+            ),
+            new TypedBinder(
+              new SiteBinder(testLoc, "tail"),
+              new S.GeneralTypeConstructor(
+                testLoc,
+                "Vec",
+                [new S.Name(testLoc, "E")],
+                [new S.Name(testLoc, "k")] // tail : Vec E k
+              )
+            )
+          ],
+          new S.GeneralTypeConstructor(
+            testLoc,
+            "Vec",
+            [new S.Name(testLoc, "E")],
+            [new S.Add1(testLoc, new S.Name(testLoc, "k"))] // Vec E (add1 k)
+          )
+        )
+      ]
+    );
+
+    const normalizedConstructors = vecDatatype.normalize_constructor(ctx, new Map());
+    console.log(inspect(normalizedConstructors, true, null, true))
+
+    expect(normalizedConstructors).toHaveLength(2);
+
+    // Check vecnil constructor
+    const vecnilConstructor = normalizedConstructors[0];
+    expect(vecnilConstructor.name).toBe("vecnil");
+    expect(vecnilConstructor.index).toBe(0);
+    expect(vecnilConstructor.type).toBe("Vec");
+    expect(vecnilConstructor.argTypes).toHaveLength(0);
+    expect(vecnilConstructor.rec_argTypes).toHaveLength(0);
+
+    // Check veccons constructor
+    const vecconsConstructor = normalizedConstructors[1];
+    expect(vecconsConstructor.name).toBe("veccons");
+    expect(vecconsConstructor.index).toBe(1);
+    expect(vecconsConstructor.type).toBe("Vec");
+
+    // veccons should have 2 non-recursive args (k : Nat, head : E) and 1 recursive arg (tail : Vec E k)
+    expect(vecconsConstructor.argTypes).toHaveLength(2); // k and head
+    expect(vecconsConstructor.rec_argTypes).toHaveLength(1); // tail
+
+    // Verify the types of non-recursive arguments
+    expect(vecconsConstructor.argTypes[0]).toBeInstanceOf(C.Nat); // k : Nat
+    // head : E would be a Free variable reference
+
+    console.log("✅ Vec with generic type parameter and index normalized successfully!");
+  });
+});
diff --git a/src/pie_interpreter/__tests__/test_telescope.ts b/src/pie_interpreter/__tests__/test_telescope.ts
new file mode 100644
index 00000000..27324ecd
--- /dev/null
+++ b/src/pie_interpreter/__tests__/test_telescope.ts
@@ -0,0 +1,10 @@
+import 'jest'
+import { evaluatePie } from '../main';
+
+describe('test_telescope', () => {
+  it('test0', () =>
+  console.log(evaluatePie(
+    `
+    (claim test (Pi ((A U) (x A)) A))`
+  )))
+})
\ No newline at end of file
diff --git a/src/pie_interpreter/evaluator/evaluator.ts b/src/pie_interpreter/evaluator/evaluator.ts
index 8fb70c3f..b5774009 100644
--- a/src/pie_interpreter/evaluator/evaluator.ts
+++ b/src/pie_interpreter/evaluator/evaluator.ts
@@ -775,4 +775,64 @@ export function doIndEither(target: V.Value, motive: V.Value, left: V.Value, rig
     }
   }
   throw new Error(`invalid input for indEither: ${[target, motive, left, right]}`);
+}
+
+export function doEliminator(name: string, target: V.Value, motive: V.Value, methods: V.Value[], methodTypes?: V.Value[], motiveType?: V.Value): V.Value {
+  const targetNow = target.now();
+
+  // Check if target is a constructor application of the inductive type
+  if (targetNow instanceof V.Constructor) {
+    if (targetNow.type != name) {
+      throw new Error(`doEliminator: wrong eliminator used. Got constructor of type: ${targetNow.type}; Expected: ${name}`);
+    }
+    const constructorIndex = targetNow.index;
+    if (constructorIndex >= 0 && constructorIndex < methods.length) {
+      const method = methods[constructorIndex];
+      let result = method;
+
+      // Apply method to constructor arguments
+      // Pattern: apply all non-recursive arguments first, then recursive arguments with their inductive hypotheses
+      for (let i = 0; i < targetNow.args.length; i++) {
+        const arg = targetNow.args[i];
+        result = doApp(result, arg);
+      }
+
+      for (let i = 0; i < targetNow.recursive_args.length; i++) {
+        const arg = targetNow.recursive_args[i];
+        result = doApp(result, arg);
+        const recursiveResult = doEliminator(name, arg, motive, methods, methodTypes, motiveType);
+        result = doApp(result, recursiveResult);
+      }
+
+      return result;
+    }
+  } else if (targetNow instanceof V.Neutral) {
+    const typeNow = targetNow.type.now();
+    if (typeNow instanceof V.InductiveTypeConstructor && typeNow.name === name) {
+      // Create neutral eliminator application
+      return new V.Neutral(
+        doApp(motive, target),
+        new N.GenericEliminator(
+          name,
+          targetNow.neutral,
+          new N.Norm(
+            motiveType ? motiveType : new V.Pi(
+              "x",
+              typeNow,
+              new HigherOrderClosure((_) => new V.Universe())
+            ),
+            motive
+          ),
+          methods.map((method, i) =>
+            new N.Norm(
+              methodTypes && methodTypes[i] ? methodTypes[i] : typeNow,  // Use provided method type or fallback
+              method
+            )
+          )
+        )
+      );
+    }
+  }
+
+  throw new Error(`doEliminator: invalid input for ${name}: ${[target, motive, methods]}`);
 }
\ No newline at end of file
diff --git a/src/pie_interpreter/evaluator/utils.ts b/src/pie_interpreter/evaluator/utils.ts
index e4a2eab2..191d3632 100644
--- a/src/pie_interpreter/evaluator/utils.ts
+++ b/src/pie_interpreter/evaluator/utils.ts
@@ -2,7 +2,7 @@ import * as V from "../types/value";
 import * as C from '../types/core';
 import * as N from '../types/neutral';
 import { fresh } from '../types/utils';
-import { bindFree, Context } from '../utils/context';
+import { bindFree, Context, ConstructorTypeBinder, valInContext } from '../utils/context';
 import { doApp, doCar, doCdr } from "./evaluator";
 
 /**
@@ -176,9 +176,50 @@ export function readBack(context: Context, type: V.Value, value: V.Value): C.Cor
     return new C.Right(
       readBack(context, typeNow.rightType, valueNow.value)!
     );
+  } else if (typeNow instanceof V.InductiveTypeConstructor
+    && valueNow instanceof V.Constructor) {
+    // Read back constructor applications
+    // We need to get the constructor's type information to read back its arguments
+    let ctorBinder: ConstructorTypeBinder | undefined;
+    for (const [name, binder] of context) {
+      if (name === valueNow.name && binder instanceof ConstructorTypeBinder) {
+        ctorBinder = binder;
+        break;
+      }
+    }
+
+    if (!ctorBinder) {
+      throw new Error(`Constructor ${valueNow.name} not found in context`);
+    }
+
+    // Get the constructor type (C.ConstructorType) and evaluate to get Value types
+    const ctorTypeCoreValue = ctorBinder.constructorType;
+    const ctorTypeValue = valInContext(context, ctorTypeCoreValue) as V.ConstructorType;
+
+    // Read back non-recursive arguments
+    const readBackArgs: C.Core[] = [];
+    for (let i = 0; i < valueNow.args.length; i++) {
+      const argType = ctorTypeValue.argTypes[i];
+      readBackArgs.push(readBack(context, argType, valueNow.args[i]));
+    }
+
+    // Read back recursive arguments
+    const readBackRecArgs: C.Core[] = [];
+    for (let i = 0; i < valueNow.recursive_args.length; i++) {
+      const recArgType = ctorTypeValue.rec_argTypes[i];
+      readBackRecArgs.push(readBack(context, recArgType, valueNow.recursive_args[i]));
+    }
+
+    return new C.Constructor(
+      valueNow.name,
+      valueNow.index,
+      valueNow.type,
+      readBackArgs,
+      readBackRecArgs
+    );
   } else if (valueNow instanceof V.Neutral) {
     return valueNow.neutral.readBackNeutral(context);
   }
-  
+
   throw new Error(`Cannot read back ${valueNow.prettyPrint()} : ${typeNow.prettyPrint()}`);
 }
\ No newline at end of file
diff --git a/src/pie_interpreter/main.ts b/src/pie_interpreter/main.ts
index 6c07f8d5..769ca28a 100644
--- a/src/pie_interpreter/main.ts
+++ b/src/pie_interpreter/main.ts
@@ -1,4 +1,5 @@
 import { schemeParse, pieDeclarationParser, Claim, Definition, SamenessCheck, DefineTactically } from './parser/parser'
+import { DefineDatatypeSource } from './typechecker/definedatatype';
 import { checkSame, normType, represent } from './typechecker/represent';
 import { go, stop } from './types/utils';
 import { prettyPrintCore } from './unparser/pretty';
@@ -11,6 +12,7 @@ import {inspect} from 'util';
 export function evaluatePie(str): string {
   const astList = schemeParse(str);
   let ctx = initCtx;
+  let renaming = new Map<string, string>();
   let output = "";
   for (const ast of astList) {
     const src = pieDeclarationParser.parseDeclaration(ast);
@@ -35,6 +37,11 @@ export function evaluatePie(str): string {
       } else if (result instanceof stop) {
         throw new Error("" + result.where + result.message);
       }
+    } else if (src instanceof DefineDatatypeSource) {
+      // Handle datatype definition
+      const [newCtx, newRenaming] = src.normalize_constructor(ctx, renaming);
+      ctx = newCtx;
+      renaming = newRenaming;
     } else if (src instanceof DefineTactically) {
       const proofManager = new ProofManager();
       let message = ''
diff --git a/src/pie_interpreter/parser/makers.ts b/src/pie_interpreter/parser/makers.ts
index f3791c34..46163015 100644
--- a/src/pie_interpreter/parser/makers.ts
+++ b/src/pie_interpreter/parser/makers.ts
@@ -3,6 +3,7 @@ import * as S from "../types/source";
 import { syntaxToLocation } from "./parser";
 import { SiteBinder, TypedBinder } from "../types/utils";
 import { EliminateNatTactic, EliminateListTactic, ExactTactic, IntroTactic, Tactic, EliminateVecTactic, EliminateEqualTactic, ExistsTactic, LeftTactic, RightTactic, EliminateEitherTactic, SpiltTactic, EliminateAbsurdTactic } from "../tactics/tactics";
+import { DefineDatatypeSource, GeneralConstructor } from "../typechecker/definedatatype";
 
 
 export function makeU(stx: Syntax): S.Source {
@@ -481,3 +482,79 @@ export function makeElimAbsurd(stx: Syntax, target: string, motive: S.Source): T
 
 }
 
+
+
+export function makeDefineDatatype(
+  stx: Syntax,
+  name: string,
+  parameters: TypedBinder[],
+  indices: TypedBinder[],
+  constructors: GeneralConstructor[],
+  eliminatorName?: string
+): DefineDatatypeSource {
+
+  return new DefineDatatypeSource(
+    syntaxToLocation(stx),
+    name,
+    parameters,
+    indices,
+    constructors,
+    eliminatorName
+  );
+
+}
+
+
+
+export function makeGeneralConstructor(
+  stx: Syntax,
+  name: string,
+  args: TypedBinder[],
+  returnType: S.GeneralTypeConstructor
+): GeneralConstructor {
+
+  return new GeneralConstructor(
+    syntaxToLocation(stx),
+    name,
+    args,
+    returnType
+  );
+
+}
+
+
+
+export function makeConstructorApplication(
+  stx: Syntax,
+  constructorName: string,
+  args: S.Source[]
+): S.ConstructorApplication {
+
+  return new S.ConstructorApplication(
+    syntaxToLocation(stx),
+    constructorName,
+    args
+  );
+
+}
+
+
+
+export function makeEliminatorApplication(
+  stx: Syntax,
+  typeName: string,
+  target: S.Source,
+  motive: S.Source,
+  methods: S.Source[]
+): S.EliminatorApplication {
+
+  return new S.EliminatorApplication(
+    syntaxToLocation(stx),
+    typeName,
+    target,
+    motive,
+    methods
+  );
+
+}
+
diff --git a/src/pie_interpreter/parser/parser.ts b/src/pie_interpreter/parser/parser.ts
index eb060c44..b5786bb1 100644
--- a/src/pie_interpreter/parser/parser.ts
+++ b/src/pie_interpreter/parser/parser.ts
@@ -8,6 +8,7 @@ import { Location, Syntax } from "../utils/locations";
 import { Location as Loc } from '../../scheme_parser/transpiler/types/location';
 import { isVarName, SiteBinder, TypedBinder } from "../types/utils";
 import { EliminateNatTactic, EliminateListTactic, ExactTactic, IntroTactic, Tactic } from "../tactics/tactics";
+import { DefineDatatypeSource, GeneralConstructor } from "../typechecker/definedatatype";
 import * as Maker from "./makers"
 
 type Element = Extended.List | Atomic.Symbol | Atomic.NumericLiteral;
@@ -399,6 +400,36 @@ export class Parser {
       );
     } else if (parsee === 'TODO') {
       return Maker.makeTODO(locationToSyntax('TODO', element.location));
+    } else if (parsee.startsWith('data-') && !parsee.startsWith('data-ind-')) {
+      // Constructor application: (data-constructor-name arg1 arg2...)
+      const constructorName = parsee.substring(5); // Remove 'data-' prefix
+      const elements = (element as Extended.List).elements;
+      const args = elements.slice(1).map(x => this.parseElements(x as Element));
+      return new S.ConstructorApplication(
+        syntaxToLocation(locationToSyntax(constructorName, element.location)),
+        constructorName,
+        args
+      );
+    } else if (parsee.startsWith('data-ind-')) {
+      // Eliminator application: (data-ind-TypeName target motive methods...)
+      const typeName = parsee.substring(9); // Remove 'data-ind-' prefix
+      const elements = (element as Extended.List).elements;
+
+      if (elements.length < 3) {
+        throw new Error(`Eliminator ${parsee} requires at least target and motive`);
+      }
+
+      const target = this.parseElements(elements[1] as Element);
+      const motive = this.parseElements(elements[2] as Element);
+      const methods = elements.slice(3).map(x => this.parseElements(x as Element));
+
+      return new S.EliminatorApplication(
+        syntaxToLocation(locationToSyntax(parsee, element.location)),
+        typeName,
+        target,
+        motive,
+        methods
+      );
     } else if (element instanceof Extended.List && (element as Extended.List).elements.length > 1) {
       let elements = (element as Extended.List).elements;
       return Maker.makeApp(
@@ -525,7 +556,7 @@ export class DefineTactically {
 
 
 
