Remove the nominal type system (#5672)

And since the only type system left is the standard isorecursive type system,
remove `TypeSystem` and its associated APIs entirely. Delete a few tests that
only made sense under the isorecursive type system.

17 files changed, 94 insertions, 941 deletions

diff --git a/CHANGELOG.md b/CHANGELOG.md
index f2d76ec92..6bad6aa3f 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -17,9 +17,9 @@ Current Trunk
 
 - Some C and JS API functions now refer to data and element segments by name
   instead of index.
-- The --nominal and --hybrid command line options have been removed. The only
-  supported type system is now the standard isorecursive (i.e. hybrid) type
-  system.
+- The --nominal and --hybrid command line options and related API functions have
+  been removed. The only supported type system is now the standard isorecursive
+  (i.e. hybrid) type system.
 
 v112
 ----
diff --git a/src/binaryen-c.cpp b/src/binaryen-c.cpp
index 01f14f924..b23d53ad6 100644
--- a/src/binaryen-c.cpp
+++ b/src/binaryen-c.cpp
@@ -406,21 +406,6 @@ BinaryenType BinaryenTypeFromHeapType(BinaryenHeapType heapType,
     .getID();
 }
 
-// TypeSystem
-
-BinaryenTypeSystem BinaryenTypeSystemNominal() {
-  return static_cast<BinaryenTypeSystem>(TypeSystem::Nominal);
-}
-BinaryenTypeSystem BinaryenTypeSystemIsorecursive() {
-  return static_cast<BinaryenTypeSystem>(TypeSystem::Isorecursive);
-}
-BinaryenTypeSystem BinaryenGetTypeSystem() {
-  return BinaryenTypeSystem(getTypeSystem());
-}
-void BinaryenSetTypeSystem(BinaryenTypeSystem typeSystem) {
-  setTypeSystem(TypeSystem(typeSystem));
-}
-
 // Expression ids
 
 BinaryenExpressionId BinaryenInvalidId(void) {
diff --git a/src/binaryen-c.h b/src/binaryen-c.h
index afbc13782..d05bdf33b 100644
--- a/src/binaryen-c.h
+++ b/src/binaryen-c.h
@@ -188,15 +188,6 @@ BINARYEN_API bool BinaryenTypeIsNullable(BinaryenType type);
 BINARYEN_API BinaryenType BinaryenTypeFromHeapType(BinaryenHeapType heapType,
                                                    bool nullable);
 
-// TypeSystem
-
-typedef uint32_t BinaryenTypeSystem;
-
-BINARYEN_API BinaryenTypeSystem BinaryenTypeSystemNominal(void);
-BINARYEN_API BinaryenTypeSystem BinaryenTypeSystemIsorecursive(void);
-BINARYEN_API BinaryenTypeSystem BinaryenGetTypeSystem(void);
-BINARYEN_API void BinaryenSetTypeSystem(BinaryenTypeSystem typeSystem);
-
 // Expression ids (call to get the value of each; you can cache them)
 
 typedef uint32_t BinaryenExpressionId;
diff --git a/src/ir/module-utils.cpp b/src/ir/module-utils.cpp
index efab9e20b..ce6fadda7 100644
--- a/src/ir/module-utils.cpp
+++ b/src/ir/module-utils.cpp
@@ -345,7 +345,6 @@ std::vector<HeapType> getPrivateHeapTypes(Module& wasm) {
 }
 
 IndexedHeapTypes getOptimizedIndexedHeapTypes(Module& wasm) {
-  TypeSystem system = getTypeSystem();
   Counts counts = getHeapTypeCounts(wasm);
 
   // Types have to be arranged into topologically ordered recursion groups.
@@ -385,32 +384,21 @@ IndexedHeapTypes getOptimizedIndexedHeapTypes(Module& wasm) {
     // Update the reference count.
     info.useCount += counts.at(type);
     // Collect predecessor groups.
-    switch (system) {
-      case TypeSystem::Isorecursive:
-        for (auto child : type.getReferencedHeapTypes()) {
-          if (!child.isBasic()) {
-            RecGroup otherGroup = child.getRecGroup();
-            if (otherGroup != group) {
-              info.preds.insert(otherGroup);
-            }
-          }
-        }
-        break;
-      case TypeSystem::Nominal:
-        if (auto super = type.getSuperType()) {
-          info.preds.insert(super->getRecGroup());
+    for (auto child : type.getReferencedHeapTypes()) {
+      if (!child.isBasic()) {
+        RecGroup otherGroup = child.getRecGroup();
+        if (otherGroup != group) {
+          info.preds.insert(otherGroup);
         }
-        break;
+      }
     }
   }
 
   // Fix up the use counts to be averages to ensure groups are used comensurate
   // with the amount of index space they occupy. Skip this for nominal types
   // since their internal group size is always 1.
-  if (system != TypeSystem::Nominal) {
-    for (auto& [group, info] : groupInfos) {
-      info.useCount /= group.size();
-    }
+  for (auto& [group, info] : groupInfos) {
+    info.useCount /= group.size();
   }
 
   // Sort the predecessors so the most used will be visited first.
diff --git a/src/tools/fuzzing/heap-types.cpp b/src/tools/fuzzing/heap-types.cpp
index 24054572d..e58c7f51d 100644
--- a/src/tools/fuzzing/heap-types.cpp
+++ b/src/tools/fuzzing/heap-types.cpp
@@ -65,8 +65,7 @@ struct HeapTypeGeneratorImpl {
     // Set up the subtype relationships. Start with some number of root types,
     // then after that start creating subtypes of existing types. Determine the
     // top-level kind of each type in advance so that we can appropriately use
-    // types we haven't constructed yet. For simplicity, always choose a
-    // supertype to bea previous type, which is valid in all type systems.
+    // types we haven't constructed yet.
     typeKinds.reserve(builder.size());
     supertypeIndices.reserve(builder.size());
     Index numRoots = 1 + rand.upTo(builder.size());
@@ -90,31 +89,23 @@ struct HeapTypeGeneratorImpl {
 
     // Initialize the recursion groups.
     recGroupEnds.reserve(builder.size());
-    if (getTypeSystem() != TypeSystem::Isorecursive) {
-      // Recursion groups don't matter and we can choose children as though we
-      // had a single large recursion group.
-      for (Index i = 0; i < builder.size(); ++i) {
-        recGroupEnds.push_back(builder.size());
-      }
-    } else {
-      // We are using isorecursive types, so create groups. Choose an expected
-      // group size uniformly at random, then create groups with random sizes on
-      // a geometric distribution based on that expected size.
-      size_t expectedSize = 1 + rand.upTo(builder.size());
-      Index groupStart = 0;
-      for (Index i = 0; i < builder.size(); ++i) {
-        if (i == builder.size() - 1 || rand.oneIn(expectedSize)) {
-          // End the old group and create a new group.
-          Index newGroupStart = i + 1;
-          builder.createRecGroup(groupStart, newGroupStart - groupStart);
-          for (Index j = groupStart; j < newGroupStart; ++j) {
-            recGroupEnds.push_back(newGroupStart);
-          }
-          groupStart = newGroupStart;
+    // Create isorecursive recursion groups. Choose an expected group size
+    // uniformly at random, then create groups with random sizes on a geometric
+    // distribution based on that expected size.
+    size_t expectedSize = 1 + rand.upTo(builder.size());
+    Index groupStart = 0;
+    for (Index i = 0; i < builder.size(); ++i) {
+      if (i == builder.size() - 1 || rand.oneIn(expectedSize)) {
+        // End the old group and create a new group.
+        Index newGroupStart = i + 1;
+        builder.createRecGroup(groupStart, newGroupStart - groupStart);
+        for (Index j = groupStart; j < newGroupStart; ++j) {
+          recGroupEnds.push_back(newGroupStart);
         }
+        groupStart = newGroupStart;
       }
-      assert(recGroupEnds.size() == builder.size());
     }
+    assert(recGroupEnds.size() == builder.size());
 
