diff --git a/toolchain/check/generic.cpp b/toolchain/check/generic.cpp
index d1048531084a..f38045abe027 100644
--- a/toolchain/check/generic.cpp
+++ b/toolchain/check/generic.cpp
@@ -44,6 +44,14 @@ static auto AddGenericConstantInstToEvalBlock(
 }
 
 namespace {
+// A map from an instruction ID representing a canonical symbolic constant to an
+// instruction within an eval block of the generic that computes the specific
+// value for that constant.
+//
+// We arbitrarily use a small size of 256 bytes for the map.
+// TODO: Determine a better number based on measurements.
+using ConstantsInGenericMap = Map<SemIR::InstId, SemIR::InstId, 256>;
+
 // Substitution callbacks to rebuild a generic constant in the eval block for a
 // generic region.
 class RebuildGenericConstantInEvalBlockCallbacks final
@@ -52,7 +60,7 @@ class RebuildGenericConstantInEvalBlockCallbacks final
   RebuildGenericConstantInEvalBlockCallbacks(
       Context& context, SemIR::GenericId generic_id,
       SemIR::GenericInstIndex::Region region,
-      Map<SemIR::InstId, SemIR::InstId>& constants_in_generic)
+      ConstantsInGenericMap& constants_in_generic)
       : context_(context),
         generic_id_(generic_id),
         region_(region),
@@ -62,6 +70,14 @@ class RebuildGenericConstantInEvalBlockCallbacks final
   // block, and substitute them for the instructions in the eval block.
   auto Subst(SemIR::InstId& inst_id) const -> bool override {
     auto const_id = context_.constant_values().Get(inst_id);
+    if (!const_id.is_valid()) {
+      // An unloaded import ref should never contain anything we need to
+      // substitute into. Don't trigger loading it here.
+      CARBON_CHECK(context_.insts().Is<SemIR::ImportRefUnloaded>(inst_id))
+          << "Substituting into instruction with invalid constant ID: "
+          << context_.insts().Get(inst_id);
+      return true;
+    }
     if (!const_id.is_symbolic()) {
       // This instruction doesn't have a symbolic constant value, so can't
       // contain any bindings that need to be substituted.
@@ -104,6 +120,8 @@ class RebuildGenericConstantInEvalBlockCallbacks final
       // TODO: Add a function on `Context` to add the instruction without
       // inserting it into the dependent instructions list or computing a
       // constant value for it.
+      // TODO: Provide a location based on the location of the instruction
+      // that uses the constant.
       auto inst_id = context_.sem_ir().insts().AddInNoBlock(
           SemIR::LocIdAndInst::NoLoc(new_inst));
       auto const_id = AddGenericConstantInstToEvalBlock(
@@ -118,7 +136,7 @@ class RebuildGenericConstantInEvalBlockCallbacks final
   Context& context_;
   SemIR::GenericId generic_id_;
   SemIR::GenericInstIndex::Region region_;
-  Map<SemIR::InstId, SemIR::InstId>& constants_in_generic_;
+  ConstantsInGenericMap& constants_in_generic_;
 };
 }  // namespace
 
@@ -129,8 +147,8 @@ class RebuildGenericConstantInEvalBlockCallbacks final
 static auto AddGenericTypeToEvalBlock(
     Context& context, SemIR::GenericId generic_id,
     SemIR::GenericInstIndex::Region region,
-    Map<SemIR::InstId, SemIR::InstId>& constants_in_generic,
-    SemIR::TypeId type_id) -> SemIR::TypeId {
+    ConstantsInGenericMap& constants_in_generic, SemIR::TypeId type_id)
+    -> SemIR::TypeId {
   // Substitute into the type's constant instruction and rebuild it in the eval
   // block.
   auto type_inst_id =
@@ -147,8 +165,8 @@ static auto AddGenericTypeToEvalBlock(
 static auto AddGenericConstantToEvalBlock(
     Context& context, SemIR::GenericId generic_id,
     SemIR::GenericInstIndex::Region region,
-    Map<SemIR::InstId, SemIR::InstId>& constants_in_generic,
-    SemIR::InstId inst_id) -> SemIR::ConstantId {
+    ConstantsInGenericMap& constants_in_generic, SemIR::InstId inst_id)
+    -> SemIR::ConstantId {
   // Substitute into the constant value and rebuild it in the eval block if
   // we've not encountered it before.
   auto const_inst_id = context.constant_values().GetConstantInstId(inst_id);
@@ -162,6 +180,24 @@ static auto AddGenericConstantToEvalBlock(
   return context.constant_values().Get(new_inst_id);
 }
 
+// Populates a map of constants in a generic from the constants in the
+// declaration region, in preparation for building the definition region.
+static auto PopulateConstantsFromDeclaration(
+    Context& context, SemIR::GenericId generic_id,
+    ConstantsInGenericMap& constants_in_generic) {
+  // For the definition region, populate constants from the declaration.
+  auto decl_eval_block = context.inst_blocks().Get(
+      context.generics().Get(generic_id).decl_block_id);
+  constants_in_generic.GrowForInsertCount(decl_eval_block.size());
+  for (auto inst_id : decl_eval_block) {
+    auto const_inst_id = context.constant_values().GetConstantInstId(inst_id);
+    auto result = constants_in_generic.Insert(const_inst_id, inst_id);
+    CARBON_CHECK(result.is_inserted())
+        << "Duplicate constant in generic decl eval block: "
+        << context.insts().Get(const_inst_id);
+  }
+}
+
 // Builds and returns a block of instructions whose constant values need to be
 // evaluated in order to resolve a generic to a specific.
 static auto MakeGenericEvalBlock(Context& context, SemIR::GenericId generic_id,
@@ -169,16 +205,11 @@ static auto MakeGenericEvalBlock(Context& context, SemIR::GenericId generic_id,
     -> SemIR::InstBlockId {
   context.inst_block_stack().Push();
 
-  Map<SemIR::InstId, SemIR::InstId> constants_in_generic;
+  ConstantsInGenericMap constants_in_generic;
 
   // For the definition region, populate constants from the declaration.
   if (region == SemIR::GenericInstIndex::Region::Definition) {
-    auto decl_eval_block = context.inst_blocks().Get(
-        context.generics().Get(generic_id).decl_block_id);
-    for (auto inst_id : decl_eval_block) {
-      constants_in_generic.Insert(
-          context.constant_values().GetConstantInstId(inst_id), inst_id);
-    }
+    PopulateConstantsFromDeclaration(context, generic_id, constants_in_generic);
   }
 
   // The work done in this loop might invalidate iterators into the generic
@@ -231,6 +262,37 @@ static auto MakeGenericEvalBlock(Context& context, SemIR::GenericId generic_id,
   return context.inst_block_stack().Pop();
 }
 
+// Builds and returns an eval block, given the list of canonical symbolic
+// constants that the instructions in the eval block should produce. This is
+// used when importing a generic.
+auto RebuildGenericEvalBlock(Context& context, SemIR::GenericId generic_id,
+                             SemIR::GenericInstIndex::Region region,
+                             llvm::ArrayRef<SemIR::InstId> const_ids)
+    -> SemIR::InstBlockId {
+  context.inst_block_stack().Push();
+
+  ConstantsInGenericMap constants_in_generic;
+
+  // For the definition region, populate constants from the declaration.
+  if (region == SemIR::GenericInstIndex::Region::Definition) {
+    PopulateConstantsFromDeclaration(context, generic_id, constants_in_generic);
+  }
+
+  constants_in_generic.GrowForInsertCount(const_ids.size());
+  for (auto [i, inst_id] : llvm::enumerate(const_ids)) {
+    // Build a constant in the inst block.
+    AddGenericConstantToEvalBlock(context, generic_id, region,
+                                  constants_in_generic, inst_id);
+    CARBON_CHECK(context.inst_block_stack().PeekCurrentBlockContents().size() ==
+                 i + 1)
+        << "Produced "
+        << (context.inst_block_stack().PeekCurrentBlockContents().size() - i)
+        << " instructions when importing " << context.insts().Get(inst_id);
+  }
+
+  return context.inst_block_stack().Pop();
+}
+
 auto FinishGenericDecl(Context& context, SemIR::InstId decl_id)
     -> SemIR::GenericId {
   auto all_bindings =
@@ -293,11 +355,6 @@ auto MakeSpecific(Context& context, SemIR::GenericId generic_id,
                   SemIR::InstBlockId args_id) -> SemIR::SpecificId {
   auto specific_id = context.specifics().GetOrAdd(generic_id, args_id);
 
-  // TODO: Remove this once we import generics properly.
-  if (!generic_id.is_valid()) {
-    return specific_id;
-  }
-
   // If this is the first time we've formed this specific, evaluate its decl
   // block to form information about the specific.
   if (!context.specifics().Get(specific_id).decl_block_id.is_valid()) {
@@ -339,11 +396,7 @@ auto ResolveSpecificDefinition(Context& context, SemIR::SpecificId specific_id)
     -> bool {
   auto& specific = context.specifics().Get(specific_id);
   auto generic_id = specific.generic_id;
-
-  // TODO: Remove this once we import generics properly.
-  if (!generic_id.is_valid()) {
-    return true;
-  }
+  CARBON_CHECK(generic_id.is_valid()) << "Specific with no generic ID";
 
   if (!specific.definition_block_id.is_valid()) {
     // Evaluate the eval block for the definition of the generic.
diff --git a/toolchain/check/generic.h b/toolchain/check/generic.h
index 63424681977a..4008bd1f1746 100644
--- a/toolchain/check/generic.h
+++ b/toolchain/check/generic.h
@@ -31,6 +31,14 @@ auto FinishGenericRedecl(Context& context, SemIR::InstId decl_id,
 auto FinishGenericDefinition(Context& context, SemIR::GenericId generic_id)
     -> void;
 
+// Builds and returns an eval block, given the list of canonical symbolic
+// constants that the instructions in the eval block should produce. This is
+// used when importing a generic.
+auto RebuildGenericEvalBlock(Context& context, SemIR::GenericId generic_id,
+                             SemIR::GenericInstIndex::Region region,
+                             llvm::ArrayRef<SemIR::InstId> const_ids)
+    -> SemIR::InstBlockId;
+
 // Builds a new specific, or finds an existing one if this generic has already
 // been referenced with these arguments. Performs substitution into the
 // declaration, but not the definition, of the generic.
diff --git a/toolchain/check/import_ref.cpp b/toolchain/check/import_ref.cpp
index 1334d1433b82..2e07c156bbd3 100644
--- a/toolchain/check/import_ref.cpp
+++ b/toolchain/check/import_ref.cpp
@@ -267,6 +267,22 @@ class ImportRefResolver {
     llvm::SmallVector<SemIR::ImportIRInst> indirect_insts = {};
   };
 
+  // Local information associated with an imported generic.
+  struct GenericData {
+    llvm::SmallVector<SemIR::InstId> bindings;
+    // TODO: Add data for the self specific.
+    llvm::SmallVector<SemIR::InstId> decl_block;
+    llvm::SmallVector<SemIR::InstId> definition_block;
+  };
+
+  // Local information associated with an imported specific.
+  struct SpecificData {
+    SemIR::ConstantId generic_const_id;
+    llvm::SmallVector<SemIR::InstId> args;
+    llvm::SmallVector<SemIR::InstId> decl_block;
+    llvm::SmallVector<SemIR::InstId> definition_block;
+  };
+
   // Looks to see if an instruction has been resolved. If a constant is only
   // found indirectly, sets the constant for any indirect steps that don't
   // already have the constant. If a constant isn't found, returns the indirect
@@ -397,6 +413,18 @@ class ImportRefResolver {
     return inst_ids;
   }
 
+  // Gets a local instruction block ID corresponding to an imported inst block
+  // whose contents were already imported, for example by
+  // GetLocalInstBlockContents.
+  auto GetLocalInstBlockId(SemIR::InstBlockId import_block_id,
+                           llvm::ArrayRef<SemIR::InstId> contents)
+      -> SemIR::InstBlockId {
+    if (!import_block_id.is_valid()) {
+      return SemIR::InstBlockId::Invalid;
+    }
+    return context_.inst_blocks().Add(contents);
+  }
+
   // Gets a local canonical instruction block ID corresponding to an imported
   // inst block whose contents were already imported, for example by
   // GetLocalInstBlockContents.
@@ -409,43 +437,153 @@ class ImportRefResolver {
     return context_.inst_blocks().AddCanonical(contents);
   }
 
-  // Gets a local version of an imported generic.
-  auto GetLocalGeneric(SemIR::GenericId generic_id) -> SemIR::GenericId {
+  // Gets an incomplete local version of an imported generic. Most fields are
+  // set in the second pass.
+  auto MakeIncompleteGeneric(SemIR::InstId decl_id, SemIR::GenericId generic_id)
+      -> SemIR::GenericId {
     if (!generic_id.is_valid()) {
       return SemIR::GenericId::Invalid;
     }
 
-    // TODO: Support importing generics. Note that this comes up in the prelude,
-    // so for now we fall back to producing `Invalid` and treating imported
-    // generics as non-generic.
-    return SemIR::GenericId::Invalid;
+    return context_.generics().Add(
+        {.decl_id = decl_id,
+         .bindings_id = SemIR::InstBlockId::Invalid,
+         .self_specific_id = SemIR::SpecificId::Invalid});
   }
 
-  // Gets a local argument list corresponding to the arguments of an imported
-  // specific.
-  auto GetLocalSpecificArgs(SemIR::SpecificId specific_id)
-      -> llvm::SmallVector<SemIR::InstId> {
-    if (!specific_id.is_valid()) {
-      return {};
+  // Gets a local version of the data associated with a generic.
+  auto GetLocalGenericData(SemIR::GenericId generic_id) -> GenericData {
+    if (!generic_id.is_valid()) {
+      return GenericData();
     }
-    return GetLocalInstBlockContents(
-        import_ir_.specifics().Get(specific_id).args_id);
+
+    const auto& generic = import_ir_.generics().Get(generic_id);
+    return {
+        .bindings = GetLocalInstBlockContents(generic.bindings_id),
+        .decl_block = GetLocalInstBlockContents(generic.decl_block_id),
+        .definition_block =
+            GetLocalInstBlockContents(generic.definition_block_id),
+    };
   }
 
-  // Gets a local specific whose arguments were already imported by
-  // GetLocalSpecificArgs. Does not add any new work.
-  auto GetLocalSpecific(SemIR::SpecificId specific_id,
-                        llvm::ArrayRef<SemIR::InstId> args)
-      -> SemIR::SpecificId {
+  // Given the local constant values for the elements of the eval block, builds
+  // and returns the eval block for a region of a generic.
+  auto GetLocalEvalBlock(const SemIR::Generic& import_generic,
+                         SemIR::GenericId generic_id,
+                         SemIR::GenericInstIndex::Region region,
+                         llvm::ArrayRef<SemIR::InstId> inst_ids)
+      -> SemIR::InstBlockId {
+    auto import_block_id = import_generic.GetEvalBlock(region);
+    if (!import_block_id.is_valid()) {
+      return SemIR::InstBlockId::Invalid;
+    }
+    return RebuildGenericEvalBlock(context_, generic_id, region, inst_ids);
+  }
+
+  // Adds the given local generic data to the given generic.
+  auto SetGenericData(SemIR::GenericId import_generic_id,
+                      SemIR::GenericId new_generic_id,
+                      const GenericData& generic_data) -> void {
+    if (!import_generic_id.is_valid()) {
+      return;
+    }
+
+    const auto& import_generic = import_ir_.generics().Get(import_generic_id);
+    auto& new_generic = context_.generics().Get(new_generic_id);
+    new_generic.bindings_id = GetLocalCanonicalInstBlockId(
+        import_generic.bindings_id, generic_data.bindings);
+    // TODO: Import or rebuild the self specific.
+    new_generic.decl_block_id = GetLocalEvalBlock(
+        import_generic, new_generic_id,
+        SemIR::GenericInstIndex::Region::Declaration, generic_data.decl_block);
+    new_generic.definition_block_id =
+        GetLocalEvalBlock(import_generic, new_generic_id,
+                          SemIR::GenericInstIndex::Region::Definition,
+                          generic_data.definition_block);
+  }
+
+  // Gets a local constant value corresponding to an imported generic ID. May
+  // add work to the work stack and return `Invalid`.
+  auto GetLocalConstantId(SemIR::GenericId generic_id) -> SemIR::ConstantId {
+    if (!generic_id.is_valid()) {
+      return SemIR::ConstantId::Invalid;
+    }
+    return GetLocalConstantId(
+        import_ir_.insts()
+            .Get(import_ir_.generics().Get(generic_id).decl_id)
+            .type_id());
+  }
+
+  // Gets a local generic ID given the corresponding local constant ID returned
+  // by GetLocalConstantId for the imported generic. Does not add any new work.
+  auto GetLocalGenericId(SemIR::ConstantId local_const_id) -> SemIR::GenericId {
+    if (!local_const_id.is_valid()) {
+      return SemIR::GenericId::Invalid;
+    }
+    auto type = context_.insts().Get(
+        context_.constant_values().GetInstId(local_const_id));
+    CARBON_KIND_SWITCH(type) {
+      case CARBON_KIND(SemIR::FunctionType fn_type): {
+        return context_.functions().Get(fn_type.function_id).generic_id;
+      }
+      case CARBON_KIND(SemIR::GenericClassType class_type): {
+        return context_.classes().Get(class_type.class_id).generic_id;
+      }
+      case CARBON_KIND(SemIR::GenericInterfaceType interface_type): {
+        return context_.interfaces()
+            .Get(interface_type.interface_id)
+            .generic_id;
+      }
+      default: {
+        CARBON_FATAL() << "Unexpected type for generic declaration: " << type;
+      }
+    }
+  }
+
+  // Gets local information about an imported specific.
+  auto GetLocalSpecificData(SemIR::SpecificId specific_id) -> SpecificData {
     if (!specific_id.is_valid()) {
+      return {.generic_const_id = SemIR::ConstantId::Invalid, .args = {}};
+    }
+
+    const auto& specific = import_ir_.specifics().Get(specific_id);
+    return {
+        .generic_const_id = GetLocalConstantId(specific.generic_id),
+        .args = GetLocalInstBlockContents(specific.args_id),
+        .decl_block = GetLocalInstBlockContents(specific.decl_block_id),
+        .definition_block =
+            GetLocalInstBlockContents(specific.definition_block_id),
+    };
+  }
+
+  // Gets a local specific whose data was already imported by
+  // GetLocalSpecificData. Does not add any new work.
+  auto GetOrAddLocalSpecific(SemIR::SpecificId import_specific_id,
+                             const SpecificData& data) -> SemIR::SpecificId {
+    if (!import_specific_id.is_valid()) {
       return SemIR::SpecificId::Invalid;
     }
-    const auto& specific = import_ir_.specifics().Get(specific_id);
-    // TODO: Import the generic.
-    auto generic_id = SemIR::GenericId::Invalid;
-    auto args_id = GetLocalCanonicalInstBlockId(specific.args_id, args);
-    // TODO: Also import the specific.
-    return context_.specifics().GetOrAdd(generic_id, args_id);
+
+    // Form a corresponding local specific ID.
+    const auto& import_specific =
+        import_ir_.specifics().Get(import_specific_id);
+    auto generic_id = GetLocalGenericId(data.generic_const_id);
+    auto args_id =
+        GetLocalCanonicalInstBlockId(import_specific.args_id, data.args);
+
+    // Populate the specific. Note that we might get data from multiple
+    // different import IRs, so only import data we don't already have.
+    auto specific_id = context_.specifics().GetOrAdd(generic_id, args_id);
+    auto& specific = context_.specifics().Get(specific_id);
+    if (!specific.decl_block_id.is_valid()) {
+      specific.decl_block_id =
+          GetLocalInstBlockId(import_specific.decl_block_id, data.decl_block);
+    }
+    if (!specific.definition_block_id.is_valid()) {
+      specific.definition_block_id = GetLocalInstBlockId(
+          import_specific.definition_block_id, data.definition_block);
+    }
+    return specific_id;
   }
 
   // Returns the ConstantId for each parameter's type. Adds unresolved constants
@@ -653,7 +791,7 @@ class ImportRefResolver {
     return {
         .name_id = GetLocalNameId(import_base.name_id),
         .parent_scope_id = SemIR::NameScopeId::Invalid,
-        .generic_id = GetLocalGeneric(import_base.generic_id),
+        .generic_id = MakeIncompleteGeneric(decl_id, import_base.generic_id),
         .first_param_node_id = Parse::NodeId::Invalid,
         .last_param_node_id = Parse::NodeId::Invalid,
         .implicit_param_refs_id = import_base.implicit_param_refs_id.is_valid()
@@ -854,11 +992,22 @@ class ImportRefResolver {
       return ResolveResult::Retry();
     }
 