-export type Declaration = Claim | Definition | SamenessCheck | DefineTactically|S.Source;
+export type Declaration = Claim | Definition | SamenessCheck | DefineTactically | DefineDatatypeSource | S.Source;
 
 
 export class pieDeclarationParser {
@@ -560,6 +591,118 @@ export class pieDeclarationParser {
         getValue(elements[1] as Element),
         (elements[2] as Extended.List).elements.map((x: Expression) => Parser.parseToTactics(x as Element))
       );
+    } else if (parsee === 'data') {
+      let elements = (ast as Extended.List).elements;
+      let loc = ast.location;
+
+      // elements[0] = 'data' (keyword)
+      // elements[1] = type name (e.g., 'Less-Than')
+      // elements[2] = parameters list (e.g., () or ((E U)))
+      // elements[3] = indices list (e.g., ((j Nat) (k Nat)))
+      // elements[4...n-1] = constructor definitions
+      // elements[n] = eliminator name (optional, e.g., 'ind-Less-Than')
+
+      const typeName = getValue(elements[1] as Element);
+      const paramsRaw = (elements[2] as Extended.List).elements || [];
+      const indicesRaw = (elements[3] as Extended.List).elements || [];
+
+      // Parse parameters: ((E U)) -> [TypedBinder(E, U)]
+      const parameters = paramsRaw.map(p => {
+        const pair = p as Extended.List;
+        return new TypedBinder(
+          syntaxToSiteBinder(elementToSyntax(pair.elements[0] as Element, pair.location)),
+          Parser.parseElements(pair.elements[1] as Element)
+        );
+      });
+
+      // Parse indices: ((j Nat) (k Nat)) -> [TypedBinder(j, Nat), TypedBinder(k, Nat)]
+      const indices = indicesRaw.map(idx => {
+        const pair = idx as Extended.List;
+        return new TypedBinder(
+          syntaxToSiteBinder(elementToSyntax(pair.elements[0] as Element, pair.location)),
+          Parser.parseElements(pair.elements[1] as Element)
+        );
+      });
+
+      // Find where constructors end (last element might be eliminator name)
+      const lastElement = elements[elements.length - 1];
+      const hasEliminator = lastElement instanceof Atomic.Symbol;
+      const constructorEndIdx = hasEliminator ? elements.length - 1 : elements.length;
+      const eliminatorName = hasEliminator ? getValue(lastElement as Element) : undefined;
+
+      // Parse constructors: (constructor-name ((args...)) (ReturnType ...))
+      const constructors = [];
+      for (let i = 4; i < constructorEndIdx; i++) {
+        const ctorElement = elements[i] as Extended.List;
+        const ctorName = getValue(ctorElement.elements[0] as Element);
+        const ctorArgsRaw = (ctorElement.elements[1] as Extended.List).elements || [];
+        const ctorReturnType = ctorElement.elements[2] as Element;
+
+        // Parse constructor arguments: ((n Nat)) or ((j Nat) (k Nat) (j<k (Less-Than j k)))
+        const ctorArgs = ctorArgsRaw.map(arg => {
+          const pair = arg as Extended.List;
+          const argType = pair.elements[1] as Element;
+
+          // Check if this is a GeneralTypeConstructor application (e.g., (Less-Than j k))
+          let parsedArgType: S.Source;
+          if (argType instanceof Extended.List && argType.elements.length > 0) {
+            const firstElem = getValue(argType.elements[0] as Element);
+            // If it starts with capital letter, treat as GeneralTypeConstructor
+            if (firstElem && firstElem[0] === firstElem[0].toUpperCase() && firstElem[0] !== firstElem[0].toLowerCase()) {
+              const typeArgs = argType.elements.slice(1).map(x => Parser.parseElements(x as Element));
+              parsedArgType = new S.GeneralTypeConstructor(
+                syntaxToLocation(elementToSyntax(argType.elements[0] as Element, argType.location)),
+                firstElem,
+                [],
+                typeArgs
+              );
+            } else {
+              parsedArgType = Parser.parseElements(argType);
+            }
+          } else {
+            parsedArgType = Parser.parseElements(argType);
+          }
+
+          return new TypedBinder(
+            syntaxToSiteBinder(elementToSyntax(pair.elements[0] as Element, pair.location)),
+            parsedArgType
+          );
+        });
+
+        // Parse return type: (Less-Than zero (add1 n))
+        // This should be a GeneralTypeConstructor application
+        const returnTypeList = ctorReturnType as Extended.List;
+        const returnTypeName = getValue(returnTypeList.elements[0] as Element);
+
+        // All remaining elements are indices (for indexed types) or parameters
+        // For now, treat all as indices since we need to match the datatype structure
+        const returnTypeArgs = returnTypeList.elements.slice(1).map(x => Parser.parseElements(x as Element));
+
+        const returnType = new S.GeneralTypeConstructor(
+          syntaxToLocation(elementToSyntax(returnTypeList.elements[0] as Element, returnTypeList.location)),
+          returnTypeName,
+          [], // parameters - will be filled based on datatype definition
+          returnTypeArgs // indices
+        );
+
+        constructors.push(
+          new GeneralConstructor(
+            syntaxToLocation(elementToSyntax(ctorElement.elements[0] as Element, ctorElement.location)),
+            ctorName,
+            ctorArgs,
+            returnType
+          )
+        );
+      }
+
+      return new DefineDatatypeSource(
+        syntaxToLocation(elementToSyntax(elements[0] as Element, loc)),
+        typeName,
+        parameters,
+        indices,
+        constructors,
+        eliminatorName
+      );
     } else {
       return Parser.parseElements(ast);
     }
diff --git a/src/pie_interpreter/try_llm/main.ts b/src/pie_interpreter/try_llm/main.ts
new file mode 100644
index 00000000..315ca535
--- /dev/null
+++ b/src/pie_interpreter/try_llm/main.ts
@@ -0,0 +1,11 @@
+import { solveTodo, todoQueue } from "./todo_solver";
+
+async function main() {
+  // Run type checker to collect TODOs
+  // Then solve each one
+  for (const todo of todoQueue) {
+    const solution = await solveTodo(todo);
+    console.log(`\n=== ${todo.location} ===`);
+    console.log(solution);
+  }
+}
\ No newline at end of file
diff --git a/src/pie_interpreter/try_llm/todo_solver.ts b/src/pie_interpreter/try_llm/todo_solver.ts
new file mode 100644
index 00000000..785a43af
--- /dev/null
+++ b/src/pie_interpreter/try_llm/todo_solver.ts
@@ -0,0 +1,201 @@
+// src/ai/todo_solver.ts
+import { GoogleGenAI } from "@google/genai";
+import * as fs from "fs/promises";
+import * as path from "path";
+import { Parser } from "../parser/parser";
+import { stop } from "../types/utils";
+import { Location } from "../utils/locations";
+import { Context, readBackContext } from "../utils/context";
+import { Value } from "../types/value";
+import { Renaming } from "../typechecker/utils";
+import { config } from "dotenv";
+
+// Load environment variables from .env file
+config();
+
+// Get API key from environment variable
+const apiKey = process.env.GOOGLE_API_KEY;
+if (!apiKey) {
+  throw new Error(
+    'GOOGLE_API_KEY environment variable is not set. ' +
+    'Please create a .env file in the project root with: GOOGLE_API_KEY=your_key_here'
+  );
+}
+
+const genAI = new GoogleGenAI({ apiKey });
+
+// Cache for project context string (in-memory)
+let cachedProjectContext: string | null = null;
+
+export interface TodoInfo {
+  location: Location;
+  context: Context;
+  expectedType: Value;
+  renaming: Renaming;
+}
+
+export const todoQueue: TodoInfo[] = [];
+
+export function addTodo(todo: TodoInfo) {
+  todoQueue.push(todo);
+}
+
+export function clearQueue() {
+  todoQueue.length = 0;
+}
+
+export function clearCache() {
+  cachedProjectContext = null;
+}
+
+// Collect all .ts files from src/pie_interpreter
+async function getProjectFiles(): Promise<Map<string, string>> {
+  const files = new Map<string, string>();
+  const dir = "src/pie_interpreter";
+
+  async function walk(dir: string) {
+    const entries = await fs.readdir(dir, { withFileTypes: true });
+    for (const entry of entries) {
+      const fullPath = path.join(dir, entry.name);
+      if (entry.isDirectory() && !entry.name.startsWith(".")) {
+        await walk(fullPath);
+      } else if (entry.name.endsWith(".ts") && !entry.name.includes("test")) {
+        files.set(fullPath, await fs.readFile(fullPath, "utf-8"));
+      }
+    }
+  }
+
+  await walk(dir);
+  return files;
+}
+
+// Build and cache project context string
+async function getOrBuildProjectContext(): Promise<string> {
+  if (cachedProjectContext) {
+    return cachedProjectContext;
+  }
+
+  const projectFiles = await getProjectFiles();
+
+  // Build comprehensive project context with file contents
+  let projectContext = "# Project structure and files:\n\n";
+
+  // Add file paths list for overview
+  projectContext += "## File listing:\n";
+  for (const [path, _] of projectFiles) {
+    projectContext += `- ${path}\n`;
+  }
+
+  // Add actual file contents (with size limit per file)
+  projectContext += "\n## File contents:\n\n";
+  for (const [path, content] of projectFiles) {
+    const lines = content.split('\n');
+    const truncatedContent = lines.slice(0, 10000).join('\n'); // Limit to first 100 lines per file
+    projectContext += `### ${path}\n\`\`\`typescript\n${truncatedContent}\n\`\`\`\n\n`;
+  }
+
+  // Cache the built context
+  cachedProjectContext = projectContext;
+  return projectContext;
+}
+
+export async function solveTodo(todo: TodoInfo): Promise<string> {
+  // Get cached or build project context
+  const projectContext = await getOrBuildProjectContext();
+
+  const startTime = Date.now();
+  const TIMEOUT_MS = 30000; // 30 seconds
+
+  // Stringify objects for AI prompt
+  const serializedContext = JSON.stringify(readBackContext(todo.context));
+  const serializedRenaming = JSON.stringify(Array.from(todo.renaming.entries()));
+  const expectedTypeStr = todo.expectedType.readBackType(todo.context).prettyPrint();
+
+  // Use the real objects for typechecking
+  const ctx = todo.context;
+  const renaming = todo.renaming;
+
+  let basePrompt = `
+You are helping to fill in TODO expressions in Pie language code (a dependently-typed language from "The Little Typer").
+
+${projectContext}
+
+## TODO Context:
+Available context (variable bindings): ${serializedContext}
+Renaming map: ${serializedRenaming}
+Expected type: ${expectedTypeStr}
+
+## Task:
+Generate ONLY a valid Pie expression (not TypeScript!) that has the expected type.
+
+Common Pie types and their values:
+- Nat: zero, (add1 zero), (add1 (add1 zero)), etc.
+- Atom: 'foo, 'bar, etc. (quoted symbols)
+- Trivial: sole (the only value of type Trivial)
+- (List T): (the (List T) nil), (:: head tail)
+  Note: nil needs explicit typing like (the (List Nat) nil)
+- (Pair A D): (cons a d)
+- (→ A B): (lambda (x) body) or (λ (x) body)
+
+Important: When you need to provide an explicit type annotation, use (the Type value).
+For example: (the Nat zero), (the (List Nat) nil)
+
+Do not include code fences, markdown, or explanations. Just the Pie expression.
+`;
+
+  let errorHistory = "";
+  let attempts = 0;
+
+  while (Date.now() - startTime < TIMEOUT_MS) {
+    attempts++;
+
+    const prompt = basePrompt + errorHistory;
+
+    try {
+      const result = await genAI.models.generateContent({
+        model: "gemini-2.5-flash",
+        contents: prompt
+      });
+
+      const pieCode = result.text.trim()
+        .replace(/^```[\w]*\n?/, '')  // Remove opening code fence
+        .replace(/\n?```$/, '')        // Remove closing code fence
+        .trim();
+
+      // Try to parse the Pie expression
+      let parsed;
+      try {
+        parsed = Parser.parsePie(pieCode);
+      } catch (parseError: any) {
+        errorHistory += `\n\nAttempt ${attempts} failed - Parse error: ${parseError.message}\nYou generated: ${pieCode}\nPlease fix the syntax and try again.`;
+        continue;
+      }
+
+      // Try to typecheck it
+      try {
+        // Use check mode since we have the expected type (already as Value)
+        const checkResult = parsed.check(ctx, renaming, todo.expectedType);
+
+        if (checkResult instanceof stop) {
+          // Typecheck failed
+          errorHistory += `\n\nAttempt ${attempts} failed - Type error: ${checkResult.message.toString()}\nYou generated: ${pieCode}\nPlease generate a correct expression.`;
+          continue;
+        }
+
+        // Success! Return the expression
+        return pieCode;
+      } catch (typecheckError: any) {
+        errorHistory += `\n\nAttempt ${attempts} failed - Typecheck error: ${typecheckError.message}\nYou generated: ${pieCode}\nPlease fix and try again.`;
+        continue;
+      }
+    } catch (error: any) {
+      errorHistory += `\n\nAttempt ${attempts} failed - API error: ${error.message}`;
+      // Wait a bit before retrying API errors
+      await new Promise(resolve => setTimeout(resolve, 1000));
+      continue;
+    }
+  }
+
+  // Timeout reached
+  throw new Error(`Failed to solve TODO after ${attempts} attempts in 30 seconds. Last errors: ${errorHistory}`);
+}
\ No newline at end of file
diff --git a/src/pie_interpreter/typechecker/definedatatype.ts b/src/pie_interpreter/typechecker/definedatatype.ts
new file mode 100644
index 00000000..e5477a1a
--- /dev/null
+++ b/src/pie_interpreter/typechecker/definedatatype.ts
@@ -0,0 +1,388 @@
+import * as S from '../types/source';
+import * as C from '../types/core';
+import * as V from '../types/value';
+import { go, Perhaps, stop, fresh, TypedBinder, Message, SiteBinder, HigherOrderClosure } from '../types/utils';
+import { Context, extendContext, InductiveDatatypeBinder, ConstructorTypeBinder, contextToEnvironment, EliminatorBinder, valInContext, bindFree, getClaim } from '../utils/context';
+import { Location, Syntax } from '../utils/locations';
+import { extendRenaming, Renaming } from './utils';
+import { Environment } from '../utils/environment';
+import { VarName } from '../types/core';
+import { synthesizer } from './synthesizer';
+import { doApp } from '../evaluator/evaluator';
+import { Position } from '../../scheme_parser/transpiler/types/location';
+
+function isRecursiveArgumentType(argType: S.Source, datatypeName: string): boolean {
+  if (argType instanceof S.Name && argType.name === datatypeName) {
+    return true;
+  }
+
+  if (argType instanceof S.GeneralTypeConstructor &&
+      argType.name === datatypeName) {
+    return true;
+  }
+
+  return false;
+}
+
+export class DefineDatatypeSource {
+  constructor(
+    public location: Location,
+    public name: string,
+    public parameters: TypedBinder[],
+    public indices: TypedBinder[],
+    public constructors: GeneralConstructor[],
+    public eliminatorName?: string
+  ) { }
+
+  normalize_constructor(ctx: Context, rename: Renaming) {
+    // Build the type: if there are parameters, wrap in Pi, otherwise just use indices
+    const validTypeTemp = (new S.GeneralType
+      (this.location,
+        this.name,
+        this.parameters,
+        this.indices
+      ).isType(ctx, rename)
+    )
+    if (validTypeTemp instanceof stop) {
+      throw new Error(validTypeTemp.message.toString())
+    }
+    const validType = (validTypeTemp as go<C.Core>).result
+
+    // Extend context with parameters so constructors can reference them
+    let extendedCtx = ctx;
+    let extendedRename = rename;
+    for (const param of this.parameters) {
+      const paramName = param.binder.varName;
+      const paramTypeResult = param.type.isType(extendedCtx, extendedRename);
+      if (paramTypeResult instanceof stop) {
+        throw new Error(paramTypeResult.message.toString());
+      }
+      const paramTypeCore = (paramTypeResult as go<C.Core>).result;
+      const paramNameHat = fresh(extendedCtx, paramName);
+      extendedCtx = bindFree(extendedCtx, paramNameHat, valInContext(extendedCtx, paramTypeCore));
+      extendedRename = extendRenaming(extendedRename, paramName, paramNameHat);
+    }
+
+    // Evaluate the type in the extended context so parameters are bound
+    const validValueType = valInContext(extendedCtx, validType);
+
+    // Add the inductive type itself to the context so recursive constructors can reference it
+    extendedCtx = extendContext(extendedCtx, this.name,
+      new InductiveDatatypeBinder(this.name, validValueType as V.InductiveType))
+
+    let normalized_constructor: C.ConstructorType[] = []
+    for (let i = 0; i < this.constructors.length; i++) {
+      // For types with no parameters, validValueType will be Universe, not Pi
+      // We need to pass the appropriate target type to checkValid
+      normalized_constructor.push(this.constructors[i].checkValid(extendedCtx, extendedRename, validValueType as any, i))
+    }
+    
+    let ret_ctx = ctx
+    let ret_rename = rename
+    ret_ctx = extendContext(ret_ctx, this.name,
+      new InductiveDatatypeBinder(this.name, validValueType as V.InductiveType))
+    normalized_constructor.forEach(element => {
+      const fresh_name = fresh(ret_ctx, element.name)
+      // Get the InductiveTypeConstructor from the constructor's result type
+      // For parameterized types, this will contain VarNames - that's OK, it's symbolic
+      let resultTypeValue: V.InductiveTypeConstructor
+
+      if (element.numTypeParams > 0) {
+        // For parameterized constructors, evaluate in the extended context where parameters were bound
+        resultTypeValue = valInContext(extendedCtx, element.resultType) as V.InductiveTypeConstructor
+      } else {
+        // For simple constructors, evaluate in base context
+        resultTypeValue = valInContext(ctx, element.resultType) as V.InductiveTypeConstructor
+      }
+
+      ret_ctx = extendContext(ret_ctx, fresh_name, new ConstructorTypeBinder(fresh_name, element, resultTypeValue))
+      ret_rename = extendRenaming(ret_rename, element.name, fresh_name)
+    })
+    return [ret_ctx, ret_rename] as [Context, Renaming]
+  }
+
+  /**
+   * Generate the motive type for the eliminator of this inductive type.
+   *
+   * The motive type has the form:
+   * (Π [i₁ : τ₁] ... [iₙ : τₙ] [target : T params... i₁...iₙ] U)
+   *
+   * Where:
+   * - i₁...iₙ are the indices of the inductive type
+   * - T is the inductive type name
+   * - params are the type parameters
+   * - target is the value being eliminated
+   *
+   * Examples:
+   * - Nat (no indices): (Π [n : Nat] U)
+   * - Vec E (one index k : Nat): (Π [k : Nat] [es : Vec E k] U)
+   * - Fin (one index n : Nat): (Π [n : Nat] [f : Fin n] U)
+   *
+   * IMPORTANT: Index variables must be captured inside closures and used to
+   * construct the target type, following the pattern from synthIndVec.
+   */
+  //TODO: add telescope to this if needed
+  // generateMotiveType(ctx: Context, rename: Renaming, params: V.Value[]): V.Value {
+  //   // Step 1: Extract index types from the Pi structure
+  //   let indexTypes: Array<[string, V.Value]> = [];
+  //   let cur: S.Source = this.indices;
+
+  //   while (cur instanceof S.Pi && cur.binders.length > 0) {
+  //     const binder = cur.binders[0];
+  //     const typeCore = binder.type.check(ctx, rename, new V.Universe());
+  //     if (typeCore instanceof stop) {
+  //       throw new Error(typeCore.message.toString());
+  //     }
+  //     const indexType = (typeCore as go<C.Core>).result;
+  //     indexTypes.push([binder.binder.varName, valInContext(ctx, indexType)]);
+  //     cur = cur.body as S.Source;
+  //   }
+
+  //   // Step 2: Build nested Pi structure recursively
+  //   // Each closure captures index values at runtime
+  //   const buildMotive = (level: number, capturedIndices: V.Value[]): V.Value => {
+  //     if (level >= indexTypes.length) {
+  //       // Base case: build (Π [target : InductiveType(name, params, capturedIndices)] U)
+  //       return new V.Pi(
+  //         'target',
+  //         new V.InductiveTypeConstructor(this.name, params, capturedIndices),
+  //         new HigherOrderClosure(_ => new V.Universe())
+  //       );
+  //     }
+
+  //     // Recursive case: build (Π [index : τ] ...)
+  //     const [indexName, indexType] = indexTypes[level];
+  //     return new V.Pi(
+  //       indexName,
+  //       indexType,
+  //       new HigherOrderClosure(indexVal =>
+  //         buildMotive(level + 1, [...capturedIndices, indexVal])
+  //       )
+  //     );
+  //   };
+
+  //   return buildMotive(0, []);
+  // }
+
+  /**
+   * Generate the eliminator method type for a specific constructor.
+   *
+   * Method type: (Π [i+x : τ₁]... (→ (P ix... xrec)... (P τ₂i... (C A... i+x...))))
+   *
+   * Following the Turnstile+ pattern:
+   * - Bind all constructor arguments
+   * - Add inductive hypotheses for recursive arguments
+   * - Result: motive applied to constructor application
+   */
+  generateMethodType(
+    ctx: Context,
+    rename: Renaming,
+    ctorType: C.ConstructorType,
+    motiveValue: V.Value,
+    params: V.Value[]
+  ): V.Value {
+    // Build environment with type parameters bound for evaluating argTypes
+    let argEnv = new Map(contextToEnvironment(ctx));
+
+    // Extract all VarNames from argTypes and rec_argTypes
+    const varNames = new Set<string>();
+    [...ctorType.argTypes, ...ctorType.rec_argTypes].forEach(at => {
+      if (at instanceof C.VarName) {
+        varNames.add(at.name);
+      }
+    });
+
+    // Bind each unique VarName to the corresponding type parameter
+    const varNameArray = Array.from(varNames);
+    for (let i = 0; i < varNameArray.length && i < params.length; i++) {
+      argEnv.set(varNameArray[i], params[i]);
+    }
+
+    // Get all argument types (non-recursive + recursive)
+    const allArgTypes = [
+      ...ctorType.argTypes.map(t => t.valOf(argEnv)),
+      ...ctorType.rec_argTypes.map(t => t.valOf(argEnv))
+    ];
+
+    // Build method type recursively with nested closures
+    const buildMethod = (level: number, capturedArgs: V.Value[]): V.Value => {
+      if (level >= allArgTypes.length) {
+        // All arguments captured, now add inductive hypotheses and result
+
+        // Step 1: Add IHs for recursive arguments (in reverse order)
+        let result: V.Value;
+
+        // First, build the result type: P applied to constructor
+        const ctorApp = new V.Constructor(
+          ctorType.name,
+          ctorType.type,
+          capturedArgs,
+          ctorType.index,
+          []  // Will be filled with recursive args
+        );
+
+        // Extract result indices from ctorType.resultType
+        const resultType = valInContext(ctx, ctorType.resultType);
+        const resultIndices = extractIndicesFromValue(resultType);
+
+        // Apply motive to indices and constructor
+        result = motiveValue;
+        for (const idx of resultIndices) {
+          result = doApp(result, idx);
+        }
+        result = doApp(result, ctorApp);
+
+        // Step 2: Wrap with inductive hypotheses (for recursive args, in reverse)
+        const numNonRec = ctorType.argTypes.length;
+        for (let i = ctorType.rec_argTypes.length - 1; i >= 0; i--) {
+          const recArgIndex = numNonRec + i;
+          const recArg = capturedArgs[recArgIndex];
+          const recArgTypeValue = allArgTypes[recArgIndex];
+
+          // Build IH type: P(indices... recArg)
+          // The recursive arg type (e.g., Vec E k) when evaluated in context
+          // has its indices as Values that reference captured arguments
+          let ihType = motiveValue;
+          if (recArgTypeValue instanceof V.InductiveTypeConstructor) {
+            for (const idx of recArgTypeValue.indices) {
+              ihType = doApp(ihType, idx);
+            }
+          }
+          ihType = doApp(ihType, recArg);
+
+          const currentResult = result;
+          result = new V.Pi(
+            `ih${i}`,
+            ihType,
+            new HigherOrderClosure(_ => currentResult)
+          );
+        }
+
+        return result;
+      }
+
+      // Recursive case: bind constructor argument
+      const argType = allArgTypes[level];
+      return new V.Pi(
+        `arg${level}`,
+        argType,
+        new HigherOrderClosure(argVal =>
+          buildMethod(level + 1, [...capturedArgs, argVal])
+        )
+      );
+    };
+
+    return buildMethod(0, []);
+  }
+
+}
+
+// Helper function to extract indices from a value
+function extractIndicesFromValue(val: V.Value): V.Value[] {
+  if (val instanceof V.InductiveTypeConstructor) {
+    return val.indices;
+  }
+  return [];
+}
+
+
+
+export class GeneralConstructor {
+  constructor(
+    public location: Location,
+    public name: string,
+    public args: TypedBinder[],
+    public returnType: S.GeneralTypeConstructor
+  ) { }
+
+  checkValid(ctx: Context, rename: Renaming, target: V.Value, index: number) {
+    let cur_ctx = ctx
+    let cur_rename = rename
+    let normalized_args = []
+    let normalized_rec_args = []
+    let numTypeParams = 0
+    let argNames: string[] = []
+
+    for (let i = 0; i < this.args.length; i++) {
+      const argName = this.args[i].binder.varName
+      const xhat = fresh(cur_ctx, argName)
+
+      // Store the original argument name
+      argNames.push(argName)
+
+      // Get the Core representation of the type annotation
+      const resultTemp = this.args[i].type.isType(cur_ctx, cur_rename)
+      if (resultTemp instanceof stop) {
+        throw new Error(resultTemp.message.toString())
+      }
+      const result = (resultTemp as go<C.Core>).result
+
+      // Check if this argument IS a type parameter (annotation is Universe at SOURCE level)
+      if (this.args[i].type instanceof S.Universe) {
+        numTypeParams++
+      }
+
+      if (isRecursiveArgumentType(this.args[i].type,this.returnType.name)) {
+        normalized_rec_args.push(result)
+      } else {
+        normalized_args.push(result)
+      }
+
+      cur_ctx = bindFree(cur_ctx, xhat, valInContext(cur_ctx, result))
+      cur_rename = extendRenaming(cur_rename, argName, xhat)
+    }
+
+    const returnTemp = this.returnType.check(cur_ctx, cur_rename, target)
+    if (returnTemp instanceof stop) {
+      throw new Error(returnTemp.message.toString())
+    }
+    const returnResult = (returnTemp as go<C.Core>).result
+    return new C.ConstructorType(
+        this.name,
+        index,
+        this.returnType.name,
+        normalized_args,
+        normalized_rec_args,
+        returnResult,
+        numTypeParams,
+        argNames
+      )
+
+
+  }
+}
+
+export class GeneralTypeSource {
+  constructor(
+    public location: Location,
+    public name: string,
+    public parameters: TypedBinder[],
+    public indices: TypedBinder[]
+  ){ }
+}
+
+// Helper function to create constructor spec
+export function makeConstructorSpec(name: string, args: TypedBinder[]): GeneralConstructor {
+  return new GeneralConstructor(
+    args.length > 0 ? args[0].binder.location : new Location(new Syntax(new Position(0, 0), new Position(0, 0), 'generated'), false),
+    name,
+    args,
+    new S.GeneralTypeConstructor(
+      args.length > 0 ? args[0].binder.location : new Location(new Syntax(new Position(0, 0), new Position(0, 0), 'generated'), false),
+      '',  // Will be set by caller
+      [],
+      []
+    )
+  );
+}
+
+// Main function to handle datatype definition and add to context
+export function handleDefineDatatype(ctx: Context, rename: Renaming, target: DefineDatatypeSource): Perhaps<Context> {
+  if (ctx.has(target.name)) {
+    return new stop(target.location, new Message([`Name already in use: ${target.name}`]));
+  }
+  let [new_ctx, new_rename] = target.normalize_constructor(ctx, rename)
+
+  
+}
+
diff --git a/src/pie_interpreter/typechecker/synthesizer.ts b/src/pie_interpreter/typechecker/synthesizer.ts
index 5995f18f..7067cada 100644
--- a/src/pie_interpreter/typechecker/synthesizer.ts
+++ b/src/pie_interpreter/typechecker/synthesizer.ts
@@ -7,12 +7,13 @@ import {
   fresh, FirstOrderClosure, HigherOrderClosure,
   TypedBinder
 } from '../types/utils';
-import { bindFree, Context, contextToEnvironment, Define, valInContext, varType } from '../utils/context';
+import { bindFree, Context, contextToEnvironment, Define, valInContext, varType, getInductiveType, InductiveDatatypeBinder, ConstructorTypeBinder } from '../utils/context';
 import { atomOk, convert, extendRenaming, makeApp, PieInfoHook, rename, Renaming, sameType } from "./utils";
 import { notForInfo } from "../utils/locations";
 import { doApp, doCar, indVecStepType } from "../evaluator/evaluator";
 import { readBack } from '../evaluator/utils';
 import { Location } from '../utils/locations';
+import { alphaEquiv } from "../utils/alphaeqv";
 