     // Create the heap types.
     for (; index < builder.size(); ++index) {
diff --git a/src/tools/tool-options.h b/src/tools/tool-options.h
index 4e9d85d00..a6e57a76e 100644
--- a/src/tools/tool-options.h
+++ b/src/tools/tool-options.h
@@ -182,10 +182,6 @@ struct ToolOptions : public Options {
   void applyFeatures(Module& module) const {
     module.features.enable(enabledFeatures);
     module.features.disable(disabledFeatures);
-    // Non-default type systems only make sense with GC enabled.
-    if (!module.features.hasGC() && getTypeSystem() == TypeSystem::Nominal) {
-      Fatal() << "Nominal typing is only allowed when GC is enabled";
-    }
   }
 
 private:
diff --git a/src/tools/wasm-fuzz-types.cpp b/src/tools/wasm-fuzz-types.cpp
index ce393d133..0dc9f9d17 100644
--- a/src/tools/wasm-fuzz-types.cpp
+++ b/src/tools/wasm-fuzz-types.cpp
@@ -228,11 +228,6 @@ void Fuzzer::checkCanonicalization() {
   // Check that structural canonicalization is working correctly by building the
   // types again, choosing randomly between equivalent possible children for
   // each definition from both the new and old sets of built types.
-  if (getTypeSystem() == TypeSystem::Nominal) {
-    // No canonicalization to check.
-    return;
-  }
-
   TypeBuilder builder(types.size());
 
   // Helper for creating new definitions of existing types, randomly choosing
@@ -274,36 +269,29 @@ void Fuzzer::checkCanonicalization() {
       // Set up recursion groups and record group ends to ensure we only select
       // valid children.
       recGroupEnds.reserve(builder.size());
-      if (getTypeSystem() != TypeSystem::Isorecursive) {
-        // No rec groups.
-        for (size_t i = 0; i < builder.size(); ++i) {
-          recGroupEnds.push_back(builder.size());
+      // Set up recursion groups
+      std::optional<RecGroup> currGroup;
+      size_t currGroupStart = 0;
+      auto finishGroup = [&](Index end) {
+        builder.createRecGroup(currGroupStart, end - currGroupStart);
+        for (Index i = currGroupStart; i < end; ++i) {
+          recGroupEnds.push_back(end);
         }
-      } else {
-        // Set up recursion groups
-        std::optional<RecGroup> currGroup;
-        size_t currGroupStart = 0;
-        auto finishGroup = [&](Index end) {
-          builder.createRecGroup(currGroupStart, end - currGroupStart);
-          for (Index i = currGroupStart; i < end; ++i) {
-            recGroupEnds.push_back(end);
-          }
-          currGroupStart = end;
-        };
-        for (Index i = 0; i < types.size(); ++i) {
-          auto type = types[i];
-          if (type.isBasic()) {
-            continue;
-          }
-          auto newGroup = type.getRecGroup();
-          if (!currGroup || newGroup != currGroup ||
-              type == types[currGroupStart]) {
-            finishGroup(i);
-            currGroup = newGroup;
-          }
+        currGroupStart = end;
+      };
+      for (Index i = 0; i < types.size(); ++i) {
+        auto type = types[i];
+        if (type.isBasic()) {
+          continue;
+        }
+        auto newGroup = type.getRecGroup();
+        if (!currGroup || newGroup != currGroup ||
+            type == types[currGroupStart]) {
+          finishGroup(i);
+          currGroup = newGroup;
         }
-        finishGroup(builder.size());
       }
+      finishGroup(builder.size());
 
       // Copy the original types
       for (; index < types.size(); ++index) {
@@ -349,7 +337,7 @@ void Fuzzer::checkCanonicalization() {
         assert(old.isBasic());
         return {OldHeapType{old}};
       }
-      if (!old.isBasic() && getTypeSystem() == TypeSystem::Isorecursive) {
+      if (!old.isBasic()) {
         // Check whether this child heap type is supposed to be a self-reference
         // into the recursion group we are defining. If it is, we must use the
         // corresponding type in the new recursion group, since anything else
@@ -514,7 +502,7 @@ void Fuzzer::checkInhabitable() {
     }
     // TODO: We could also check that the transformed types are the same as the
     // original types up to nullability.
-  } else if (getTypeSystem() == TypeSystem::Isorecursive) {
+  } else {
     // Verify the produced inhabitable types are the same as the original types
     // (which also implies that they are indeed inhabitable).
     if (types.size() != inhabitable.size()) {
diff --git a/src/wasm-type.h b/src/wasm-type.h
index d72f5477d..ad0606d59 100644
--- a/src/wasm-type.h
+++ b/src/wasm-type.h
@@ -40,17 +40,6 @@
 
 namespace wasm {
 
-enum class TypeSystem {
-  Isorecursive,
-  Nominal,
-};
-
-// This should only ever be called before any Types or HeapTypes have been
-// created. The default system is equirecursive.
-void setTypeSystem(TypeSystem system);
-
-TypeSystem getTypeSystem();
-
 // Dangerous! Frees all types and heap types that have ever been created and
 // resets the type system's internal state. This is only really meant to be used
 // for tests.
diff --git a/src/wasm/wasm-binary.cpp b/src/wasm/wasm-binary.cpp
index e85740614..967356210 100644
--- a/src/wasm/wasm-binary.cpp
+++ b/src/wasm/wasm-binary.cpp
@@ -229,40 +229,22 @@ void WasmBinaryWriter::writeTypes() {
   // the type section. With nominal typing there is always one group and with
   // equirecursive typing there is one group per type.
   size_t numGroups = 0;
-  // MVP types are structural and do not use recursion groups.
-  TypeSystem typeSystem = getTypeSystem();
-  if (!wasm->features.hasGC()) {
-    typeSystem = TypeSystem::Isorecursive;
-  }
-  switch (typeSystem) {
-    case TypeSystem::Nominal:
-      numGroups = 1;
-      break;
-    case TypeSystem::Isorecursive: {
-      std::optional<RecGroup> lastGroup;
-      for (auto type : indexedTypes.types) {
-        auto currGroup = type.getRecGroup();
-        numGroups += lastGroup != currGroup;
-        lastGroup = currGroup;
-      }
+  {
+    std::optional<RecGroup> lastGroup;
+    for (auto type : indexedTypes.types) {
+      auto currGroup = type.getRecGroup();
+      numGroups += lastGroup != currGroup;
+      lastGroup = currGroup;
     }
   }
   BYN_TRACE("== writeTypes\n");
   auto start = startSection(BinaryConsts::Section::Type);
   o << U32LEB(numGroups);
-  if (typeSystem == TypeSystem::Nominal) {
-    // The nominal recursion group contains every type.
-    o << S32LEB(BinaryConsts::EncodedType::Rec)
-      << U32LEB(indexedTypes.types.size());
-  }
   std::optional<RecGroup> lastGroup = std::nullopt;
   for (Index i = 0; i < indexedTypes.types.size(); ++i) {
     auto type = indexedTypes.types[i];
     // Check whether we need to start a new recursion group. Recursion groups of
-    // size 1 are implicit, so only emit a group header for larger groups. This
-    // gracefully handles non-isorecursive type systems, which only have groups
-    // of size 1 internally (even though nominal types are emitted as a single
-    // large group).
+    // size 1 are implicit, so only emit a group header for larger groups.
     auto currGroup = type.getRecGroup();
     if (lastGroup != currGroup && currGroup.size() > 1) {
       o << S32LEB(BinaryConsts::EncodedType::Rec) << U32LEB(currGroup.size());
diff --git a/src/wasm/wasm-type.cpp b/src/wasm/wasm-type.cpp
index 8b1dfb0af..c9c35ac49 100644
--- a/src/wasm/wasm-type.cpp
+++ b/src/wasm/wasm-type.cpp
@@ -44,12 +44,6 @@
 