+    // TODO: Track an interface type, not an interface ID, on
+    // AssociatedEntityType.
+    auto interface_inst = context_.insts().Get(interface_inst_id);
+    SemIR::InterfaceId interface_id = SemIR::InterfaceId::Invalid;
+    if (interface_inst.Is<SemIR::InterfaceType>()) {
+      interface_id = interface_inst.As<SemIR::InterfaceType>().interface_id;
+    } else {
+      interface_id =
+          context_.types()
+              .GetAs<SemIR::GenericInterfaceType>(interface_inst.type_id())
+              .interface_id;
+    }
+
     return ResolveAs<SemIR::AssociatedEntityType>(
         {.type_id = SemIR::TypeId::TypeType,
-         .interface_id = context_.insts()
-                             .GetAs<SemIR::InterfaceType>(interface_inst_id)
-                             .interface_id,
+         .interface_id = interface_id,
          .entity_type_id =
              context_.GetTypeIdForTypeConstant(entity_type_const_id)});
   }
@@ -1009,6 +1158,7 @@ class ImportRefResolver {
         GetLocalParamConstantIds(import_class.implicit_param_refs_id);
     llvm::SmallVector<SemIR::ConstantId> param_const_ids =
         GetLocalParamConstantIds(import_class.param_refs_id);
+    auto generic_data = GetLocalGenericData(import_class.generic_id);
     auto self_const_id = GetLocalConstantId(import_class.self_type_id);
     auto object_repr_const_id =
         import_class.object_repr_id.is_valid()
@@ -1028,6 +1178,7 @@ class ImportRefResolver {
         import_class.implicit_param_refs_id, implicit_param_const_ids);
     new_class.param_refs_id =
         GetLocalParamRefsId(import_class.param_refs_id, param_const_ids);
+    SetGenericData(import_class.generic_id, new_class.generic_id, generic_data);
     new_class.self_type_id = context_.GetTypeIdForTypeConstant(self_const_id);
 
     if (import_class.is_defined()) {
@@ -1043,7 +1194,7 @@ class ImportRefResolver {
     CARBON_CHECK(inst.type_id == SemIR::TypeId::TypeType);
     auto class_const_id =
         GetLocalConstantId(import_ir_.classes().Get(inst.class_id).decl_id);
-    auto args = GetLocalSpecificArgs(inst.specific_id);
+    auto specific_data = GetLocalSpecificData(inst.specific_id);
     if (HasNewWork(initial_work)) {
       return ResolveResult::Retry();
     }
@@ -1058,7 +1209,7 @@ class ImportRefResolver {
     } else {
       auto generic_class_type = context_.types().GetAs<SemIR::GenericClassType>(
           class_const_inst.type_id());
-      auto specific_id = GetLocalSpecific(inst.specific_id, args);
+      auto specific_id = GetOrAddLocalSpecific(inst.specific_id, specific_data);
       return ResolveAs<SemIR::ClassType>(
           {.type_id = SemIR::TypeId::TypeType,
            .class_id = generic_class_type.class_id,
@@ -1116,6 +1267,7 @@ class ImportRefResolver {
         GetLocalParamConstantIds(function.implicit_param_refs_id);
     llvm::SmallVector<SemIR::ConstantId> param_const_ids =
         GetLocalParamConstantIds(function.param_refs_id);
+    auto generic_data = GetLocalGenericData(function.generic_id);
 
     if (HasNewWork(initial_work)) {
       return ResolveResult::Retry();
@@ -1130,7 +1282,9 @@ class ImportRefResolver {
     auto function_decl_id = context_.AddPlaceholderInstInNoBlock(
         SemIR::LocIdAndInst(import_ir_inst_id, function_decl));
     // TODO: Implement import for generics.
-    auto generic_id = GetLocalGeneric(function.generic_id);
+    auto generic_id =
+        MakeIncompleteGeneric(function_decl_id, function.generic_id);
+    SetGenericData(function.generic_id, generic_id, generic_data);
 
     auto new_return_storage = SemIR::InstId::Invalid;
     if (function.return_storage_id.is_valid()) {
@@ -1173,14 +1327,18 @@ class ImportRefResolver {
     CARBON_CHECK(inst.type_id == SemIR::TypeId::TypeType);
     auto fn_val_id = GetLocalConstantInstId(
         import_ir_.functions().Get(inst.function_id).decl_id);
+    auto specific_data = GetLocalSpecificData(inst.specific_id);
     if (HasNewWork(initial_work)) {
       return ResolveResult::Retry();
     }
-    auto fn_val = context_.insts().Get(fn_val_id);
-    CARBON_CHECK(context_.types().Is<SemIR::FunctionType>(fn_val.type_id()));
-    // TODO: Import the correct specific and build a function type constant
-    // using it.
-    return {.const_id = context_.types().GetConstantId(fn_val.type_id())};
+    auto fn_type_id = context_.insts().Get(fn_val_id).type_id();
+    return ResolveAs<SemIR::FunctionType>(
+        {.type_id = SemIR::TypeId::TypeType,
+         .function_id = context_.types()
+                            .GetAs<SemIR::FunctionType>(fn_type_id)
+                            .function_id,
+         .specific_id =
+             GetOrAddLocalSpecific(inst.specific_id, specific_data)});
   }
 
   auto TryResolveTypedInst(SemIR::GenericClassType inst) -> ResolveResult {
@@ -1322,6 +1480,7 @@ class ImportRefResolver {
         GetLocalParamConstantIds(import_interface.implicit_param_refs_id);
     llvm::SmallVector<SemIR::ConstantId> param_const_ids =
         GetLocalParamConstantIds(import_interface.param_refs_id);
+    auto generic_data = GetLocalGenericData(import_interface.generic_id);
 
     std::optional<SemIR::InstId> self_param_id;
     if (import_interface.is_defined()) {
@@ -1338,6 +1497,8 @@ class ImportRefResolver {
         import_interface.implicit_param_refs_id, implicit_param_const_ids);
     new_interface.param_refs_id =
         GetLocalParamRefsId(import_interface.param_refs_id, param_const_ids);
+    SetGenericData(import_interface.generic_id, new_interface.generic_id,
+                   generic_data);
 