 
 export class synthesizer {
@@ -30,16 +31,16 @@ export class synthesizer {
     );
   }
 
-  public static synthArrow(context: Context, r: Renaming, location: Location, arg1 : S.Source, arg2 : S.Source, args : S.Source[]): Perhaps<C.The> {
+  public static synthArrow(context: Context, r: Renaming, location: Location, arg1: S.Source, arg2: S.Source, args: S.Source[]): Perhaps<C.The> {
     if (args.length === 0) {
       const z = freshBinder(context, arg2, 'x');
       const Aout = new PerhapsM<C.Core>("Aout");
       const Bout = new PerhapsM<C.Core>('Bout');
       return goOn(
         [
-          [Aout, () => 
+          [Aout, () =>
             arg1.check(context, r, new V.Universe())],
-          [Bout, () => 
+          [Bout, () =>
             arg2.check(
               bindFree(context, z, valInContext(context, Aout.value)),
               r,
@@ -68,11 +69,11 @@ export class synthesizer {
           [Aout, () => arg1.check(context, r, new V.Universe())],
           [tout, () =>
             new S.Arrow(notForInfo(location), arg2, first, rest)
-                .check(
-                  bindFree(context, z, valInContext(context, Aout.value)),
-                  r,
-                  new V.Universe()
-                )
+              .check(
+                bindFree(context, z, valInContext(context, Aout.value)),
+                r,
+                new V.Universe()
+              )
           ]
         ],
         () => {
@@ -316,7 +317,7 @@ export class synthesizer {
     return goOn(
       [
         [tgtout, () => target.check(context, r, new V.Nat())],
-        [motout, () => motive.check(context, r, 
+        [motout, () => motive.check(context, r,
           new V.Pi(
             'n',
             new V.Nat(),
@@ -384,12 +385,12 @@ export class synthesizer {
     return goOn(
       [
         [Aout, () => first.check(context, r, new V.Universe())],
-        [Dout, () => 
+        [Dout, () =>
           second.check(
             bindFree(context, a, valInContext(context, Aout.value)),
             r,
             new V.Universe()
-        )],
+          )],
       ],
       () => new go<C.The>(
         new C.The(
@@ -446,7 +447,7 @@ export class synthesizer {
       return goOn(
         [
           [Aout, () => type.check(context, r, new V.Universe())],
-          [Dout, () => 
+          [Dout, () =>
             new S.Sigma(
               notForInfo(location),
               rest,
@@ -564,7 +565,7 @@ export class synthesizer {
     )
   }
 
-  public static synthIndList(context: Context, r: Renaming, 
+  public static synthIndList(context: Context, r: Renaming,
     location: Location, target: S.Source, motive: S.Source, base: S.Source, step: S.Source,): Perhaps<C.The> {
     const tgtout = new PerhapsM<C.The>('tgtout');
     const motout = new PerhapsM<C.Core>('motout');
@@ -583,7 +584,7 @@ export class synthesizer {
           return goOn(
             [
               [
-                motout, 
+                motout,
                 () => motive.check(
                   context,
                   r,
@@ -654,7 +655,7 @@ export class synthesizer {
   }
 
 
-  public static synthRecList(context: Context, r: Renaming, 
+  public static synthRecList(context: Context, r: Renaming,
     location: Location, target: S.Source, base: S.Source, step: S.Source,): Perhaps<C.The> {
     const tgtout = new PerhapsM<C.The>('tgtout');
     return goOn(
@@ -671,7 +672,7 @@ export class synthesizer {
             [
               [bout, () => base.synth(context, r)],
               [btval, () => new go(valInContext(context, bout.value.type))],
-              [sout, () => 
+              [sout, () =>
                 step.check(
                   context,
                   r,
@@ -742,7 +743,7 @@ export class synthesizer {
     return goOn(
       [
         [fstout, () => x.synth(context, r)],
-        [restout, () => 
+        [restout, () =>
           xs.check(
             context,
             r,
@@ -1014,7 +1015,7 @@ export class synthesizer {
           const [Av, fromv, tov] = [result.type, result.from, result.to];
           return goOn(
             [
-              [motout, () => 
+              [motout, () =>
                 motive.check(
                   context,
                   r,
@@ -1034,7 +1035,7 @@ export class synthesizer {
                 )
               ],
               [motv, () => new go(valInContext(context, motout.value))],
-              [baseout, () => 
+              [baseout, () =>
                 base.check(
                   context,
                   r,
@@ -1157,7 +1158,7 @@ export class synthesizer {
   }
 
   public static synthIndVec(context: Context, r: Renaming, location: Location,
-      length: S.Source, target: S.Source, motive: S.Source, base: S.Source, step: S.Source): Perhaps<C.The> {
+    length: S.Source, target: S.Source, motive: S.Source, base: S.Source, step: S.Source): Perhaps<C.The> {
     const lenout = new PerhapsM<C.Core>('lenout');
     const lenv = new PerhapsM<V.Value>('lenv');
     const vecout = new PerhapsM<C.The>('vecout');
@@ -1255,7 +1256,7 @@ export class synthesizer {
 
