diff --git a/tools/hls-fuzzer/BasicCGenerator.h b/tools/hls-fuzzer/BasicCGenerator.h
index 6812336e4..2242a5467 100644
--- a/tools/hls-fuzzer/BasicCGenerator.h
+++ b/tools/hls-fuzzer/BasicCGenerator.h
@@ -200,11 +200,12 @@ class BasicCGenerator {
           [&](auto elementIndex, auto &&transferFn) {
             constexpr std::size_t index = decltype(elementIndex){};
             if constexpr (index < sizeof...(SubElements)) {
-              if (transferFn.getInputDependencies().empty() ||
-                  transferFn.getInputDependencies() ==
-                      llvm::ArrayRef{INPUT_DEPENDENCY}) {
-                // No dependency (besides the parent context which is
-                // satisfied).
+              if (llvm::all_of(
+                      transferFn.getInputDependencies(), [](std::size_t index) {
+                        return index == INPUT_DEPENDENCY || isWeak(index);
+                      })) {
+                // No dependency (besides the input context and weak ones which
+                // are satisfied by default).
                 worklist[workListSize++] = index;
                 return;
               }
@@ -212,7 +213,7 @@ class BasicCGenerator {
               // Build the outgoing edge list but do keep track of the
               // number of incoming edges.
               for (auto fromIndex : transferFn.getInputDependencies())
-                if (fromIndex != INPUT_DEPENDENCY) {
+                if (fromIndex != INPUT_DEPENDENCY && !isWeak(fromIndex)) {
                   forwardEdgeList[fromIndex][forwardEdgeCount[fromIndex]++] =
                       index;
                   ++incomingEdgeCount[index];
diff --git a/tools/hls-fuzzer/LimitTypeSystem.h b/tools/hls-fuzzer/LimitTypeSystem.h
index 21018141a..34f78157c 100644
--- a/tools/hls-fuzzer/LimitTypeSystem.h
+++ b/tools/hls-fuzzer/LimitTypeSystem.h
@@ -135,17 +135,27 @@ class LimitTypeSystem : public TypeSystem<LimitTypingContext, LimitTypeSystem> {
   }
 
   TransferFnArray<ast::StatementList> getStatementListTransferFns() override {
-    // TODO: This needlessly forces in which order statements are to be
-    //       generated!
-    //       In reality, the type system does not care whether the statement
-    //       gets generated first or the rest of the statement list, just that
-    //       their respective statement number is propagated to the other.
-    //       This is a missing feature!
     return {
-        copyFrom<ast::StatementList, ast::StatementList::STATEMENT>(),
-        copyFromInput<ast::StatementList>(),
+        /*statement list=*/copyFirstOf<ast::StatementList,
+                                       weak(ast::StatementList::STATEMENT),
+                                       INPUT_DEPENDENCY>(),
+        /*statement=*/
+        copyFirstOf<ast::StatementList,
+                    weak(ast::StatementList::STATEMENT_LIST),
+                    INPUT_DEPENDENCY>(),
         /*output=*/
-        copyToOutput<ast::StatementList, ast::StatementList::STATEMENT_LIST>(),
+        OutputTransferFn<ast::StatementList>(
+            std::index_sequence<ast::StatementList::STATEMENT,
+                                ast::StatementList::STATEMENT_LIST>{},
+            [](const ast::StatementList &, LimitTypingContext statement,
+               const LimitTypingContext &statementList) {
+              // Regardless of which of the two was generated first, we can
+              // extract the total number of statements by taking their maximum.
+              statement.totalNumberOfStatements =
+                  std::max(statement.totalNumberOfStatements,
+                           statementList.totalNumberOfStatements);
+              return statement;
+            }),
     };
   }
 
diff --git a/tools/hls-fuzzer/TypeSystem.h b/tools/hls-fuzzer/TypeSystem.h
index ecbe9ed3a..7ccdd1f86 100644
--- a/tools/hls-fuzzer/TypeSystem.h
+++ b/tools/hls-fuzzer/TypeSystem.h
@@ -127,6 +127,32 @@ class OpaqueContext {
 /// Sentinel value representing a dependency on the input context.
 constexpr std::size_t INPUT_DEPENDENCY = -1;
 