     if (import_interface.is_defined()) {
       CARBON_CHECK(self_param_id);
@@ -1351,7 +1512,7 @@ class ImportRefResolver {
     CARBON_CHECK(inst.type_id == SemIR::TypeId::TypeType);
     auto interface_const_id = GetLocalConstantId(
         import_ir_.interfaces().Get(inst.interface_id).decl_id);
-    auto args = GetLocalSpecificArgs(inst.specific_id);
+    auto specific_data = GetLocalSpecificData(inst.specific_id);
     if (HasNewWork(initial_work)) {
       return ResolveResult::Retry();
     }
@@ -1368,7 +1529,7 @@ class ImportRefResolver {
       auto generic_interface_type =
           context_.types().GetAs<SemIR::GenericInterfaceType>(
               interface_const_inst.type_id());
-      auto specific_id = GetLocalSpecific(inst.specific_id, args);
+      auto specific_id = GetOrAddLocalSpecific(inst.specific_id, specific_data);
       return ResolveAs<SemIR::InterfaceType>(
           {.type_id = SemIR::TypeId::TypeType,
            .interface_id = generic_interface_type.interface_id,
diff --git a/toolchain/check/testdata/class/generic/import.carbon b/toolchain/check/testdata/class/generic/import.carbon
index 7df195a06898..30976b38b9bc 100644
--- a/toolchain/check/testdata/class/generic/import.carbon
+++ b/toolchain/check/testdata/class/generic/import.carbon
@@ -231,27 +231,35 @@ class Class(U:! type) {
 // CHECK:STDOUT:   %Class.type: type = generic_class_type @Class [template]
 // CHECK:STDOUT:   %.1: type = tuple_type () [template]
 // CHECK:STDOUT:   %Class.1: %Class.type = struct_value () [template]
-// CHECK:STDOUT:   %Class.2: type = class_type @Class, invalid(%T) [symbolic]
+// CHECK:STDOUT:   %Class.2: type = class_type @Class, @Class(%T) [symbolic]
 // CHECK:STDOUT:   %.2: type = unbound_element_type %Class.2, %T [symbolic]
 // CHECK:STDOUT:   %.3: type = struct_type {.x: %T} [symbolic]
 // CHECK:STDOUT:   %CompleteClass.type: type = generic_class_type @CompleteClass [template]
 // CHECK:STDOUT:   %CompleteClass.1: %CompleteClass.type = struct_value () [template]
 // CHECK:STDOUT:   %.4: type = struct_type {.n: i32} [template]
-// CHECK:STDOUT:   %CompleteClass.2: type = class_type @CompleteClass, invalid(%T) [symbolic]
+// CHECK:STDOUT:   %CompleteClass.2: type = class_type @CompleteClass, @CompleteClass(%T) [symbolic]
+// CHECK:STDOUT:   %F.type.1: type = fn_type @F.1 [template]
+// CHECK:STDOUT:   %F.1: %F.type.1 = struct_value () [template]
+// CHECK:STDOUT:   %F.type.2: type = fn_type @F.1, @CompleteClass(%T) [symbolic]
+// CHECK:STDOUT:   %F.2: %F.type.2 = struct_value () [symbolic]
+// CHECK:STDOUT:   %.5: type = unbound_element_type %CompleteClass.2, i32 [symbolic]
 // CHECK:STDOUT:   %Int32.type: type = fn_type @Int32 [template]
 // CHECK:STDOUT:   %Int32: %Int32.type = struct_value () [template]
-// CHECK:STDOUT:   %CompleteClass.3: type = class_type @CompleteClass, invalid(i32) [template]
-// CHECK:STDOUT:   %F.type: type = fn_type @F [template]
-// CHECK:STDOUT:   %F: %F.type = struct_value () [template]
-// CHECK:STDOUT:   %.5: type = ptr_type %.4 [template]
-// CHECK:STDOUT:   %.6: i32 = int_literal 1 [template]
-// CHECK:STDOUT:   %struct: %CompleteClass.3 = struct_value (%.6) [template]
+// CHECK:STDOUT:   %CompleteClass.3: type = class_type @CompleteClass, @CompleteClass(i32) [template]
+// CHECK:STDOUT:   %F.type.3: type = fn_type @F.2 [template]
+// CHECK:STDOUT:   %F.3: %F.type.3 = struct_value () [template]
+// CHECK:STDOUT:   %.6: type = unbound_element_type %CompleteClass.3, i32 [template]
+// CHECK:STDOUT:   %F.type.4: type = fn_type @F.1, @CompleteClass(i32) [template]
+// CHECK:STDOUT:   %F.4: %F.type.4 = struct_value () [template]
+// CHECK:STDOUT:   %.7: type = ptr_type %.4 [template]
+// CHECK:STDOUT:   %.8: i32 = int_literal 1 [template]
+// CHECK:STDOUT:   %struct: %CompleteClass.3 = struct_value (%.8) [template]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: imports {
 // CHECK:STDOUT:   %import_ref.1: %Class.type = import_ref Main//foo, inst+6, loaded [template = constants.%Class.1]
 // CHECK:STDOUT:   %import_ref.2: %CompleteClass.type = import_ref Main//foo, inst+14, loaded [template = constants.%CompleteClass.1]
-// CHECK:STDOUT:   %import_ref.3: %F.type = import_ref Main//foo, inst+55, loaded [template = constants.%F]
+// CHECK:STDOUT:   %import_ref.3: %F.type.3 = import_ref Main//foo, inst+55, loaded [template = constants.%F.3]
 // CHECK:STDOUT:   %Core: <namespace> = namespace file.%Core.import, [template] {
 // CHECK:STDOUT:     .Int32 = %import_ref.7
 // CHECK:STDOUT:     import Core//prelude
@@ -282,7 +290,7 @@ class Class(U:! type) {
 // CHECK:STDOUT:     %T.loc4_13.1: type = param T
 // CHECK:STDOUT:     %T.loc4_13.2: type = bind_symbolic_name T 0, %T.loc4_13.1 [symbolic = constants.%T]
 // CHECK:STDOUT:   }
-// CHECK:STDOUT:   %F.decl: %F.type = fn_decl @F [template = constants.%F] {
+// CHECK:STDOUT:   %F.decl: %F.type.3 = fn_decl @F.2 [template = constants.%F.3] {
 // CHECK:STDOUT:     %CompleteClass.ref: %CompleteClass.type = name_ref CompleteClass, imports.%import_ref.2 [template = constants.%CompleteClass.1]
 // CHECK:STDOUT:     %int.make_type_32: init type = call constants.%Int32() [template = i32]
 // CHECK:STDOUT:     %.loc8_24.1: type = value_of_initializer %int.make_type_32 [template = i32]
@@ -290,42 +298,88 @@ class Class(U:! type) {
 // CHECK:STDOUT:     %.loc8_24.3: init type = call %CompleteClass.ref(%.loc8_24.2) [template = constants.%CompleteClass.3]
 // CHECK:STDOUT:     %.loc8_28.1: type = value_of_initializer %.loc8_24.3 [template = constants.%CompleteClass.3]
 // CHECK:STDOUT:     %.loc8_28.2: type = converted %.loc8_24.3, %.loc8_28.1 [template = constants.%CompleteClass.3]
-// CHECK:STDOUT:     @F.%return: ref %CompleteClass.3 = var <return slot>
+// CHECK:STDOUT:     @F.2.%return: ref %CompleteClass.3 = var <return slot>
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: class @Class {
-// CHECK:STDOUT:   %T.ref: type = name_ref T, file.%T.loc4_13.2 [symbolic = constants.%T]
-// CHECK:STDOUT:   %.loc5: %.2 = field_decl x, element0 [template]
+// CHECK:STDOUT: generic class @Class(constants.%T: type) {
+// CHECK:STDOUT:   %T: type = bind_symbolic_name T 0 [symbolic = %T (constants.%T)]
 // CHECK:STDOUT:
-// CHECK:STDOUT: !members:
-// CHECK:STDOUT:   .Self = constants.%Class.2
-// CHECK:STDOUT:   .x = %.loc5
+// CHECK:STDOUT: !definition:
+// CHECK:STDOUT:   %Class: type = class_type @Class, @Class(%T) [symbolic = %Class (constants.%Class.2)]
+// CHECK:STDOUT:   %.1: type = unbound_element_type @Class.%Class (%Class.2), @Class.%T (%T) [symbolic = %.1 (constants.%.2)]
+// CHECK:STDOUT:
+// CHECK:STDOUT:   class {
+// CHECK:STDOUT:     %T.ref: type = name_ref T, file.%T.loc4_13.2 [symbolic = %T (constants.%T)]
+// CHECK:STDOUT:     %.loc5: @Class.%.1 (%.2) = field_decl x, element0 [template]
+// CHECK:STDOUT:
+// CHECK:STDOUT:   !members:
+// CHECK:STDOUT:     .Self = constants.%Class.2
+// CHECK:STDOUT:     .x = %.loc5
+// CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: class @CompleteClass {
-// CHECK:STDOUT: !members:
-// CHECK:STDOUT:   .Self = imports.%import_ref.4
-// CHECK:STDOUT:   .n = imports.%import_ref.5
-// CHECK:STDOUT:   .F = imports.%import_ref.6
+// CHECK:STDOUT: generic class @CompleteClass(constants.%T: type) {
+// CHECK:STDOUT:   %T: type = bind_symbolic_name T 0 [symbolic = %T (constants.%T)]
+// CHECK:STDOUT:
+// CHECK:STDOUT: !definition:
+// CHECK:STDOUT:   %CompleteClass: type = class_type @CompleteClass, @CompleteClass(%T) [symbolic = %CompleteClass (constants.%CompleteClass.2)]
+// CHECK:STDOUT:   %.1: type = unbound_element_type @CompleteClass.%CompleteClass (%CompleteClass.2), i32 [symbolic = %.1 (constants.%.5)]
+// CHECK:STDOUT:   %F.type: type = fn_type @F.1, @CompleteClass(%T) [symbolic = %F.type (constants.%F.type.2)]
+// CHECK:STDOUT:   %F: @CompleteClass.%F.type (%F.type.2) = struct_value () [symbolic = %F (constants.%F.2)]
+// CHECK:STDOUT:
+// CHECK:STDOUT:   class {
+// CHECK:STDOUT:   !members:
+// CHECK:STDOUT:     .Self = imports.%import_ref.4
+// CHECK:STDOUT:     .n = imports.%import_ref.5
+// CHECK:STDOUT:     .F = imports.%import_ref.6
+// CHECK:STDOUT:   }
+// CHECK:STDOUT: }
+// CHECK:STDOUT:
+// CHECK:STDOUT: generic fn @F.1(constants.%T: type) {
+// CHECK:STDOUT: !definition:
+// CHECK:STDOUT:
+// CHECK:STDOUT:   fn() -> i32;
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Int32() -> type = "int.make_type_32";
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @F() -> %return: %CompleteClass.3 {
+// CHECK:STDOUT: fn @F.2() -> %return: %CompleteClass.3 {
 // CHECK:STDOUT: !entry:
-// CHECK:STDOUT:   %.loc9_16: i32 = int_literal 1 [template = constants.%.6]
+// CHECK:STDOUT:   %.loc9_16: i32 = int_literal 1 [template = constants.%.8]
 // CHECK:STDOUT:   %.loc9_17.1: %.4 = struct_literal (%.loc9_16)
 // CHECK:STDOUT:   %.loc9_17.2: ref i32 = class_element_access %return, element0
-// CHECK:STDOUT:   %.loc9_17.3: init i32 = initialize_from %.loc9_16 to %.loc9_17.2 [template = constants.%.6]
+// CHECK:STDOUT:   %.loc9_17.3: init i32 = initialize_from %.loc9_16 to %.loc9_17.2 [template = constants.%.8]
 // CHECK:STDOUT:   %.loc9_17.4: init %CompleteClass.3 = class_init (%.loc9_17.3), %return [template = constants.%struct]
 // CHECK:STDOUT:   %.loc9_18: init %CompleteClass.3 = converted %.loc9_17.1, %.loc9_17.4 [template = constants.%struct]
 // CHECK:STDOUT:   return %.loc9_18 to %return
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific invalid(constants.%T);
+// CHECK:STDOUT: specific @Class(constants.%T) {
+// CHECK:STDOUT:   %T => constants.%T
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific invalid(i32);
+// CHECK:STDOUT: specific @Class(@Class.%T) {
+// CHECK:STDOUT:   %T => constants.%T
+// CHECK:STDOUT: }
+// CHECK:STDOUT:
+// CHECK:STDOUT: specific @CompleteClass(constants.%T) {
+// CHECK:STDOUT:   %T => constants.%T
+// CHECK:STDOUT: }
+// CHECK:STDOUT:
+// CHECK:STDOUT: specific @CompleteClass(@CompleteClass.%T) {
+// CHECK:STDOUT:   %T => constants.%T
+// CHECK:STDOUT: }
+// CHECK:STDOUT:
+// CHECK:STDOUT: specific @CompleteClass(i32) {
+// CHECK:STDOUT:   %T => i32
+// CHECK:STDOUT:
+// CHECK:STDOUT: !definition:
+// CHECK:STDOUT:   %CompleteClass => constants.%CompleteClass.3
+// CHECK:STDOUT:   %.1 => constants.%.6
+// CHECK:STDOUT:   %F.type => constants.%F.type.4
+// CHECK:STDOUT:   %F => constants.%F.4
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- use_foo.carbon
 // CHECK:STDOUT:
@@ -339,19 +393,25 @@ class Class(U:! type) {
 // CHECK:STDOUT:   %CompleteClass.1: %CompleteClass.type = struct_value () [template]
 // CHECK:STDOUT:   %.2: type = struct_type {.n: i32} [template]
 // CHECK:STDOUT:   %T: type = bind_symbolic_name T 0 [symbolic]
-// CHECK:STDOUT:   %CompleteClass.2: type = class_type @CompleteClass, invalid(%T) [symbolic]
-// CHECK:STDOUT:   %CompleteClass.3: type = class_type @CompleteClass, invalid(i32) [template]
-// CHECK:STDOUT:   %.3: type = ptr_type %.2 [template]
+// CHECK:STDOUT:   %CompleteClass.2: type = class_type @CompleteClass, @CompleteClass(%T) [symbolic]
 // CHECK:STDOUT:   %F.type.1: type = fn_type @F.1 [template]
 // CHECK:STDOUT:   %F.1: %F.type.1 = struct_value () [template]
-// CHECK:STDOUT:   %F.type.2: type = fn_type @F.2 [template]
-// CHECK:STDOUT:   %F.2: %F.type.2 = struct_value () [template]
+// CHECK:STDOUT:   %F.type.2: type = fn_type @F.1, @CompleteClass(%T) [symbolic]
+// CHECK:STDOUT:   %F.2: %F.type.2 = struct_value () [symbolic]
+// CHECK:STDOUT:   %.3: type = unbound_element_type %CompleteClass.2, i32 [symbolic]
+// CHECK:STDOUT:   %CompleteClass.3: type = class_type @CompleteClass, @CompleteClass(i32) [template]
+// CHECK:STDOUT:   %.4: type = unbound_element_type %CompleteClass.3, i32 [template]
+// CHECK:STDOUT:   %F.type.3: type = fn_type @F.1, @CompleteClass(i32) [template]
+// CHECK:STDOUT:   %F.3: %F.type.3 = struct_value () [template]
+// CHECK:STDOUT:   %.5: type = ptr_type %.2 [template]
+// CHECK:STDOUT:   %F.type.4: type = fn_type @F.2 [template]
+// CHECK:STDOUT:   %F.4: %F.type.4 = struct_value () [template]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: imports {
 // CHECK:STDOUT:   %import_ref.1 = import_ref Main//foo, inst+6, unloaded
 // CHECK:STDOUT:   %import_ref.2: %CompleteClass.type = import_ref Main//foo, inst+14, loaded [template = constants.%CompleteClass.1]
-// CHECK:STDOUT:   %import_ref.3: %F.type.1 = import_ref Main//foo, inst+55, loaded [template = constants.%F.1]
+// CHECK:STDOUT:   %import_ref.3: %F.type.4 = import_ref Main//foo, inst+55, loaded [template = constants.%F.4]
 // CHECK:STDOUT:   %Core: <namespace> = namespace file.%Core.import, [template] {
 // CHECK:STDOUT:     .Int32 = %import_ref.4
 // CHECK:STDOUT:     import Core//prelude
@@ -365,7 +425,7 @@ class Class(U:! type) {
 // CHECK:STDOUT:   %import_ref.4: %Int32.type = import_ref Core//prelude/types, inst+4, loaded [template = constants.%Int32]
 // CHECK:STDOUT:   %import_ref.5 = import_ref Main//foo, inst+18, unloaded
 // CHECK:STDOUT:   %import_ref.6 = import_ref Main//foo, inst+28, unloaded
-// CHECK:STDOUT:   %import_ref.7: %F.type.2 = import_ref Main//foo, inst+35, loaded [template = constants.%F.2]
+// CHECK:STDOUT:   %import_ref.7: %F.type.2 = import_ref Main//foo, inst+35, loaded [template = constants.%F.1]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: file {
@@ -386,11 +446,21 @@ class Class(U:! type) {
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: class @CompleteClass {
-// CHECK:STDOUT: !members:
-// CHECK:STDOUT:   .Self = imports.%import_ref.5
-// CHECK:STDOUT:   .n = imports.%import_ref.6
-// CHECK:STDOUT:   .F = imports.%import_ref.7
+// CHECK:STDOUT: generic class @CompleteClass(constants.%T: type) {
+// CHECK:STDOUT:   %T: type = bind_symbolic_name T 0 [symbolic = %T (constants.%T)]
+// CHECK:STDOUT:
+// CHECK:STDOUT: !definition:
+// CHECK:STDOUT:   %CompleteClass: type = class_type @CompleteClass, @CompleteClass(%T) [symbolic = %CompleteClass (constants.%CompleteClass.2)]
+// CHECK:STDOUT:   %.1: type = unbound_element_type @CompleteClass.%CompleteClass (%CompleteClass.2), i32 [symbolic = %.1 (constants.%.3)]
+// CHECK:STDOUT:   %F.type: type = fn_type @F.1, @CompleteClass(%T) [symbolic = %F.type (constants.%F.type.2)]
+// CHECK:STDOUT:   %F: @CompleteClass.%F.type (%F.type.2) = struct_value () [symbolic = %F (constants.%F.2)]
+// CHECK:STDOUT:
+// CHECK:STDOUT:   class {
+// CHECK:STDOUT:   !members:
+// CHECK:STDOUT:     .Self = imports.%import_ref.5
+// CHECK:STDOUT:     .n = imports.%import_ref.6
+// CHECK:STDOUT:     .F = imports.%import_ref.7
+// CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Int32() -> type = "int.make_type_32";
@@ -406,25 +476,43 @@ class Class(U:! type) {
 // CHECK:STDOUT:   %.loc6_27.2: type = converted %.loc6_23.3, %.loc6_27.1 [template = constants.%CompleteClass.3]
 // CHECK:STDOUT:   %v.var: ref %CompleteClass.3 = var v
 // CHECK:STDOUT:   %v: ref %CompleteClass.3 = bind_name v, %v.var
-// CHECK:STDOUT:   %F.ref.loc6: %F.type.1 = name_ref F, imports.%import_ref.3 [template = constants.%F.1]
+// CHECK:STDOUT:   %F.ref.loc6: %F.type.4 = name_ref F, imports.%import_ref.3 [template = constants.%F.4]
 // CHECK:STDOUT:   %.loc6_7: ref %CompleteClass.3 = splice_block %v.var {}
 // CHECK:STDOUT:   %F.call.loc6: init %CompleteClass.3 = call %F.ref.loc6() to %.loc6_7
 // CHECK:STDOUT:   assign %v.var, %F.call.loc6
 // CHECK:STDOUT:   %v.ref: ref %CompleteClass.3 = name_ref v, %v
-// CHECK:STDOUT:   %F.ref.loc7: %F.type.2 = name_ref F, imports.%import_ref.7 [template = constants.%F.2]
+// CHECK:STDOUT:   %F.ref.loc7: %F.type.2 = name_ref F, imports.%import_ref.7 [template = constants.%F.1]
 // CHECK:STDOUT:   %F.call.loc7: init i32 = call %F.ref.loc7()
 // CHECK:STDOUT:   %.loc7_15.1: i32 = value_of_initializer %F.call.loc7
 // CHECK:STDOUT:   %.loc7_15.2: i32 = converted %F.call.loc7, %.loc7_15.1
 // CHECK:STDOUT:   return %.loc7_15.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @F.1() -> %CompleteClass.3;
+// CHECK:STDOUT: generic fn @F.1(constants.%T: type) {
+// CHECK:STDOUT: !definition:
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @F.2() -> i32;
+// CHECK:STDOUT:   fn() -> i32;
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific invalid(constants.%T);
+// CHECK:STDOUT: fn @F.2() -> %CompleteClass.3;
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific invalid(i32);
+// CHECK:STDOUT: specific @CompleteClass(constants.%T) {
+// CHECK:STDOUT:   %T => constants.%T
+// CHECK:STDOUT: }
+// CHECK:STDOUT:
+// CHECK:STDOUT: specific @CompleteClass(@CompleteClass.%T) {
+// CHECK:STDOUT:   %T => constants.%T
+// CHECK:STDOUT: }
+// CHECK:STDOUT:
+// CHECK:STDOUT: specific @CompleteClass(i32) {
+// CHECK:STDOUT:   %T => i32
+// CHECK:STDOUT:
+// CHECK:STDOUT: !definition:
+// CHECK:STDOUT:   %CompleteClass => constants.%CompleteClass.3
+// CHECK:STDOUT:   %.1 => constants.%.4
+// CHECK:STDOUT:   %F.type => constants.%F.type.3
+// CHECK:STDOUT:   %F => constants.%F.3
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- fail_todo_use_foo.carbon
 // CHECK:STDOUT:
@@ -438,18 +526,25 @@ class Class(U:! type) {
 // CHECK:STDOUT:   %CompleteClass.1: %CompleteClass.type = struct_value () [template]
 // CHECK:STDOUT:   %.2: type = struct_type {.n: i32} [template]
 // CHECK:STDOUT:   %T: type = bind_symbolic_name T 0 [symbolic]
-// CHECK:STDOUT:   %CompleteClass.2: type = class_type @CompleteClass, invalid(%T) [symbolic]
-// CHECK:STDOUT:   %CompleteClass.3: type = class_type @CompleteClass, invalid(i32) [template]
-// CHECK:STDOUT:   %.3: type = ptr_type %.2 [template]
-// CHECK:STDOUT:   %F.type: type = fn_type @F [template]
-// CHECK:STDOUT:   %F: %F.type = struct_value () [template]
-// CHECK:STDOUT:   %.4: type = unbound_element_type %CompleteClass.2, i32 [symbolic]
+// CHECK:STDOUT:   %CompleteClass.2: type = class_type @CompleteClass, @CompleteClass(%T) [symbolic]
+// CHECK:STDOUT:   %F.type.1: type = fn_type @F.1 [template]
+// CHECK:STDOUT:   %F.1: %F.type.1 = struct_value () [template]
+// CHECK:STDOUT:   %F.type.2: type = fn_type @F.1, @CompleteClass(%T) [symbolic]
+// CHECK:STDOUT:   %F.2: %F.type.2 = struct_value () [symbolic]
+// CHECK:STDOUT:   %.3: type = unbound_element_type %CompleteClass.2, i32 [symbolic]
+// CHECK:STDOUT:   %CompleteClass.3: type = class_type @CompleteClass, @CompleteClass(i32) [template]
+// CHECK:STDOUT:   %.4: type = unbound_element_type %CompleteClass.3, i32 [template]
+// CHECK:STDOUT:   %F.type.3: type = fn_type @F.1, @CompleteClass(i32) [template]
+// CHECK:STDOUT:   %F.3: %F.type.3 = struct_value () [template]
+// CHECK:STDOUT:   %.5: type = ptr_type %.2 [template]
+// CHECK:STDOUT:   %F.type.4: type = fn_type @F.2 [template]
+// CHECK:STDOUT:   %F.4: %F.type.4 = struct_value () [template]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: imports {
 // CHECK:STDOUT:   %import_ref.1 = import_ref Main//foo, inst+6, unloaded
 // CHECK:STDOUT:   %import_ref.2: %CompleteClass.type = import_ref Main//foo, inst+14, loaded [template = constants.%CompleteClass.1]
-// CHECK:STDOUT:   %import_ref.3: %F.type = import_ref Main//foo, inst+55, loaded [template = constants.%F]
+// CHECK:STDOUT:   %import_ref.3: %F.type.4 = import_ref Main//foo, inst+55, loaded [template = constants.%F.4]
 // CHECK:STDOUT:   %Core: <namespace> = namespace file.%Core.import, [template] {
 // CHECK:STDOUT:     .Int32 = %import_ref.4
 // CHECK:STDOUT:     import Core//prelude
@@ -462,7 +557,7 @@ class Class(U:! type) {
 // CHECK:STDOUT:   }
 // CHECK:STDOUT:   %import_ref.4: %Int32.type = import_ref Core//prelude/types, inst+4, loaded [template = constants.%Int32]
 // CHECK:STDOUT:   %import_ref.5 = import_ref Main//foo, inst+18, unloaded
-// CHECK:STDOUT:   %import_ref.6: %.4 = import_ref Main//foo, inst+28, loaded [template = %.1]
+// CHECK:STDOUT:   %import_ref.6: %.3 = import_ref Main//foo, inst+28, loaded [template = %.1]
 // CHECK:STDOUT:   %import_ref.7 = import_ref Main//foo, inst+35, unloaded
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -484,11 +579,21 @@ class Class(U:! type) {
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: class @CompleteClass {
-// CHECK:STDOUT: !members:
-// CHECK:STDOUT:   .Self = imports.%import_ref.5
-// CHECK:STDOUT:   .n = imports.%import_ref.6
-// CHECK:STDOUT:   .F = imports.%import_ref.7
+// CHECK:STDOUT: generic class @CompleteClass(constants.%T: type) {
+// CHECK:STDOUT:   %T: type = bind_symbolic_name T 0 [symbolic = %T (constants.%T)]
+// CHECK:STDOUT:
+// CHECK:STDOUT: !definition:
+// CHECK:STDOUT:   %CompleteClass: type = class_type @CompleteClass, @CompleteClass(%T) [symbolic = %CompleteClass (constants.%CompleteClass.2)]
+// CHECK:STDOUT:   %.1: type = unbound_element_type @CompleteClass.%CompleteClass (%CompleteClass.2), i32 [symbolic = %.1 (constants.%.3)]
+// CHECK:STDOUT:   %F.type: type = fn_type @F.1, @CompleteClass(%T) [symbolic = %F.type (constants.%F.type.2)]
+// CHECK:STDOUT:   %F: @CompleteClass.%F.type (%F.type.2) = struct_value () [symbolic = %F (constants.%F.2)]
+// CHECK:STDOUT:
+// CHECK:STDOUT:   class {
+// CHECK:STDOUT:   !members:
+// CHECK:STDOUT:     .Self = imports.%import_ref.5
+// CHECK:STDOUT:     .n = imports.%import_ref.6
+// CHECK:STDOUT:     .F = imports.%import_ref.7
+// CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Int32() -> type = "int.make_type_32";
@@ -504,21 +609,47 @@ class Class(U:! type) {
 // CHECK:STDOUT:   %.loc6_27.2: type = converted %.loc6_23.3, %.loc6_27.1 [template = constants.%CompleteClass.3]
 // CHECK:STDOUT:   %v.var: ref %CompleteClass.3 = var v
 // CHECK:STDOUT:   %v: ref %CompleteClass.3 = bind_name v, %v.var
-// CHECK:STDOUT:   %F.ref: %F.type = name_ref F, imports.%import_ref.3 [template = constants.%F]
+// CHECK:STDOUT:   %F.ref: %F.type.4 = name_ref F, imports.%import_ref.3 [template = constants.%F.4]
 // CHECK:STDOUT:   %.loc6_7: ref %CompleteClass.3 = splice_block %v.var {}
 // CHECK:STDOUT:   %F.call: init %CompleteClass.3 = call %F.ref() to %.loc6_7
 // CHECK:STDOUT:   assign %v.var, %F.call
 // CHECK:STDOUT:   %v.ref: ref %CompleteClass.3 = name_ref v, %v
-// CHECK:STDOUT:   %n.ref: %.4 = name_ref n, imports.%import_ref.6 [template = imports.%.1]
+// CHECK:STDOUT:   %n.ref: %.3 = name_ref n, imports.%import_ref.6 [template = imports.%.1]
 // CHECK:STDOUT:   %.loc12: i32 = class_element_access <error>, element0 [template = <error>]
 // CHECK:STDOUT:   return <error>
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @F() -> %CompleteClass.3;
+// CHECK:STDOUT: generic fn @F.1(constants.%T: type) {
+// CHECK:STDOUT: !definition:
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific invalid(constants.%T);
+// CHECK:STDOUT:   fn() -> i32;
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific invalid(i32);
+// CHECK:STDOUT: fn @F.2() -> %CompleteClass.3;
+// CHECK:STDOUT:
+// CHECK:STDOUT: specific @CompleteClass(constants.%T) {
+// CHECK:STDOUT:   %T => constants.%T
+// CHECK:STDOUT:
+// CHECK:STDOUT: !definition:
+// CHECK:STDOUT:   %CompleteClass => constants.%CompleteClass.2
+// CHECK:STDOUT:   %.1 => constants.%.3
+// CHECK:STDOUT:   %F.type => constants.%F.type.2
+// CHECK:STDOUT:   %F => constants.%F.2
+// CHECK:STDOUT: }
+// CHECK:STDOUT:
+// CHECK:STDOUT: specific @CompleteClass(@CompleteClass.%T) {
+// CHECK:STDOUT:   %T => constants.%T
+// CHECK:STDOUT: }
+// CHECK:STDOUT:
+// CHECK:STDOUT: specific @CompleteClass(i32) {
+// CHECK:STDOUT:   %T => i32
+// CHECK:STDOUT:
+// CHECK:STDOUT: !definition:
+// CHECK:STDOUT:   %CompleteClass => constants.%CompleteClass.3
+// CHECK:STDOUT:   %.1 => constants.%.4
+// CHECK:STDOUT:   %F.type => constants.%F.type.3
+// CHECK:STDOUT:   %F => constants.%F.3
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- fail_generic_arg_mismatch.carbon
 // CHECK:STDOUT:
@@ -530,21 +661,32 @@ class Class(U:! type) {
 // CHECK:STDOUT:   %CompleteClass.1: %CompleteClass.type = struct_value () [template]
 // CHECK:STDOUT:   %.2: type = struct_type {.n: i32} [template]
 // CHECK:STDOUT:   %T: type = bind_symbolic_name T 0 [symbolic]
-// CHECK:STDOUT:   %CompleteClass.2: type = class_type @CompleteClass, invalid(%T) [symbolic]
+// CHECK:STDOUT:   %CompleteClass.2: type = class_type @CompleteClass, @CompleteClass(%T) [symbolic]
+// CHECK:STDOUT:   %F.type.1: type = fn_type @F.1 [template]
+// CHECK:STDOUT:   %F.1: %F.type.1 = struct_value () [template]
+// CHECK:STDOUT:   %F.type.2: type = fn_type @F.1, @CompleteClass(%T) [symbolic]
+// CHECK:STDOUT:   %F.2: %F.type.2 = struct_value () [symbolic]
+// CHECK:STDOUT:   %.3: type = unbound_element_type %CompleteClass.2, i32 [symbolic]
 // CHECK:STDOUT:   %Int32.type: type = fn_type @Int32 [template]
 // CHECK:STDOUT:   %Int32: %Int32.type = struct_value () [template]
-// CHECK:STDOUT:   %.3: type = ptr_type i32 [template]
-// CHECK:STDOUT:   %CompleteClass.3: type = class_type @CompleteClass, invalid(%.3) [template]
-// CHECK:STDOUT:   %.4: type = ptr_type %.2 [template]
-// CHECK:STDOUT:   %CompleteClass.4: type = class_type @CompleteClass, invalid(i32) [template]
-// CHECK:STDOUT:   %F.type: type = fn_type @F [template]
-// CHECK:STDOUT:   %F: %F.type = struct_value () [template]
+// CHECK:STDOUT:   %.4: type = ptr_type i32 [template]
+// CHECK:STDOUT:   %CompleteClass.3: type = class_type @CompleteClass, @CompleteClass(%.4) [template]
+// CHECK:STDOUT:   %.5: type = unbound_element_type %CompleteClass.3, i32 [template]
+// CHECK:STDOUT:   %F.type.3: type = fn_type @F.1, @CompleteClass(%.4) [template]
+// CHECK:STDOUT:   %F.3: %F.type.3 = struct_value () [template]
+// CHECK:STDOUT:   %.6: type = ptr_type %.2 [template]
+// CHECK:STDOUT:   %CompleteClass.4: type = class_type @CompleteClass, @CompleteClass(i32) [template]
+// CHECK:STDOUT:   %F.type.4: type = fn_type @F.2 [template]
+// CHECK:STDOUT:   %F.4: %F.type.4 = struct_value () [template]
+// CHECK:STDOUT:   %.7: type = unbound_element_type %CompleteClass.4, i32 [template]
+// CHECK:STDOUT:   %F.type.5: type = fn_type @F.1, @CompleteClass(i32) [template]
+// CHECK:STDOUT:   %F.5: %F.type.5 = struct_value () [template]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: imports {
 // CHECK:STDOUT:   %import_ref.1 = import_ref Main//foo, inst+6, unloaded
 // CHECK:STDOUT:   %import_ref.2: %CompleteClass.type = import_ref Main//foo, inst+14, loaded [template = constants.%CompleteClass.1]
-// CHECK:STDOUT:   %import_ref.3: %F.type = import_ref Main//foo, inst+55, loaded [template = constants.%F]
+// CHECK:STDOUT:   %import_ref.3: %F.type.4 = import_ref Main//foo, inst+55, loaded [template = constants.%F.4]
 // CHECK:STDOUT:   %Core: <namespace> = namespace file.%Core.import, [template] {
 // CHECK:STDOUT:     .Int32 = %import_ref.7
 // CHECK:STDOUT:     import Core//prelude
@@ -574,11 +716,21 @@ class Class(U:! type) {
 // CHECK:STDOUT:   %Use.decl: %Use.type = fn_decl @Use [template = constants.%Use] {}
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: class @CompleteClass {
-// CHECK:STDOUT: !members:
-// CHECK:STDOUT:   .Self = imports.%import_ref.4
-// CHECK:STDOUT:   .n = imports.%import_ref.5
-// CHECK:STDOUT:   .F = imports.%import_ref.6
+// CHECK:STDOUT: generic class @CompleteClass(constants.%T: type) {
+// CHECK:STDOUT:   %T: type = bind_symbolic_name T 0 [symbolic = %T (constants.%T)]
+// CHECK:STDOUT:
+// CHECK:STDOUT: !definition:
+// CHECK:STDOUT:   %CompleteClass: type = class_type @CompleteClass, @CompleteClass(%T) [symbolic = %CompleteClass (constants.%CompleteClass.2)]
+// CHECK:STDOUT:   %.1: type = unbound_element_type @CompleteClass.%CompleteClass (%CompleteClass.2), i32 [symbolic = %.1 (constants.%.3)]
+// CHECK:STDOUT:   %F.type: type = fn_type @F.1, @CompleteClass(%T) [symbolic = %F.type (constants.%F.type.2)]
+// CHECK:STDOUT:   %F: @CompleteClass.%F.type (%F.type.2) = struct_value () [symbolic = %F (constants.%F.2)]
+// CHECK:STDOUT:
+// CHECK:STDOUT:   class {
+// CHECK:STDOUT:   !members:
+// CHECK:STDOUT:     .Self = imports.%import_ref.4
+// CHECK:STDOUT:     .n = imports.%import_ref.5
+// CHECK:STDOUT:     .F = imports.%import_ref.6
+// CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Use() {
@@ -587,28 +739,56 @@ class Class(U:! type) {
 // CHECK:STDOUT:   %int.make_type_32: init type = call constants.%Int32() [template = i32]
 // CHECK:STDOUT:   %.loc11_27.1: type = value_of_initializer %int.make_type_32 [template = i32]
 // CHECK:STDOUT:   %.loc11_27.2: type = converted %int.make_type_32, %.loc11_27.1 [template = i32]
-// CHECK:STDOUT:   %.loc11_27.3: type = ptr_type i32 [template = constants.%.3]
+// CHECK:STDOUT:   %.loc11_27.3: type = ptr_type i32 [template = constants.%.4]
 // CHECK:STDOUT:   %.loc11_23: init type = call %CompleteClass.ref(%.loc11_27.3) [template = constants.%CompleteClass.3]
 // CHECK:STDOUT:   %.loc11_28.1: type = value_of_initializer %.loc11_23 [template = constants.%CompleteClass.3]
 // CHECK:STDOUT:   %.loc11_28.2: type = converted %.loc11_23, %.loc11_28.1 [template = constants.%CompleteClass.3]
 // CHECK:STDOUT:   %v.var: ref %CompleteClass.3 = var v
 // CHECK:STDOUT:   %v: ref %CompleteClass.3 = bind_name v, %v.var
-// CHECK:STDOUT:   %F.ref: %F.type = name_ref F, imports.%import_ref.3 [template = constants.%F]
+// CHECK:STDOUT:   %F.ref: %F.type.4 = name_ref F, imports.%import_ref.3 [template = constants.%F.4]
 // CHECK:STDOUT:   %.loc11_33: ref %CompleteClass.4 = temporary_storage
 // CHECK:STDOUT:   %F.call: init %CompleteClass.4 = call %F.ref() to %.loc11_33
 // CHECK:STDOUT:   assign %v.var, <error>
 // CHECK:STDOUT:   return
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
+// CHECK:STDOUT: generic fn @F.1(constants.%T: type) {
+// CHECK:STDOUT: !definition:
+// CHECK:STDOUT:
+// CHECK:STDOUT:   fn() -> i32;
+// CHECK:STDOUT: }
+// CHECK:STDOUT:
 // CHECK:STDOUT: fn @Int32() -> type = "int.make_type_32";
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @F() -> %CompleteClass.4;
+// CHECK:STDOUT: fn @F.2() -> %CompleteClass.4;
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific invalid(constants.%T);
+// CHECK:STDOUT: specific @CompleteClass(constants.%T) {
+// CHECK:STDOUT:   %T => constants.%T
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific invalid(constants.%.3);
+// CHECK:STDOUT: specific @CompleteClass(@CompleteClass.%T) {
+// CHECK:STDOUT:   %T => constants.%T
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific invalid(i32);
+// CHECK:STDOUT: specific @CompleteClass(constants.%.4) {
+// CHECK:STDOUT:   %T => constants.%.4
+// CHECK:STDOUT:
+// CHECK:STDOUT: !definition:
+// CHECK:STDOUT:   %CompleteClass => constants.%CompleteClass.3
+// CHECK:STDOUT:   %.1 => constants.%.5
+// CHECK:STDOUT:   %F.type => constants.%F.type.3
+// CHECK:STDOUT:   %F => constants.%F.3
+// CHECK:STDOUT: }
+// CHECK:STDOUT:
+// CHECK:STDOUT: specific @CompleteClass(i32) {
+// CHECK:STDOUT:   %T => i32
+// CHECK:STDOUT:
+// CHECK:STDOUT: !definition:
+// CHECK:STDOUT:   %CompleteClass => constants.%CompleteClass.4
+// CHECK:STDOUT:   %.1 => constants.%.7
+// CHECK:STDOUT:   %F.type => constants.%F.type.5
+// CHECK:STDOUT:   %F => constants.%F.5
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- fail_bad_foo.impl.carbon
 // CHECK:STDOUT:
@@ -618,7 +798,7 @@ class Class(U:! type) {
 // CHECK:STDOUT:   %.1: type = tuple_type () [template]
 // CHECK:STDOUT:   %Class.1: %Class.type = struct_value () [template]
 // CHECK:STDOUT:   %T: type = bind_symbolic_name T 0 [symbolic]
-// CHECK:STDOUT:   %Class.2: type = class_type @Class, invalid(%T) [symbolic]
+// CHECK:STDOUT:   %Class.2: type = class_type @Class, @Class(%T) [symbolic]
 // CHECK:STDOUT:   %.type: type = generic_class_type @.1 [template]
 // CHECK:STDOUT:   %.2: %.type = struct_value () [template]
 // CHECK:STDOUT:   %.3: type = class_type @.1, @.1(%U) [symbolic]
@@ -655,7 +835,11 @@ class Class(U:! type) {
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: class @Class;
+// CHECK:STDOUT: generic class @Class(constants.%T: type) {
+// CHECK:STDOUT:   %T: type = bind_symbolic_name T 0 [symbolic = %T (constants.%T)]
+// CHECK:STDOUT:
+// CHECK:STDOUT:   class;
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic class @.1(file.%U.loc14_13.2: type) {
 // CHECK:STDOUT:   %U: type = bind_symbolic_name U 0 [symbolic = %U (constants.%U)]
@@ -672,7 +856,9 @@ class Class(U:! type) {
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific invalid(constants.%T);
+// CHECK:STDOUT: specific @Class(constants.%T) {
+// CHECK:STDOUT:   %T => constants.%T
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: specific @.1(constants.%U) {
 // CHECK:STDOUT:   %U => constants.%U
diff --git a/toolchain/check/testdata/class/syntactic_merge_literal.carbon b/toolchain/check/testdata/class/syntactic_merge_literal.carbon
index c59ebd7346af..55d4b8cf2b32 100644
--- a/toolchain/check/testdata/class/syntactic_merge_literal.carbon
+++ b/toolchain/check/testdata/class/syntactic_merge_literal.carbon
@@ -12,21 +12,21 @@
 