 
   public static synthIndEither(context: Context, r: Renaming, location: Location, target: S.Source,
-      motive: S.Source, baseLeft: S.Source, baseRight: S.Source,): Perhaps<C.The> {
+    motive: S.Source, baseLeft: S.Source, baseRight: S.Source,): Perhaps<C.The> {
     const tgtout = new PerhapsM<C.The>('tgtout');
     const motout = new PerhapsM<C.Core>('motout');
     const motval = new PerhapsM<V.Value>('motval');
@@ -1269,7 +1270,7 @@ export class synthesizer {
           const [Lv, Rv] = [result.leftType, result.rightType];
           return goOn(
             [
-              [motout, () => 
+              [motout, () =>
                 motive.check(
                   context,
                   r,
@@ -1360,7 +1361,7 @@ export class synthesizer {
             const argout = new PerhapsM<C.Core>('argout');
             return goOn(
               [[argout, () => arg.check(context, r, A)]],
-              () => 
+              () =>
                 new go(
                   new C.The(
                     c.valOfClosure(valInContext(context, argout.value)).readBackType(context),
@@ -1453,6 +1454,20 @@ export class synthesizer {
         if (result instanceof Define) {
           PieInfoHook(location, 'definition');
         }
+        // If it's an inductive datatype, return the type constructor, not a variable reference
+        if (result instanceof InductiveDatatypeBinder) {
+          const inductiveType = result.type;
+          return new go(
+            new C.The(
+              new C.Universe(),
+              new C.InductiveTypeConstructor(
+                inductiveType.name,
+                inductiveType.parameterTypes.map(p => p.readBackType(context)),
+                inductiveType.indexTypes.map(i => i.readBackType(context))
+              )
+            )
+          );
+        }
         return new go(
           new C.The(
             x_tv.value.readBackType(context),
@@ -1489,4 +1504,425 @@ export class synthesizer {
       );
     }
   }
-}
\ No newline at end of file
+
+  // ==================== INDUCTIVE DATATYPES ====================
+
+  /**
+   * Synthesize constructor application for user-defined inductive types
+   */
+  public static synthConstructorApplication(ctx: Context, r: Renaming, ctorApp: S.ConstructorApplication): Perhaps<C.The> {
+    // Look up constructor in context
+    const constructorBinder = ctx.get(ctorApp.constructorName);
+    if (!constructorBinder || !(constructorBinder instanceof ConstructorTypeBinder)) {
+      throw new Error(`Unknown constructor: ${ctorApp.constructorName}`);
+    }
+
+    const ctorType = constructorBinder.constructorType
+    const argTypes = ctorType.argTypes.concat(ctorType.rec_argTypes)
+
+    let cur_ctx = ctx
+    let cur_rename = r
+
+    if(argTypes.length !== ctorApp.args.length) {
+      return new stop(ctorApp.location,
+        new Message([`Expected ${argTypes.length} arguments, got ${ctorApp.args.length}`]));
+    }
+
+    const checkedArgs: C.Core[] = [];
+
+    // Build an environment for checking arguments
+    // For parameterized constructors, we need to bind type parameters first
+    let argCheckEnv = new Map(contextToEnvironment(ctx));
+
+    // First pass: check type parameters and build environment
+    const typeParamValues: V.Value[] = [];
+    for (let i = 0; i < ctorType.numTypeParams && i < ctorApp.args.length; i++) {
+      // Type parameter: should check against Universe
+      const argCheck = ctorApp.args[i].check(cur_ctx, cur_rename, new V.Universe());
+      if (argCheck instanceof stop) return argCheck;
+      const checkedArg = (argCheck as go<C.Core>).result;
+      checkedArgs.push(checkedArg);
+
+      // Store the actual type value
+      const paramValue = valInContext(ctx, checkedArg);
+      typeParamValues.push(paramValue);
+
+      // Try to extract parameter name from argTypes to bind in environment
+      // argTypes[i] for type params might be Universe or VarName
+      // We need to find VarNames in subsequent argTypes and bind them
+      const extractAndBindVarNames = (core: C.Core, value: V.Value) => {
+        if (core instanceof C.VarName) {
+          argCheckEnv.set(core.name, value);
+        }
+      };
+
+      // Look through remaining argTypes to find references to this parameter
+      for (let j = i + 1; j < argTypes.length; j++) {
+        if (argTypes[j] instanceof C.VarName) {
+          // This might be the parameter we just checked
+          // Bind it speculatively - if it's the wrong one, it won't match anyway
+          argCheckEnv.set((argTypes[j] as C.VarName).name, paramValue);
+        }
+      }
+    }
+
+    // Second pass: check remaining arguments with type parameters bound
+    for (let i = ctorType.numTypeParams; i < ctorApp.args.length; i++) {
+      // Regular argument: check against its type (evaluated with type params bound)
+      const argType = argTypes[i].valOf(argCheckEnv);
+      const argCheck = ctorApp.args[i].check(cur_ctx, cur_rename, argType);
+      if (argCheck instanceof stop) return argCheck;
+      const checkedArg = (argCheck as go<C.Core>).result;
+      checkedArgs.push(checkedArg);
+
+      // Bind this argument's value in the environment using its actual name
+      // Now we have argNames available from the constructor type!
+      if (i < ctorType.argNames.length) {
+        const argName = ctorType.argNames[i];
+        const argValue = valInContext(ctx, checkedArg);
+        argCheckEnv.set(argName, argValue);
+      }
+    }
+
+    // Compute the specific result type by substituting type parameters
+    let specificResultType: V.Value;
+
+    if (ctorType.numTypeParams > 0) {
+      // For parameterized constructors: substitute type parameters with actual values
+      // Build an environment where type parameter variables are bound to actual type values
+      const typeParamEnv = new Map(contextToEnvironment(ctx));
+
+      // The result type contains VarName references to type parameters (like 'E')
+      // We need to evaluate it in an environment where those are bound to the actual types
+      // Extract actual type parameter values
+      const typeParamValues: V.Value[] = [];
+      for (let i = 0; i < ctorType.numTypeParams; i++) {
+        typeParamValues.push(valInContext(ctx, checkedArgs[i]));
+      }
+
+      // Create environment with type parameters bound
+      // We need to know the NAMES of the type parameters from the constructor definition
+      // These names are embedded in the resultType as VarNames
+      // For MyList, resultType is: InductiveTypeConstructor('MyList', [VarName('E')], [])
+
+      // Extract VarNames from resultType to find parameter names
+      const extractVarNames = (core: C.Core): string[] => {
+        if (core instanceof C.VarName) return [core.name];
+        if (core instanceof C.InductiveTypeConstructor) {
+          // Extract from both parameters AND indices
+          return [
+            ...core.parameters.flatMap(p => extractVarNames(p)),
+            ...core.indices.flatMap(i => extractVarNames(i))
+          ];
+        }
+        if (core instanceof C.Add1) {
+          return extractVarNames(core.n);
+        }
+        return [];
+      };
+
+      const paramNames = extractVarNames(ctorType.resultType);
+
+      // Bind each parameter name to its actual value in a temporary environment
+      for (let i = 0; i < Math.min(paramNames.length, typeParamValues.length); i++) {
+        typeParamEnv.set(paramNames[i], typeParamValues[i]);
+      }
+
+      // Also bind all checked arguments (including non-type-parameter args like 'k' in MyVec)
+      // We need to bind ALL constructor arguments, not just type parameters
+      // Extract all arg type VarNames and bind them to corresponding checked values
+      const allArgNames: string[] = [];
+      for (let i = 0; i < argTypes.length; i++) {
+        const argVarNames = extractVarNames(argTypes[i]);
+        if (argVarNames.length === 0 && argTypes[i] instanceof C.VarName) {
+          // The argType itself might not contain VarNames, but we need its name
+          // Actually, we need to find the parameter NAME from the original constructor definition
+          // For now, let's just bind all checked argument values by index
+        }
+      }
+
+      // Bind each checked argument value to the environment
+      // We need to figure out the variable names for constructor arguments
+      // For myveccons: args are [E, k, head, tail]
+      // argTypes are [Universe, Nat, VarName('E'), InductiveTypeConstructor('MyVec', [VarName('E')], [VarName('k')])]
+      // We need to bind k -> checkedArgs[1] value
+      // The challenge is knowing that argTypes[1] corresponds to variable name 'k'
+
+      // Alternative approach: bind all checked args with sequential names or by extracting from Core
+      // Actually, the best approach is to evaluate the resultType with ALL arguments bound
+      // Let's find all VarNames in argTypes and bind them to checked argument values
+      const bindArgValue = (argTypeCore: C.Core, argIndex: number) => {
+        // This arg type might reference previous args by name
+        // We should have bound them already in argCheckEnv
+        // For the current arg, if we can determine its name, bind its value
+      };
+
+      // Simpler approach: extend typeParamEnv with all values from argCheckEnv that were bound
+      // during argument checking
+      for (const [name, value] of argCheckEnv) {
+        if (!typeParamEnv.has(name)) {
+          typeParamEnv.set(name, value);
+        }
+      }
+
+      // Now evaluate the result type with the substituted environment
+      specificResultType = ctorType.resultType.valOf(typeParamEnv);
+    } else {
+      // For non-parameterized constructors: still need to use argCheckEnv
+      // to bind any constructor arguments referenced in the result type
+      specificResultType = ctorType.resultType.valOf(argCheckEnv);
+    }
+
+    return new go(new C.The(
+      specificResultType.readBackType(ctx),
+      new C.Constructor(
+        ctorApp.constructorName,
+        ctorType.index,
+        ctorType.type,
+        checkedArgs.slice(0, ctorType.argTypes.length),
+        checkedArgs.slice(ctorType.argTypes.length)
+      )
+    ));
+
+  }
+
+  /**
+   * Synthesize eliminator application for user-defined inductive types
+   */
+  public static synthGeneralEliminator(ctx: Context, r: Renaming, elimApp: S.EliminatorApplication): Perhaps<C.The> {
+    // PHASE 1: Look up inductive datatype in context
+    const inductiveTypeResult = getInductiveType(ctx, elimApp.location, elimApp.typeName);
+    if (inductiveTypeResult instanceof stop) return inductiveTypeResult;
+
+    const inductiveBinder = (inductiveTypeResult as go<InductiveDatatypeBinder>).result;
+    const inductiveTypeValue = inductiveBinder.type; // V.InductiveType
+
+    // PHASE 2: Synthesize & Check Target
+    const targetSynth = elimApp.target.synth(ctx, r);
+    if (targetSynth instanceof stop) return targetSynth;
+
+    const targetThe = (targetSynth as go<C.The>).result;
+    const targetTypeValue = valInContext(ctx, targetThe.type);
+
+    // Verify target type matches the inductive type
+    if (!(targetTypeValue instanceof V.InductiveTypeConstructor) ||
+        targetTypeValue.name !== elimApp.typeName) {
+      return new stop(elimApp.location,
+        new Message([`Expected type ${elimApp.typeName}, got ${targetTypeValue.readBackType(ctx)}`]));
+    }
+
+    // PHASE 3: Generate & Check Motive Type
+    // Generate expected motive type: (Π [target : T] U)
+    let indexTypes = inductiveTypeValue.indexTypes
+    const buildMotive = (level: number, capturedIndices: V.Value[]): V.Value => {
+          if (level >= indexTypes.length) {
+            // Base case: build (Π [target : InductiveType(name, params, capturedIndices)] U)
+            return new V.Pi(
+              'target',
+              new V.InductiveTypeConstructor(targetTypeValue.name, targetTypeValue.parameters, capturedIndices),
+              new HigherOrderClosure(_ => new V.Universe())
+            );
+          }
+    
+          // Recursive case: build (Π [index : τ] ...)
+          const indexType = indexTypes[level];
+          return new V.Pi(
+            fresh(ctx, 'idx'),
+            indexType,
+            new HigherOrderClosure(indexVal =>
+              buildMotive(level + 1, [...capturedIndices, indexVal])
+            )
+          );
+        };
+    
+    const expectedMotiveType = buildMotive(0, [])
+
+    const motiveCheck = elimApp.motive.check(ctx, r, expectedMotiveType);
+    if (motiveCheck instanceof stop) return motiveCheck;
+
+    const motiveCore = (motiveCheck as go<C.Core>).result;
+    const motiveValue = valInContext(ctx, motiveCore);
+    const motiveTypeCore = expectedMotiveType.readBackType(ctx);  // Store motive type for Neutral handling
+
+    // PHASE 4: Get constructor types and check methods
+    const constructorTypes = this.getConstructorTypesForDatatype(ctx, elimApp.typeName);
+
+    if (elimApp.methods.length !== constructorTypes.length) {
+      return new stop(elimApp.location,
+        new Message([`Expected ${constructorTypes.length} methods, got ${elimApp.methods.length}`]));
+    }
+
+    const checkedMethods: C.Core[] = [];
+    const methodTypeCores: C.Core[] = [];  // Store method types as Core
+    for (let i = 0; i < elimApp.methods.length; i++) {
+      const expectedMethodType = this.generateMethodTypeForConstructor(
+        ctx,
+        constructorTypes[i],
+        motiveValue,
+        targetTypeValue.parameters
+      );
+
+      // Store the method type as Core for later use in evaluation
+      methodTypeCores.push(expectedMethodType.readBackType(ctx));
+
+      const methodCheck = elimApp.methods[i].check(ctx, r, expectedMethodType);
+      if (methodCheck instanceof stop) return methodCheck;
+
+      checkedMethods.push((methodCheck as go<C.Core>).result);
+    }
+
+    // PHASE 5: Compute Result Type & Build Core
+    // For indexed types, apply motive to indices first, then target
+    let resultType: V.Value = motiveValue;
+
+    // Apply to each index value from the target's type
+    for (const indexValue of targetTypeValue.indices) {
+      resultType = doApp(resultType, indexValue);
+    }
+
+    // Finally apply to the target value itself
+    resultType = doApp(resultType, valInContext(ctx, targetThe.expr));
+
+    const eliminatorCore = new C.Eliminator(
+      elimApp.typeName,
+      targetThe.expr,
+      motiveCore,
+      checkedMethods,
+      methodTypeCores,  // Pass method types for proper Neutral handling
+      motiveTypeCore  // Pass motive type for proper Neutral handling with indexed types
+    );
+
+    return new go(new C.The(
+      resultType.readBackType(ctx),
+      eliminatorCore
+    ));
+  }
+
+  /**
+   * Get constructor types for a datatype from context
+   */
+  private static getConstructorTypesForDatatype(ctx: Context, typeName: string): C.ConstructorType[] {
+    const constructorTypes: C.ConstructorType[] = [];
+
+    for (const [name, binder] of ctx) {
+      if (binder instanceof ConstructorTypeBinder) {
+        const ctor = binder.constructorType;
+        if (ctor.type === typeName) {
+          constructorTypes.push(binder.constructorType);
+        }
+      }
+    }
+
+    return constructorTypes.sort((a, b) => a.index - b.index);
+  }
+
+  /**
+   * Generate method type for a constructor
+   * Form: (Π [args...] (→ [IHs...] (P ctor)))
+   */
+  private static generateMethodTypeForConstructor(
+    ctx: Context,
+    ctorType: C.ConstructorType,
+    motiveValue: V.Value,
+    typeParams: V.Value[]
+  ): V.Value {
+    // Build environment with type parameters bound for evaluating argTypes
+    let argEnv = new Map(contextToEnvironment(ctx));
+
+    // Extract all VarNames from argTypes and rec_argTypes
+    const varNames = new Set<string>();
+    [...ctorType.argTypes, ...ctorType.rec_argTypes].forEach(at => {
+      if (at instanceof C.VarName) {
+        varNames.add(at.name);
+      }
+    });
+
+    // Bind each unique VarName to the corresponding type parameter
+    // Assumption: type parameters appear in order, and VarNames reference them by position
+    const varNameArray = Array.from(varNames);
+    for (let i = 0; i < varNameArray.length && i < typeParams.length; i++) {
+      argEnv.set(varNameArray[i], typeParams[i]);
+    }
+
+    // Build the result type: motive applied to constructor application
+    const allArgTypes = [
+      ...ctorType.argTypes.map(t => t.valOf(argEnv)),
+      ...ctorType.rec_argTypes.map(t => t.valOf(argEnv))
+    ];
+
+    const buildMethod = (level: number, capturedArgs: V.Value[]): V.Value => {
+          if (level >= allArgTypes.length) {
+            // All arguments captured, now add inductive hypotheses and result
+    
+            // Step 1: Add IHs for recursive arguments (in reverse order)
+            let result: V.Value;
+    
+            // First, build the result type: P applied to constructor
+            const ctorApp = new V.Constructor(
+              ctorType.name,
+              ctorType.type,
+              capturedArgs,
+              ctorType.index,
+              []  // Will be filled with recursive args
+            );
+    
+            // Extract result indices from ctorType.resultType
+            const resultType = valInContext(ctx, ctorType.resultType);
+            const resultIndices = extractIndicesFromValue(resultType);
+    
+            // Apply motive to indices and constructor
+            result = motiveValue;
+            for (const idx of resultIndices) {
+              result = doApp(result, idx);
+            }
+            result = doApp(result, ctorApp);
+    
+            // Step 2: Wrap with inductive hypotheses (for recursive args, in reverse)
+            const numNonRec = ctorType.argTypes.length;
+            for (let i = ctorType.rec_argTypes.length - 1; i >= 0; i--) {
+              const recArgIndex = numNonRec + i;
+              const recArg = capturedArgs[recArgIndex];
+              const recArgTypeValue = allArgTypes[recArgIndex];
+
+              // Build IH type: P(indices... recArg)
+              // The recursive arg type (e.g., Vec E k) when evaluated in context
+              // has its indices as Values that reference captured arguments
+              let ihType = motiveValue;
+              if (recArgTypeValue instanceof V.InductiveTypeConstructor) {
+                for (const idx of recArgTypeValue.indices) {
+                  ihType = doApp(ihType, idx);
+                }
+              }
+              ihType = doApp(ihType, recArg);
+
+              const currentResult = result;
+              result = new V.Pi(
+                `ih${i}`,
+                ihType,
+                new HigherOrderClosure(_ => currentResult)
+              );
+            }
+    
+            return result;
+          }
+    
+          // Recursive case: bind constructor argument
+          const argType = allArgTypes[level];
+          return new V.Pi(
+            `arg${level}`,
+            argType,
+            new HigherOrderClosure(argVal =>
+              buildMethod(level + 1, [...capturedArgs, argVal])
+            )
+          );
+        };
+    return buildMethod(0, []);
+  }
+}
+
+function extractIndicesFromValue(val: V.Value): V.Value[] {
+  if (val instanceof V.InductiveTypeConstructor) {
+    return val.indices;
+  }
+  return [];
+}
diff --git a/src/pie_interpreter/typechecker/utils.ts b/src/pie_interpreter/typechecker/utils.ts
index 316723e2..47cb84f4 100644
--- a/src/pie_interpreter/typechecker/utils.ts
+++ b/src/pie_interpreter/typechecker/utils.ts
@@ -8,19 +8,38 @@ import { go, stop, Perhaps, Message } from "../types/utils";
 import { alphaEquiv } from "../utils/alphaeqv";
 import { readBack } from "../evaluator/utils";
 import { inspect } from "util";
+import { todoQueue } from "../try_llm/todo_solver";
 
 
 type What = 'definition'
   | ['binding-site', Core]
   | ['is-type', Core]
   | ['has-type', Core]
-  | ['TODO', SerializableContext, Core];
+  | ['TODO', SerializableContext, Core, Renaming];
 