 namespace wasm {
 
-static TypeSystem typeSystem = TypeSystem::Isorecursive;
-
-void setTypeSystem(TypeSystem system) { typeSystem = system; }
-
-TypeSystem getTypeSystem() { return typeSystem; }
-
 namespace {
 
 struct TypeInfo {
@@ -104,11 +98,10 @@ struct HeapTypeInfo {
   // Otherwise, the type definition tree is still being constructed via the
   // TypeBuilder interface, so hashing and equality use pointer identity.
   bool isFinalized = true;
-  // In nominal or isorecursive mode, the supertype of this HeapType, if it
-  // exists.
+  // The supertype of this HeapType, if it exists.
   HeapTypeInfo* supertype = nullptr;
-  // In isorecursive mode, the recursion group of this type or null if the
-  // recursion group is trivial (i.e. contains only this type).
+  // The recursion group of this type or null if the recursion group is trivial
+  // (i.e. contains only this type).
   RecGroupInfo* recGroup = nullptr;
   size_t recGroupIndex = 0;
   enum Kind {
@@ -714,12 +707,6 @@ private:
       return *canonical;
     }
     std::lock_guard<std::recursive_mutex> lock(mutex);
-    // Nominal HeapTypes are always unique, so don't bother deduplicating them.
-    if constexpr (std::is_same_v<Info, HeapTypeInfo>) {
-      if (typeSystem == TypeSystem::Nominal) {
-        return insertNew();
-      }
-    }
     // Check whether we already have a type for this structural Info.
     auto indexIt = typeIDs.find(std::cref(info));
     if (indexIt != typeIDs.end()) {
@@ -759,34 +746,6 @@ template<typename Info> bool Store<Info>::isGlobalStore() {
 }
 #endif
 
-// Cache canonical nominal signature types. See comment in
-// `HeapType::HeapType(Signature)`.
-struct SignatureTypeCache {
-  std::unordered_map<Signature, HeapType> cache;
-  std::mutex mutex;
-
-  HeapType getType(Signature sig) {
-    std::lock_guard<std::mutex> lock(mutex);
-    // Try inserting a placeholder type, then replace it with a real type if we
-    // don't already have a canonical type for this signature.
-    auto [entry, inserted] = cache.insert({sig, {}});
-    auto& [_, type] = *entry;
-    if (inserted) {
-      type = globalHeapTypeStore.insert(sig);
-    }
-    return type;
-  }
-
-  void insertType(HeapType type) {
-    std::lock_guard<std::mutex> lock(mutex);
-    cache.insert({type.getSignature(), type});
-  }
-
-  void clear() { cache.clear(); }
-};
-
-static SignatureTypeCache nominalSignatureCache;
-
 // Keep track of the constructed recursion groups.
 struct RecGroupStore {
   std::mutex mutex;
@@ -841,7 +800,6 @@ static RecGroupStore globalRecGroupStore;
 void destroyAllTypesForTestingPurposesOnly() {
   globalTypeStore.clear();
   globalHeapTypeStore.clear();
-  nominalSignatureCache.clear();
   globalRecGroupStore.clear();
 }
 
@@ -1222,24 +1180,8 @@ const Type& Type::Iterator::operator*() const {
 HeapType::HeapType(Signature sig) {
   assert(!isTemp(sig.params) && "Leaking temporary type!");
   assert(!isTemp(sig.results) && "Leaking temporary type!");
-  switch (getTypeSystem()) {
-    case TypeSystem::Nominal:
-      // Special case the creation of signature types in nominal mode to return
-      // a "canonical" type for the signature, which happens to be the first one
-      // created. We depend on being able to create new function signatures in
-      // many places, and historically they have always been structural, so
-      // creating a copy of an existing signature did not result in any code
-      // bloat or semantic changes. To avoid regressions or significant changes
-      // of behavior in nominal mode, we cache the canonical heap types for each
-      // signature to emulate structural behavior.
-      new (this) HeapType(nominalSignatureCache.getType(sig));
-      return;
-    case TypeSystem::Isorecursive:
-      new (this) HeapType(
-        globalRecGroupStore.insert(std::make_unique<HeapTypeInfo>(sig)));
-      return;
-  }
-  WASM_UNREACHABLE("unexpected type system");
+  new (this)
+    HeapType(globalRecGroupStore.insert(std::make_unique<HeapTypeInfo>(sig)));
 }
 
 HeapType::HeapType(const Struct& struct_) {
@@ -1248,16 +1190,8 @@ HeapType::HeapType(const Struct& struct_) {
     assert(!isTemp(field.type) && "Leaking temporary type!");
   }
 #endif
-  switch (getTypeSystem()) {
-    case TypeSystem::Nominal:
-      new (this) HeapType(globalHeapTypeStore.insert(struct_));
-      return;
-    case TypeSystem::Isorecursive:
-      new (this) HeapType(
-        globalRecGroupStore.insert(std::make_unique<HeapTypeInfo>(struct_)));
-      return;
-  }
-  WASM_UNREACHABLE("unexpected type system");
+  new (this) HeapType(
+    globalRecGroupStore.insert(std::make_unique<HeapTypeInfo>(struct_)));
 }
 
 HeapType::HeapType(Struct&& struct_) {
@@ -1266,30 +1200,14 @@ HeapType::HeapType(Struct&& struct_) {
     assert(!isTemp(field.type) && "Leaking temporary type!");
   }
 #endif
-  switch (getTypeSystem()) {
-    case TypeSystem::Nominal:
-      new (this) HeapType(globalHeapTypeStore.insert(std::move(struct_)));
-      return;
-    case TypeSystem::Isorecursive:
-      new (this) HeapType(globalRecGroupStore.insert(
-        std::make_unique<HeapTypeInfo>(std::move(struct_))));
-      return;
-  }
-  WASM_UNREACHABLE("unexpected type system");
+  new (this) HeapType(globalRecGroupStore.insert(
+    std::make_unique<HeapTypeInfo>(std::move(struct_))));
 }
 
 HeapType::HeapType(Array array) {
   assert(!isTemp(array.element.type) && "Leaking temporary type!");
-  switch (getTypeSystem()) {
-    case TypeSystem::Nominal:
-      new (this) HeapType(globalHeapTypeStore.insert(array));
-      return;
-    case TypeSystem::Isorecursive:
-      new (this) HeapType(
-        globalRecGroupStore.insert(std::make_unique<HeapTypeInfo>(array)));
-      return;
-  }
-  WASM_UNREACHABLE("unexpected type system");
+  new (this)
+    HeapType(globalRecGroupStore.insert(std::make_unique<HeapTypeInfo>(array)));
 }
 
 bool HeapType::isFunction() const {
@@ -2774,39 +2692,6 @@ validateSubtyping(const std::vector<HeapType>& types) {
   return {};
 }
 