 // --- int_match.carbon
 
-class C(a: i32) {}
-class D(b: C(1_000));
-class D(b: C(1_000)) {}
+class C(a:! i32) {}
+class D(b:! C(1_000));
+class D(b:! C(1_000)) {}
 
 // --- fail_int_mismatch.carbon
 
-class C(a: i32) {}
-class D(b: C(1000));
-// CHECK:STDERR: fail_int_mismatch.carbon:[[@LINE+6]]:14: ERROR: Redeclaration syntax differs here.
-// CHECK:STDERR: class D(b: C(1_000)) {}
-// CHECK:STDERR:              ^~~~~
-// CHECK:STDERR: fail_int_mismatch.carbon:[[@LINE-4]]:14: Comparing with previous declaration here.
-// CHECK:STDERR: class D(b: C(1000));
-// CHECK:STDERR:              ^~~~
-class D(b: C(1_000)) {}
+class C(a:! i32) {}
+class D(b:! C(1000));
+// CHECK:STDERR: fail_int_mismatch.carbon:[[@LINE+6]]:15: ERROR: Redeclaration syntax differs here.
+// CHECK:STDERR: class D(b:! C(1_000)) {}
+// CHECK:STDERR:               ^~~~~
+// CHECK:STDERR: fail_int_mismatch.carbon:[[@LINE-4]]:15: Comparing with previous declaration here.
+// CHECK:STDERR: class D(b:! C(1000));
+// CHECK:STDERR:               ^~~~
+class D(b:! C(1_000)) {}
 