 
 // TODO: Implement PieInfoHook
 
 export function PieInfoHook(where: Location, what: What): void {
-
+  if (Array.isArray(what) && what[0] === 'TODO') {
+    const [_, serializedCtx, expectedTypeCore, renaming] = what;
+
+    // Reconstruct the actual Context from SerializableContext
+    // For now, we'll use a simpler approach - just pass empty context
+    // TODO: Properly deserialize SerializableContext to Context
+    const ctx = new Map();
+
+    // Convert Core type to Value for storage
+    const expectedTypeValue = expectedTypeCore.valOf(new Map());
+
+    // Queue for processing with real objects
+    todoQueue.push({
+      location: where,
+      context: ctx,
+      expectedType: expectedTypeValue,
+      renaming: renaming
+    });
+  }
 }
 
 export function SendPieInfo(where: Location, what: What): void {
@@ -96,4 +115,5 @@ function isAlphabetic(char: string): boolean {
 // Helper to concoct a function application form in source syntax
 export function makeApp(a: Source, b: Source, cs: Source[]): Source {
   return new Application(a.location, a, b, cs);
-}
\ No newline at end of file
+}
+
diff --git a/src/pie_interpreter/types/core.ts b/src/pie_interpreter/types/core.ts
index cf6cf729..3320829a 100644
--- a/src/pie_interpreter/types/core.ts
+++ b/src/pie_interpreter/types/core.ts
@@ -2,7 +2,7 @@ import * as V from "./value";
 import * as N from './neutral';
 
 import * as Evaluator from '../evaluator/evaluator';
-import { Environment, getValueFromEnvironment} from '../utils/environment';
+import { Environment, getValueFromEnvironment } from '../utils/environment';
 import { SourceLocation } from '../utils/locations';
 import { FirstOrderClosure, isVarName } from './utils';
 
@@ -254,7 +254,7 @@ export class Pi extends Core {
 
   public valOf(env: Environment): V.Value {
     const typeVal = this.type.toLazy(env);
-    return new V.Pi(this.name, typeVal, 
+    return new V.Pi(this.name, typeVal,
       new FirstOrderClosure(env, this.name, this.body)
     );
   }
@@ -278,7 +278,7 @@ export class Lambda extends Core {
   ) { super() }
 
   public valOf(env: Environment): V.Value {
-    return new V.Lambda(this.param, 
+    return new V.Lambda(this.param,
       new FirstOrderClosure(env, this.param, this.body));
   }
 
@@ -337,7 +337,7 @@ export class Sigma extends Core {
 
   public valOf(env: Environment): V.Value {
     const typeVal = this.type.toLazy(env);
-    return new V.Sigma(this.name, typeVal, 
+    return new V.Sigma(this.name, typeVal,
       new FirstOrderClosure(env, this.name, this.body));
   }
 
@@ -534,7 +534,7 @@ export class IndList extends Core {
 }
 
 export class Trivial extends Core {
-  
+
   public valOf(env: Environment): V.Value {
     return new V.Trivial();
   }
@@ -626,7 +626,7 @@ export class Equal extends Core {
   public prettyPrint(): string {
     return `(= ${this.type.prettyPrint()} 
               ${this.left.prettyPrint()} 
-              ${this.right.prettyPrint()})`;  
+              ${this.right.prettyPrint()})`;
   }
 
   public toString(): string {
@@ -754,7 +754,7 @@ export class Symm extends Core {
 }
 
 export class IndEqual extends Core {
-  
+
   constructor(
     public target: Core,
     public motive: Core,
@@ -789,7 +789,7 @@ export class Vec extends Core {
 
   public valOf(env: Environment): V.Value {
     return new V.Vec(
-      this.type.toLazy(env), 
+      this.type.toLazy(env),
       this.length.toLazy(env)
     );
   }
@@ -937,7 +937,7 @@ export class Either extends Core {
   public toString(): string {
     return this.prettyPrint();
   }
-  
+
 }
 
 export class Left extends Core {
@@ -1080,4 +1080,153 @@ export class VarName extends Core {
     return this.prettyPrint();
   }
 
-}
\ No newline at end of file
+}
+
+export class InductiveTypeConstructor extends Core {
+  public valOf(env: Environment): V.Value {
+    return new V.InductiveTypeConstructor(
+      this.typeName,
+      this.parameters.map(p => p.toLazy(env)),
+      this.indices.map(i => i.toLazy(env)),
+    );
+  }
+  constructor(
+    public typeName: string,
+    public parameters: Core[],
+    public indices: Core[],
+  ) { super(); }
+
+  public prettyPrint(): string {
+    return `${this.typeName}${this.parameters.length > 0 ? ' ' + this.parameters.map(p => p.prettyPrint()).join(' ') : ''}${this.indices.length > 0 ? ' ' + this.indices.map(i => i.prettyPrint()).join(' ') : ''}`;
+  }
+
+  public toString(): string {
+    return this.prettyPrint();
+  }
+}
+
+export class InductiveType extends Core {
+  public valOf(env: Environment): V.Value {
+    return new V.InductiveType(
+      this.typeName,
+      this.parameterTypes.map(p => p.toLazy(env)),
+      this.indexTypes.map(i => i.toLazy(env)),
+    );
+  }
+  constructor(
+    public typeName: string,
+    public parameterTypes: Core[],
+    public indexTypes: Core[],
+  ) { super(); }
+
+  public prettyPrint(): string {
+    return `${this.typeName}${this.parameterTypes.length > 0 ? ' ' + this.parameterTypes.map(p => p.prettyPrint()).join(' ') : ''}${this.indexTypes.length > 0 ? ' ' + this.indexTypes.map(i => i.prettyPrint()).join(' ') : ''}`;
+  }
+}
+
+export class Constructor extends Core {
+
+  constructor(
+    public name: string,
+    public index: number,
+    public type: string,
+    public args: Core[],
+    public recursive_args: Core[]
+  ) { super(); }
+
+  public valOf(env: Environment): V.Constructor {
+    return new V.Constructor(
+      this.name,
+      this.type,
+      this.args.map(a => a.toLazy(env)),
+      this.index,
+      this.recursive_args.map(a => a.toLazy(env))
+    )
+  }
+
+  public prettyPrint(): string {
+    const args = this.args.map(a => a.prettyPrint()).join(' ');
+    return `(${this.name}${args.length > 0 ? ' ' + args : ''})`;
+  }
+}
+
+export class ConstructorType extends Core {
+
+  constructor(
+    public name: string,
+    public index: number,
+    public type: string,
+    public argTypes: Core[],
+    public rec_argTypes: Core[],
+    public resultType: Core,
+    public numTypeParams: number = 0,  // Number of leading args that are type parameters
+    public argNames: string[] = []  // Names of ALL arguments (for binding during instantiation)
+  ) { super(); }
+
+  public valOf(env: Environment): V.Value {
+    return new V.ConstructorType(
+      this.name,
+      this.index,
+      this.type,
+      this.argTypes.map(a => a.toLazy(env)),
+      this.rec_argTypes.map(a => a.toLazy(env)),
+      this.resultType,
+      this.numTypeParams,
+      this.argNames
+    )
+  }
+
+  public prettyPrint(): string {
+    return `ConstructorType ${this.name} : ${this.argTypes.map(a => a.prettyPrint()).join(' -> ')} -> ${this.resultType.prettyPrint()}`;
+  }
+}
+
+export class Eliminator extends Core {
+
+  constructor(
+    public typeName: string,
+    public target: Core,
+    public motive: Core,
+    public methods: Core[],
+    public methodTypes?: Core[],  // Optional: method types for proper Neutral handling
+    public motiveType?: Core  // Optional: motive type for proper Neutral handling with indexed types
+  ) { super(); }
+
+  public valOf(env: Environment): V.Value {
+    return Evaluator.doEliminator(
+      this.typeName,
+      this.target.toLazy(env),
+      this.motive.toLazy(env),
+      this.methods.map(m => m.toLazy(env)),
+      this.methodTypes ? this.methodTypes.map(t => t.toLazy(env)) : undefined,
+      this.motiveType ? this.motiveType.toLazy(env) : undefined
+    );
+  }
+  public prettyPrint(): string {
+    const methods = this.methods.map(m => m.prettyPrint()).join(' ');
+    return `(elim-${this.typeName} ${this.target.prettyPrint()} ${this.motive.prettyPrint()} ${methods})`;
+  }
+}
+
+export class EliminatorType extends Core {
+
+  constructor(
+    public typeName: string,
+    public targetType: Core,
+    public motiveType: Core,
+    public methodTypes: Core[]
+  ) { super(); }
+
+  public valOf(env: Environment): V.Value {
+    return new V.EliminatorType(
+      this.typeName,
+      this.targetType.toLazy(env),
+      this.motiveType.toLazy(env),
+      this.methodTypes.map(m => m.toLazy(env))
+    );
+  }
+
+  public prettyPrint(): string {
+    return `EliminatorType ${this.typeName} ${this.targetType.prettyPrint()} ${this.motiveType.prettyPrint()} ${this.methodTypes.map(m => m.prettyPrint()).join(' ')}`;
+  }
+}
diff --git a/src/pie_interpreter/types/neutral.ts b/src/pie_interpreter/types/neutral.ts
index c567acdb..63f6e3ef 100644
--- a/src/pie_interpreter/types/neutral.ts
+++ b/src/pie_interpreter/types/neutral.ts
@@ -517,6 +517,31 @@ export class IndEither extends Neutral {
   }
 }
 
+export class GenericEliminator extends Neutral {
+
+  constructor(
+    public typeName: string,
+    public target: Neutral,
+    public motive: Norm,
+    public methods: Norm[]
+  ) {
+    super();
+  }
+
+  public readBackNeutral(context: Context): C.Core {
+    return new C.Eliminator(
+      this.typeName,
+      this.target.readBackNeutral(context),
+      readBack(context, this.motive.type, this.motive.value),
+      this.methods.map(method => readBack(context, method.type, method.value))
+    );
+  }
+
+  public prettyPrint() {
+    return `N-GenericEliminator-${this.typeName}`;
+  }
+}
+
 export class Application extends Neutral {
 
   constructor(public operator: Neutral, public operand: Norm) {
diff --git a/src/pie_interpreter/types/source.ts b/src/pie_interpreter/types/source.ts
index fbfbbc0a..de0d1910 100644
--- a/src/pie_interpreter/types/source.ts
+++ b/src/pie_interpreter/types/source.ts
@@ -5,7 +5,7 @@ import * as S from './source';
 
 import { PieInfoHook, Renaming, SendPieInfo, extendRenaming, makeApp, rename} from '../typechecker/utils';
 import { Location, notForInfo } from '../utils/locations';
-import { bindFree, Context, readBackContext, valInContext } from '../utils/context';
+import { bindFree, Context, readBackContext, valInContext, getInductiveType, InductiveDatatypeBinder, ConstructorTypeBinder, EliminatorBinder, contextToEnvironment } from '../utils/context';
 
 import { go, stop, goOn, occurringBinderNames, Perhaps, 
   PerhapsM, SiteBinder, TypedBinder, Message, freshBinder, 
@@ -1907,7 +1907,7 @@ export class TODO extends Source {
 
   public checkOut(ctx: Context, renames: Renaming, type: V.Value): Perhaps<C.Core> {
     const typeVal = type.readBackType(ctx);
-    SendPieInfo(this.location, ['TODO', readBackContext(ctx), typeVal]);
+    SendPieInfo(this.location, ['TODO', readBackContext(ctx), typeVal, renames]);
     return new go(new C.TODO(this.location.locationToSrcLoc(), typeVal));
   }
 
@@ -1929,7 +1929,7 @@ export class Application extends Source {
     public arg: Source,
     public args: Source[],
   ) { super(location); }
-  
+
   protected synthHelper(ctx: Context, renames: Renaming): Perhaps<C.The> {
     return Synth.synthApplication(ctx, renames, this.location, this.func, this.arg, this.args);
   }
@@ -1947,4 +1947,242 @@ export class Application extends Source {
   public toString(): string {
     return this.prettyPrint();
   }
+
+  // Override getType to handle inductive type applications
+  public getType(ctx: Context, renames: Renaming): Perhaps<C.Core> {
+    // Check if func is a Name referring to an inductive type
+    if (this.func instanceof Name) {
+      const funcName = this.func.name;
+      const binder = ctx.get(funcName);
+
+      // If it's an inductive type, treat this as a GeneralTypeConstructor application
+      if (binder instanceof InductiveDatatypeBinder) {
+        // Create a GeneralTypeConstructor with the indices from args
+        const allArgs = [this.arg, ...this.args];
+        const generalTypeCtor = new GeneralTypeConstructor(
+          this.location,
+          funcName,
+          [], // parameters - will be inferred from context
+          allArgs
+        );
+        return generalTypeCtor.getType(ctx, renames);
+      }
+    }
+
+    // Otherwise, use default behavior (check against Universe)
+    return super.getType(ctx, renames);
+  }
+}
+
+export class GeneralType extends Source {
+  constructor(
+    public location: Location,
+    public name: string,
+    public paramType: TypedBinder[],
+    public indicesType: TypedBinder[]
+  ) {super(location)}
+
+  public findNames(): string[] {
+    throw new Error('Method not implemented.');
+  }
+  public prettyPrint(): string {
+    throw new Error('Method not implemented.');
+  }
+  protected synthHelper(ctx: Context, renames: Renaming): Perhaps<C.The> {
+    throw new Error('Method not implemented.');
+  }
+
+  public getType(ctx: Context, rename: Renaming): Perhaps<C.Core> {
+
+    let cur_ctx = ctx
+    let cur_rename = rename 
+    let normalizedParamType = []
+    let normalizedIndicesType = []
+    for (let i = 0; i < this.paramType.length; i++) {
+      const fresh_name = fresh(cur_ctx, this.paramType[i].binder.varName)
+      const resultTemp = this.paramType[i].type.isType(cur_ctx, cur_rename)
+      cur_rename = extendRenaming(cur_rename, this.paramType[i].binder.varName, fresh_name)
+      if (resultTemp instanceof stop) {
+        return resultTemp
+      } 
+      cur_ctx = bindFree(cur_ctx, fresh_name,
+        valInContext(cur_ctx, (resultTemp as go<C.Core>).result)
+      )
+      normalizedParamType.push((resultTemp as go<C.Core>).result)
+    }
+    for (let i = 0; i < this.indicesType.length; i++) {
+      const fresh_name = fresh(cur_ctx, this.indicesType[i].binder.varName)
+      const resultTemp = this.indicesType[i].type.isType(cur_ctx, cur_rename)
+      cur_rename = extendRenaming(cur_rename, this.indicesType[i].binder.varName, fresh_name)
+      if (resultTemp instanceof stop) {
+        return resultTemp
+      } 
+      cur_ctx = bindFree(cur_ctx, fresh_name,
+        valInContext(cur_ctx, (resultTemp as go<C.Core>).result)
+      )
+      normalizedIndicesType.push((resultTemp as go<C.Core>).result)
+    }
+
+    return new go(new C.InductiveType(this.name, normalizedParamType, normalizedIndicesType))
+
+
+  }
+
+}
+
+export class GeneralTypeConstructor extends Source {
+  public findNames(): string[] {
+    throw new Error('Method not implemented.');
+  }
+  public prettyPrint(): string {
+    throw new Error('Method not implemented.');
+  }
+  protected synthHelper(ctx: Context, renames: Renaming): Perhaps<C.The> {
+    throw new Error('Method not implemented.');
+  }
+  constructor(
+    public location: Location,
+    public name: string,
+    public params: S.Source[],
+    public indices: S.Source[]
+  ) { super(location) }
+
+  public getType(ctx: Context, renames: Renaming): Perhaps<C.Core> {
+    // GeneralTypeConstructor represents an applied inductive type, which has type Universe
+    // First verify that the inductive type exists and check parameters/indices
+    const inductiveResult = getInductiveType(ctx, this.location, this.name);
+    if (inductiveResult instanceof stop) return inductiveResult;
+
+    const inductiveBinder = (inductiveResult as go<InductiveDatatypeBinder>).result;
+    const inductiveType = inductiveBinder.type;
+
+    // Check that parameter and index counts match
+    if (this.params.length !== inductiveType.parameterTypes.length ||
+        this.indices.length !== inductiveType.indexTypes.length) {
+      return new stop(this.location,
+        new Message(['Parameter/index count mismatch for type ' + this.name]));
+    }
+
+    // Check each parameter and index and collect their Core representations
+    const normalizedParams: C.Core[] = [];
+    for (let i = 0; i < this.params.length; i++) {
+      const paramCheck = this.params[i].check(ctx, renames, inductiveType.parameterTypes[i].now());
+      if (paramCheck instanceof stop) return paramCheck;
+      normalizedParams.push((paramCheck as go<C.Core>).result);
+    }
+
+    const normalizedIndices: C.Core[] = [];
+    for (let i = 0; i < this.indices.length; i++) {
+      const indexCheck = this.indices[i].check(ctx, renames, inductiveType.indexTypes[i].now());
+      if (indexCheck instanceof stop) return indexCheck;
+      normalizedIndices.push((indexCheck as go<C.Core>).result);
+    }
+
+    // Return the InductiveTypeConstructor expression itself
+    return new go(new C.InductiveTypeConstructor(this.name, normalizedParams, normalizedIndices));
+  }
+
+  public checkOut(ctx: Context, renames: Renaming, target: V.Value): Perhaps<C.Core> {
+    let cur_val = target.now()
+    let cur_ctx = ctx
+    let cur_rename = renames
+    let normalized_params = []
+    let normalized_indices = []
+
+    //TODO: verify name sameness check is not necessary
+
+    if(!(cur_val instanceof V.InductiveType)) {
+      return new stop(this.location, new Message(['target type is not user defined inductive type, or use the wrong type']))
+    }
+
+    const targetType: V.InductiveType = cur_val as V.InductiveType
+    let paramTypes = targetType.parameterTypes
+    let idxTypes = targetType.indexTypes
+
+    if((this.params.length != paramTypes.length) || (this.indices.length != idxTypes.length)) {
+      return new stop(this.location, new Message(['the number of parameters/indices is inconsistent in constructor']))
+    }
+
+    for (let i = 0; i < this.params.length; i++) {
+      const result = this.params[i].check(ctx, renames, paramTypes[i].now())
+      if (result instanceof stop) {
+        return stop
+      }
+      normalized_params.push((result as go<C.Core>).result)
+    }
+
+    for (let i = 0; i < this.indices.length; i++) {
+      const result = this.indices[i].check(ctx, renames, idxTypes[i].now())
+      if (result instanceof stop) {
+        return stop
+      }
+      normalized_indices.push((result as go<C.Core>).result)
+    }
+
+    return new go(new C.InductiveTypeConstructor(this.name, normalized_params, normalized_indices))
+
+  }
+}
+
+export class GeneralEliminator extends Source {
+  public findNames(): string[] {
+    throw new Error('Method not implemented.');
+  }
+  public prettyPrint(): string {
+    throw new Error('Method not implemented.');
+  }
+  protected synthHelper(ctx: Context, renames: Renaming): Perhaps<C.The> {
+    throw new Error('Method not implemented.');
+  }
+
+}
+
+// Generic eliminator application for user-defined inductive types
+export class EliminatorApplication extends Source {
+  constructor(
+    public location: Location,
+    public typeName: string,      // e.g., "MyList", "Bool"
+    public target: Source,         // The value to eliminate
+    public motive: Source,         // The motive function
+    public methods: Source[]       // One method per constructor
+  ) { super(location); }
+
+  public findNames(): string[] {
+    return [this.typeName]
+      .concat(this.target.findNames())
+      .concat(this.motive.findNames())
+      .concat(this.methods.flatMap(m => m.findNames()));
+  }
+
+  public prettyPrint(): string {
+    const methods = this.methods.map(m => m.prettyPrint()).join(' ');
+    return `(elim-${this.typeName} ${this.target.prettyPrint()} ${this.motive.prettyPrint()} ${methods})`;
+  }
+
+  protected synthHelper(ctx: Context, renames: Renaming): Perhaps<C.The> {
+    return Synth.synthGeneralEliminator(ctx, renames, this);
+  }
+}
+
+// Constructor application for user-defined inductive types
+export class ConstructorApplication extends Source {
+  constructor(
+    public location: Location,
+    public constructorName: string,
+    public args: Source[]
+  ) { super(location); }
+
+  public findNames(): string[] {
+    return [this.constructorName]
+      .concat(this.args.flatMap(a => a.findNames()));
+  }
+
+  public prettyPrint(): string {
+    const args = this.args.map(a => a.prettyPrint()).join(' ');
+    return `(${this.constructorName}${args.length > 0 ? ' ' + args : ''})`;
+  }
+
+  protected synthHelper(ctx: Context, renames: Renaming): Perhaps<C.The> {
+    return Synth.synthConstructorApplication(ctx, renames, this);
+  }
 }
\ No newline at end of file
diff --git a/src/pie_interpreter/types/utils.ts b/src/pie_interpreter/types/utils.ts
index 6f878c4d..97b3ae87 100644
--- a/src/pie_interpreter/types/utils.ts
+++ b/src/pie_interpreter/types/utils.ts
@@ -14,6 +14,10 @@ export class SiteBinder {
     public location: Location,
     public varName: string,
   ) { }
+
+  public prettyPrint(): string {
+    return `${this.varName}`;
+  }
 }
 
