Redefine * between ::Zero and ::Any

Author: YingboMa

src/differential_arithmetic.jl

@@ -32,15 +32,19 @@ Base.:*(::DoesNotExist, ::Zero) = Zero()
 Base.:*(::Zero, ::DoesNotExist) = Zero()
 
 
-Base.:+(::Zero, b::Zero) = Zero()
+Base.:+(::Zero, ::Zero) = Zero()
 Base.:*(::Zero, ::Zero) = Zero()
 for T in (:One, :AbstractThunk, :Any)
     @eval Base.:+(::Zero, b::$T) = b
     @eval Base.:+(a::$T, ::Zero) = a
 
-    @eval Base.:*(::Zero, ::$T) = Zero()
-    @eval Base.:*(::$T, ::Zero) = Zero()
+    if T !== :Any
+        @eval Base.:*(::Zero, ::$T) = Zero()
+        @eval Base.:*(::$T, ::Zero) = Zero()
+    end
 end
+Base.:*(::Zero, x) = zero(x)
+Base.:*(x, ::Zero) = zero(x)
 
 
 Base.:+(a::One, b::One) = extern(a) + extern(b)

test/differentials/zero.jl

@@ -1,15 +1,15 @@
 @testset "Zero" begin
     z = Zero()
     @test extern(z) === false
-    @test z + z == z
-    @test z + 1 == 1
-    @test 1 + z == 1
-    @test z * z == z
-    @test z * 1 == z
-    @test 1 * z == z
+    @test z + z === z
+    @test z + 1 === 1
+    @test 1 + z === 1
+    @test z * z === z
+    @test z * 1 === 0
+    @test 1 * z === 0
     for x in z
         @test x === z
     end
     @test broadcastable(z) isa Ref{Zero}
-    @test conj(z) == z
+    @test conj(z) === z
 end