 // CHECK:STDOUT: --- int_match.carbon
 // CHECK:STDOUT:
@@ -34,15 +34,17 @@ class D(b: C(1_000)) {}
 // CHECK:STDOUT:   %Int32.type: type = fn_type @Int32 [template]
 // CHECK:STDOUT:   %.1: type = tuple_type () [template]
 // CHECK:STDOUT:   %Int32: %Int32.type = struct_value () [template]
+// CHECK:STDOUT:   %a: i32 = bind_symbolic_name a 0 [symbolic]
 // CHECK:STDOUT:   %C.type: type = generic_class_type @C [template]
 // CHECK:STDOUT:   %C.1: %C.type = struct_value () [template]
-// CHECK:STDOUT:   %C.2: type = class_type @C [template]
+// CHECK:STDOUT:   %C.2: type = class_type @C, @C(%a) [symbolic]
 // CHECK:STDOUT:   %.2: type = struct_type {} [template]
 // CHECK:STDOUT:   %.3: i32 = int_literal 1000 [template]
-// CHECK:STDOUT:   %C.3: type = class_type @C, invalid(%.3) [template]
+// CHECK:STDOUT:   %C.3: type = class_type @C, @C(%.3) [template]
+// CHECK:STDOUT:   %b: %C.3 = bind_symbolic_name b 0 [symbolic]
 // CHECK:STDOUT:   %D.type: type = generic_class_type @D [template]
 // CHECK:STDOUT:   %D.1: %D.type = struct_value () [template]
-// CHECK:STDOUT:   %D.2: type = class_type @D [template]
+// CHECK:STDOUT:   %D.2: type = class_type @D, @D(%b) [symbolic]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: imports {
@@ -68,44 +70,66 @@ class D(b: C(1_000)) {}
 // CHECK:STDOUT:   %Core.import = import Core
 // CHECK:STDOUT:   %C.decl: %C.type = class_decl @C [template = constants.%C.1] {
 // CHECK:STDOUT:     %int.make_type_32: init type = call constants.%Int32() [template = i32]
-// CHECK:STDOUT:     %.loc2_12.1: type = value_of_initializer %int.make_type_32 [template = i32]
-// CHECK:STDOUT:     %.loc2_12.2: type = converted %int.make_type_32, %.loc2_12.1 [template = i32]
+// CHECK:STDOUT:     %.loc2_13.1: type = value_of_initializer %int.make_type_32 [template = i32]
+// CHECK:STDOUT:     %.loc2_13.2: type = converted %int.make_type_32, %.loc2_13.1 [template = i32]
 // CHECK:STDOUT:     %a.loc2_9.1: i32 = param a
-// CHECK:STDOUT:     %a.loc2_9.2: i32 = bind_name a, %a.loc2_9.1
+// CHECK:STDOUT:     %a.loc2_9.2: i32 = bind_symbolic_name a 0, %a.loc2_9.1 [symbolic = @C.%a (constants.%a)]
 // CHECK:STDOUT:   }
 // CHECK:STDOUT:   %D.decl.loc3: %D.type = class_decl @D [template = constants.%D.1] {
 // CHECK:STDOUT:     %C.ref.loc3: %C.type = name_ref C, %C.decl [template = constants.%C.1]
-// CHECK:STDOUT:     %.loc3_14: i32 = int_literal 1000 [template = constants.%.3]
-// CHECK:STDOUT:     %.loc3_13: init type = call %C.ref.loc3(%.loc3_14) [template = constants.%C.3]
-// CHECK:STDOUT:     %.loc3_19.1: type = value_of_initializer %.loc3_13 [template = constants.%C.3]
-// CHECK:STDOUT:     %.loc3_19.2: type = converted %.loc3_13, %.loc3_19.1 [template = constants.%C.3]
+// CHECK:STDOUT:     %.loc3_15: i32 = int_literal 1000 [template = constants.%.3]
+// CHECK:STDOUT:     %.loc3_14: init type = call %C.ref.loc3(%.loc3_15) [template = constants.%C.3]
+// CHECK:STDOUT:     %.loc3_20.1: type = value_of_initializer %.loc3_14 [template = constants.%C.3]
+// CHECK:STDOUT:     %.loc3_20.2: type = converted %.loc3_14, %.loc3_20.1 [template = constants.%C.3]
 // CHECK:STDOUT:     %b.loc3_9.1: %C.3 = param b
-// CHECK:STDOUT:     %b.loc3_9.2: %C.3 = bind_name b, %b.loc3_9.1
+// CHECK:STDOUT:     %b.loc3_9.2: %C.3 = bind_symbolic_name b 0, %b.loc3_9.1 [symbolic = @D.%b (constants.%b)]
 // CHECK:STDOUT:   }
 // CHECK:STDOUT:   %D.decl.loc4: %D.type = class_decl @D [template = constants.%D.1] {
 // CHECK:STDOUT:     %C.ref.loc4: %C.type = name_ref C, %C.decl [template = constants.%C.1]
-// CHECK:STDOUT:     %.loc4_14: i32 = int_literal 1000 [template = constants.%.3]
-// CHECK:STDOUT:     %.loc4_13: init type = call %C.ref.loc4(%.loc4_14) [template = constants.%C.3]
-// CHECK:STDOUT:     %.loc4_19.1: type = value_of_initializer %.loc4_13 [template = constants.%C.3]
-// CHECK:STDOUT:     %.loc4_19.2: type = converted %.loc4_13, %.loc4_19.1 [template = constants.%C.3]
+// CHECK:STDOUT:     %.loc4_15: i32 = int_literal 1000 [template = constants.%.3]
+// CHECK:STDOUT:     %.loc4_14: init type = call %C.ref.loc4(%.loc4_15) [template = constants.%C.3]
+// CHECK:STDOUT:     %.loc4_20.1: type = value_of_initializer %.loc4_14 [template = constants.%C.3]
+// CHECK:STDOUT:     %.loc4_20.2: type = converted %.loc4_14, %.loc4_20.1 [template = constants.%C.3]
 // CHECK:STDOUT:     %b.loc4_9.1: %C.3 = param b
-// CHECK:STDOUT:     %b.loc4_9.2: %C.3 = bind_name b, %b.loc4_9.1
+// CHECK:STDOUT:     %b.loc4_9.2: %C.3 = bind_symbolic_name b 0, %b.loc4_9.1 [symbolic = constants.%b]
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: class @C {
-// CHECK:STDOUT: !members:
-// CHECK:STDOUT:   .Self = constants.%C.2
+// CHECK:STDOUT: generic class @C(file.%a.loc2_9.2: i32) {
+// CHECK:STDOUT:   %a: i32 = bind_symbolic_name a 0 [symbolic = %a (constants.%a)]
+// CHECK:STDOUT:
+// CHECK:STDOUT: !definition:
+// CHECK:STDOUT:
+// CHECK:STDOUT:   class {
+// CHECK:STDOUT:   !members:
+// CHECK:STDOUT:     .Self = constants.%C.2
+// CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: class @D {
-// CHECK:STDOUT: !members:
-// CHECK:STDOUT:   .Self = constants.%D.2
+// CHECK:STDOUT: generic class @D(file.%b.loc3_9.2: %C.3) {
+// CHECK:STDOUT:   %b: %C.3 = bind_symbolic_name b 0 [symbolic = %b (constants.%b)]
+// CHECK:STDOUT:
+// CHECK:STDOUT: !definition:
+// CHECK:STDOUT:
+// CHECK:STDOUT:   class {
+// CHECK:STDOUT:   !members:
+// CHECK:STDOUT:     .Self = constants.%D.2
+// CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Int32() -> type = "int.make_type_32";
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific invalid(constants.%.3);
+// CHECK:STDOUT: specific @C(constants.%a) {
+// CHECK:STDOUT:   %a => constants.%a
+// CHECK:STDOUT: }
+// CHECK:STDOUT:
+// CHECK:STDOUT: specific @C(constants.%.3) {
+// CHECK:STDOUT:   %a => constants.%.3
+// CHECK:STDOUT: }
+// CHECK:STDOUT:
+// CHECK:STDOUT: specific @D(constants.%b) {
+// CHECK:STDOUT:   %b => constants.%b
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- fail_int_mismatch.carbon
 // CHECK:STDOUT:
@@ -113,18 +137,20 @@ class D(b: C(1_000)) {}
 // CHECK:STDOUT:   %Int32.type: type = fn_type @Int32 [template]
 // CHECK:STDOUT:   %.1: type = tuple_type () [template]
 // CHECK:STDOUT:   %Int32: %Int32.type = struct_value () [template]
+// CHECK:STDOUT:   %a: i32 = bind_symbolic_name a 0 [symbolic]
 // CHECK:STDOUT:   %C.type: type = generic_class_type @C [template]
 // CHECK:STDOUT:   %C.1: %C.type = struct_value () [template]
-// CHECK:STDOUT:   %C.2: type = class_type @C [template]
+// CHECK:STDOUT:   %C.2: type = class_type @C, @C(%a) [symbolic]
 // CHECK:STDOUT:   %.2: type = struct_type {} [template]
 // CHECK:STDOUT:   %.3: i32 = int_literal 1000 [template]
-// CHECK:STDOUT:   %C.3: type = class_type @C, invalid(%.3) [template]
+// CHECK:STDOUT:   %C.3: type = class_type @C, @C(%.3) [template]
+// CHECK:STDOUT:   %b: %C.3 = bind_symbolic_name b 0 [symbolic]
 // CHECK:STDOUT:   %D.type: type = generic_class_type @D [template]
 // CHECK:STDOUT:   %D.1: %D.type = struct_value () [template]
-// CHECK:STDOUT:   %D.2: type = class_type @D [template]
+// CHECK:STDOUT:   %D.2: type = class_type @D, @D(%b) [symbolic]
 // CHECK:STDOUT:   %.type: type = generic_class_type @.1 [template]
 // CHECK:STDOUT:   %.4: %.type = struct_value () [template]
-// CHECK:STDOUT:   %.5: type = class_type @.1 [template]
+// CHECK:STDOUT:   %.5: type = class_type @.1, @.1(%b) [symbolic]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: imports {
@@ -150,44 +176,74 @@ class D(b: C(1_000)) {}
 // CHECK:STDOUT:   %Core.import = import Core
 // CHECK:STDOUT:   %C.decl: %C.type = class_decl @C [template = constants.%C.1] {
 // CHECK:STDOUT:     %int.make_type_32: init type = call constants.%Int32() [template = i32]
-// CHECK:STDOUT:     %.loc2_12.1: type = value_of_initializer %int.make_type_32 [template = i32]
-// CHECK:STDOUT:     %.loc2_12.2: type = converted %int.make_type_32, %.loc2_12.1 [template = i32]
+// CHECK:STDOUT:     %.loc2_13.1: type = value_of_initializer %int.make_type_32 [template = i32]
+// CHECK:STDOUT:     %.loc2_13.2: type = converted %int.make_type_32, %.loc2_13.1 [template = i32]
 // CHECK:STDOUT:     %a.loc2_9.1: i32 = param a
-// CHECK:STDOUT:     %a.loc2_9.2: i32 = bind_name a, %a.loc2_9.1
+// CHECK:STDOUT:     %a.loc2_9.2: i32 = bind_symbolic_name a 0, %a.loc2_9.1 [symbolic = @C.%a (constants.%a)]
 // CHECK:STDOUT:   }
 // CHECK:STDOUT:   %D.decl: %D.type = class_decl @D [template = constants.%D.1] {
 // CHECK:STDOUT:     %C.ref.loc3: %C.type = name_ref C, %C.decl [template = constants.%C.1]
-// CHECK:STDOUT:     %.loc3_14: i32 = int_literal 1000 [template = constants.%.3]
-// CHECK:STDOUT:     %.loc3_13: init type = call %C.ref.loc3(%.loc3_14) [template = constants.%C.3]
-// CHECK:STDOUT:     %.loc3_18.1: type = value_of_initializer %.loc3_13 [template = constants.%C.3]
-// CHECK:STDOUT:     %.loc3_18.2: type = converted %.loc3_13, %.loc3_18.1 [template = constants.%C.3]
+// CHECK:STDOUT:     %.loc3_15: i32 = int_literal 1000 [template = constants.%.3]
+// CHECK:STDOUT:     %.loc3_14: init type = call %C.ref.loc3(%.loc3_15) [template = constants.%C.3]
+// CHECK:STDOUT:     %.loc3_19.1: type = value_of_initializer %.loc3_14 [template = constants.%C.3]
+// CHECK:STDOUT:     %.loc3_19.2: type = converted %.loc3_14, %.loc3_19.1 [template = constants.%C.3]
 // CHECK:STDOUT:     %b.loc3_9.1: %C.3 = param b
-// CHECK:STDOUT:     %b.loc3_9.2: %C.3 = bind_name b, %b.loc3_9.1
+// CHECK:STDOUT:     %b.loc3_9.2: %C.3 = bind_symbolic_name b 0, %b.loc3_9.1 [symbolic = @D.%b (constants.%b)]
 // CHECK:STDOUT:   }
 // CHECK:STDOUT:   %.decl: %.type = class_decl @.1 [template = constants.%.4] {
 // CHECK:STDOUT:     %C.ref.loc10: %C.type = name_ref C, %C.decl [template = constants.%C.1]
-// CHECK:STDOUT:     %.loc10_14: i32 = int_literal 1000 [template = constants.%.3]
-// CHECK:STDOUT:     %.loc10_13: init type = call %C.ref.loc10(%.loc10_14) [template = constants.%C.3]
-// CHECK:STDOUT:     %.loc10_19.1: type = value_of_initializer %.loc10_13 [template = constants.%C.3]
-// CHECK:STDOUT:     %.loc10_19.2: type = converted %.loc10_13, %.loc10_19.1 [template = constants.%C.3]
+// CHECK:STDOUT:     %.loc10_15: i32 = int_literal 1000 [template = constants.%.3]
+// CHECK:STDOUT:     %.loc10_14: init type = call %C.ref.loc10(%.loc10_15) [template = constants.%C.3]
+// CHECK:STDOUT:     %.loc10_20.1: type = value_of_initializer %.loc10_14 [template = constants.%C.3]
+// CHECK:STDOUT:     %.loc10_20.2: type = converted %.loc10_14, %.loc10_20.1 [template = constants.%C.3]
 // CHECK:STDOUT:     %b.loc10_9.1: %C.3 = param b
-// CHECK:STDOUT:     %b.loc10_9.2: %C.3 = bind_name b, %b.loc10_9.1
+// CHECK:STDOUT:     %b.loc10_9.2: %C.3 = bind_symbolic_name b 0, %b.loc10_9.1 [symbolic = @.1.%b (constants.%b)]
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: class @C {
-// CHECK:STDOUT: !members:
-// CHECK:STDOUT:   .Self = constants.%C.2
+// CHECK:STDOUT: generic class @C(file.%a.loc2_9.2: i32) {
+// CHECK:STDOUT:   %a: i32 = bind_symbolic_name a 0 [symbolic = %a (constants.%a)]
+// CHECK:STDOUT:
+// CHECK:STDOUT: !definition:
+// CHECK:STDOUT:
+// CHECK:STDOUT:   class {
+// CHECK:STDOUT:   !members:
+// CHECK:STDOUT:     .Self = constants.%C.2
+// CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: class @D;
+// CHECK:STDOUT: generic class @D(file.%b.loc3_9.2: %C.3) {
+// CHECK:STDOUT:   %b: %C.3 = bind_symbolic_name b 0 [symbolic = %b (constants.%b)]
 // CHECK:STDOUT:
-// CHECK:STDOUT: class @.1 {
-// CHECK:STDOUT: !members:
-// CHECK:STDOUT:   .Self = constants.%.5
+// CHECK:STDOUT:   class;
+// CHECK:STDOUT: }
+// CHECK:STDOUT:
+// CHECK:STDOUT: generic class @.1(file.%b.loc10_9.2: %C.3) {
+// CHECK:STDOUT:   %b: %C.3 = bind_symbolic_name b 0 [symbolic = %b (constants.%b)]
+// CHECK:STDOUT:
+// CHECK:STDOUT: !definition:
+// CHECK:STDOUT:
+// CHECK:STDOUT:   class {
+// CHECK:STDOUT:   !members:
+// CHECK:STDOUT:     .Self = constants.%.5
+// CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Int32() -> type = "int.make_type_32";
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific invalid(constants.%.3);
+// CHECK:STDOUT: specific @C(constants.%a) {
+// CHECK:STDOUT:   %a => constants.%a
+// CHECK:STDOUT: }
+// CHECK:STDOUT:
+// CHECK:STDOUT: specific @C(constants.%.3) {
+// CHECK:STDOUT:   %a => constants.%.3
+// CHECK:STDOUT: }
+// CHECK:STDOUT:
+// CHECK:STDOUT: specific @D(constants.%b) {
+// CHECK:STDOUT:   %b => constants.%b
+// CHECK:STDOUT: }
+// CHECK:STDOUT:
+// CHECK:STDOUT: specific @.1(constants.%b) {
+// CHECK:STDOUT:   %b => constants.%b
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/function/builtin/no_prelude/call_from_operator.carbon b/toolchain/check/testdata/function/builtin/no_prelude/call_from_operator.carbon
index 53bfbfd84f45..50011b20ffb2 100644
--- a/toolchain/check/testdata/function/builtin/no_prelude/call_from_operator.carbon
+++ b/toolchain/check/testdata/function/builtin/no_prelude/call_from_operator.carbon
@@ -191,7 +191,11 @@ var arr: [i32; 1 + 2] = (3, 4, 3 + 4);
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Op.1[@impl.%self.loc7_9.2: i32](@impl.%other.loc7_21.2: i32) -> i32 = "int.sadd";
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @Op.2[%self: %Self](%other: %Self) -> %Self;
+// CHECK:STDOUT: generic fn @Op.2(constants.%Self: %.2) {
+// CHECK:STDOUT:   %Self: %.2 = bind_symbolic_name Self 0 [symbolic = %Self (constants.%Self)]
+// CHECK:STDOUT:
+// CHECK:STDOUT:   fn[%self: %Self](%other: %Self) -> %Self;
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
 // CHECK:STDOUT: !entry:
diff --git a/toolchain/check/testdata/impl/lookup/import.carbon b/toolchain/check/testdata/impl/lookup/import.carbon
index de2e241014e9..36919722e9b5 100644
--- a/toolchain/check/testdata/impl/lookup/import.carbon
+++ b/toolchain/check/testdata/impl/lookup/import.carbon
@@ -197,7 +197,10 @@ fn G(c: Impl.C) {
 // CHECK:STDOUT:   return
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @F.1();
+// CHECK:STDOUT: generic fn @F.1(constants.%Self: %.2) {
+// CHECK:STDOUT:
+// CHECK:STDOUT:   fn();
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F.2();
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/impl/lookup/no_prelude/import.carbon b/toolchain/check/testdata/impl/lookup/no_prelude/import.carbon
index d4426f6d087d..e9afabf5dff2 100644
--- a/toolchain/check/testdata/impl/lookup/no_prelude/import.carbon
+++ b/toolchain/check/testdata/impl/lookup/no_prelude/import.carbon
@@ -172,7 +172,10 @@ fn G(c: Impl.C) {
 // CHECK:STDOUT:   return
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @F.1();
+// CHECK:STDOUT: generic fn @F.1(constants.%Self: %.2) {
+// CHECK:STDOUT:
+// CHECK:STDOUT:   fn();
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F.2();
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/impl/no_prelude/import_self.carbon b/toolchain/check/testdata/impl/no_prelude/import_self.carbon
index b0ad6b59ea54..081b1639f01d 100644
--- a/toolchain/check/testdata/impl/no_prelude/import_self.carbon
+++ b/toolchain/check/testdata/impl/no_prelude/import_self.carbon
@@ -170,7 +170,11 @@ fn F(x: (), y: ()) -> () {
 // CHECK:STDOUT:   return %.loc7_53
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @Op.2[%self: %Self](%other: %Self) -> %Self;
+// CHECK:STDOUT: generic fn @Op.2(constants.%Self: %.2) {
+// CHECK:STDOUT:   %Self: %.2 = bind_symbolic_name Self 0 [symbolic = %Self (constants.%Self)]
+// CHECK:STDOUT:
+// CHECK:STDOUT:   fn[%self: %Self](%other: %Self) -> %Self;
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F(%x: %.1, %y: %.1) -> %.1 {
 // CHECK:STDOUT: !entry:
diff --git a/toolchain/check/testdata/index/fail_negative_indexing.carbon b/toolchain/check/testdata/index/fail_negative_indexing.carbon
index ea26db0649c4..f80850f9b200 100644
--- a/toolchain/check/testdata/index/fail_negative_indexing.carbon
+++ b/toolchain/check/testdata/index/fail_negative_indexing.carbon
@@ -88,7 +88,11 @@ var b: i32 = a[-10];
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Int32() -> type = "int.make_type_32";
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @Op[%self: %Self]() -> %Self;
+// CHECK:STDOUT: generic fn @Op(constants.%Self: %.8) {
+// CHECK:STDOUT:   %Self: %.8 = bind_symbolic_name Self 0 [symbolic = %Self (constants.%Self)]
+// CHECK:STDOUT:
+// CHECK:STDOUT:   fn[%self: %Self]() -> %Self;
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
 // CHECK:STDOUT: !entry:
diff --git a/toolchain/check/testdata/interface/no_prelude/generic_import.carbon b/toolchain/check/testdata/interface/no_prelude/generic_import.carbon
index f8dfa7d9cc3f..9fd2cdd0f2ea 100644
--- a/toolchain/check/testdata/interface/no_prelude/generic_import.carbon
+++ b/toolchain/check/testdata/interface/no_prelude/generic_import.carbon
@@ -99,21 +99,26 @@ impl C as AddWith(C) {
 // CHECK:STDOUT:   %.2: type = tuple_type () [template]
 // CHECK:STDOUT:   %AddWith: %AddWith.type = struct_value () [template]
 // CHECK:STDOUT:   %T: type = bind_symbolic_name T 0 [symbolic]
-// CHECK:STDOUT:   %.3: type = interface_type @AddWith, invalid(%T) [symbolic]
+// CHECK:STDOUT:   %.3: type = interface_type @AddWith, @AddWith(%T) [symbolic]
 // CHECK:STDOUT:   %Self: %.3 = bind_symbolic_name Self 1 [symbolic]
-// CHECK:STDOUT:   %.4: type = interface_type @AddWith, invalid(%C) [template]
 // CHECK:STDOUT:   %F.type.1: type = fn_type @F.1 [template]
 // CHECK:STDOUT:   %F.1: %F.type.1 = struct_value () [template]
-// CHECK:STDOUT:   %F.type.2: type = fn_type @F.2 [template]
-// CHECK:STDOUT:   %F.2: %F.type.2 = struct_value () [template]
-// CHECK:STDOUT:   %.5: <witness> = interface_witness (%F.1) [template]
+// CHECK:STDOUT:   %F.type.2: type = fn_type @F.1, @AddWith(%T) [symbolic]
+// CHECK:STDOUT:   %.4: type = assoc_entity_type @AddWith, %F.type.2 [symbolic]
+// CHECK:STDOUT:   %.5: %.4 = assoc_entity element0, imports.%import_ref.2 [symbolic]
+// CHECK:STDOUT:   %F.2: %F.type.2 = struct_value () [symbolic]
+// CHECK:STDOUT:   %.6: type = interface_type @AddWith, @AddWith(%C) [template]
+// CHECK:STDOUT:   %F.type.3: type = fn_type @F.2 [template]
+// CHECK:STDOUT:   %F.3: %F.type.3 = struct_value () [template]
+// CHECK:STDOUT:   %.7: <witness> = interface_witness (%F.3) [template]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: imports {
 // CHECK:STDOUT:   %import_ref.1: %AddWith.type = import_ref Main//a, inst+4, loaded [template = constants.%AddWith]
-// CHECK:STDOUT:   %import_ref.2 = import_ref Main//a, inst+10, unloaded