+/// Marks a dependency as weak. This is a noop for 'INPUT_DEPENDENCY' as it
+/// cannot be weak.
+/// See the 'TypeSystem' documentation for what 'weak' means.
+constexpr std::size_t weak(std::size_t dependency) {
+  // We use the top bit being set as an encoding for a dependency being weak.
+  // Since 'INPUT_DEPENDENCY' is encoded as all 1s, this operation is also a
+  // noop for 'INPUT_DEPENDENCY'.
+  return dependency | (1ull << (std::numeric_limits<std::size_t>::digits - 1));
+}
+
+/// Returns true if 'dependency' is weak.
+/// See the 'TypeSystem' documentation for what 'weak' means.
+constexpr bool isWeak(std::size_t dependency) {
+  return dependency != INPUT_DEPENDENCY && weak(dependency) == dependency;
+}
+
+/// If 'dependency' is weak, then it returns the original non-weak dependency.
+/// Otherwise, returns 'dependency'.
+/// See the 'TypeSystem' documentation for what 'weak' means.
+constexpr std::size_t unwrapWeak(std::size_t dependency) {
+  if (dependency == INPUT_DEPENDENCY)
+    return INPUT_DEPENDENCY;
+
+  return dependency & ~weak(0);
+}
+
 /// Class responsible for telling the generator how to calculate the input
 /// 'TypingContext' for a given subelement of 'ASTNode'.
 /// The subelement whose input-context we are calculating for is given by its
@@ -139,12 +165,28 @@ constexpr std::size_t INPUT_DEPENDENCY = -1;
 /// this instance depends on within 'ASTNode::SubElements'.
 /// The special value 'INPUT_DEPENDENCY' represents depending on the
 /// input-context of 'ASTNode'.
-/// It is the user's responsibility to not create cyclic dependencies.
+///
+/// Dependencies can additionally be marked 'weak'. In that case, the element
+/// and context will be passed to the transfer function if and only if they
+/// have been generated previously. Otherwise, an empty optional and nullptr
+/// are passed for the AST-node and context of that dependency instead.
+///
+/// This is the big difference to normal dependencies: They do not force an
+/// AST-node to have been generated previously (i.e., do not participate in the
+/// topological sort performed by the generator). This makes it legal to have
+/// cycles involving weak dependencies.
+///
+/// It is the user's responsibility to not create cyclic non-weak dependencies.
 template <typename TypingContext, typename ASTNode, std::size_t... inputIndices>
 class TransferFn {
 
   template <typename Tuple, std::size_t current, std::size_t... remaining>
   struct CalcCompFn {
+    using SubElementType = std::tuple_element_t<
+        std::min(unwrapWeak(current),
+                 std::tuple_size_v<typename ASTNode::SubElements> - 1),
+        typename ASTNode::SubElements>;
+
     // Recursive case.
     using type = typename CalcCompFn<
         decltype(std::tuple_cat(
@@ -155,12 +197,11 @@ class TransferFn {
                 std::tuple<const TypingContext &>,
                 // Add both the context and the ASTNode to the arguments.
                 std::tuple<
-                    const TypingContext &,
-                    const std::tuple_element_t<
-                        std::min(current, std::tuple_size_v<
-                                              typename ASTNode::SubElements> -
-                                              1),
-                        typename ASTNode::SubElements> &>>>())),
+                    std::conditional_t<isWeak(current), const TypingContext *,
+                                       const TypingContext &>,
+                    const std::conditional_t<isWeak(current),
+                                             std::optional<SubElementType>,
+                                             SubElementType> &>>>())),
         remaining...>::type;
   };
 