-std::optional<TypeBuilder::Error>
-canonicalizeNominal(CanonicalizationState& state) {
-  for (auto& info : state.newInfos) {
-    info->recGroup = nullptr;
-  }
-
-  // Nominal types do not require separate canonicalization, so just validate
-  // that their subtyping is correct.
-
-  // Ensure there are no cycles in the subtype graph. This is the classic DFA
-  // algorithm for detecting cycles, but in the form of a simple loop because
-  // each node (type) has at most one child (supertype).
-  std::unordered_set<HeapTypeInfo*> checked;
-  for (size_t i = 0; i < state.results.size(); ++i) {
-    HeapType type = state.results[i];
-    if (type.isBasic()) {
-      continue;
-    }
-    std::unordered_set<HeapTypeInfo*> path;
-    for (auto* curr = getHeapTypeInfo(type);
-         curr != nullptr && !checked.count(curr);
-         curr = curr->supertype) {
-      if (!path.insert(curr).second) {
-        return TypeBuilder::Error{i, TypeBuilder::ErrorReason::SelfSupertype};
-      }
-    }
-    // None of the types in `path` reach themselves.
-    checked.insert(path.begin(), path.end());
-  }
-
-  return {};
-}
-
 std::optional<TypeBuilder::Error> canonicalizeIsorecursive(
   CanonicalizationState& state,
   std::vector<std::unique_ptr<RecGroupInfo>>& recGroupInfos) {
@@ -2992,17 +2877,8 @@ TypeBuilder::BuildResult TypeBuilder::build() {
   auto start = std::chrono::steady_clock::now();
 #endif
 
-  switch (typeSystem) {
-    case TypeSystem::Nominal:
-      if (auto error = canonicalizeNominal(state)) {
-        return {*error};
-      }
-      break;
-    case TypeSystem::Isorecursive:
-      if (auto error = canonicalizeIsorecursive(state, impl->recGroups)) {
-        return {*error};
-      }
-      break;
+  if (auto error = canonicalizeIsorecursive(state, impl->recGroups)) {
+    return {*error};
   }
 
 #if TIME_CANONICALIZATION
@@ -3026,17 +2902,6 @@ TypeBuilder::BuildResult TypeBuilder::build() {
     return {*error};
   }
 
-  // Note built signature types. See comment in `HeapType::HeapType(Signature)`.
-  for (auto type : state.results) {
-    // Do not cache types with explicit supertypes (that is, whose supertype is
-    // not HeapType::func). We don't want to reuse such types because then we'd
-    // be adding subtyping relationships that are not in the input.
-    if (type.isSignature() && (getTypeSystem() == TypeSystem::Nominal) &&
-        !type.getSuperType()) {
-      nominalSignatureCache.insertType(type);
-    }
-  }
-
   return {state.results};
 }
 
diff --git a/test/example/c-api-kitchen-sink.c b/test/example/c-api-kitchen-sink.c
index 01cc6a9c0..760f4be1d 100644
--- a/test/example/c-api-kitchen-sink.c
+++ b/test/example/c-api-kitchen-sink.c
@@ -2122,23 +2122,7 @@ void test_func_opt() {
   BinaryenModuleDispose(module);
 }
 
-void test_typesystem() {
-  BinaryenTypeSystem defaultTypeSystem = BinaryenGetTypeSystem();
-  assert(defaultTypeSystem == BinaryenTypeSystemIsorecursive());
-  BinaryenSetTypeSystem(BinaryenTypeSystemNominal());
-  assert(BinaryenGetTypeSystem() == BinaryenTypeSystemNominal());
-  printf("BinaryenTypeSystemNominal: %d\n", BinaryenTypeSystemNominal());
-  BinaryenSetTypeSystem(BinaryenTypeSystemIsorecursive());
-  assert(BinaryenGetTypeSystem() == BinaryenTypeSystemIsorecursive());
-  printf("BinaryenTypeSystemIsorecursive: %d\n",
-         BinaryenTypeSystemIsorecursive());
-  BinaryenSetTypeSystem(defaultTypeSystem);
-}
-
 void test_typebuilder() {
-  BinaryenTypeSystem defaultTypeSystem = BinaryenGetTypeSystem();
-  BinaryenSetTypeSystem(BinaryenTypeSystemIsorecursive());
-
   printf("TypeBuilderErrorReasonSelfSupertype: %d\n",
          TypeBuilderErrorReasonSelfSupertype());
   printf("TypeBuilderErrorReasonInvalidSupertype: %d\n",
@@ -2344,8 +2328,6 @@ void test_typebuilder() {
   printf("module with recursive GC types:\n");
   BinaryenModulePrint(module);
   BinaryenModuleDispose(module);
-
-  BinaryenSetTypeSystem(defaultTypeSystem);
 }
 
 int main() {
@@ -2360,7 +2342,6 @@ int main() {
   test_color_status();
   test_for_each();
   test_func_opt();
-  test_typesystem();
   test_typebuilder();
 