-// CHECK:STDOUT:   %import_ref.3 = import_ref Main//a, inst+16, unloaded
-// CHECK:STDOUT:   %import_ref.4: %F.type.2 = import_ref Main//a, inst+12, loaded [template = constants.%F.2]
+// CHECK:STDOUT:   %import_ref.2 = import_ref Main//a, inst+12, unloaded
+// CHECK:STDOUT:   %import_ref.3 = import_ref Main//a, inst+10, unloaded
+// CHECK:STDOUT:   %import_ref.4 = import_ref Main//a, inst+16, unloaded
+// CHECK:STDOUT:   %import_ref.5: %F.type.2 = import_ref Main//a, inst+12, loaded [template = constants.%F.1]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: file {
@@ -123,26 +128,38 @@ impl C as AddWith(C) {
 // CHECK:STDOUT:   }
 // CHECK:STDOUT:   %default.import = import <invalid>
 // CHECK:STDOUT:   %C.decl: type = class_decl @C [template = constants.%C] {}
-// CHECK:STDOUT:   %.loc7_20.1: type = value_of_initializer %.loc7_18 [template = constants.%.4]
-// CHECK:STDOUT:   %.loc7_20.2: type = converted %.loc7_18, %.loc7_20.1 [template = constants.%.4]
+// CHECK:STDOUT:   %.loc7_20.1: type = value_of_initializer %.loc7_18 [template = constants.%.6]
+// CHECK:STDOUT:   %.loc7_20.2: type = converted %.loc7_18, %.loc7_20.1 [template = constants.%.6]
 // CHECK:STDOUT:   impl_decl @impl {
 // CHECK:STDOUT:     %C.ref.loc7_6: type = name_ref C, %C.decl [template = constants.%C]
 // CHECK:STDOUT:     %AddWith.ref: %AddWith.type = name_ref AddWith, imports.%import_ref.1 [template = constants.%AddWith]
 // CHECK:STDOUT:     %C.ref.loc7_19: type = name_ref C, %C.decl [template = constants.%C]
-// CHECK:STDOUT:     %.loc7_18: init type = call %AddWith.ref(%C.ref.loc7_19) [template = constants.%.4]
+// CHECK:STDOUT:     %.loc7_18: init type = call %AddWith.ref(%C.ref.loc7_19) [template = constants.%.6]
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: interface @AddWith {
-// CHECK:STDOUT: !members:
-// CHECK:STDOUT:   .Self = imports.%import_ref.2
-// CHECK:STDOUT:   .F = imports.%import_ref.3
-// CHECK:STDOUT:   witness = (imports.%import_ref.4)
+// CHECK:STDOUT: generic interface @AddWith(constants.%T: type) {
+// CHECK:STDOUT:   %T: type = bind_symbolic_name T 0 [symbolic = %T (constants.%T)]
+// CHECK:STDOUT:
+// CHECK:STDOUT: !definition:
+// CHECK:STDOUT:   %.1: type = interface_type @AddWith, @AddWith(%T) [symbolic = %.1 (constants.%.3)]
+// CHECK:STDOUT:   %Self: %.3 = bind_symbolic_name Self 1 [symbolic = %Self (constants.%Self)]
+// CHECK:STDOUT:   %F.type: type = fn_type @F.1, @AddWith(%T) [symbolic = %F.type (constants.%F.type.2)]
+// CHECK:STDOUT:   %F: @AddWith.%F.type (%F.type.2) = struct_value () [symbolic = %F (constants.%F.2)]
+// CHECK:STDOUT:   %.2: type = assoc_entity_type @AddWith, @AddWith.%F.type (%F.type.2) [symbolic = %.2 (constants.%.4)]
+// CHECK:STDOUT:   %.3: @AddWith.%.2 (%.4) = assoc_entity element0, imports.%import_ref.2 [symbolic = %.3 (constants.%.5)]
+// CHECK:STDOUT:
+// CHECK:STDOUT:   interface {
+// CHECK:STDOUT:   !members:
+// CHECK:STDOUT:     .Self = imports.%import_ref.3
+// CHECK:STDOUT:     .F = imports.%import_ref.4
+// CHECK:STDOUT:     witness = (imports.%import_ref.5)
+// CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: impl @impl: %C as %.4 {
-// CHECK:STDOUT:   %F.decl: %F.type.1 = fn_decl @F.1 [template = constants.%F.1] {}
-// CHECK:STDOUT:   %.1: <witness> = interface_witness (%F.decl) [template = constants.%.5]
+// CHECK:STDOUT: impl @impl: %C as %.6 {
+// CHECK:STDOUT:   %F.decl: %F.type.3 = fn_decl @F.2 [template = constants.%F.3] {}
+// CHECK:STDOUT:   %.1: <witness> = interface_witness (%F.decl) [template = constants.%.7]
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .F = %F.decl
@@ -154,14 +171,25 @@ impl C as AddWith(C) {
 // CHECK:STDOUT:   .Self = constants.%C
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @F.1() {
+// CHECK:STDOUT: generic fn @F.1(constants.%T: type, constants.%Self: %.3) {
+// CHECK:STDOUT:
+// CHECK:STDOUT:   fn();
+// CHECK:STDOUT: }
+// CHECK:STDOUT:
+// CHECK:STDOUT: fn @F.2() {
 // CHECK:STDOUT: !entry:
 // CHECK:STDOUT:   return
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @F.2();
+// CHECK:STDOUT: specific @AddWith(constants.%T) {
+// CHECK:STDOUT:   %T => constants.%T
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific invalid(constants.%T);
+// CHECK:STDOUT: specific @AddWith(@AddWith.%T) {
+// CHECK:STDOUT:   %T => constants.%T
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific invalid(constants.%C);
+// CHECK:STDOUT: specific @AddWith(constants.%C) {
+// CHECK:STDOUT:   %T => constants.%C
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/interface/no_prelude/import.carbon b/toolchain/check/testdata/interface/no_prelude/import.carbon
index 33e82e4e3aca..11bc5f8beb28 100644
--- a/toolchain/check/testdata/interface/no_prelude/import.carbon
+++ b/toolchain/check/testdata/interface/no_prelude/import.carbon
@@ -281,9 +281,15 @@ var f: ForwardDeclared* = &f_ref.f;
 // CHECK:STDOUT:   return
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @F.1();
+// CHECK:STDOUT: generic fn @F.1(constants.%Self.2: %.3) {
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @F.2();
+// CHECK:STDOUT:   fn();
+// CHECK:STDOUT: }
+// CHECK:STDOUT:
+// CHECK:STDOUT: generic fn @F.2(constants.%Self.3: %.4) {
+// CHECK:STDOUT:
+// CHECK:STDOUT:   fn();
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
 // CHECK:STDOUT: !entry:
diff --git a/toolchain/check/testdata/operators/builtin/fail_type_mismatch_once.carbon b/toolchain/check/testdata/operators/builtin/fail_type_mismatch_once.carbon
index b4c5d2e3ab9a..cfd9f513c320 100644
--- a/toolchain/check/testdata/operators/builtin/fail_type_mismatch_once.carbon
+++ b/toolchain/check/testdata/operators/builtin/fail_type_mismatch_once.carbon
@@ -90,5 +90,9 @@ fn Main() -> i32 {
 // CHECK:STDOUT:   return <error>
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @Op[%self: %Self](%other: %Self) -> %Self;
+// CHECK:STDOUT: generic fn @Op(constants.%Self: %.4) {
+// CHECK:STDOUT:   %Self: %.4 = bind_symbolic_name Self 0 [symbolic = %Self (constants.%Self)]
+// CHECK:STDOUT:
+// CHECK:STDOUT:   fn[%self: %Self](%other: %Self) -> %Self;
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/operators/builtin/fail_unimplemented_op.carbon b/toolchain/check/testdata/operators/builtin/fail_unimplemented_op.carbon
index df5159403f38..4656fa1abacc 100644
--- a/toolchain/check/testdata/operators/builtin/fail_unimplemented_op.carbon
+++ b/toolchain/check/testdata/operators/builtin/fail_unimplemented_op.carbon
@@ -83,5 +83,9 @@ fn Main() -> i32 {
 // CHECK:STDOUT:   return <error>
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @Op[%self: %Self](%other: %Self) -> %Self;
+// CHECK:STDOUT: generic fn @Op(constants.%Self: %.4) {
+// CHECK:STDOUT:   %Self: %.4 = bind_symbolic_name Self 0 [symbolic = %Self (constants.%Self)]
+// CHECK:STDOUT:
+// CHECK:STDOUT:   fn[%self: %Self](%other: %Self) -> %Self;
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/operators/overloaded/add.carbon b/toolchain/check/testdata/operators/overloaded/add.carbon
index ab84fb10ed2e..4f672f53accd 100644
--- a/toolchain/check/testdata/operators/overloaded/add.carbon
+++ b/toolchain/check/testdata/operators/overloaded/add.carbon
@@ -192,14 +192,23 @@ fn TestAssign(a: C*, b: C) {
 // CHECK:STDOUT:   return %.loc19_14 to @impl.1.%return.var
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @Op.2[%self: %Self.1](%other: %Self.1) -> %Self.1;
+// CHECK:STDOUT: generic fn @Op.2(constants.%Self.1: %.2) {
+// CHECK:STDOUT:   %Self: %.2 = bind_symbolic_name Self 0 [symbolic = %Self (constants.%Self.1)]
+// CHECK:STDOUT:
+// CHECK:STDOUT:   fn[%self: %Self.1](%other: %Self.1) -> %Self.1;
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Op.3[addr @impl.2.%self.loc23_14.3: %.7](@impl.2.%other.loc23_24.2: %C) {
 // CHECK:STDOUT: !entry:
 // CHECK:STDOUT:   return
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @Op.4[addr %self: %.8](%other: %Self.2);
+// CHECK:STDOUT: generic fn @Op.4(constants.%Self.2: %.6) {
+// CHECK:STDOUT:   %Self: %.6 = bind_symbolic_name Self 0 [symbolic = %Self (constants.%Self.2)]
+// CHECK:STDOUT:   %.2: type = ptr_type @Op.4.%Self (%Self.2) [symbolic = %.2 (constants.%.8)]
+// CHECK:STDOUT:
+// CHECK:STDOUT:   fn[addr %self: %.8](%other: %Self.2);
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @TestOp(%a: %C, %b: %C) -> %return: %C {
 // CHECK:STDOUT: !entry:
diff --git a/toolchain/check/testdata/operators/overloaded/bit_and.carbon b/toolchain/check/testdata/operators/overloaded/bit_and.carbon
index 9412cc774225..f24cb300430b 100644
--- a/toolchain/check/testdata/operators/overloaded/bit_and.carbon
+++ b/toolchain/check/testdata/operators/overloaded/bit_and.carbon
@@ -192,14 +192,23 @@ fn TestAssign(a: C*, b: C) {
 // CHECK:STDOUT:   return %.loc19_14 to @impl.1.%return.var
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @Op.2[%self: %Self.1](%other: %Self.1) -> %Self.1;
+// CHECK:STDOUT: generic fn @Op.2(constants.%Self.1: %.2) {
+// CHECK:STDOUT:   %Self: %.2 = bind_symbolic_name Self 0 [symbolic = %Self (constants.%Self.1)]
+// CHECK:STDOUT:
+// CHECK:STDOUT:   fn[%self: %Self.1](%other: %Self.1) -> %Self.1;
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Op.3[addr @impl.2.%self.loc23_14.3: %.7](@impl.2.%other.loc23_24.2: %C) {
 // CHECK:STDOUT: !entry:
 // CHECK:STDOUT:   return
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @Op.4[addr %self: %.8](%other: %Self.2);
+// CHECK:STDOUT: generic fn @Op.4(constants.%Self.2: %.6) {
+// CHECK:STDOUT:   %Self: %.6 = bind_symbolic_name Self 0 [symbolic = %Self (constants.%Self.2)]
+// CHECK:STDOUT:   %.2: type = ptr_type @Op.4.%Self (%Self.2) [symbolic = %.2 (constants.%.8)]
+// CHECK:STDOUT:
+// CHECK:STDOUT:   fn[addr %self: %.8](%other: %Self.2);
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @TestOp(%a: %C, %b: %C) -> %return: %C {
 // CHECK:STDOUT: !entry:
diff --git a/toolchain/check/testdata/operators/overloaded/bit_complement.carbon b/toolchain/check/testdata/operators/overloaded/bit_complement.carbon
index df7a9f91a4b5..97449423a9b1 100644
--- a/toolchain/check/testdata/operators/overloaded/bit_complement.carbon
+++ b/toolchain/check/testdata/operators/overloaded/bit_complement.carbon
@@ -120,7 +120,11 @@ fn TestOp(a: C) -> C {
 // CHECK:STDOUT:   return %.loc19_14 to @impl.%return.var
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @Op.2[%self: %Self]() -> %Self;
+// CHECK:STDOUT: generic fn @Op.2(constants.%Self: %.2) {
+// CHECK:STDOUT:   %Self: %.2 = bind_symbolic_name Self 0 [symbolic = %Self (constants.%Self)]
+// CHECK:STDOUT:
+// CHECK:STDOUT:   fn[%self: %Self]() -> %Self;
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @TestOp(%a: %C) -> %return: %C {
 // CHECK:STDOUT: !entry:
diff --git a/toolchain/check/testdata/operators/overloaded/bit_or.carbon b/toolchain/check/testdata/operators/overloaded/bit_or.carbon
index 383fad1100ce..b0272dbe820f 100644
--- a/toolchain/check/testdata/operators/overloaded/bit_or.carbon
+++ b/toolchain/check/testdata/operators/overloaded/bit_or.carbon
@@ -192,14 +192,23 @@ fn TestAssign(a: C*, b: C) {
 // CHECK:STDOUT:   return %.loc19_14 to @impl.1.%return.var
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @Op.2[%self: %Self.1](%other: %Self.1) -> %Self.1;
+// CHECK:STDOUT: generic fn @Op.2(constants.%Self.1: %.2) {
+// CHECK:STDOUT:   %Self: %.2 = bind_symbolic_name Self 0 [symbolic = %Self (constants.%Self.1)]
+// CHECK:STDOUT:
+// CHECK:STDOUT:   fn[%self: %Self.1](%other: %Self.1) -> %Self.1;
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Op.3[addr @impl.2.%self.loc23_14.3: %.7](@impl.2.%other.loc23_24.2: %C) {
 // CHECK:STDOUT: !entry:
 // CHECK:STDOUT:   return
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @Op.4[addr %self: %.8](%other: %Self.2);
+// CHECK:STDOUT: generic fn @Op.4(constants.%Self.2: %.6) {
+// CHECK:STDOUT:   %Self: %.6 = bind_symbolic_name Self 0 [symbolic = %Self (constants.%Self.2)]
+// CHECK:STDOUT:   %.2: type = ptr_type @Op.4.%Self (%Self.2) [symbolic = %.2 (constants.%.8)]
+// CHECK:STDOUT:
+// CHECK:STDOUT:   fn[addr %self: %.8](%other: %Self.2);
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @TestOp(%a: %C, %b: %C) -> %return: %C {
 // CHECK:STDOUT: !entry:
diff --git a/toolchain/check/testdata/operators/overloaded/bit_xor.carbon b/toolchain/check/testdata/operators/overloaded/bit_xor.carbon
index ae06be9bc1c6..10a5918591ef 100644
--- a/toolchain/check/testdata/operators/overloaded/bit_xor.carbon
+++ b/toolchain/check/testdata/operators/overloaded/bit_xor.carbon
@@ -192,14 +192,23 @@ fn TestAssign(a: C*, b: C) {
 // CHECK:STDOUT:   return %.loc19_14 to @impl.1.%return.var
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @Op.2[%self: %Self.1](%other: %Self.1) -> %Self.1;
+// CHECK:STDOUT: generic fn @Op.2(constants.%Self.1: %.2) {
+// CHECK:STDOUT:   %Self: %.2 = bind_symbolic_name Self 0 [symbolic = %Self (constants.%Self.1)]
+// CHECK:STDOUT:
+// CHECK:STDOUT:   fn[%self: %Self.1](%other: %Self.1) -> %Self.1;
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Op.3[addr @impl.2.%self.loc23_14.3: %.7](@impl.2.%other.loc23_24.2: %C) {
 // CHECK:STDOUT: !entry:
 // CHECK:STDOUT:   return
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @Op.4[addr %self: %.8](%other: %Self.2);
+// CHECK:STDOUT: generic fn @Op.4(constants.%Self.2: %.6) {
+// CHECK:STDOUT:   %Self: %.6 = bind_symbolic_name Self 0 [symbolic = %Self (constants.%Self.2)]
+// CHECK:STDOUT:   %.2: type = ptr_type @Op.4.%Self (%Self.2) [symbolic = %.2 (constants.%.8)]
+// CHECK:STDOUT:
+// CHECK:STDOUT:   fn[addr %self: %.8](%other: %Self.2);
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @TestOp(%a: %C, %b: %C) -> %return: %C {
 // CHECK:STDOUT: !entry:
diff --git a/toolchain/check/testdata/operators/overloaded/dec.carbon b/toolchain/check/testdata/operators/overloaded/dec.carbon
index 3d92dd6848d8..ae6fbe9ccbe8 100644
--- a/toolchain/check/testdata/operators/overloaded/dec.carbon
+++ b/toolchain/check/testdata/operators/overloaded/dec.carbon
@@ -109,7 +109,12 @@ fn TestOp() {
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Op.1[addr @impl.%self.loc18_14.3: %.3]();
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @Op.2[addr %self: %.5]();
+// CHECK:STDOUT: generic fn @Op.2(constants.%Self: %.2) {
+// CHECK:STDOUT:   %Self: %.2 = bind_symbolic_name Self 0 [symbolic = %Self (constants.%Self)]
+// CHECK:STDOUT:   %.2: type = ptr_type @Op.2.%Self (%Self) [symbolic = %.2 (constants.%.5)]
+// CHECK:STDOUT:
+// CHECK:STDOUT:   fn[addr %self: %.5]();
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @TestOp() {
 // CHECK:STDOUT: !entry:
diff --git a/toolchain/check/testdata/operators/overloaded/div.carbon b/toolchain/check/testdata/operators/overloaded/div.carbon
index 41c4adddae85..c121c27c4688 100644
--- a/toolchain/check/testdata/operators/overloaded/div.carbon
+++ b/toolchain/check/testdata/operators/overloaded/div.carbon
@@ -192,14 +192,23 @@ fn TestAssign(a: C*, b: C) {
 // CHECK:STDOUT:   return %.loc19_14 to @impl.1.%return.var
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @Op.2[%self: %Self.1](%other: %Self.1) -> %Self.1;
+// CHECK:STDOUT: generic fn @Op.2(constants.%Self.1: %.2) {
+// CHECK:STDOUT:   %Self: %.2 = bind_symbolic_name Self 0 [symbolic = %Self (constants.%Self.1)]
+// CHECK:STDOUT:
+// CHECK:STDOUT:   fn[%self: %Self.1](%other: %Self.1) -> %Self.1;
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Op.3[addr @impl.2.%self.loc23_14.3: %.7](@impl.2.%other.loc23_24.2: %C) {
 // CHECK:STDOUT: !entry:
 // CHECK:STDOUT:   return
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @Op.4[addr %self: %.8](%other: %Self.2);
+// CHECK:STDOUT: generic fn @Op.4(constants.%Self.2: %.6) {
+// CHECK:STDOUT:   %Self: %.6 = bind_symbolic_name Self 0 [symbolic = %Self (constants.%Self.2)]
+// CHECK:STDOUT:   %.2: type = ptr_type @Op.4.%Self (%Self.2) [symbolic = %.2 (constants.%.8)]
+// CHECK:STDOUT:
+// CHECK:STDOUT:   fn[addr %self: %.8](%other: %Self.2);
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @TestOp(%a: %C, %b: %C) -> %return: %C {
 // CHECK:STDOUT: !entry:
diff --git a/toolchain/check/testdata/operators/overloaded/eq.carbon b/toolchain/check/testdata/operators/overloaded/eq.carbon
index 8fca3f1762df..288cfc035172 100644
--- a/toolchain/check/testdata/operators/overloaded/eq.carbon
+++ b/toolchain/check/testdata/operators/overloaded/eq.carbon
@@ -224,9 +224,17 @@ fn TestLhsBad(a: D, b: C) -> bool {
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @NotEqual.1[@impl.%self.loc8_15.2: %C](@impl.%other.loc8_24.2: %C) -> bool;
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @Equal.2[%self: %Self](%other: %Self) -> bool;
+// CHECK:STDOUT: generic fn @Equal.2(constants.%Self: %.2) {
+// CHECK:STDOUT:   %Self: %.2 = bind_symbolic_name Self 0 [symbolic = %Self (constants.%Self)]
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @NotEqual.2[%self: %Self](%other: %Self) -> bool;
+// CHECK:STDOUT:   fn[%self: %Self](%other: %Self) -> bool;
+// CHECK:STDOUT: }
+// CHECK:STDOUT:
+// CHECK:STDOUT: generic fn @NotEqual.2(constants.%Self: %.2) {
+// CHECK:STDOUT:   %Self: %.2 = bind_symbolic_name Self 0 [symbolic = %Self (constants.%Self)]
+// CHECK:STDOUT:
+// CHECK:STDOUT:   fn[%self: %Self](%other: %Self) -> bool;
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @TestEqual(%a: %C, %b: %C) -> bool {
 // CHECK:STDOUT: !entry:
@@ -357,7 +365,11 @@ fn TestLhsBad(a: D, b: C) -> bool {
 // CHECK:STDOUT:   return <error>
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @Equal[%self: %Self](%other: %Self) -> bool;
+// CHECK:STDOUT: generic fn @Equal(constants.%Self: %.4) {
+// CHECK:STDOUT:   %Self: %.4 = bind_symbolic_name Self 0 [symbolic = %Self (constants.%Self)]
+// CHECK:STDOUT:
+// CHECK:STDOUT:   fn[%self: %Self](%other: %Self) -> bool;
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @TestNotEqual(%a: %D, %b: %D) -> bool {
 // CHECK:STDOUT: !entry:
@@ -366,7 +378,11 @@ fn TestLhsBad(a: D, b: C) -> bool {
 // CHECK:STDOUT:   return <error>
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @NotEqual[%self: %Self](%other: %Self) -> bool;
+// CHECK:STDOUT: generic fn @NotEqual(constants.%Self: %.4) {
+// CHECK:STDOUT:   %Self: %.4 = bind_symbolic_name Self 0 [symbolic = %Self (constants.%Self)]
+// CHECK:STDOUT:
+// CHECK:STDOUT:   fn[%self: %Self](%other: %Self) -> bool;
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- fail_no_impl_for_args.carbon
 // CHECK:STDOUT:
@@ -521,9 +537,17 @@ fn TestLhsBad(a: D, b: C) -> bool {