 // Define TypedBinder, which is a SiteBinder associated with a expression in Pie.
@@ -23,6 +27,14 @@ export class TypedBinder {
     public binder: SiteBinder,
     public type: Source,
   ) {}
+
+  public prettyPrint(): string {
+    return `${this.binder.prettyPrint()} : ${this.type.prettyPrint()}`;
+  }
+
+  public findNames(): string {
+    return this.binder.varName;
+  }
 }
 
 export function isPieKeywords(str : string) : boolean {
@@ -209,7 +221,7 @@ export class HigherOrderClosure extends Closure {
   }
 
   public prettyPrint(): string {
-    return `(HOCLOS)`;
+    return this.proc.toString();
   }
 
   public toString(): string {
diff --git a/src/pie_interpreter/types/value.ts b/src/pie_interpreter/types/value.ts
index ac428f86..bab64868 100644
--- a/src/pie_interpreter/types/value.ts
+++ b/src/pie_interpreter/types/value.ts
@@ -621,4 +621,159 @@ export class Absurd extends Value {
     return this.prettyPrint();
   }
   
-}
\ No newline at end of file
+}
+
+export class InductiveTypeConstructor extends Value {
+  constructor(
+    public name: string,
+    public parameters: Value[],
+    public indices: Value[],
+  ) { super() }
+
+  public readBackType(context: Context): C.Core {
+    return new C.InductiveTypeConstructor(
+      this.name,
+      this.parameters.map(p => p.readBackType(context)),
+      this.indices.map(i => {
+        // Check if this is a Delay that hasn't been forced yet
+        if (i instanceof Delay) {
+          const boxContent = i.val.get();
+          if (boxContent instanceof DelayClosure) {
+            // It's a closure - try to force it, but if it fails, return the Core expression directly
+            try {
+              const iNow = i.now();
+              if (iNow instanceof Neutral) {
+                return iNow.neutral.readBackNeutral(context);
+              } else {
+                return readBack(context, new Nat(), iNow);
+              }
+            } catch (e) {
+              // If evaluation fails due to free variables, return the Core expression as-is
+              // This preserves VarNames and other constructs
+              return boxContent.expr;
+            }
+          } else {
+            // Already evaluated
+            const val = boxContent as Value;
+            if (val instanceof Neutral) {
+              return val.neutral.readBackNeutral(context);
+            } else {
+              return readBack(context, new Nat(), val);
+            }
+          }
+        } else {
+          // Not a Delay
+          const iNow = i.now();
+          if (iNow instanceof Neutral) {
+            return iNow.neutral.readBackNeutral(context);
+          } else {
+            return readBack(context, new Nat(), iNow);
+          }
+        }
+      }),
+    )
+  }
+
+  public prettyPrint(): string {
+    return `InductiveType ${this.name}`;
+  }
+
+  public toString(): string {
+    return this.prettyPrint();
+  }
+}
+
+export class InductiveType extends Value {
+  constructor(
+    public name: string,
+    public parameterTypes: Value[],
+    public indexTypes: Value[],
+  ) { super() }
+
+  public readBackType(context: Context): C.Core {
+    return new C.InductiveType(
+      this.name,
+      this.parameterTypes.map(p => p.readBackType(context)),
+      this.indexTypes.map(i => i.readBackType(context)),
+    )
+  }
+
+  public prettyPrint(): string {
+    return `InductiveType ${this.name}`;
+  }
+
+  public toString(): string {
+    return this.prettyPrint();
+  }
+}
+
+export class Constructor extends Value {
+
+  constructor(
+    public name: string,
+    public type: string,
+    public args: Value[],
+    public index: number,
+    public recursive_args: Value[],
+  ) { super() }
+
+  public readBackType(context: Context): C.Core {
+    throw new Error("No readBackType for Constructor.");
+  }
+
+  public prettyPrint(): string {
+    const args = this.args.map(a => a.prettyPrint()).join(' ');
+    return `(${this.name}${args.length > 0 ? ' ' + args : ''})`;
+  }
+
+  public toString(): string {
+    return this.prettyPrint();
+  }
+}
+
+export class ConstructorType extends Value {
+  constructor(
+    public name: string,
+    public index: number,
+    public type: string,
+    public argTypes: Value[],
+    public rec_argTypes: Value[],
+    public resultType: C.Core,
+    public numTypeParams: number = 0,  // Number of leading args that are type parameters
+    public argNames: string[] = []  // Names of ALL arguments (for binding during instantiation)
+
+  ) {super()}
+  public readBackType(context: Context): C.Core {
+    throw Error('Method not implemented')
+  }
+  public prettyPrint(): string {
+    return `ConstructorType (${this.argTypes.map(a => a.prettyPrint()).join(' ')})`;
+  }
+
+}
+
+export class EliminatorType extends Value {
+  constructor(
+    public typeName: string,
+    public targetType: Value,
+    public motiveType: Value,
+    public methodTypes: Value[]
+  ) { super(); }
+
+  public readBackType(context: Context): C.Core {
+    return new C.EliminatorType(
+      this.typeName,
+      this.targetType.readBackType(context),
+      this.motiveType.readBackType(context),
+      this.methodTypes.map(m => m.readBackType(context))
+    );
+  }
+
+  public prettyPrint(): string {
+    return `EliminatorType ${this.typeName} ${this.targetType.prettyPrint()} ${this.motiveType.prettyPrint()} ${this.methodTypes.map(m => m.prettyPrint()).join(' ')}`;
+  }
+
+  public toString(): string {
+    return this.prettyPrint();
+  }
+}
diff --git a/src/pie_interpreter/utils/alphaeqv.ts b/src/pie_interpreter/utils/alphaeqv.ts
index b2c4e7c9..537ff178 100644
--- a/src/pie_interpreter/utils/alphaeqv.ts
+++ b/src/pie_interpreter/utils/alphaeqv.ts
@@ -242,6 +242,18 @@ function alphaEquivAux(lvl: number, b1: Bindings, b2: Bindings, e1: C.Core, e2:
       alphaEquivAux(lvl, b1, b2, e1.baseRight, e2.baseRight);
   } else if (e1 instanceof C.TODO && e2 instanceof C.TODO) {
     return sameLocation(e1.loc, e2.loc) && alphaEquivAux(lvl, b1, b2, e1.type, e2.type);
+  } else if (e1 instanceof C.InductiveTypeConstructor && e2 instanceof C.InductiveTypeConstructor) {
+    // Check that names match and parameters/indices are alpha-equivalent
+    if (e1.typeName !== e2.typeName) return false;
+    if (e1.parameters.length !== e2.parameters.length) return false;
+    if (e1.indices.length !== e2.indices.length) return false;
+    for (let i = 0; i < e1.parameters.length; i++) {
+      if (!alphaEquivAux(lvl, b1, b2, e1.parameters[i], e2.parameters[i])) return false;
+    }
+    for (let i = 0; i < e1.indices.length; i++) {
+      if (!alphaEquivAux(lvl, b1, b2, e1.indices[i], e2.indices[i])) return false;
+    }
+    return true;
   }
   // if none of the above cases are met, return false.
   else {
diff --git a/src/pie_interpreter/utils/context.ts b/src/pie_interpreter/utils/context.ts
index 936aa6cb..159e5eea 100644
--- a/src/pie_interpreter/utils/context.ts
+++ b/src/pie_interpreter/utils/context.ts
@@ -1,13 +1,14 @@
 import * as C from '../types/core';
-import { Neutral, Value } from '../types/value';
+import { InductiveType, Neutral, Universe, Value, Constructor, InductiveTypeConstructor } from '../types/value';
 
 import { Location } from './locations';
 import { go, stop, Perhaps, goOn, PerhapsM, Message } from '../types/utils';
 import { Environment } from './environment';
 import { readBack } from '../evaluator/utils';
-import { Source } from '../types/source';
+import { Source} from '../types/source';
 import { Variable } from '../types/neutral';
 import { inspect } from 'util';
+import { Eliminator } from '../types/core';
 /*
     ## Contexts ##
     A context maps free variable names to binders.
@@ -128,11 +129,21 @@ export function contextToEnvironment(ctx: Context): Environment {
       env.set(name, binder.value);
     } else if (binder instanceof Free) {
       env.set(name, new Neutral(binder.type, new Variable(name)));
+    } else if (binder instanceof InductiveDatatypeBinder) {
+      env.set(name, binder.type);
     } // else continue;
   }
   return env;
 }
 
+export function getInductiveType(ctx: Context, where: Location, name:string): Perhaps<InductiveDatatypeBinder> {
+  for (const [n, binder] of ctx) {
+    if (binder instanceof InductiveDatatypeBinder && n === name) {
+      return new go(binder);
+    }
+  }
+  return new stop(where, new Message([`No inductive type found for ${name} at ${where}`]));
+}
 
 export const initCtx: Context = new Map();
 
@@ -159,6 +170,32 @@ export class Free extends Binder {
   constructor(public type: Value) { super() }
 }
 
+export class InductiveDatatypeBinder extends Binder {
+  constructor(
+    public name: string, 
+    public type: InductiveType) {
+      super()
+    }
+}
+
+export class ConstructorTypeBinder extends Binder {
+  constructor(
+    public name: string,
+    public constructorType: C.ConstructorType,
+    public type: InductiveTypeConstructor
+  ) {
+      super()
+    }
+}
+
+export class EliminatorBinder extends Binder {
+  constructor(
+    public name: string, 
+    public type: Value) {
+      super()
+    }
+}
+
 export function varType(ctx: Context, where: Location, x: string): Perhaps<Value> {
   if (ctx.size === 0) {
     throw new Error(`The context ${JSON.stringify(ctx)} is empty, but we are looking for ${x}`);
@@ -167,6 +204,10 @@ export function varType(ctx: Context, where: Location, x: string): Perhaps<Value
     if (binder instanceof Claim) {
       continue;
     } else if (x === y) {
+      // Inductive datatypes have type Universe
+      if (binder instanceof InductiveDatatypeBinder) {
+        return new go(new Universe());
+      }
       return new go(binder.type);
     }
   }
diff --git a/test_eliminator_simple.ts b/test_eliminator_simple.ts
new file mode 100644
index 00000000..5e810e40
--- /dev/null
+++ b/test_eliminator_simple.ts
@@ -0,0 +1,90 @@
+import 'jest';
+import * as S from './src/pie_interpreter/types/source';
+import * as V from './src/pie_interpreter/types/value';
+import * as C from './src/pie_interpreter/types/core';
+import { Location, Syntax } from './src/pie_interpreter/utils/locations';
+import { Position } from './src/scheme_parser/transpiler/types/location';
+import { DefineDatatypeSource, handleDefineDatatype, makeConstructorSpec, makeTypedBinder, GeneralConstructor } from './src/pie_interpreter/typechecker/definedatatype';
+import { Context, contextToEnvironment } from './src/pie_interpreter/utils/context';
+import { go, stop } from './src/pie_interpreter/types/utils';
+
+// Test location
+const testLoc = new Location(new Syntax(new Position(1, 1), new Position(1, 1), 'test'), false);
+
+describe("Simple Eliminator Test", () => {
+  it("should define Bool and create an eliminator", () => {
+    const ctx: Context = new Map();
+
+    // Create Bool datatype with simple constructors
+    const trueConstructor = new GeneralConstructor(
+      testLoc,
+      "true",
+      [],
+      new S.GeneralTypeConstructor(testLoc, "Bool", [], [])
+    );
+
+    const falseConstructor = new GeneralConstructor(
+      testLoc,
+      "false",
+      [],
+      new S.GeneralTypeConstructor(testLoc, "Bool", [], [])
+    );
+
+    const boolDatatype = new DefineDatatypeSource(
+      testLoc,
+      "Bool",
+      [],
+      new S.Pi(testLoc, [], new S.Universe(testLoc)),
+      [trueConstructor, falseConstructor]
+    );
+
+    // Handle the datatype definition
+    const result = handleDefineDatatype(ctx, new Map(), boolDatatype);
+    expect(result).toBeInstanceOf(go);
+
+    if (result instanceof stop) {
+      throw new Error(`Failed to define Bool: ${result.message}`);
+    }
+
+    const updatedCtx = (result as go<Context>).result;
+
+    // Verify everything was added to context
+    console.log("Context keys:", Array.from(updatedCtx.keys()));
+    expect(updatedCtx.has("Bool")).toBe(true);
+    expect(updatedCtx.has("true")).toBe(true);
+    expect(updatedCtx.has("false")).toBe(true);
+    expect(updatedCtx.has("elim-Bool")).toBe(true);
+
+    // Create constructor applications
+    const trueSource = new S.ConstructorApplication(testLoc, "true", []);
+    const falseSource = new S.ConstructorApplication(testLoc, "false", []);
+
+    // Test synthesis
+    const trueSynth = trueSource.synth(updatedCtx, new Map());
+    const falseSynth = falseSource.synth(updatedCtx, new Map());
+
+    expect(trueSynth).toBeInstanceOf(go);
+    expect(falseSynth).toBeInstanceOf(go);
+
+    // Create eliminator
+    const eliminator = new S.EliminatorApplication(
+      testLoc,
+      "Bool",
+      trueSource,
+      new S.Nat(testLoc),
+      [new S.Zero(testLoc), new S.Add1(testLoc, new S.Zero(testLoc))]
+    );
+
+    // Test eliminator synthesis
+    const elimSynth = eliminator.synth(updatedCtx, new Map());
+    console.log("Eliminator synthesis result:", elimSynth);
+
+    if (elimSynth instanceof stop) {
+      console.error("Eliminator failed:", elimSynth.message);
+    }
+
+    expect(elimSynth).toBeInstanceOf(go);
+
+    console.log("✅ Bool eliminator test passed!");
+  });
+});
diff --git a/yarn.lock b/yarn.lock
index bb1c716a..9f3af54e 100644
--- a/yarn.lock
+++ b/yarn.lock
@@ -980,7 +980,7 @@
     minimatch "^3.1.2"
     strip-json-comments "^3.1.1"
 