   return 0;
diff --git a/test/example/c-api-kitchen-sink.txt b/test/example/c-api-kitchen-sink.txt
index dcfd6de8c..1c1a3b956 100644
--- a/test/example/c-api-kitchen-sink.txt
+++ b/test/example/c-api-kitchen-sink.txt
@@ -3147,8 +3147,6 @@ optimized:
   (i32.const 4)
  )
 )
-BinaryenTypeSystemNominal: 1
-BinaryenTypeSystemIsorecursive: 0
 TypeBuilderErrorReasonSelfSupertype: 0
 TypeBuilderErrorReasonInvalidSupertype: 1
 TypeBuilderErrorReasonForwardSupertypeReference: 2
diff --git a/test/example/type-builder-nominal.cpp b/test/example/type-builder-nominal.cpp
deleted file mode 100644
index a3e8695ac..000000000
--- a/test/example/type-builder-nominal.cpp
+++ /dev/null
@@ -1,428 +0,0 @@
-#include <cassert>
-#include <iostream>
-
-#include "wasm-builder.h"
-#include "wasm-type-printing.h"
-#include "wasm-type.h"
-
-using namespace wasm;
-
-// Construct Signature, Struct, and Array heap types using undefined types.
-void test_builder() {
-  std::cout << ";; Test TypeBuilder\n";
-
-  // (type $sig (func (param (ref $struct)) (result (ref $array) i32)))
-  // (type $struct (struct (field (ref null $array))))
-  // (type $array (array (mut anyref)))
-
-  TypeBuilder builder;
-  assert(builder.size() == 0);
-  builder.grow(3);
-  assert(builder.size() == 3);
-
-  Type refSig = builder.getTempRefType(builder[0], NonNullable);
-  Type refStruct = builder.getTempRefType(builder[1], NonNullable);
-  Type refArray = builder.getTempRefType(builder[2], NonNullable);
-  Type refNullArray = builder.getTempRefType(builder[2], Nullable);
-  Type refNullAny(HeapType::any, Nullable);
-
-  Signature sig(refStruct, builder.getTempTupleType({refArray, Type::i32}));
-  Struct struct_({Field(refNullArray, Immutable)});
-  Array array(Field(refNullAny, Mutable));
-
-  {
-    IndexedTypeNameGenerator print(builder);
-    std::cout << "Before setting heap types:\n";
-    std::cout << "$sig => " << print(builder[0]) << "\n";
-    std::cout << "$struct => " << print(builder[1]) << "\n";
-    std::cout << "$array => " << print(builder[2]) << "\n";
-    std::cout << "(ref $sig) => " << print(refSig) << "\n";
-    std::cout << "(ref $struct) => " << print(refStruct) << "\n";
-    std::cout << "(ref $array) => " << print(refArray) << "\n";
-    std::cout << "(ref null $array) => " << print(refNullArray) << "\n";
-  }
-
-  builder[0] = sig;
-  builder[1] = struct_;
-  builder[2] = array;
-
-  {
-    IndexedTypeNameGenerator print(builder);
-    std::cout << "After setting heap types:\n";
-    std::cout << "$sig => " << print(builder[0]) << "\n";
-    std::cout << "$struct => " << print(builder[1]) << "\n";
-    std::cout << "$array => " << print(builder[2]) << "\n";
-    std::cout << "(ref $sig) => " << print(refSig) << "\n";
-    std::cout << "(ref $struct) => " << print(refStruct) << "\n";
-    std::cout << "(ref $array) => " << print(refArray) << "\n";
-    std::cout << "(ref null $array) => " << print(refNullArray) << "\n";
-  }
-
-  std::vector<HeapType> built = *builder.build();
-
-  Type newRefSig = Type(built[0], NonNullable);
-  Type newRefStruct = Type(built[1], NonNullable);
-  Type newRefArray = Type(built[2], NonNullable);
-  Type newRefNullArray = Type(built[2], Nullable);
-
-  {
-    IndexedTypeNameGenerator print(built);
-    std::cout << "After building types:\n";
-    std::cout << "$sig => " << print(built[0]) << "\n";
-    std::cout << "$struct => " << print(built[1]) << "\n";
-    std::cout << "$array => " << print(built[2]) << "\n";
-    std::cout << "(ref $sig) => " << print(newRefSig) << "\n";
-    std::cout << "(ref $struct) => " << print(newRefStruct) << "\n";
-    std::cout << "(ref $array) => " << print(newRefArray) << "\n";
-    std::cout << "(ref null $array) => " << print(newRefNullArray) << "\n";
-  }
-}
-
-// Check that the builder works when there are duplicate definitions
-void test_canonicalization() {
-  std::cout << ";; Test canonicalization\n";
-
-  // (type $struct (struct (field (ref null $sig) (ref null $sig))))
-  // (type $sig (func))
-  HeapType sig = Signature(Type::none, Type::none);
-  HeapType struct_ = Struct({Field(Type(sig, Nullable), Immutable),
-                             Field(Type(sig, Nullable), Immutable)});
-
-  TypeBuilder builder(4);
-
-  Type tempSigRef1 = builder.getTempRefType(builder[2], Nullable);
-  Type tempSigRef2 = builder.getTempRefType(builder[3], Nullable);
-
-  assert(tempSigRef1 != tempSigRef2);
-  assert(tempSigRef1 != Type(sig, Nullable));
-  assert(tempSigRef2 != Type(sig, Nullable));
-
-  builder[0] =
-    Struct({Field(tempSigRef1, Immutable), Field(tempSigRef1, Immutable)});
-  builder[1] =
-    Struct({Field(tempSigRef2, Immutable), Field(tempSigRef2, Immutable)});
-  builder[2] = Signature(Type::none, Type::none);
-  builder[3] = Signature(Type::none, Type::none);
-
-  std::vector<HeapType> built = *builder.build();
-
-  assert(built[0] != struct_);
-  assert(built[1] != struct_);
-  assert(built[0] != built[1]);
-  assert(built[2] != sig);
-  assert(built[3] != sig);
-  assert(built[2] != built[3]);
-}
-
-// Check that defined basic HeapTypes are handled correctly.
-void test_basic() {
-  std::cout << ";; Test basic\n";
-
-  Type canonAnyref = Type(HeapType::any, Nullable);
-  Type canonI31ref = Type(HeapType::i31, NonNullable);
-
-  TypeBuilder builder(6);
-
-  Type anyref = builder.getTempRefType(builder[4], Nullable);
-  Type i31ref = builder.getTempRefType(builder[5], NonNullable);
-
-  builder[0] = Signature(canonAnyref, canonI31ref);
-  builder[1] = Signature(anyref, canonI31ref);
-  builder[2] = Signature(canonAnyref, i31ref);
-  builder[3] = Signature(anyref, i31ref);
-  builder[4] = HeapType::any;
-  builder[5] = HeapType::i31;
-
-  std::vector<HeapType> built = *builder.build();
-
-  assert(built[0].getSignature() == Signature(canonAnyref, canonI31ref));
-  assert(built[1].getSignature() == built[0].getSignature());
-  assert(built[2].getSignature() == built[1].getSignature());
-  assert(built[3].getSignature() == built[2].getSignature());
-  assert(built[4] == HeapType::any);
-  assert(built[5] == HeapType::i31);
-}
-
-// Check that signatures created with TypeBuilders are properly recorded as
-// canonical.
-void test_signatures(bool warm) {
-  std::cout << ";; Test canonical signatures\n";
-
-  Type canonAnyref = Type(HeapType::any, Nullable);
-  Type canonI31ref = Type(HeapType::i31, NonNullable);
-
-  TypeBuilder builder(2);
-  Type tempRef = builder.getTempRefType(builder[0], Nullable);
-  builder[0] = Signature(canonI31ref, canonAnyref);
-  builder[1] = Signature(tempRef, tempRef);
-  std::vector<HeapType> built = *builder.build();
-
-  HeapType small = Signature(canonI31ref, canonAnyref);
-  HeapType big = Signature(Type(Signature(canonI31ref, canonAnyref), Nullable),
-                           Type(Signature(canonI31ref, canonAnyref), Nullable));
-  if (warm) {
-    assert(built[0] != small);
-    assert(built[1] != big);
-  } else {
-    assert(built[0] == small);
-    assert(built[1] == big);
-  }
-}
-
-void test_recursive() {
-  std::cout << ";; Test recursive types\n";
-
-  {
-    // Trivial recursion
-    std::vector<HeapType> built;
-    {
-      TypeBuilder builder(1);
-      Type temp = builder.getTempRefType(builder[0], Nullable);
-      builder[0] = Signature(Type::none, temp);
-      built = *builder.build();
-    }
-    IndexedTypeNameGenerator print(built);
-    std::cout << print(built[0]) << "\n\n";
-    assert(built[0] == built[0].getSignature().results.getHeapType());
-    assert(Type(built[0], Nullable) == built[0].getSignature().results);
-  }
-
-  {
-    // Mutual recursion
-    std::vector<HeapType> built;
-    {
-      TypeBuilder builder(2);
-      Type temp0 = builder.getTempRefType(builder[0], Nullable);
-      Type temp1 = builder.getTempRefType(builder[1], Nullable);
-      builder[0] = Signature(Type::none, temp1);
-      builder[1] = Signature(Type::none, temp0);
-      built = *builder.build();
-    }
-    IndexedTypeNameGenerator print(built);
-    std::cout << print(built[0]) << "\n";
-    std::cout << print(built[1]) << "\n\n";
-    assert(built[0].getSignature().results.getHeapType() == built[1]);
-    assert(built[1].getSignature().results.getHeapType() == built[0]);
-    assert(built[0] != built[1]);
-  }
-
-  {
-    // A longer chain of recursion
-    std::vector<HeapType> built;
-    {
-      TypeBuilder builder(5);
-      Type temp0 = builder.getTempRefType(builder[0], Nullable);
-      Type temp1 = builder.getTempRefType(builder[1], Nullable);
-      Type temp2 = builder.getTempRefType(builder[2], Nullable);
-      Type temp3 = builder.getTempRefType(builder[3], Nullable);
-      Type temp4 = builder.getTempRefType(builder[4], Nullable);
-      builder[0] = Signature(Type::none, temp1);
-      builder[1] = Signature(Type::none, temp2);
-      builder[2] = Signature(Type::none, temp3);
-      builder[3] = Signature(Type::none, temp4);
-      builder[4] = Signature(Type::none, temp0);
-      built = *builder.build();
-    }
-    IndexedTypeNameGenerator print(built);
-    std::cout << print(built[0]) << "\n";
-    std::cout << print(built[1]) << "\n";
-    std::cout << print(built[2]) << "\n";
-    std::cout << print(built[3]) << "\n";
-    std::cout << print(built[4]) << "\n\n";
-    assert(built[0].getSignature().results.getHeapType() == built[1]);
-    assert(built[1].getSignature().results.getHeapType() == built[2]);
-    assert(built[2].getSignature().results.getHeapType() == built[3]);
-    assert(built[3].getSignature().results.getHeapType() == built[4]);
-    assert(built[4].getSignature().results.getHeapType() == built[0]);
-    assert(built[0] != built[1]);
-    assert(built[0] != built[2]);
-    assert(built[0] != built[3]);
-    assert(built[0] != built[4]);
-    assert(built[1] != built[2]);
-    assert(built[1] != built[3]);
-    assert(built[1] != built[4]);
-    assert(built[2] != built[3]);
-    assert(built[2] != built[4]);
-    assert(built[3] != built[4]);
-  }
-
-  {
-    // Check canonicalization for non-recursive parents and children of
-    // recursive HeapTypes.
-    std::vector<HeapType> built;
-    {
-      TypeBuilder builder(6);
-      Type temp0 = builder.getTempRefType(builder[0], Nullable);
-      Type temp1 = builder.getTempRefType(builder[1], Nullable);
-      Type temp2 = builder.getTempRefType(builder[2], Nullable);
-      Type temp3 = builder.getTempRefType(builder[3], Nullable);
-      Type tuple0_2 = builder.getTempTupleType({temp0, temp2});
-      Type tuple1_3 = builder.getTempTupleType({temp1, temp3});
-      builder[0] = Signature(Type::none, tuple0_2);
-      builder[1] = Signature(Type::none, tuple1_3);