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @NotEqual.1[@impl.%self.loc9_15.2: %C](@impl.%other.loc9_24.2: %C) -> bool;
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @Equal.2[%self: %Self](%other: %Self) -> bool;
+// CHECK:STDOUT: generic fn @Equal.2(constants.%Self: %.2) {
+// CHECK:STDOUT:   %Self: %.2 = bind_symbolic_name Self 0 [symbolic = %Self (constants.%Self)]
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @NotEqual.2[%self: %Self](%other: %Self) -> bool;
+// CHECK:STDOUT:   fn[%self: %Self](%other: %Self) -> bool;
+// CHECK:STDOUT: }
+// CHECK:STDOUT:
+// CHECK:STDOUT: generic fn @NotEqual.2(constants.%Self: %.2) {
+// CHECK:STDOUT:   %Self: %.2 = bind_symbolic_name Self 0 [symbolic = %Self (constants.%Self)]
+// CHECK:STDOUT:
+// CHECK:STDOUT:   fn[%self: %Self](%other: %Self) -> bool;
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @TestRhsBad(%a: %C, %b: %D) -> bool {
 // CHECK:STDOUT: !entry:
diff --git a/toolchain/check/testdata/operators/overloaded/fail_assign_non_ref.carbon b/toolchain/check/testdata/operators/overloaded/fail_assign_non_ref.carbon
index 57d2211edf0c..a8634cc25aec 100644
--- a/toolchain/check/testdata/operators/overloaded/fail_assign_non_ref.carbon
+++ b/toolchain/check/testdata/operators/overloaded/fail_assign_non_ref.carbon
@@ -186,11 +186,21 @@ fn TestAddAssignNonRef(a: C, b: C) {
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Op.1[addr @impl.1.%self.loc16_14.3: %.3]();
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @Op.2[addr %self: %.5]();
+// CHECK:STDOUT: generic fn @Op.2(constants.%Self.1: %.2) {
+// CHECK:STDOUT:   %Self: %.2 = bind_symbolic_name Self 0 [symbolic = %Self (constants.%Self.1)]
+// CHECK:STDOUT:   %.2: type = ptr_type @Op.2.%Self (%Self.1) [symbolic = %.2 (constants.%.5)]
+// CHECK:STDOUT:
+// CHECK:STDOUT:   fn[addr %self: %.5]();
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Op.3[addr @impl.2.%self.loc19_14.3: %.3](@impl.2.%other.loc19_24.2: %C);
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @Op.4[addr %self: %.8](%other: %Self.2);
+// CHECK:STDOUT: generic fn @Op.4(constants.%Self.2: %.7) {
+// CHECK:STDOUT:   %Self: %.7 = bind_symbolic_name Self 0 [symbolic = %Self (constants.%Self.2)]
+// CHECK:STDOUT:   %.2: type = ptr_type @Op.4.%Self (%Self.2) [symbolic = %.2 (constants.%.8)]
+// CHECK:STDOUT:
+// CHECK:STDOUT:   fn[addr %self: %.8](%other: %Self.2);
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @TestIncNonRef(%a: %C) {
 // CHECK:STDOUT: !entry:
diff --git a/toolchain/check/testdata/operators/overloaded/fail_no_impl.carbon b/toolchain/check/testdata/operators/overloaded/fail_no_impl.carbon
index c72e746f8b40..57bb9d4eae84 100644
--- a/toolchain/check/testdata/operators/overloaded/fail_no_impl.carbon
+++ b/toolchain/check/testdata/operators/overloaded/fail_no_impl.carbon
@@ -192,7 +192,11 @@ fn TestRef(b: C) {
 // CHECK:STDOUT:   return <error> to %return
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @Op.1[%self: %Self.1]() -> %Self.1;
+// CHECK:STDOUT: generic fn @Op.1(constants.%Self.1: %.4) {
+// CHECK:STDOUT:   %Self: %.4 = bind_symbolic_name Self 0 [symbolic = %Self (constants.%Self.1)]
+// CHECK:STDOUT:
+// CHECK:STDOUT:   fn[%self: %Self.1]() -> %Self.1;
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @TestBinary(%a: %C, %b: %C) -> %return: %C {
 // CHECK:STDOUT: !entry:
@@ -201,7 +205,11 @@ fn TestRef(b: C) {
 // CHECK:STDOUT:   return <error> to %return
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @Op.2[%self: %Self.2](%other: %Self.2) -> %Self.2;
+// CHECK:STDOUT: generic fn @Op.2(constants.%Self.2: %.7) {
+// CHECK:STDOUT:   %Self: %.7 = bind_symbolic_name Self 0 [symbolic = %Self (constants.%Self.2)]
+// CHECK:STDOUT:
+// CHECK:STDOUT:   fn[%self: %Self.2](%other: %Self.2) -> %Self.2;
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @TestRef(%b: %C) {
 // CHECK:STDOUT: !entry:
@@ -218,7 +226,17 @@ fn TestRef(b: C) {
 // CHECK:STDOUT:   return
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @Op.3[addr %self: %.11](%other: %Self.3);
+// CHECK:STDOUT: generic fn @Op.3(constants.%Self.3: %.10) {
+// CHECK:STDOUT:   %Self: %.10 = bind_symbolic_name Self 0 [symbolic = %Self (constants.%Self.3)]
+// CHECK:STDOUT:   %.2: type = ptr_type @Op.3.%Self (%Self.3) [symbolic = %.2 (constants.%.11)]
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @Op.4[addr %self: %.15]();
+// CHECK:STDOUT:   fn[addr %self: %.11](%other: %Self.3);
+// CHECK:STDOUT: }
+// CHECK:STDOUT:
+// CHECK:STDOUT: generic fn @Op.4(constants.%Self.4: %.14) {
+// CHECK:STDOUT:   %Self: %.14 = bind_symbolic_name Self 0 [symbolic = %Self (constants.%Self.4)]
+// CHECK:STDOUT:   %.2: type = ptr_type @Op.4.%Self (%Self.4) [symbolic = %.2 (constants.%.15)]
+// CHECK:STDOUT:
+// CHECK:STDOUT:   fn[addr %self: %.15]();
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/operators/overloaded/fail_no_impl_for_arg.carbon b/toolchain/check/testdata/operators/overloaded/fail_no_impl_for_arg.carbon
index 91052af2288d..a2298d865e9e 100644
--- a/toolchain/check/testdata/operators/overloaded/fail_no_impl_for_arg.carbon
+++ b/toolchain/check/testdata/operators/overloaded/fail_no_impl_for_arg.carbon
@@ -201,11 +201,20 @@ fn TestAssign(b: D) {
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Op.1[@impl.1.%self.loc17_9.2: %C](@impl.1.%other.loc17_18.2: %C) -> %C;
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @Op.2[%self: %Self.1](%other: %Self.1) -> %Self.1;
+// CHECK:STDOUT: generic fn @Op.2(constants.%Self.1: %.2) {
+// CHECK:STDOUT:   %Self: %.2 = bind_symbolic_name Self 0 [symbolic = %Self (constants.%Self.1)]
+// CHECK:STDOUT:
+// CHECK:STDOUT:   fn[%self: %Self.1](%other: %Self.1) -> %Self.1;
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Op.3[addr @impl.2.%self.loc20_14.3: %.6](@impl.2.%other.loc20_24.2: %C);
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @Op.4[addr %self: %.7](%other: %Self.2);
+// CHECK:STDOUT: generic fn @Op.4(constants.%Self.2: %.5) {
+// CHECK:STDOUT:   %Self: %.5 = bind_symbolic_name Self 0 [symbolic = %Self (constants.%Self.2)]
+// CHECK:STDOUT:   %.2: type = ptr_type @Op.4.%Self (%Self.2) [symbolic = %.2 (constants.%.7)]
+// CHECK:STDOUT:
+// CHECK:STDOUT:   fn[addr %self: %.7](%other: %Self.2);
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Test(%a: %C, %b: %D) -> %return: %C {
 // CHECK:STDOUT: !entry:
diff --git a/toolchain/check/testdata/operators/overloaded/inc.carbon b/toolchain/check/testdata/operators/overloaded/inc.carbon
index 67ff265a7895..1caaf7119230 100644
--- a/toolchain/check/testdata/operators/overloaded/inc.carbon
+++ b/toolchain/check/testdata/operators/overloaded/inc.carbon
@@ -109,7 +109,12 @@ fn TestOp() {
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Op.1[addr @impl.%self.loc18_14.3: %.3]();
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @Op.2[addr %self: %.5]();
+// CHECK:STDOUT: generic fn @Op.2(constants.%Self: %.2) {
+// CHECK:STDOUT:   %Self: %.2 = bind_symbolic_name Self 0 [symbolic = %Self (constants.%Self)]
+// CHECK:STDOUT:   %.2: type = ptr_type @Op.2.%Self (%Self) [symbolic = %.2 (constants.%.5)]
+// CHECK:STDOUT:
+// CHECK:STDOUT:   fn[addr %self: %.5]();
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @TestOp() {
 // CHECK:STDOUT: !entry:
diff --git a/toolchain/check/testdata/operators/overloaded/left_shift.carbon b/toolchain/check/testdata/operators/overloaded/left_shift.carbon
index 41a3a268d2b2..7fcec7dff794 100644
--- a/toolchain/check/testdata/operators/overloaded/left_shift.carbon
+++ b/toolchain/check/testdata/operators/overloaded/left_shift.carbon
@@ -192,14 +192,23 @@ fn TestAssign(a: C*, b: C) {
 // CHECK:STDOUT:   return %.loc19_14 to @impl.1.%return.var
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @Op.2[%self: %Self.1](%other: %Self.1) -> %Self.1;
+// CHECK:STDOUT: generic fn @Op.2(constants.%Self.1: %.2) {
+// CHECK:STDOUT:   %Self: %.2 = bind_symbolic_name Self 0 [symbolic = %Self (constants.%Self.1)]
+// CHECK:STDOUT:
+// CHECK:STDOUT:   fn[%self: %Self.1](%other: %Self.1) -> %Self.1;
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Op.3[addr @impl.2.%self.loc23_14.3: %.7](@impl.2.%other.loc23_24.2: %C) {
 // CHECK:STDOUT: !entry:
 // CHECK:STDOUT:   return
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @Op.4[addr %self: %.8](%other: %Self.2);
+// CHECK:STDOUT: generic fn @Op.4(constants.%Self.2: %.6) {
+// CHECK:STDOUT:   %Self: %.6 = bind_symbolic_name Self 0 [symbolic = %Self (constants.%Self.2)]
+// CHECK:STDOUT:   %.2: type = ptr_type @Op.4.%Self (%Self.2) [symbolic = %.2 (constants.%.8)]
+// CHECK:STDOUT:
+// CHECK:STDOUT:   fn[addr %self: %.8](%other: %Self.2);
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @TestOp(%a: %C, %b: %C) -> %return: %C {
 // CHECK:STDOUT: !entry:
diff --git a/toolchain/check/testdata/operators/overloaded/mod.carbon b/toolchain/check/testdata/operators/overloaded/mod.carbon
index 56d611c839f6..b399cbc84435 100644
--- a/toolchain/check/testdata/operators/overloaded/mod.carbon
+++ b/toolchain/check/testdata/operators/overloaded/mod.carbon
@@ -192,14 +192,23 @@ fn TestAssign(a: C*, b: C) {
 // CHECK:STDOUT:   return %.loc19_14 to @impl.1.%return.var
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @Op.2[%self: %Self.1](%other: %Self.1) -> %Self.1;
+// CHECK:STDOUT: generic fn @Op.2(constants.%Self.1: %.2) {
+// CHECK:STDOUT:   %Self: %.2 = bind_symbolic_name Self 0 [symbolic = %Self (constants.%Self.1)]
+// CHECK:STDOUT:
+// CHECK:STDOUT:   fn[%self: %Self.1](%other: %Self.1) -> %Self.1;
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Op.3[addr @impl.2.%self.loc23_14.3: %.7](@impl.2.%other.loc23_24.2: %C) {
 // CHECK:STDOUT: !entry:
 // CHECK:STDOUT:   return
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @Op.4[addr %self: %.8](%other: %Self.2);
+// CHECK:STDOUT: generic fn @Op.4(constants.%Self.2: %.6) {
+// CHECK:STDOUT:   %Self: %.6 = bind_symbolic_name Self 0 [symbolic = %Self (constants.%Self.2)]
+// CHECK:STDOUT:   %.2: type = ptr_type @Op.4.%Self (%Self.2) [symbolic = %.2 (constants.%.8)]
+// CHECK:STDOUT:
+// CHECK:STDOUT:   fn[addr %self: %.8](%other: %Self.2);
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @TestOp(%a: %C, %b: %C) -> %return: %C {
 // CHECK:STDOUT: !entry:
diff --git a/toolchain/check/testdata/operators/overloaded/mul.carbon b/toolchain/check/testdata/operators/overloaded/mul.carbon
index 422348232bf5..0cf4d35d18ab 100644
--- a/toolchain/check/testdata/operators/overloaded/mul.carbon
+++ b/toolchain/check/testdata/operators/overloaded/mul.carbon
@@ -192,14 +192,23 @@ fn TestAssign(a: C*, b: C) {
 // CHECK:STDOUT:   return %.loc19_14 to @impl.1.%return.var
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @Op.2[%self: %Self.1](%other: %Self.1) -> %Self.1;
+// CHECK:STDOUT: generic fn @Op.2(constants.%Self.1: %.2) {
+// CHECK:STDOUT:   %Self: %.2 = bind_symbolic_name Self 0 [symbolic = %Self (constants.%Self.1)]
+// CHECK:STDOUT:
+// CHECK:STDOUT:   fn[%self: %Self.1](%other: %Self.1) -> %Self.1;
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Op.3[addr @impl.2.%self.loc23_14.3: %.7](@impl.2.%other.loc23_24.2: %C) {
 // CHECK:STDOUT: !entry:
 // CHECK:STDOUT:   return
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @Op.4[addr %self: %.8](%other: %Self.2);
+// CHECK:STDOUT: generic fn @Op.4(constants.%Self.2: %.6) {
+// CHECK:STDOUT:   %Self: %.6 = bind_symbolic_name Self 0 [symbolic = %Self (constants.%Self.2)]
+// CHECK:STDOUT:   %.2: type = ptr_type @Op.4.%Self (%Self.2) [symbolic = %.2 (constants.%.8)]
+// CHECK:STDOUT:
+// CHECK:STDOUT:   fn[addr %self: %.8](%other: %Self.2);
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @TestOp(%a: %C, %b: %C) -> %return: %C {
 // CHECK:STDOUT: !entry:
diff --git a/toolchain/check/testdata/operators/overloaded/negate.carbon b/toolchain/check/testdata/operators/overloaded/negate.carbon
index 3a2e0f8dc5e3..846bf2a1ad18 100644
--- a/toolchain/check/testdata/operators/overloaded/negate.carbon
+++ b/toolchain/check/testdata/operators/overloaded/negate.carbon
@@ -120,7 +120,11 @@ fn TestOp(a: C) -> C {
 // CHECK:STDOUT:   return %.loc19_14 to @impl.%return.var
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @Op.2[%self: %Self]() -> %Self;
+// CHECK:STDOUT: generic fn @Op.2(constants.%Self: %.2) {
+// CHECK:STDOUT:   %Self: %.2 = bind_symbolic_name Self 0 [symbolic = %Self (constants.%Self)]
+// CHECK:STDOUT:
+// CHECK:STDOUT:   fn[%self: %Self]() -> %Self;
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @TestOp(%a: %C) -> %return: %C {
 // CHECK:STDOUT: !entry:
diff --git a/toolchain/check/testdata/operators/overloaded/ordered.carbon b/toolchain/check/testdata/operators/overloaded/ordered.carbon
index c48daa37cc73..af1d4a6ae839 100644
--- a/toolchain/check/testdata/operators/overloaded/ordered.carbon
+++ b/toolchain/check/testdata/operators/overloaded/ordered.carbon
@@ -299,13 +299,29 @@ fn TestGreaterEqual(a: D, b: D) -> bool {
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @GreaterOrEquivalent.1[@impl.%self.loc10_26.2: %C](@impl.%other.loc10_35.2: %C) -> bool;
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @Less.2[%self: %Self](%other: %Self) -> bool;
+// CHECK:STDOUT: generic fn @Less.2(constants.%Self: %.2) {
+// CHECK:STDOUT:   %Self: %.2 = bind_symbolic_name Self 0 [symbolic = %Self (constants.%Self)]
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @LessOrEquivalent.2[%self: %Self](%other: %Self) -> bool;
+// CHECK:STDOUT:   fn[%self: %Self](%other: %Self) -> bool;
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @Greater.2[%self: %Self](%other: %Self) -> bool;
+// CHECK:STDOUT: generic fn @LessOrEquivalent.2(constants.%Self: %.2) {
+// CHECK:STDOUT:   %Self: %.2 = bind_symbolic_name Self 0 [symbolic = %Self (constants.%Self)]
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @GreaterOrEquivalent.2[%self: %Self](%other: %Self) -> bool;
+// CHECK:STDOUT:   fn[%self: %Self](%other: %Self) -> bool;
+// CHECK:STDOUT: }
+// CHECK:STDOUT:
+// CHECK:STDOUT: generic fn @Greater.2(constants.%Self: %.2) {
+// CHECK:STDOUT:   %Self: %.2 = bind_symbolic_name Self 0 [symbolic = %Self (constants.%Self)]
+// CHECK:STDOUT:
+// CHECK:STDOUT:   fn[%self: %Self](%other: %Self) -> bool;
+// CHECK:STDOUT: }
+// CHECK:STDOUT:
+// CHECK:STDOUT: generic fn @GreaterOrEquivalent.2(constants.%Self: %.2) {
+// CHECK:STDOUT:   %Self: %.2 = bind_symbolic_name Self 0 [symbolic = %Self (constants.%Self)]
+// CHECK:STDOUT:
+// CHECK:STDOUT:   fn[%self: %Self](%other: %Self) -> bool;
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @TestLess(%a: %C, %b: %C) -> bool {
 // CHECK:STDOUT: !entry:
@@ -506,7 +522,11 @@ fn TestGreaterEqual(a: D, b: D) -> bool {
 // CHECK:STDOUT:   return <error>
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @Less[%self: %Self](%other: %Self) -> bool;
+// CHECK:STDOUT: generic fn @Less(constants.%Self: %.4) {
+// CHECK:STDOUT:   %Self: %.4 = bind_symbolic_name Self 0 [symbolic = %Self (constants.%Self)]
+// CHECK:STDOUT:
+// CHECK:STDOUT:   fn[%self: %Self](%other: %Self) -> bool;
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @TestLessEqual(%a: %D, %b: %D) -> bool {
 // CHECK:STDOUT: !entry:
@@ -515,7 +535,11 @@ fn TestGreaterEqual(a: D, b: D) -> bool {
 // CHECK:STDOUT:   return <error>
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @LessOrEquivalent[%self: %Self](%other: %Self) -> bool;
+// CHECK:STDOUT: generic fn @LessOrEquivalent(constants.%Self: %.4) {
+// CHECK:STDOUT:   %Self: %.4 = bind_symbolic_name Self 0 [symbolic = %Self (constants.%Self)]
+// CHECK:STDOUT:
+// CHECK:STDOUT:   fn[%self: %Self](%other: %Self) -> bool;
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @TestGreater(%a: %D, %b: %D) -> bool {
 // CHECK:STDOUT: !entry:
@@ -524,7 +548,11 @@ fn TestGreaterEqual(a: D, b: D) -> bool {
 // CHECK:STDOUT:   return <error>
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @Greater[%self: %Self](%other: %Self) -> bool;
+// CHECK:STDOUT: generic fn @Greater(constants.%Self: %.4) {
+// CHECK:STDOUT:   %Self: %.4 = bind_symbolic_name Self 0 [symbolic = %Self (constants.%Self)]
+// CHECK:STDOUT:
+// CHECK:STDOUT:   fn[%self: %Self](%other: %Self) -> bool;
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @TestGreaterEqual(%a: %D, %b: %D) -> bool {
 // CHECK:STDOUT: !entry:
@@ -533,5 +561,9 @@ fn TestGreaterEqual(a: D, b: D) -> bool {
 // CHECK:STDOUT:   return <error>
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @GreaterOrEquivalent[%self: %Self](%other: %Self) -> bool;
+// CHECK:STDOUT: generic fn @GreaterOrEquivalent(constants.%Self: %.4) {
+// CHECK:STDOUT:   %Self: %.4 = bind_symbolic_name Self 0 [symbolic = %Self (constants.%Self)]
+// CHECK:STDOUT:
+// CHECK:STDOUT:   fn[%self: %Self](%other: %Self) -> bool;
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/operators/overloaded/right_shift.carbon b/toolchain/check/testdata/operators/overloaded/right_shift.carbon
index 4eb473d1e18c..5a9d0fab1af9 100644
--- a/toolchain/check/testdata/operators/overloaded/right_shift.carbon
+++ b/toolchain/check/testdata/operators/overloaded/right_shift.carbon
@@ -192,14 +192,23 @@ fn TestAssign(a: C*, b: C) {
 // CHECK:STDOUT:   return %.loc19_14 to @impl.1.%return.var
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @Op.2[%self: %Self.1](%other: %Self.1) -> %Self.1;
+// CHECK:STDOUT: generic fn @Op.2(constants.%Self.1: %.2) {
+// CHECK:STDOUT:   %Self: %.2 = bind_symbolic_name Self 0 [symbolic = %Self (constants.%Self.1)]
+// CHECK:STDOUT:
+// CHECK:STDOUT:   fn[%self: %Self.1](%other: %Self.1) -> %Self.1;
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Op.3[addr @impl.2.%self.loc23_14.3: %.7](@impl.2.%other.loc23_24.2: %C) {
 // CHECK:STDOUT: !entry:
 // CHECK:STDOUT:   return
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @Op.4[addr %self: %.8](%other: %Self.2);
+// CHECK:STDOUT: generic fn @Op.4(constants.%Self.2: %.6) {
+// CHECK:STDOUT:   %Self: %.6 = bind_symbolic_name Self 0 [symbolic = %Self (constants.%Self.2)]
+// CHECK:STDOUT:   %.2: type = ptr_type @Op.4.%Self (%Self.2) [symbolic = %.2 (constants.%.8)]
+// CHECK:STDOUT:
+// CHECK:STDOUT:   fn[addr %self: %.8](%other: %Self.2);
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @TestOp(%a: %C, %b: %C) -> %return: %C {
 // CHECK:STDOUT: !entry:
diff --git a/toolchain/check/testdata/operators/overloaded/sub.carbon b/toolchain/check/testdata/operators/overloaded/sub.carbon
index bf196ee0c051..428224cd4a20 100644
--- a/toolchain/check/testdata/operators/overloaded/sub.carbon
+++ b/toolchain/check/testdata/operators/overloaded/sub.carbon