-"@eslint/js@9.22.0", "@eslint/js@^9.15.0":
+"@eslint/js@^9.15.0", "@eslint/js@9.22.0":
   version "9.22.0"
   resolved "https://registry.npmjs.org/@eslint/js/-/js-9.22.0.tgz"
   integrity sha512-vLFajx9o8d1/oL2ZkpMYbkLv8nDB6yaIwFNt7nI4+I80U/z03SxmfOMsLbvWr3p7C+Wnoh//aOu2pQW8cS0HCQ==
@@ -998,6 +998,19 @@
     "@eslint/core" "^0.12.0"
     levn "^0.4.1"
 
+"@google/genai@^1.25.0":
+  version "1.25.0"
+  resolved "https://registry.npmjs.org/@google/genai/-/genai-1.25.0.tgz"
+  integrity sha512-IBNyel/umavam98SQUfvQSvh/Rp6Ql2fysQLqPyWZr5K8d768X9AO+JZU4o+3qvFDUBA0dVYUSkxyYonVcICvA==
+  dependencies:
+    google-auth-library "^9.14.2"
+    ws "^8.18.0"
+
+"@google/generative-ai@^0.24.1":
+  version "0.24.1"
+  resolved "https://registry.npmjs.org/@google/generative-ai/-/generative-ai-0.24.1.tgz"
+  integrity sha512-MqO+MLfM6kjxcKoy0p1wRzG3b4ZZXtPI+z2IE26UogS2Cm/XHO+7gGRBh6gcJsOiIVoH93UwKvW4HdgiOZCy9Q==
+
 "@humanfs/core@^0.19.1":
   version "0.19.1"
   resolved "https://registry.npmjs.org/@humanfs/core/-/core-0.19.1.tgz"
@@ -1261,7 +1274,7 @@
     "@jridgewell/gen-mapping" "^0.3.5"
     "@jridgewell/trace-mapping" "^0.3.25"
 
-"@jridgewell/sourcemap-codec@^1.4.10", "@jridgewell/sourcemap-codec@^1.4.14", "@jridgewell/sourcemap-codec@^1.5.0":
+"@jridgewell/sourcemap-codec@^1.4.10", "@jridgewell/sourcemap-codec@^1.4.14":
   version "1.5.0"
   resolved "https://registry.npmjs.org/@jridgewell/sourcemap-codec/-/sourcemap-codec-1.5.0.tgz"
   integrity sha512-gv3ZRaISU3fjPAgNsriBRqGWQL6quFx04YMPW/zD8XMLsU32mhCCbfbO6KZFLjvYpCZ8zyDEgqsgf+PwPaM7GQ==
@@ -1295,15 +1308,6 @@
     "@nodelib/fs.scandir" "2.1.5"
     fastq "^1.6.0"
 
-"@rollup/plugin-inject@^5.0.4":
-  version "5.0.5"
-  resolved "https://registry.npmjs.org/@rollup/plugin-inject/-/plugin-inject-5.0.5.tgz"
-  integrity sha512-2+DEJbNBoPROPkgTDNe8/1YXWcqxbN5DTjASVIOx8HS+pITXushyNiBV56RB08zuptzz8gT3YfkqriTBVycepg==
-  dependencies:
-    "@rollup/pluginutils" "^5.0.1"
-    estree-walker "^2.0.2"
-    magic-string "^0.30.3"
-
 "@rollup/plugin-node-resolve@^16.0.0":
   version "16.0.1"
   resolved "https://registry.npmjs.org/@rollup/plugin-node-resolve/-/plugin-node-resolve-16.0.1.tgz"
@@ -1493,7 +1497,7 @@
   dependencies:
     "@babel/types" "^7.20.7"
 
-"@types/estree@1.0.6", "@types/estree@^1.0.0", "@types/estree@^1.0.6":
+"@types/estree@^1.0.0", "@types/estree@^1.0.6", "@types/estree@1.0.6":
   version "1.0.6"
   resolved "https://registry.npmjs.org/@types/estree/-/estree-1.0.6.tgz"
   integrity sha512-AYnb1nQyY49te+VRAVgmzfcgjYS91mY5P0TKUDCLEM+gNnA+3T6rWITXRLYCpahpqSQbN5cE+gHpnPyXjHWxcw==
@@ -1586,7 +1590,7 @@
     natural-compare "^1.4.0"
     ts-api-utils "^2.0.1"
 
-"@typescript-eslint/parser@8.26.1":
+"@typescript-eslint/parser@^8.0.0 || ^8.0.0-alpha.0", "@typescript-eslint/parser@8.26.1":
   version "8.26.1"
   resolved "https://registry.npmjs.org/@typescript-eslint/parser/-/parser-8.26.1.tgz"
   integrity sha512-w6HZUV4NWxqd8BdeFf81t07d7/YV9s7TCWrQQbG5uhuvGUAW+fq1usZ1Hmz9UPNLniFnD8GLSsDpjP0hm1S4lQ==
@@ -1662,6 +1666,11 @@ acorn-jsx@^5.3.2:
   resolved "https://registry.npmjs.org/acorn/-/acorn-8.14.1.tgz"
   integrity sha512-OvQ/2pUDKmgfCg++xsTX1wGxfTaszcHVcTctW4UJB4hibJx2HXxxO5UmVgyjMa+ZDsiaf5wWLXYpRWMmBI0QHg==
 
+agent-base@^7.1.2:
+  version "7.1.4"
+  resolved "https://registry.npmjs.org/agent-base/-/agent-base-7.1.4.tgz"
+  integrity sha512-MnA+YT8fwfJPgBx3m60MNqakm30XOkyIoH1y6huTQvC0PwZG7ki8NacLBcrPbNoo8vEZy7Jpuk7+jMO+CUovTQ==
+
 ajv@^6.12.4:
   version "6.12.6"
   resolved "https://registry.npmjs.org/ajv/-/ajv-6.12.6.tgz"
@@ -1698,6 +1707,13 @@ ansi-styles@^4.0.0:
   dependencies:
     color-convert "^2.0.1"
 
+ansi-styles@^4.1.0:
+  version "4.3.0"
+  resolved "https://registry.npmjs.org/ansi-styles/-/ansi-styles-4.3.0.tgz"
+  integrity sha512-zbB9rCJAT1rbjiVDb2hqKFHNYLxgtk8NURxZ3IZwD3F6NtxbXZQCnnSi1Lkx+IDohdPlFp222wVALIheZJQSEg==
+  dependencies:
+    color-convert "^2.0.1"
+
 ansi-styles@^5.0.0:
   version "5.2.0"
   resolved "https://registry.npmjs.org/ansi-styles/-/ansi-styles-5.2.0.tgz"
@@ -1908,6 +1924,16 @@ balanced-match@^1.0.0:
   resolved "https://registry.npmjs.org/balanced-match/-/balanced-match-1.0.2.tgz"
   integrity sha512-3oSeUO0TMV67hN1AmbXsK4yaqU7tjiHlbxRDZOpH0KW9+CeX4bRAaX0Anxt0tx2MrpRpWwQaPwIlISEJhYU5Pw==
 
+base64-js@^1.3.0:
+  version "1.5.1"
+  resolved "https://registry.npmjs.org/base64-js/-/base64-js-1.5.1.tgz"
+  integrity sha512-AKpaYlHn8t4SVbOHCy+b5+KKgvR4vrsD8vbvrbiQJps7fKDTkjkDry6ji0rUJjC0kzbNePLwzxq8iypo41qeWA==
+
+bignumber.js@^9.0.0:
+  version "9.3.1"
+  resolved "https://registry.npmjs.org/bignumber.js/-/bignumber.js-9.3.1.tgz"
+  integrity sha512-Ko0uX15oIUS7wJ3Rb30Fs6SkVbLmPBAKdlm7q9+ak9bbIeFf0MwuBsQV6z7+X768/cHsfg+WlysDWJcmthjsjQ==
+
 brace-expansion@^1.1.7:
   version "1.1.11"
   resolved "https://registry.npmjs.org/brace-expansion/-/brace-expansion-1.1.11.tgz"
@@ -1954,6 +1980,11 @@ bser@2.1.1:
   dependencies:
     node-int64 "^0.4.0"
 
+buffer-equal-constant-time@^1.0.1:
+  version "1.0.1"
+  resolved "https://registry.npmjs.org/buffer-equal-constant-time/-/buffer-equal-constant-time-1.0.1.tgz"
+  integrity sha512-zRpUiDwd/xk6ADqPMATG8vc9VPrkck7T07OIx0gnjmJAnHnTVXNQG3vfvWNuiZIkwu9KrKdA1iJKfsfTVxE6NA==
+
 buffer-from@^1.0.0:
   version "1.1.2"
   resolved "https://registry.npmjs.org/buffer-from/-/buffer-from-1.1.2.tgz"
@@ -2022,6 +2053,14 @@ chalk@^4.0.0:
     ansi-styles "^4.1.0"
     supports-color "^7.1.0"
 
+chalk@^4.0.2:
+  version "4.1.2"
+  resolved "https://registry.npmjs.org/chalk/-/chalk-4.1.2.tgz"
+  integrity sha512-oKnbhFyRIXpUuez8iBMmyEa4nbj4IOQyuhc/wy9kY7/WVPcwIO9VA668Pu8RkO7+0G76SLROeyw9CpQ061i4mA==
+  dependencies:
+    ansi-styles "^4.1.0"
+    supports-color "^7.1.0"
+
 char-regex@^1.0.2:
   version "1.0.2"
   resolved "https://registry.npmjs.org/char-regex/-/char-regex-1.0.2.tgz"
@@ -2070,11 +2109,6 @@ color-convert@^2.0.1:
   dependencies:
     color-name "~1.1.4"
 
-color-name@1.1.3:
-  version "1.1.3"
-  resolved "https://registry.npmjs.org/color-name/-/color-name-1.1.3.tgz"
-  integrity sha512-72fSenhMw2HZMTVHeCA9KCmpEIbzWiQsjN+BHcBbS9vr1mtt+vJjPdksIBNUmKAW8TFUDPJK5SUU3QhE9NEXDw==
-
 color-name@~1.1.4:
   version "1.1.4"
   resolved "https://registry.npmjs.org/color-name/-/color-name-1.1.4.tgz"
@@ -2160,7 +2194,7 @@ data-view-byte-offset@^1.0.1:
     es-errors "^1.3.0"
     is-data-view "^1.0.1"
 
-debug@^4.1.0, debug@^4.1.1, debug@^4.3.1, debug@^4.3.2, debug@^4.3.4:
+debug@^4.1.0, debug@^4.1.1, debug@^4.3.1, debug@^4.3.2, debug@^4.3.4, debug@4:
   version "4.4.0"
   resolved "https://registry.npmjs.org/debug/-/debug-4.4.0.tgz"
   integrity sha512-6WTZ/IxCY/T6BALoZHaE4ctp9xm+Z5kY/pzYaCHRFeyVhojxlrm+46y68HA6hr0TcwEssoxNiDEUJQjfPZ/RYA==
@@ -2217,6 +2251,11 @@ doctrine@^2.1.0:
   dependencies:
     esutils "^2.0.2"
 
+dotenv@^17.2.3:
+  version "17.2.3"
+  resolved "https://registry.npmjs.org/dotenv/-/dotenv-17.2.3.tgz"
+  integrity sha512-JVUnt+DUIzu87TABbhPmNfVdBDt18BLOWjMUFJMSi/Qqg7NTYtabbvSNJGOJ7afbRuv9D/lngizHtP7QyLQ+9w==
+
 dunder-proto@^1.0.0, dunder-proto@^1.0.1:
   version "1.0.1"
   resolved "https://registry.npmjs.org/dunder-proto/-/dunder-proto-1.0.1.tgz"
@@ -2226,6 +2265,13 @@ dunder-proto@^1.0.0, dunder-proto@^1.0.1:
     es-errors "^1.3.0"
     gopd "^1.2.0"
 
+ecdsa-sig-formatter@^1.0.11, ecdsa-sig-formatter@1.0.11:
+  version "1.0.11"
+  resolved "https://registry.npmjs.org/ecdsa-sig-formatter/-/ecdsa-sig-formatter-1.0.11.tgz"
+  integrity sha512-nagl3RYrbNv6kQkeJIpt6NJZy8twLB/2vtz6yN9Z4vRKHN4/QZJIEbqohALSgwKdnksuY3k5Addp5lg8sVoVcQ==
+  dependencies:
+    safe-buffer "^5.0.1"
+
 ejs@^3.1.10:
   version "3.1.10"
   resolved "https://registry.npmjs.org/ejs/-/ejs-3.1.10.tgz"
@@ -2439,7 +2485,7 @@ eslint-visitor-keys@^4.2.0:
   resolved "https://registry.npmjs.org/eslint-visitor-keys/-/eslint-visitor-keys-4.2.0.tgz"
   integrity sha512-UyLnSehNt62FFhSwjZlHmeokpRK59rcz29j+F1/aDgbkbRTk7wIc9XzdoasMUbRNKDM0qQt/+BJ4BrpFeABemw==
 
-eslint@^9.15.0:
+"eslint@^3 || ^4 || ^5 || ^6 || ^7 || ^8 || ^9.7", "eslint@^6.0.0 || ^7.0.0 || >=8.0.0", "eslint@^8.57.0 || ^9.0.0", eslint@^9.15.0:
   version "9.22.0"
   resolved "https://registry.npmjs.org/eslint/-/eslint-9.22.0.tgz"
   integrity sha512-9V/QURhsRN40xuHXWjV64yvrzMjcz7ZyNoF2jJFmy9j/SLk0u1OLSZgXi28MrXjymnjEGSR80WCdab3RGMDveQ==
@@ -2554,6 +2600,11 @@ expect@^29.0.0, expect@^29.7.0:
     jest-message-util "^29.7.0"
     jest-util "^29.7.0"
 
+extend@^3.0.2:
+  version "3.0.2"
+  resolved "https://registry.npmjs.org/extend/-/extend-3.0.2.tgz"
+  integrity sha512-fjquC59cD7CyW6urNXK0FBufkZcoiGG80wTuPujX590cB5Ttln20E2UB4S/WARVqhXffZl2LNgS+gQdPIIim/g==
+
 fast-deep-equal@^3.1.1, fast-deep-equal@^3.1.3:
   version "3.1.3"
   resolved "https://registry.npmjs.org/fast-deep-equal/-/fast-deep-equal-3.1.3.tgz"
@@ -2683,6 +2734,26 @@ functions-have-names@^1.2.3:
   resolved "https://registry.npmjs.org/functions-have-names/-/functions-have-names-1.2.3.tgz"
   integrity sha512-xckBUXyTIqT97tq2x2AMb+g163b5JFysYk0x4qxNFwbfQkmNZoiRHb6sPzI9/QV33WeuvVYBUIiD4NzNIyqaRQ==
 
+gaxios@^6.0.0, gaxios@^6.1.1:
+  version "6.7.1"
+  resolved "https://registry.npmjs.org/gaxios/-/gaxios-6.7.1.tgz"
+  integrity sha512-LDODD4TMYx7XXdpwxAVRAIAuB0bzv0s+ywFonY46k126qzQHT9ygyoa9tncmOiQmmDrik65UYsEkv3lbfqQ3yQ==
+  dependencies:
+    extend "^3.0.2"
+    https-proxy-agent "^7.0.1"
+    is-stream "^2.0.0"
+    node-fetch "^2.6.9"
+    uuid "^9.0.1"
+
+gcp-metadata@^6.1.0:
+  version "6.1.1"
+  resolved "https://registry.npmjs.org/gcp-metadata/-/gcp-metadata-6.1.1.tgz"
+  integrity sha512-a4tiq7E0/5fTjxPAaH4jpjkSv/uCaU2p5KC6HVGrvl0cDjA8iBZv4vv1gyzlmK0ZUKqwpOyQMKzZQe3lTit77A==
+  dependencies:
+    gaxios "^6.1.1"
+    google-logging-utils "^0.0.2"
+    json-bigint "^1.0.0"
+
 gensync@^1.0.0-beta.2:
   version "1.0.0-beta.2"
   resolved "https://registry.npmjs.org/gensync/-/gensync-1.0.0-beta.2.tgz"
@@ -2785,6 +2856,23 @@ globalthis@^1.0.4:
     define-properties "^1.2.1"
     gopd "^1.0.1"
 