-      builder[2] = Signature();
-      builder[3] = Signature();
-      builder[4] = Signature(Type::none, temp0);
-      builder[5] = Signature(Type::none, temp1);
-      built = *builder.build();
-    }
-    IndexedTypeNameGenerator print(built);
-    std::cout << print(built[0]) << "\n";
-    std::cout << print(built[1]) << "\n";
-    std::cout << print(built[2]) << "\n";
-    std::cout << print(built[3]) << "\n";
-    std::cout << print(built[4]) << "\n";
-    std::cout << print(built[5]) << "\n\n";
-    assert(built[0] != built[1]);
-    assert(built[2] != built[3]);
-    assert(built[4] != built[5]);
-    assert(built[4].getSignature().results.getHeapType() == built[0]);
-    assert(built[5].getSignature().results.getHeapType() == built[1]);
-    assert(built[0].getSignature().results ==
-           Type({Type(built[0], Nullable), Type(built[2], Nullable)}));
-    assert(built[1].getSignature().results ==
-           Type({Type(built[1], Nullable), Type(built[3], Nullable)}));
-  }
-
-  {
-    // Folded and unfolded
-    std::vector<HeapType> built;
-    {
-      TypeBuilder builder(2);
-      Type temp0 = builder.getTempRefType(builder[0], Nullable);
-      builder[0] = Signature(Type::none, temp0);
-      builder[1] = Signature(Type::none, temp0);
-      built = *builder.build();
-    }
-    IndexedTypeNameGenerator print(built);
-    std::cout << print(built[0]) << "\n";
-    std::cout << print(built[1]) << "\n\n";
-    assert(built[0].getSignature().results.getHeapType() == built[0]);
-    assert(built[1].getSignature().results.getHeapType() == built[0]);
-    assert(built[0] != built[1]);
-  }
-}
-
-void test_subtypes() {
-  std::cout << ";; Test subtyping\n";
-
-  Type anyref = Type(HeapType::any, Nullable);
-  Type eqref = Type(HeapType::eq, Nullable);
-
-  auto LUB = [&](HeapType a, HeapType b) {
-    Type refA = Type(a, Nullable);
-    Type refB = Type(b, Nullable);
-    Type lubAB = Type::getLeastUpperBound(refA, refB);
-    Type lubBA = Type::getLeastUpperBound(refB, refA);
-    assert(lubAB == lubBA);
-    assert(lubAB != Type::none);
-    HeapType lub = lubAB.getHeapType();
-    assert(Type::hasLeastUpperBound(refA, refB));
-    assert(Type::hasLeastUpperBound(refB, refA));
-    assert(Type::isSubType(refA, lubAB));
-    assert(Type::isSubType(refB, lubAB));
-    assert(HeapType::isSubType(a, lub));
-    assert(HeapType::isSubType(b, lub));
-    assert(lub == a || !HeapType::isSubType(lub, a));
-    assert(lub == b || !HeapType::isSubType(lub, b));
-    return lub;
-  };
-
-  {
-    // Subtype declarations, but still no subtypes
-    std::vector<HeapType> built;
-    {
-      TypeBuilder builder(3);
-      builder[0].subTypeOf(builder[1]);
-      builder[0] = Struct{};
-      builder[1] = Struct{};
-      builder[2] = Struct{};
-      built = *builder.build();
-    }
-    assert(LUB(built[0], built[2]) == HeapType::struct_);
-  }
-
-  {
-    // Subtyping of identical types
-    std::vector<HeapType> built;
-    {
-      TypeBuilder builder(6);
-      builder[0].subTypeOf(builder[1]);
-      builder[2].subTypeOf(builder[3]);
-      builder[4].subTypeOf(builder[5]);
-      builder[0] = Struct({Field(Type::i32, Mutable), Field(anyref, Mutable)});
-      builder[1] = Struct({Field(Type::i32, Mutable), Field(anyref, Mutable)});
-      builder[2] = Signature(Type::i32, anyref);
-      builder[3] = Signature(Type::i32, anyref);
-      builder[4] = Array(Field(Type::i32, Mutable));
-      builder[5] = Array(Field(Type::i32, Mutable));
-      built = *builder.build();
-    }
-    assert(LUB(built[0], built[1]) == built[1]);
-    assert(LUB(built[2], built[3]) == built[3]);
-    assert(LUB(built[4], built[5]) == built[5]);
-  }
-
-  {
-    // Width subtyping
-    std::vector<HeapType> built;
-    {
-      TypeBuilder builder(2);
-      builder[0] = Struct({Field(Type::i32, Immutable)});
-      builder[1] =
-        Struct({Field(Type::i32, Immutable), Field(Type::i32, Immutable)});
-      builder[1].subTypeOf(builder[0]);
-      built = *builder.build();
-    }
-    assert(LUB(built[1], built[0]) == built[0]);
-  }
-
-  {
-    // Depth subtyping
-    std::vector<HeapType> built;
-    {
-      TypeBuilder builder(2);
-      builder[0] = Struct({Field(anyref, Immutable)});
-      builder[1] = Struct({Field(eqref, Immutable)});
-      builder[1].subTypeOf(builder[0]);
-      built = *builder.build();
-    }
-    assert(LUB(built[1], built[0]) == built[0]);
-  }
-
-  {
-    // Mutually recursive subtyping
-    std::vector<HeapType> built;
-    {
-      TypeBuilder builder(4);
-      Type a = builder.getTempRefType(builder[0], Nullable);
-      Type b = builder.getTempRefType(builder[1], Nullable);
-      Type c = builder.getTempRefType(builder[2], Nullable);
-      Type d = builder.getTempRefType(builder[3], Nullable);
-      builder[1].subTypeOf(builder[0]);
-      builder[3].subTypeOf(builder[2]);
-      builder[0] = Struct({Field(c, Immutable)});
-      builder[1] = Struct({Field(d, Immutable)});
-      builder[2] = Struct({Field(a, Immutable)});
-      builder[3] = Struct({Field(b, Immutable)});
-      built = *builder.build();
-    }
-    assert(LUB(built[0], built[1]) == built[0]);
-    assert(LUB(built[2], built[3]) == built[2]);
-  }
-}
-
-int main() {
-  wasm::setTypeSystem(TypeSystem::Nominal);
-
-  // Run the tests twice to ensure things still work when the global stores are
-  // already populated.
-  for (size_t i = 0; i < 2; ++i) {
-    test_builder();
-    test_canonicalization();
-    test_basic();
-    test_signatures(i == 1);
-    test_recursive();
-    test_subtypes();
-  }
-}
diff --git a/test/example/type-builder-nominal.txt b/test/example/type-builder-nominal.txt
deleted file mode 100644
index 4da8857f2..000000000
--- a/test/example/type-builder-nominal.txt
+++ /dev/null
@@ -1,102 +0,0 @@
-;; Test TypeBuilder
-Before setting heap types:
-$sig => (type $0 (; temp ;) (func))
-$struct => (type $1 (; temp ;) (func))
-$array => (type $2 (; temp ;) (func))
-(ref $sig) => (; temp ;) (ref $0)
-(ref $struct) => (; temp ;) (ref $1)
-(ref $array) => (; temp ;) (ref $2)
-(ref null $array) => (; temp ;) (ref null $2)
-After setting heap types:
-$sig => (type $0 (; temp ;) (func (param (; temp ;) (ref $1)) (result (; temp ;) (ref $2) i32)))
-$struct => (type $1 (; temp ;) (struct (field (; temp ;) (ref null $2))))
-$array => (type $2 (; temp ;) (array (mut anyref)))
-(ref $sig) => (; temp ;) (ref $0)
-(ref $struct) => (; temp ;) (ref $1)
-(ref $array) => (; temp ;) (ref $2)
-(ref null $array) => (; temp ;) (ref null $2)
-After building types:
-$sig => (type $0 (func (param (ref $1)) (result (ref $2) i32)))
-$struct => (type $1 (struct (field (ref null $2))))
-$array => (type $2 (array (mut anyref)))
-(ref $sig) => (ref $0)
-(ref $struct) => (ref $1)
-(ref $array) => (ref $2)
-(ref null $array) => (ref null $2)
-;; Test canonicalization
-;; Test basic
-;; Test canonical signatures
-;; Test recursive types
-(type $0 (func (result (ref null $0))))
-
-(type $0 (func (result (ref null $1))))
-(type $1 (func (result (ref null $0))))
-
-(type $0 (func (result (ref null $1))))
-(type $1 (func (result (ref null $2))))
-(type $2 (func (result (ref null $3))))
-(type $3 (func (result (ref null $4))))
-(type $4 (func (result (ref null $0))))
-
-(type $0 (func (result (ref null $0) (ref null $2))))
-(type $1 (func (result (ref null $1) (ref null $3))))
-(type $2 (func))
-(type $3 (func))
-(type $4 (func (result (ref null $0))))
-(type $5 (func (result (ref null $1))))
-
-(type $0 (func (result (ref null $0))))
-(type $1 (func (result (ref null $0))))
-
-;; Test subtyping
-;; Test TypeBuilder
-Before setting heap types:
-$sig => (type $0 (; temp ;) (func))
-$struct => (type $1 (; temp ;) (func))
-$array => (type $2 (; temp ;) (func))
-(ref $sig) => (; temp ;) (ref $0)
-(ref $struct) => (; temp ;) (ref $1)
-(ref $array) => (; temp ;) (ref $2)
-(ref null $array) => (; temp ;) (ref null $2)
-After setting heap types:
-$sig => (type $0 (; temp ;) (func (param (; temp ;) (ref $1)) (result (; temp ;) (ref $2) i32)))
-$struct => (type $1 (; temp ;) (struct (field (; temp ;) (ref null $2))))
-$array => (type $2 (; temp ;) (array (mut anyref)))
-(ref $sig) => (; temp ;) (ref $0)
-(ref $struct) => (; temp ;) (ref $1)
-(ref $array) => (; temp ;) (ref $2)
-(ref null $array) => (; temp ;) (ref null $2)
-After building types:
-$sig => (type $0 (func (param (ref $1)) (result (ref $2) i32)))
-$struct => (type $1 (struct (field (ref null $2))))
-$array => (type $2 (array (mut anyref)))
-(ref $sig) => (ref $0)
-(ref $struct) => (ref $1)
-(ref $array) => (ref $2)
-(ref null $array) => (ref null $2)
-;; Test canonicalization
-;; Test basic
-;; Test canonical signatures
-;; Test recursive types
-(type $0 (func (result (ref null $0))))
-
-(type $0 (func (result (ref null $1))))
-(type $1 (func (result (ref null $0))))
-
-(type $0 (func (result (ref null $1))))
-(type $1 (func (result (ref null $2))))
-(type $2 (func (result (ref null $3))))
-(type $3 (func (result (ref null $4))))
-(type $4 (func (result (ref null $0))))
-
-(type $0 (func (result (ref null $0) (ref null $2))))
-(type $1 (func (result (ref null $1) (ref null $3))))
-(type $2 (func))
-(type $3 (func))
-(type $4 (func (result (ref null $0))))
-(type $5 (func (result (ref null $1))))
-
-(type $0 (func (result (ref null $0))))
-(type $1 (func (result (ref null $0))))
-
-;; Test subtyping
diff --git a/test/gtest/possible-contents.cpp b/test/gtest/possible-contents.cpp
index dc10c00bf..85a4e86fd 100644
--- a/test/gtest/possible-contents.cpp
+++ b/test/gtest/possible-contents.cpp
@@ -66,11 +66,6 @@ static std::unique_ptr<Module> parse(std::string module) {
 // that.
 class PossibleContentsTest : public testing::Test {
 protected:
-  void SetUp() override {
-    // Use nominal typing to test struct types.
-    wasm::setTypeSystem(TypeSystem::Nominal);
-  }
-
   Type anyref = Type(HeapType::any, Nullable);
   Type funcref = Type(HeapType::func, Nullable);
   Type i31ref = Type(HeapType::i31, Nullable);
@@ -542,6 +537,7 @@ TEST_F(PossibleContentsTest, TestStructCones) {
             D
   */
   TypeBuilder builder(5);
+  builder.createRecGroup(0, 5);
   builder.setHeapType(0, Struct(FieldList{}));
   builder.setHeapType(1, Struct(FieldList{}));
   builder.setHeapType(2, Struct(FieldList{}));
diff --git a/test/gtest/type-builder.cpp b/test/gtest/type-builder.cpp
index af6613bd2..7d5f5aa98 100644
--- a/test/gtest/type-builder.cpp
+++ b/test/gtest/type-builder.cpp
@@ -156,7 +156,7 @@ TEST_F(TypeTest, ModuleTypePrinter) {
   EXPECT_EQ(stream.str(), "(type $1 (struct (field i32)))");
 }
 