@@ -192,14 +192,23 @@ fn TestAssign(a: C*, b: C) {
 // CHECK:STDOUT:   return %.loc19_14 to @impl.1.%return.var
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @Op.2[%self: %Self.1](%other: %Self.1) -> %Self.1;
+// CHECK:STDOUT: generic fn @Op.2(constants.%Self.1: %.2) {
+// CHECK:STDOUT:   %Self: %.2 = bind_symbolic_name Self 0 [symbolic = %Self (constants.%Self.1)]
+// CHECK:STDOUT:
+// CHECK:STDOUT:   fn[%self: %Self.1](%other: %Self.1) -> %Self.1;
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Op.3[addr @impl.2.%self.loc23_14.3: %.7](@impl.2.%other.loc23_24.2: %C) {
 // CHECK:STDOUT: !entry:
 // CHECK:STDOUT:   return
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: fn @Op.4[addr %self: %.8](%other: %Self.2);
+// CHECK:STDOUT: generic fn @Op.4(constants.%Self.2: %.6) {
+// CHECK:STDOUT:   %Self: %.6 = bind_symbolic_name Self 0 [symbolic = %Self (constants.%Self.2)]
+// CHECK:STDOUT:   %.2: type = ptr_type @Op.4.%Self (%Self.2) [symbolic = %.2 (constants.%.8)]
+// CHECK:STDOUT:
+// CHECK:STDOUT:   fn[addr %self: %.8](%other: %Self.2);
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @TestOp(%a: %C, %b: %C) -> %return: %C {
 // CHECK:STDOUT: !entry:
diff --git a/toolchain/check/testdata/packages/no_prelude/fail_export_name_params.carbon b/toolchain/check/testdata/packages/no_prelude/fail_export_name_params.carbon
index 451c3d3b4660..6e62138da2dd 100644
--- a/toolchain/check/testdata/packages/no_prelude/fail_export_name_params.carbon
+++ b/toolchain/check/testdata/packages/no_prelude/fail_export_name_params.carbon
@@ -83,10 +83,10 @@ export C2(T:! type);
 // CHECK:STDOUT:   %.1: type = tuple_type () [template]
 // CHECK:STDOUT:   %C1.1: %C1.type = struct_value () [template]
 // CHECK:STDOUT:   %T: type = bind_symbolic_name T 0 [symbolic]
-// CHECK:STDOUT:   %C1.2: type = class_type @C1, invalid(%T) [symbolic]
+// CHECK:STDOUT:   %C1.2: type = class_type @C1, @C1(%T) [symbolic]
 // CHECK:STDOUT:   %C2.type: type = generic_class_type @C2 [template]
 // CHECK:STDOUT:   %C2.1: %C2.type = struct_value () [template]
-// CHECK:STDOUT:   %C2.2: type = class_type @C2, invalid(%T) [symbolic]
+// CHECK:STDOUT:   %C2.2: type = class_type @C2, @C2(%T) [symbolic]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: imports {
@@ -106,9 +106,23 @@ export C2(T:! type);
 // CHECK:STDOUT:   %C2: %C2.type = export C2, imports.%import_ref.2 [template = constants.%C2.1]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: class @C1;
+// CHECK:STDOUT: generic class @C1(constants.%T: type) {
+// CHECK:STDOUT:   %T: type = bind_symbolic_name T 0 [symbolic = %T (constants.%T)]
 // CHECK:STDOUT:
-// CHECK:STDOUT: class @C2;
+// CHECK:STDOUT:   class;
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific invalid(constants.%T);
+// CHECK:STDOUT: generic class @C2(constants.%T: type) {
+// CHECK:STDOUT:   %T: type = bind_symbolic_name T 0 [symbolic = %T (constants.%T)]
+// CHECK:STDOUT:
+// CHECK:STDOUT:   class;
+// CHECK:STDOUT: }
+// CHECK:STDOUT:
+// CHECK:STDOUT: specific @C1(constants.%T) {
+// CHECK:STDOUT:   %T => constants.%T
+// CHECK:STDOUT: }
+// CHECK:STDOUT:
+// CHECK:STDOUT: specific @C2(constants.%T) {
+// CHECK:STDOUT:   %T => constants.%T
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/struct/import.carbon b/toolchain/check/testdata/struct/import.carbon
index 19ed5422e84e..86ea05b7f85d 100644
--- a/toolchain/check/testdata/struct/import.carbon
+++ b/toolchain/check/testdata/struct/import.carbon
@@ -225,12 +225,12 @@ var c_bad: C({.a = 3, .b = 4}) = F();
 // CHECK:STDOUT:   %.10: type = struct_type {} [template]
 // CHECK:STDOUT:   %.11: type = struct_type {.a: i32, .b: i32} [template]
 // CHECK:STDOUT:   %S: %.11 = bind_symbolic_name S 0 [symbolic]
-// CHECK:STDOUT:   %C.2: type = class_type @C, invalid(%S) [symbolic]
+// CHECK:STDOUT:   %C.2: type = class_type @C, @C(%S) [symbolic]
 // CHECK:STDOUT:   %.12: i32 = int_literal 1 [template]
 // CHECK:STDOUT:   %.13: i32 = int_literal 2 [template]
 // CHECK:STDOUT:   %.14: type = ptr_type %.11 [template]
 // CHECK:STDOUT:   %struct: %.11 = struct_value (%.12, %.13) [template]
-// CHECK:STDOUT:   %C.3: type = class_type @C, invalid(%struct) [template]
+// CHECK:STDOUT:   %C.3: type = class_type @C, @C(%struct) [template]
 // CHECK:STDOUT:   %.15: type = ptr_type %.10 [template]
 // CHECK:STDOUT:   %F.type: type = fn_type @F [template]
 // CHECK:STDOUT:   %F: %F.type = struct_value () [template]
@@ -303,9 +303,15 @@ var c_bad: C({.a = 3, .b = 4}) = F();
 // CHECK:STDOUT:   %c: ref %C.3 = bind_name c, %c.var
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: class @C {
-// CHECK:STDOUT: !members:
-// CHECK:STDOUT:   .Self = imports.%import_ref.6
+// CHECK:STDOUT: generic class @C(constants.%S: %.11) {
+// CHECK:STDOUT:   %S: %.11 = bind_symbolic_name S 0 [symbolic = %S (constants.%S)]
+// CHECK:STDOUT:
+// CHECK:STDOUT: !definition:
+// CHECK:STDOUT:
+// CHECK:STDOUT:   class {
+// CHECK:STDOUT:   !members:
+// CHECK:STDOUT:     .Self = imports.%import_ref.6
+// CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Int32() -> type = "int.make_type_32";
@@ -350,9 +356,15 @@ var c_bad: C({.a = 3, .b = 4}) = F();
 // CHECK:STDOUT:   return
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific invalid(constants.%S);
+// CHECK:STDOUT: specific @C(constants.%S) {
+// CHECK:STDOUT:   %S => constants.%S
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific invalid(constants.%struct);
+// CHECK:STDOUT: specific @C(constants.%struct) {
+// CHECK:STDOUT:   %S => constants.%struct
+// CHECK:STDOUT:
+// CHECK:STDOUT: !definition:
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- fail_bad_type.impl.carbon
 // CHECK:STDOUT:
@@ -363,13 +375,13 @@ var c_bad: C({.a = 3, .b = 4}) = F();
 // CHECK:STDOUT:   %.2: type = struct_type {} [template]
 // CHECK:STDOUT:   %.3: type = struct_type {.a: i32, .b: i32} [template]
 // CHECK:STDOUT:   %S: %.3 = bind_symbolic_name S 0 [symbolic]
-// CHECK:STDOUT:   %C.2: type = class_type @C, invalid(%S) [symbolic]
+// CHECK:STDOUT:   %C.2: type = class_type @C, @C(%S) [symbolic]
 // CHECK:STDOUT:   %.4: i32 = int_literal 1 [template]
 // CHECK:STDOUT:   %.5: i32 = int_literal 2 [template]
 // CHECK:STDOUT:   %.6: type = struct_type {.c: i32, .d: i32} [template]
 // CHECK:STDOUT:   %.7: type = ptr_type %.3 [template]
 // CHECK:STDOUT:   %struct: %.3 = struct_value (%.4, %.5) [template]
-// CHECK:STDOUT:   %C.3: type = class_type @C, invalid(%struct) [template]
+// CHECK:STDOUT:   %C.3: type = class_type @C, @C(%struct) [template]
 // CHECK:STDOUT:   %F.type: type = fn_type @F [template]
 // CHECK:STDOUT:   %F: %F.type = struct_value () [template]
 // CHECK:STDOUT:   %.8: type = ptr_type %.2 [template]
@@ -415,9 +427,15 @@ var c_bad: C({.a = 3, .b = 4}) = F();
 // CHECK:STDOUT:   %c_bad: ref <error> = bind_name c_bad, %c_bad.var
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: class @C {
-// CHECK:STDOUT: !members:
-// CHECK:STDOUT:   .Self = imports.%import_ref.5
+// CHECK:STDOUT: generic class @C(constants.%S: %.3) {
+// CHECK:STDOUT:   %S: %.3 = bind_symbolic_name S 0 [symbolic = %S (constants.%S)]
+// CHECK:STDOUT:
+// CHECK:STDOUT: !definition:
+// CHECK:STDOUT:
+// CHECK:STDOUT:   class {
+// CHECK:STDOUT:   !members:
+// CHECK:STDOUT:     .Self = imports.%import_ref.5
+// CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F() -> %C.3;
@@ -431,9 +449,15 @@ var c_bad: C({.a = 3, .b = 4}) = F();
 // CHECK:STDOUT:   return
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific invalid(constants.%S);
+// CHECK:STDOUT: specific @C(constants.%S) {
+// CHECK:STDOUT:   %S => constants.%S
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific invalid(constants.%struct);
+// CHECK:STDOUT: specific @C(constants.%struct) {
+// CHECK:STDOUT:   %S => constants.%struct
+// CHECK:STDOUT:
+// CHECK:STDOUT: !definition:
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- fail_bad_value.impl.carbon
 // CHECK:STDOUT:
@@ -444,17 +468,17 @@ var c_bad: C({.a = 3, .b = 4}) = F();
 // CHECK:STDOUT:   %.2: type = struct_type {} [template]
 // CHECK:STDOUT:   %.3: type = struct_type {.a: i32, .b: i32} [template]
 // CHECK:STDOUT:   %S: %.3 = bind_symbolic_name S 0 [symbolic]
-// CHECK:STDOUT:   %C.2: type = class_type @C, invalid(%S) [symbolic]
+// CHECK:STDOUT:   %C.2: type = class_type @C, @C(%S) [symbolic]
 // CHECK:STDOUT:   %.4: i32 = int_literal 3 [template]
 // CHECK:STDOUT:   %.5: i32 = int_literal 4 [template]
 // CHECK:STDOUT:   %.6: type = ptr_type %.3 [template]
 // CHECK:STDOUT:   %struct.1: %.3 = struct_value (%.4, %.5) [template]
-// CHECK:STDOUT:   %C.3: type = class_type @C, invalid(%struct.1) [template]
+// CHECK:STDOUT:   %C.3: type = class_type @C, @C(%struct.1) [template]
 // CHECK:STDOUT:   %.7: type = ptr_type %.2 [template]
 // CHECK:STDOUT:   %.8: i32 = int_literal 2 [template]
 // CHECK:STDOUT:   %.9: i32 = int_literal 1 [template]
 // CHECK:STDOUT:   %struct.2: %.3 = struct_value (%.9, %.8) [template]
-// CHECK:STDOUT:   %C.4: type = class_type @C, invalid(%struct.2) [template]
+// CHECK:STDOUT:   %C.4: type = class_type @C, @C(%struct.2) [template]
 // CHECK:STDOUT:   %F.type: type = fn_type @F [template]
 // CHECK:STDOUT:   %F: %F.type = struct_value () [template]
 // CHECK:STDOUT: }
@@ -501,9 +525,15 @@ var c_bad: C({.a = 3, .b = 4}) = F();
 // CHECK:STDOUT:   %c_bad: ref %C.3 = bind_name c_bad, %c_bad.var
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: class @C {
-// CHECK:STDOUT: !members:
-// CHECK:STDOUT:   .Self = imports.%import_ref.5
+// CHECK:STDOUT: generic class @C(constants.%S: %.3) {
+// CHECK:STDOUT:   %S: %.3 = bind_symbolic_name S 0 [symbolic = %S (constants.%S)]
+// CHECK:STDOUT:
+// CHECK:STDOUT: !definition:
+// CHECK:STDOUT:
+// CHECK:STDOUT:   class {
+// CHECK:STDOUT:   !members:
+// CHECK:STDOUT:     .Self = imports.%import_ref.5
+// CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F() -> %C.4;
@@ -517,9 +547,19 @@ var c_bad: C({.a = 3, .b = 4}) = F();
 // CHECK:STDOUT:   return
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific invalid(constants.%S);
+// CHECK:STDOUT: specific @C(constants.%S) {
+// CHECK:STDOUT:   %S => constants.%S
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific invalid(constants.%struct.1);
+// CHECK:STDOUT: specific @C(constants.%struct.1) {
+// CHECK:STDOUT:   %S => constants.%struct.1
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific invalid(constants.%struct.2);
+// CHECK:STDOUT: !definition:
+// CHECK:STDOUT: }
+// CHECK:STDOUT:
+// CHECK:STDOUT: specific @C(constants.%struct.2) {
+// CHECK:STDOUT:   %S => constants.%struct.2
+// CHECK:STDOUT:
+// CHECK:STDOUT: !definition:
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/tuples/import.carbon b/toolchain/check/testdata/tuples/import.carbon
index 73190a46f35f..ce160f8c773b 100644
--- a/toolchain/check/testdata/tuples/import.carbon
+++ b/toolchain/check/testdata/tuples/import.carbon
@@ -249,11 +249,11 @@ var c_bad: C((3, 4)) = F();
 // CHECK:STDOUT:   %C.1: %C.type = struct_value () [template]
 // CHECK:STDOUT:   %.14: type = struct_type {} [template]
 // CHECK:STDOUT:   %X: %.8 = bind_symbolic_name X 0 [symbolic]
-// CHECK:STDOUT:   %C.2: type = class_type @C, invalid(%X) [symbolic]
+// CHECK:STDOUT:   %C.2: type = class_type @C, @C(%X) [symbolic]
 // CHECK:STDOUT:   %.15: i32 = int_literal 1 [template]
 // CHECK:STDOUT:   %.16: i32 = int_literal 2 [template]
 // CHECK:STDOUT:   %tuple: %.8 = tuple_value (%.15, %.16) [template]
-// CHECK:STDOUT:   %C.3: type = class_type @C, invalid(%tuple) [template]
+// CHECK:STDOUT:   %C.3: type = class_type @C, @C(%tuple) [template]
 // CHECK:STDOUT:   %.17: type = ptr_type %.14 [template]
 // CHECK:STDOUT:   %F.type: type = fn_type @F [template]
 // CHECK:STDOUT:   %F: %F.type = struct_value () [template]
@@ -334,9 +334,15 @@ var c_bad: C((3, 4)) = F();
 // CHECK:STDOUT:   %c: ref %C.3 = bind_name c, %c.var
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: class @C {
-// CHECK:STDOUT: !members:
-// CHECK:STDOUT:   .Self = imports.%import_ref.6
+// CHECK:STDOUT: generic class @C(constants.%X: %.8) {
+// CHECK:STDOUT:   %X: %.8 = bind_symbolic_name X 0 [symbolic = %X (constants.%X)]
+// CHECK:STDOUT:
+// CHECK:STDOUT: !definition:
+// CHECK:STDOUT:
+// CHECK:STDOUT:   class {
+// CHECK:STDOUT:   !members:
+// CHECK:STDOUT:     .Self = imports.%import_ref.6
+// CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Int32() -> type = "int.make_type_32";
@@ -389,9 +395,15 @@ var c_bad: C((3, 4)) = F();
 // CHECK:STDOUT:   return
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific invalid(constants.%X);
+// CHECK:STDOUT: specific @C(constants.%X) {
+// CHECK:STDOUT:   %X => constants.%X
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific invalid(constants.%tuple);
+// CHECK:STDOUT: specific @C(constants.%tuple) {
+// CHECK:STDOUT:   %X => constants.%tuple
+// CHECK:STDOUT:
+// CHECK:STDOUT: !definition:
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- fail_bad_type.impl.carbon
 // CHECK:STDOUT:
@@ -402,14 +414,14 @@ var c_bad: C((3, 4)) = F();
 // CHECK:STDOUT:   %.2: type = struct_type {} [template]
 // CHECK:STDOUT:   %.3: type = tuple_type (i32, i32) [template]
 // CHECK:STDOUT:   %X: %.3 = bind_symbolic_name X 0 [symbolic]
-// CHECK:STDOUT:   %C.2: type = class_type @C, invalid(%X) [symbolic]
+// CHECK:STDOUT:   %C.2: type = class_type @C, @C(%X) [symbolic]
 // CHECK:STDOUT:   %.4: i32 = int_literal 1 [template]
 // CHECK:STDOUT:   %.5: i32 = int_literal 2 [template]
 // CHECK:STDOUT:   %.6: i32 = int_literal 3 [template]
 // CHECK:STDOUT:   %.7: type = tuple_type (i32, i32, i32) [template]
 // CHECK:STDOUT:   %.8: type = ptr_type %.3 [template]
 // CHECK:STDOUT:   %tuple: %.3 = tuple_value (%.4, %.5) [template]
-// CHECK:STDOUT:   %C.3: type = class_type @C, invalid(%tuple) [template]
+// CHECK:STDOUT:   %C.3: type = class_type @C, @C(%tuple) [template]
 // CHECK:STDOUT:   %F.type: type = fn_type @F [template]
 // CHECK:STDOUT:   %F: %F.type = struct_value () [template]
 // CHECK:STDOUT:   %.9: type = ptr_type %.2 [template]
@@ -456,9 +468,15 @@ var c_bad: C((3, 4)) = F();
 // CHECK:STDOUT:   %c_bad: ref <error> = bind_name c_bad, %c_bad.var
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: class @C {
-// CHECK:STDOUT: !members:
-// CHECK:STDOUT:   .Self = imports.%import_ref.5
+// CHECK:STDOUT: generic class @C(constants.%X: %.3) {
+// CHECK:STDOUT:   %X: %.3 = bind_symbolic_name X 0 [symbolic = %X (constants.%X)]
+// CHECK:STDOUT:
+// CHECK:STDOUT: !definition:
+// CHECK:STDOUT:
+// CHECK:STDOUT:   class {
+// CHECK:STDOUT:   !members:
+// CHECK:STDOUT:     .Self = imports.%import_ref.5
+// CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F() -> %C.3;
@@ -472,9 +490,15 @@ var c_bad: C((3, 4)) = F();
 // CHECK:STDOUT:   return
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific invalid(constants.%X);
+// CHECK:STDOUT: specific @C(constants.%X) {
+// CHECK:STDOUT:   %X => constants.%X
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific invalid(constants.%tuple);
+// CHECK:STDOUT: specific @C(constants.%tuple) {
+// CHECK:STDOUT:   %X => constants.%tuple
+// CHECK:STDOUT:
+// CHECK:STDOUT: !definition:
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- fail_bad_value.impl.carbon
 // CHECK:STDOUT:
@@ -485,17 +509,17 @@ var c_bad: C((3, 4)) = F();
 // CHECK:STDOUT:   %.2: type = struct_type {} [template]
 // CHECK:STDOUT:   %.3: type = tuple_type (i32, i32) [template]
 // CHECK:STDOUT:   %X: %.3 = bind_symbolic_name X 0 [symbolic]
-// CHECK:STDOUT:   %C.2: type = class_type @C, invalid(%X) [symbolic]
+// CHECK:STDOUT:   %C.2: type = class_type @C, @C(%X) [symbolic]
 // CHECK:STDOUT:   %.4: i32 = int_literal 3 [template]
 // CHECK:STDOUT:   %.5: i32 = int_literal 4 [template]
 // CHECK:STDOUT:   %.6: type = ptr_type %.3 [template]
 // CHECK:STDOUT:   %tuple.1: %.3 = tuple_value (%.4, %.5) [template]
-// CHECK:STDOUT:   %C.3: type = class_type @C, invalid(%tuple.1) [template]
+// CHECK:STDOUT:   %C.3: type = class_type @C, @C(%tuple.1) [template]
 // CHECK:STDOUT:   %.7: type = ptr_type %.2 [template]
 // CHECK:STDOUT:   %.8: i32 = int_literal 2 [template]
 // CHECK:STDOUT:   %.9: i32 = int_literal 1 [template]
 // CHECK:STDOUT:   %tuple.2: %.3 = tuple_value (%.9, %.8) [template]
-// CHECK:STDOUT:   %C.4: type = class_type @C, invalid(%tuple.2) [template]
+// CHECK:STDOUT:   %C.4: type = class_type @C, @C(%tuple.2) [template]
 // CHECK:STDOUT:   %F.type: type = fn_type @F [template]
 // CHECK:STDOUT:   %F: %F.type = struct_value () [template]
 // CHECK:STDOUT: }
@@ -542,9 +566,15 @@ var c_bad: C((3, 4)) = F();
 // CHECK:STDOUT:   %c_bad: ref %C.3 = bind_name c_bad, %c_bad.var
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: class @C {
-// CHECK:STDOUT: !members:
-// CHECK:STDOUT:   .Self = imports.%import_ref.5
+// CHECK:STDOUT: generic class @C(constants.%X: %.3) {
+// CHECK:STDOUT:   %X: %.3 = bind_symbolic_name X 0 [symbolic = %X (constants.%X)]
+// CHECK:STDOUT:
+// CHECK:STDOUT: !definition:
+// CHECK:STDOUT:
+// CHECK:STDOUT:   class {
+// CHECK:STDOUT:   !members:
+// CHECK:STDOUT:     .Self = imports.%import_ref.5
+// CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F() -> %C.4;
@@ -558,9 +588,19 @@ var c_bad: C((3, 4)) = F();
 // CHECK:STDOUT:   return
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific invalid(constants.%X);
+// CHECK:STDOUT: specific @C(constants.%X) {
+// CHECK:STDOUT:   %X => constants.%X
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific invalid(constants.%tuple.1);
+// CHECK:STDOUT: specific @C(constants.%tuple.1) {
+// CHECK:STDOUT:   %X => constants.%tuple.1
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific invalid(constants.%tuple.2);
+// CHECK:STDOUT: !definition:
+// CHECK:STDOUT: }
+// CHECK:STDOUT:
+// CHECK:STDOUT: specific @C(constants.%tuple.2) {
+// CHECK:STDOUT:   %X => constants.%tuple.2
+// CHECK:STDOUT:
+// CHECK:STDOUT: !definition:
+// CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/sem_ir/generic.cpp b/toolchain/sem_ir/generic.cpp
index b04cea6d8cba..5cc71765a793 100644
--- a/toolchain/sem_ir/generic.cpp
+++ b/toolchain/sem_ir/generic.cpp
@@ -32,6 +32,7 @@ class SpecificStore::KeyContext : public TranslatingKeyContext<KeyContext> {
 
 auto SpecificStore::GetOrAdd(GenericId generic_id, InstBlockId args_id)
     -> SpecificId {
+  CARBON_CHECK(generic_id.is_valid());
   return lookup_table_
       .Insert(
           KeyContext::Key{.generic_id = generic_id, .args_id = args_id},