+google-auth-library@^9.14.2:
+  version "9.15.1"
+  resolved "https://registry.npmjs.org/google-auth-library/-/google-auth-library-9.15.1.tgz"
+  integrity sha512-Jb6Z0+nvECVz+2lzSMt9u98UsoakXxA2HGHMCxh+so3n90XgYWkq5dur19JAJV7ONiJY22yBTyJB1TSkvPq9Ng==
+  dependencies:
+    base64-js "^1.3.0"
+    ecdsa-sig-formatter "^1.0.11"
+    gaxios "^6.1.1"
+    gcp-metadata "^6.1.0"
+    gtoken "^7.0.0"
+    jws "^4.0.0"
+
+google-logging-utils@^0.0.2:
+  version "0.0.2"
+  resolved "https://registry.npmjs.org/google-logging-utils/-/google-logging-utils-0.0.2.tgz"
+  integrity sha512-NEgUnEcBiP5HrPzufUkBzJOD/Sxsco3rLNo1F1TNf7ieU8ryUzBhqba8r756CjLX7rn3fHl6iLEwPYuqpoKgQQ==
+
 gopd@^1.0.1, gopd@^1.2.0:
   version "1.2.0"
   resolved "https://registry.npmjs.org/gopd/-/gopd-1.2.0.tgz"
@@ -2800,6 +2888,14 @@ graphemer@^1.4.0:
   resolved "https://registry.npmjs.org/graphemer/-/graphemer-1.4.0.tgz"
   integrity sha512-EtKwoO6kxCL9WO5xipiHTZlSzBm7WLT627TqC/uVRd0HKmq8NXyebnNYxDoBi7wt8eTWrUrKXCOVaFq9x1kgag==
 
+gtoken@^7.0.0:
+  version "7.1.0"
+  resolved "https://registry.npmjs.org/gtoken/-/gtoken-7.1.0.tgz"
+  integrity sha512-pCcEwRi+TKpMlxAQObHDQ56KawURgyAf6jtIY046fJ5tIv3zDe/LEIubckAO8fj6JnAxLdmWkUfNyulQ2iKdEw==
+  dependencies:
+    gaxios "^6.0.0"
+    jws "^4.0.0"
+
 has-bigints@^1.0.2:
   version "1.1.0"
   resolved "https://registry.npmjs.org/has-bigints/-/has-bigints-1.1.0.tgz"
@@ -2853,6 +2949,14 @@ html-escaper@^2.0.0:
   resolved "https://registry.npmjs.org/html-escaper/-/html-escaper-2.0.2.tgz"
   integrity sha512-H2iMtd0I4Mt5eYiapRdIDjp+XzelXQ0tFE4JS7YFwFevXXMmOp9myNrUvCg0D6ws8iqkRPBfKHgbwig1SmlLfg==
 
+https-proxy-agent@^7.0.1:
+  version "7.0.6"
+  resolved "https://registry.npmjs.org/https-proxy-agent/-/https-proxy-agent-7.0.6.tgz"
+  integrity sha512-vK9P5/iUfdl95AI+JVyUuIcVtd4ofvtrOr3HNtM2yxC9bnMbEdp3x01OhQNnjb8IJYi38VlTE3mBXwcfvywuSw==
+  dependencies:
+    agent-base "^7.1.2"
+    debug "4"
+
 human-signals@^2.1.0:
   version "2.1.0"
   resolved "https://registry.npmjs.org/human-signals/-/human-signals-2.1.0.tgz"
@@ -3581,6 +3685,13 @@ jsesc@~3.0.2:
   resolved "https://registry.npmjs.org/jsesc/-/jsesc-3.0.2.tgz"
   integrity sha512-xKqzzWXDttJuOcawBt4KnKHHIf5oQ/Cxax+0PWFG+DFDgHNAdi+TXECADI+RYiFUMmx8792xsMbbgXj4CwnP4g==
 
+json-bigint@^1.0.0:
+  version "1.0.0"
+  resolved "https://registry.npmjs.org/json-bigint/-/json-bigint-1.0.0.tgz"
+  integrity sha512-SiPv/8VpZuWbvLSMtTDU8hEfrZWg/mH/nV/b4o0CYbSxu1UIQPLdwKOCIyLQX+VIPO5vrLX3i8qtqFyhdPSUSQ==
+  dependencies:
+    bignumber.js "^9.0.0"
+
 json-buffer@3.0.1:
   version "3.0.1"
   resolved "https://registry.npmjs.org/json-buffer/-/json-buffer-3.0.1.tgz"
@@ -3616,6 +3727,23 @@ json5@^2.2.3:
     object.assign "^4.1.4"
     object.values "^1.1.6"
 
+jwa@^2.0.0:
+  version "2.0.1"
+  resolved "https://registry.npmjs.org/jwa/-/jwa-2.0.1.tgz"
+  integrity sha512-hRF04fqJIP8Abbkq5NKGN0Bbr3JxlQ+qhZufXVr0DvujKy93ZCbXZMHDL4EOtodSbCWxOqR8MS1tXA5hwqCXDg==
+  dependencies:
+    buffer-equal-constant-time "^1.0.1"
+    ecdsa-sig-formatter "1.0.11"
+    safe-buffer "^5.0.1"
+
+jws@^4.0.0:
+  version "4.0.0"
+  resolved "https://registry.npmjs.org/jws/-/jws-4.0.0.tgz"
+  integrity sha512-KDncfTmOZoOMTFG4mBlG0qUIOlc03fmzH+ru6RgYVZhPkyiy/92Owlt/8UEN+a4TXR1FQetfIpJE8ApdvdVxTg==
+  dependencies:
+    jwa "^2.0.0"
+    safe-buffer "^5.0.1"
+
 keyv@^4.5.4:
   version "4.5.4"
   resolved "https://registry.npmjs.org/keyv/-/keyv-4.5.4.tgz"
@@ -3689,13 +3817,6 @@ lru-cache@^5.1.1:
   dependencies:
     yallist "^3.0.2"
 
-magic-string@^0.30.3:
-  version "0.30.17"
-  resolved "https://registry.npmjs.org/magic-string/-/magic-string-0.30.17.tgz"
-  integrity sha512-sNPKHvyjVf7gyjwS4xGTaW/mCnF8wnjtifKBEhxfZ7E/S8tQ0rssrwGNn6q8JH/ohItJfSQp9mBtQYuTlH5QnA==
-  dependencies:
-    "@jridgewell/sourcemap-codec" "^1.5.0"
-
 make-dir@^4.0.0:
   version "4.0.0"
   resolved "https://registry.npmjs.org/make-dir/-/make-dir-4.0.0.tgz"
@@ -3774,6 +3895,13 @@ natural-compare@^1.4.0:
   resolved "https://registry.npmjs.org/natural-compare/-/natural-compare-1.4.0.tgz"
   integrity sha512-OWND8ei3VtNC9h7V60qff3SVobHr996CTwgxubgyQYEpg290h9J0buyECNNJexkFm5sOajh5G116RYA1c8ZMSw==
 
+node-fetch@^2.6.9:
+  version "2.7.0"
+  resolved "https://registry.npmjs.org/node-fetch/-/node-fetch-2.7.0.tgz"
+  integrity sha512-c4FRfUm/dbcWZ7U+1Wq0AwCyFL+3nt2bEw05wfxSz+DWpWsitgmSgYmy2dQdWyKC1694ELPqMs/YzUSNozLt8A==
+  dependencies:
+    whatwg-url "^5.0.0"
+
 node-int64@^0.4.0:
   version "0.4.0"
   resolved "https://registry.npmjs.org/node-int64/-/node-int64-0.4.0.tgz"
@@ -4177,14 +4305,7 @@ reusify@^1.0.4:
   resolved "https://registry.npmjs.org/reusify/-/reusify-1.1.0.tgz"
   integrity sha512-g6QUff04oZpHs0eG5p83rFLhHeV00ug/Yf9nZM6fLeUrPguBTkTQOdpAWWspMh55TZfVQDPaN3NQJfbVRAxdIw==
 
-rollup-plugin-polyfill-node@^0.13.0:
-  version "0.13.0"
-  resolved "https://registry.yarnpkg.com/rollup-plugin-polyfill-node/-/rollup-plugin-polyfill-node-0.13.0.tgz#28e5705b59438da894e55133a0fe7a86b57d9b0a"
-  integrity sha512-FYEvpCaD5jGtyBuBFcQImEGmTxDTPbiHjJdrYIp+mFIwgXiXabxvKUK7ZT9P31ozu2Tqm9llYQMRWsfvTMTAOw==
-  dependencies:
-    "@rollup/plugin-inject" "^5.0.4"
-
-rollup@^4.37.0:
+rollup@^1.20.0||^2.0.0||^3.0.0||^4.0.0, rollup@^2.0.0||^3.0.0||^4.0.0, rollup@^2.14.0||^3.0.0||^4.0.0, rollup@^2.78.0||^3.0.0||^4.0.0, rollup@^4.37.0:
   version "4.37.0"
   resolved "https://registry.npmjs.org/rollup/-/rollup-4.37.0.tgz"
   integrity sha512-iAtQy/L4QFU+rTJ1YUjXqJOJzuwEghqWzCEYD2FEghT7Gsy1VdABntrO4CLopA5IkflTyqNiLNwPcOJ3S7UKLg==
@@ -4231,7 +4352,7 @@ safe-array-concat@^1.1.3:
     has-symbols "^1.1.0"
     isarray "^2.0.5"
 
-safe-buffer@^5.1.0:
+safe-buffer@^5.0.1, safe-buffer@^5.1.0:
   version "5.2.1"
   resolved "https://registry.npmjs.org/safe-buffer/-/safe-buffer-5.2.1.tgz"
   integrity sha512-rp3So07KcdmmKbGvgaNxQSJr7bGVSVk5S9Eq1F+ppbRo70+YeaDxkw5Dd8NPN+GD6bjnYm2VuPuCXmpuYvmCXQ==
@@ -4263,6 +4384,21 @@ semver@^7.5.3:
   resolved "https://registry.npmjs.org/semver/-/semver-7.7.1.tgz"
   integrity sha512-hlq8tAfn0m/61p4BVRcPzIGr6LKiMwo4VM6dGi6pt4qcRkmNzTcWq6eCEjEh+qXjkMDvPlOFFSGwQjoEa6gyMA==
 
+semver@^7.5.4:
+  version "7.7.1"
+  resolved "https://registry.npmjs.org/semver/-/semver-7.7.1.tgz"
+  integrity sha512-hlq8tAfn0m/61p4BVRcPzIGr6LKiMwo4VM6dGi6pt4qcRkmNzTcWq6eCEjEh+qXjkMDvPlOFFSGwQjoEa6gyMA==
+
+semver@^7.6.0:
+  version "7.7.1"
+  resolved "https://registry.npmjs.org/semver/-/semver-7.7.1.tgz"
+  integrity sha512-hlq8tAfn0m/61p4BVRcPzIGr6LKiMwo4VM6dGi6pt4qcRkmNzTcWq6eCEjEh+qXjkMDvPlOFFSGwQjoEa6gyMA==
+
+semver@^7.7.1:
+  version "7.7.1"
+  resolved "https://registry.npmjs.org/semver/-/semver-7.7.1.tgz"
+  integrity sha512-hlq8tAfn0m/61p4BVRcPzIGr6LKiMwo4VM6dGi6pt4qcRkmNzTcWq6eCEjEh+qXjkMDvPlOFFSGwQjoEa6gyMA==
+
 serialize-javascript@^6.0.1:
   version "6.0.2"
   resolved "https://registry.npmjs.org/serialize-javascript/-/serialize-javascript-6.0.2.tgz"
@@ -4373,14 +4509,6 @@ smob@^1.0.0:
   resolved "https://registry.npmjs.org/smob/-/smob-1.5.0.tgz"
   integrity sha512-g6T+p7QO8npa+/hNx9ohv1E5pVCmWrVCUzUXJyLdMmftX6ER0oiWY/w9knEonLpnOp6b6FenKnMfR8gqwWdwig==
 
-source-map-support@0.5.13:
-  version "0.5.13"
-  resolved "https://registry.npmjs.org/source-map-support/-/source-map-support-0.5.13.tgz"
-  integrity sha512-SHSKFHadjVA5oR4PPqhtAVdcBWwRYVd6g6cAXnIbRiIwc2EhPrTuKUBdSLvlEKyIP3GCf89fltvcZiP9MMFA1w==
-  dependencies:
-    buffer-from "^1.0.0"
-    source-map "^0.6.0"
-
 source-map-support@~0.5.20:
   version "0.5.21"
   resolved "https://registry.npmjs.org/source-map-support/-/source-map-support-0.5.21.tgz"
@@ -4389,6 +4517,14 @@ source-map-support@~0.5.20:
     buffer-from "^1.0.0"
     source-map "^0.6.0"
 
+source-map-support@0.5.13:
+  version "0.5.13"
+  resolved "https://registry.npmjs.org/source-map-support/-/source-map-support-0.5.13.tgz"
+  integrity sha512-SHSKFHadjVA5oR4PPqhtAVdcBWwRYVd6g6cAXnIbRiIwc2EhPrTuKUBdSLvlEKyIP3GCf89fltvcZiP9MMFA1w==
+  dependencies:
+    buffer-from "^1.0.0"
+    source-map "^0.6.0"
+
 source-map@^0.6.0, source-map@^0.6.1:
   version "0.6.1"
   resolved "https://registry.npmjs.org/source-map/-/source-map-0.6.1.tgz"
@@ -4566,6 +4702,11 @@ to-regex-range@^5.0.1:
   dependencies:
     is-number "^7.0.0"
 
+tr46@~0.0.3:
+  version "0.0.3"
+  resolved "https://registry.npmjs.org/tr46/-/tr46-0.0.3.tgz"
+  integrity sha512-N3WMsuqV66lT30CrXNbEjx4GEwlow3v6rr4mCcv6prnfwhS01rkgyFdjPNBYd9br7LpXV1+Emh01fHnq2Gdgrw==
+
 ts-api-utils@^2.0.1:
   version "2.0.1"
   resolved "https://registry.npmjs.org/ts-api-utils/-/ts-api-utils-2.0.1.tgz"
@@ -4720,6 +4861,11 @@ uri-js@^4.2.2:
   dependencies:
     punycode "^2.1.0"
 
+uuid@^9.0.1:
+  version "9.0.1"
+  resolved "https://registry.npmjs.org/uuid/-/uuid-9.0.1.tgz"
+  integrity sha512-b+1eJOlsR9K8HJpow9Ok3fiWOWSIcIzXodvv0rQjVoOVNpWMpxf1wZNpt4y9h10odCNrqnYp1OBzRktckBe3sA==
+
 v8-to-istanbul@^9.0.1:
   version "9.3.0"
   resolved "https://registry.npmjs.org/v8-to-istanbul/-/v8-to-istanbul-9.3.0.tgz"
@@ -4736,6 +4882,19 @@ walker@^1.0.8:
   dependencies:
     makeerror "1.0.12"
 
+webidl-conversions@^3.0.0:
+  version "3.0.1"
+  resolved "https://registry.npmjs.org/webidl-conversions/-/webidl-conversions-3.0.1.tgz"
+  integrity sha512-2JAn3z8AR6rjK8Sm8orRC0h/bcl/DqL7tRPdGZ4I1CjdF+EaMLmYxBHyXuKL849eucPFhvBoxMsflfOb8kxaeQ==
+
+whatwg-url@^5.0.0:
+  version "5.0.0"
+  resolved "https://registry.npmjs.org/whatwg-url/-/whatwg-url-5.0.0.tgz"
+  integrity sha512-saE57nupxk6v3HY35+jzBwYa0rKSy0XR8JSxZPwgLr7ys0IBzhGviA1/TUGJLmSVqs8pb9AnvICXEuOHLprYTw==
+  dependencies:
+    tr46 "~0.0.3"
+    webidl-conversions "^3.0.0"
+
 which-boxed-primitive@^1.1.0, which-boxed-primitive@^1.1.1:
   version "1.1.1"
   resolved "https://registry.npmjs.org/which-boxed-primitive/-/which-boxed-primitive-1.1.1.tgz"
@@ -4823,6 +4982,11 @@ write-file-atomic@^4.0.2:
     imurmurhash "^0.1.4"
     signal-exit "^3.0.7"
 
+ws@^8.18.0:
+  version "8.18.3"
+  resolved "https://registry.npmjs.org/ws/-/ws-8.18.3.tgz"
+  integrity sha512-PEIGCY5tSlUt50cqyMXfCzX+oOPqN0vuGqWzbcJ2xvnkzkq46oOpz7dQaTDBdfICb4N14+GARUDw2XV2N4tvzg==
+
 y18n@^5.0.5:
   version "5.0.8"
   resolved "https://registry.npmjs.org/y18n/-/y18n-5.0.8.tgz"