-TEST_F(IsorecursiveTest, Basics) {
+TEST_F(TypeTest, Basics) {
   // (type $sig (func (param (ref $struct)) (result (ref $array) i32)))
   // (type $struct (struct (field (ref null $array))))
   // (type $array (array (mut anyref)))
@@ -207,7 +207,7 @@ TEST_F(IsorecursiveTest, Basics) {
   EXPECT_NE(newRefNullArray, refNullArray);
 }
 
-static void testDirectSelfSupertype() {
+TEST_F(TypeTest, DirectSelfSupertype) {
   // Type is directly a supertype of itself.
   TypeBuilder builder(1);
   builder[0] = Struct{};
@@ -218,19 +218,11 @@ static void testDirectSelfSupertype() {
 
   const auto* error = result.getError();
   ASSERT_TRUE(error);
-  if (getTypeSystem() == TypeSystem::Nominal) {
-    EXPECT_EQ(error->reason, TypeBuilder::ErrorReason::SelfSupertype);
-  } else if (getTypeSystem() == TypeSystem::Isorecursive) {
-    EXPECT_EQ(error->reason,
-              TypeBuilder::ErrorReason::ForwardSupertypeReference);
-  }
+  EXPECT_EQ(error->reason, TypeBuilder::ErrorReason::ForwardSupertypeReference);
   EXPECT_EQ(error->index, 0u);
 }
 
