Refactor `dmul(This, Differential)` to `dmul<T:Real>(T, Differential)` (#3029)

* Refactor `dmul(This, Differential)` to `dmul<T:Real>(T, Differential)`

 - Add AST synthesis support for generic containers
 - Refactor relevant tests

* Merge dmul synthesis with dadd and dzero, and disambiguate using an enum

* Fix trailing spaces

1 files changed, 33 insertions, 2 deletions

diff --git a/source/slang/slang-check-impl.h b/source/slang/slang-check-impl.h
index 04112743a..575d4aff7 100644
--- a/source/slang/slang-check-impl.h
+++ b/source/slang/slang-check-impl.h
@@ -1467,6 +1467,13 @@ namespace Slang
             DeclRef<FuncDecl> requiredMemberDeclRef,
             List<Expr*>& synArgs,
             ThisExpr*& synThis);
+        
+        GenericDecl* synthesizeGenericSignatureForRequirementWitness(
+            ConformanceCheckingContext* context,
+            DeclRef<GenericDecl> requiredMemberDeclRef,
+            List<Expr*>& synArgs,
+            List<Expr*>& synGenericArgs,
+            ThisExpr*& synThis);
 
         void _addMethodWitness(
             WitnessTable* witnessTable,
@@ -1503,15 +1510,39 @@ namespace Slang
             LookupResult const&         lookupResult,
             DeclRef<Decl>               requiredMemberDeclRef,
             RefPtr<WitnessTable>        witnessTable);
+        
 
-            /// Attempt to synthesize `zero`, `dadd` and `dmul` methods for a type that conforms to
+        enum SynthesisPattern
+        {
+            // Synthesized method inducts over all arguments.
+            // T fn(T x, T y, T z, ...) 
+            // { 
+            //     typeof(T::member0)::fn(x.member0, y.member0, z.member0, ...);
+            //     typeof(T::member1)::fn(x.member1, y.member1, z.member1, ...);
+            //     ...
+            // }
+            // 
+            AllInductive,
+
+            // Synthesized method inducts over all arguments except the first.
+            // T fn(U x, T y, T z)
+            // {
+            //     typeof(T::member0)::fn(x, y.member0, z.member0, ...);
+            //     typeof(T::member1)::fn(x, y.member1, z.member1, ...);
+            //     ...
+            // }
+            FixedFirstArg
+        };
+
+            /// Attempt to synthesize `zero`, `dadd` & `dmul` methods for a type that conforms to
             /// `IDifferentiable`.
             /// On success, installs the syntethesized functions and returns `true`.
             /// Otherwise, returns `false`.
         bool trySynthesizeDifferentialMethodRequirementWitness(
             ConformanceCheckingContext* context,
             DeclRef<Decl> requirementDeclRef,
-            RefPtr<WitnessTable> witnessTable);
+            RefPtr<WitnessTable> witnessTable,
+            SynthesisPattern pattern);
 
             /// Attempt to synthesize an associated `Differential` type for a type that conforms to
             /// `IDifferentiable`.