@@ -191,17 +232,28 @@ class TransferFn {
   /// Specifically, for every element of 'inputIndices' and in the order as
   /// given in 'inputIndices', the arguments are:
   /// * The input 'TypingContext' if the value is 'INPUT_DEPENDENCY'
-  /// * The output 'TypingContext' of the 'i'th subelement of 'ASTNode' followed
+  /// * If 'i' is not weak, the output 'TypingContext' of the 'i'th subelement
+  /// of 'ASTNode' followed
   ///   by the subelement's AST node itself.
+  /// * If 'i' is weak, a pointer to the output 'TypingContext' of the 'i'th
+  ///   subelement of 'ASTNode' or null if not present, followed by an optional
+  ///   of the subelement's AST node itself if already generated.
   ///
   /// Example:
   /// Dependency<Context, ast::BinaryExpression,
-  ///   /*rhs=*/ast::BINARY_EXPRESSION::RHS, INPUT_DEPENDENCY>(
+  ///   ast::BINARY_EXPRESSION::RHS, INPUT_DEPENDENCY>(
   ///   [](const Context& rhsContext, const ast::Expression& rhs,
   ///      const Context& inputContext) -> Context {
   ///     ...
   ///   }
   /// )
+  /// Dependency<Context, ast::BinaryExpression,
+  ///   weak(ast::BINARY_EXPRESSION::RHS), INPUT_DEPENDENCY>(
+  ///   [](const Context* rhsContext, const std::optional<ast::Expression>& rhs,
+  ///      const Context& inputContext) -> Context {
+  ///     ...
+  ///   }
+  /// )
   ///
   /// The function should always return a 'TypingContext'. All parameters are
   /// passed as const-references.
@@ -220,7 +272,7 @@ class TransferFn {
   }
 
 private:
-  static_assert(((inputIndices <
+  static_assert(((unwrapWeak(inputIndices) <
                       std::tuple_size_v<typename ASTNode::SubElements> ||
                   inputIndices == INPUT_DEPENDENCY) &&
                  ...),
@@ -284,11 +336,19 @@ class OpaqueTransferFn {
                   *reinterpret_cast<const TypingContext *>(
                       std::get<std::tuple_size_v<ContextTuple> - 1>(contexts)));
             } else {
-              // Subelement context + ASTNode.
-              return std::forward_as_tuple(
-                  *reinterpret_cast<const TypingContext *>(
-                      std::get<index>(contexts)),
-                  *std::get<index>(subElements));
+              if constexpr (isWeak(index)) {
+                // Subelement context + ASTNode.
+                return std::make_tuple(
+                    reinterpret_cast<const TypingContext *>(
+                        std::get<unwrapWeak(index)>(contexts)),
+                    std::cref(std::get<unwrapWeak(index)>(subElements)));
+              } else {
+                // Subelement context + ASTNode.
+                return std::forward_as_tuple(
+                    *reinterpret_cast<const TypingContext *>(
+                        std::get<index>(contexts)),
+                    *std::get<index>(subElements));
+              }
             }
           }(std::integral_constant<std::size_t, inputIndices>{})...);
 
@@ -721,6 +781,37 @@ class TypeSystem : public AbstractTypeSystem {
         [](const TypingContext &context, auto &&...) { return context; });
   }
 
+  /// Returns an instance of 'TransferFn' which forwards the first present
+  /// context from the possibly-weak dependencies in 'indices'.
+  /// At least one dependency must not be weak.
+  template <typename ASTNode, std::size_t... indices>
+  static auto copyFirstOf() {
+    static_assert((!isWeak(indices) || ...),
+                  "at least one of 'indices' must not be weak");
+
+    return TransferFn<ASTNode, indices...>([](auto &&...args) {
+      std::optional<TypingContext> result;
+      foreachInTuples(
+          [&](auto &&element) {
+            if (result)
+              return;
+
+            if constexpr (std::is_same_v<std::decay_t<decltype(element)>,
+                                         TypingContext>) {
+              result = element;
+            }
+            if constexpr (std::is_same_v<std::decay_t<decltype(element)>,
+                                         const TypingContext *>) {
+              if (element)
+                result = *element;
+            }
+          },
+          std::forward_as_tuple(std::forward<decltype(args)>(args)...));
+
+      return std::move(*result);
+    });
+  }
+
   /// Returns a noop 'OutputTransferFn' that keeps the output context
   /// equal to the input context.
   template <typename ASTNode>