-TEST_F(NominalTest, DirectSelfSupertype) { testDirectSelfSupertype(); }
-TEST_F(IsorecursiveTest, DirectSelfSupertype) { testDirectSelfSupertype(); }
-
-static void testIndirectSelfSupertype() {
+TEST_F(TypeTest, IndirectSelfSupertype) {
   // Type is indirectly a supertype of itself.
   TypeBuilder builder(2);
   builder.createRecGroup(0, 2);
@@ -244,21 +236,11 @@ static void testIndirectSelfSupertype() {
 
   const auto* error = result.getError();
   ASSERT_TRUE(error);
-  if (getTypeSystem() == TypeSystem::Nominal) {
-    EXPECT_EQ(error->reason, TypeBuilder::ErrorReason::SelfSupertype);
-  } else if (getTypeSystem() == TypeSystem::Isorecursive) {
-    EXPECT_EQ(error->reason,
-              TypeBuilder::ErrorReason::ForwardSupertypeReference);
-  } else {
-    WASM_UNREACHABLE("unexpected type system");
-  }
+  EXPECT_EQ(error->reason, TypeBuilder::ErrorReason::ForwardSupertypeReference);
   EXPECT_EQ(error->index, 0u);
 }
 
-TEST_F(NominalTest, IndirectSelfSupertype) { testIndirectSelfSupertype(); }
-TEST_F(IsorecursiveTest, IndirectSelfSupertype) { testIndirectSelfSupertype(); }
-
-static void testInvalidSupertype() {
+TEST_F(TypeTest, InvalidSupertype) {
   TypeBuilder builder(2);
   builder.createRecGroup(0, 2);
   builder[0] = Struct({Field(Type::i32, Immutable)});
@@ -274,10 +256,7 @@ static void testInvalidSupertype() {
   EXPECT_EQ(error->index, 1u);
 }
 
-TEST_F(NominalTest, InvalidSupertype) { testInvalidSupertype(); }
-TEST_F(IsorecursiveTest, InvalidSupertype) { testInvalidSupertype(); }
-
-TEST_F(IsorecursiveTest, ForwardReferencedChild) {
+TEST_F(TypeTest, ForwardReferencedChild) {
   TypeBuilder builder(3);
   builder.createRecGroup(0, 2);
   Type refA1 = builder.getTempRefType(builder[1], Nullable);
@@ -297,7 +276,7 @@ TEST_F(IsorecursiveTest, ForwardReferencedChild) {
   EXPECT_EQ(error->index, 1u);
 }
 
-TEST_F(IsorecursiveTest, RecGroupIndices) {
+TEST_F(TypeTest, RecGroupIndices) {
   TypeBuilder builder(5);
 
   builder.createRecGroup(0, 2);
@@ -324,7 +303,7 @@ TEST_F(IsorecursiveTest, RecGroupIndices) {
   EXPECT_EQ(built[4].getRecGroupIndex(), 2u);
 }
 
-TEST_F(IsorecursiveTest, CanonicalizeGroups) {
+TEST_F(TypeTest, CanonicalizeGroups) {
   // Trivial types in the same group are not equivalent.
   TypeBuilder builderA(2);
   builderA.createRecGroup(0, 2);
@@ -374,7 +353,7 @@ TEST_F(IsorecursiveTest, CanonicalizeGroups) {
   EXPECT_EQ(builtB2[0], builtB[0]);
 }
 
-TEST_F(IsorecursiveTest, CanonicalizeUses) {
+TEST_F(TypeTest, CanonicalizeUses) {
   TypeBuilder builder(8);
   builder[0] = makeStruct(builder, {});
   builder[1] = makeStruct(builder, {});
@@ -402,7 +381,7 @@ TEST_F(IsorecursiveTest, CanonicalizeUses) {
   EXPECT_NE(built[4], built[6]);
 }
 
-TEST_F(IsorecursiveTest, CanonicalizeSelfReferences) {
+TEST_F(TypeTest, CanonicalizeSelfReferences) {
   TypeBuilder builder(5);
   // Single self-reference
   builder[0] = makeStruct(builder, {0});
@@ -428,7 +407,7 @@ TEST_F(IsorecursiveTest, CanonicalizeSelfReferences) {
   EXPECT_NE(built[3], built[4]);
 }
 
-TEST_F(IsorecursiveTest, CanonicalizeSupertypes) {
+TEST_F(TypeTest, CanonicalizeSupertypes) {
   TypeBuilder builder(6);
   builder[0] = Struct{};
   builder[1] = Struct{};
@@ -455,7 +434,7 @@ TEST_F(IsorecursiveTest, CanonicalizeSupertypes) {
   EXPECT_NE(built[4], built[5]);
 }
 
-TEST_F(IsorecursiveTest, HeapTypeConstructors) {
+TEST_F(TypeTest, HeapTypeConstructors) {
   HeapType sig(Signature(Type::i32, Type::i32));
   HeapType struct_(Struct({Field(Type(sig, Nullable), Mutable)}));
   HeapType array(Field(Type(struct_, Nullable), Mutable));
@@ -484,7 +463,7 @@ TEST_F(IsorecursiveTest, HeapTypeConstructors) {
   EXPECT_EQ(array, array2);
 }
 
-TEST_F(IsorecursiveTest, CanonicalizeTypesBeforeSubtyping) {
+TEST_F(TypeTest, CanonicalizeTypesBeforeSubtyping) {
   TypeBuilder builder(6);
   // A rec group
   builder.createRecGroup(0, 2);
@@ -510,7 +489,7 @@ TEST_F(IsorecursiveTest, CanonicalizeTypesBeforeSubtyping) {
   EXPECT_TRUE(result);
 }
 
-TEST_F(IsorecursiveTest, CanonicalizeBasicTypes) {
+TEST_F(TypeTest, CanonicalizeBasicTypes) {
   TypeBuilder builder(5);
 
   Type anyref = builder.getTempRefType(builder[0], Nullable);
@@ -532,7 +511,7 @@ TEST_F(IsorecursiveTest, CanonicalizeBasicTypes) {
   EXPECT_EQ(built[3], built[4]);
 }
 
-TEST_F(IsorecursiveTest, TestHeapTypeRelations) {
+TEST_F(TypeTest, TestHeapTypeRelations) {
   HeapType ext = HeapType::ext;
   HeapType func = HeapType::func;
   HeapType any = HeapType::any;
@@ -829,7 +808,7 @@ TEST_F(IsorecursiveTest, TestHeapTypeRelations) {
   }
 }
 
-TEST_F(IsorecursiveTest, TestSubtypeErrors) {
+TEST_F(TypeTest, TestSubtypeErrors) {
   Type anyref = Type(HeapType::any, Nullable);
   Type eqref = Type(HeapType::eq, Nullable);
   Type funcref = Type(HeapType::func, Nullable);
@@ -872,7 +851,7 @@ TEST_F(IsorecursiveTest, TestSubtypeErrors) {
 }
 
 // Test SubTypes utility code.
-TEST_F(NominalTest, TestSubTypes) {
+TEST_F(TypeTest, TestSubTypes) {
   Type anyref = Type(HeapType::any, Nullable);
   Type eqref = Type(HeapType::eq, Nullable);
 
@@ -907,40 +886,7 @@ TEST_F(NominalTest, TestSubTypes) {
 }
 
 // Test reuse of a previously built type as supertype.
-TEST_F(NominalTest, TestExistingSuperType) {
-  // Build an initial type A
-  Type A;
-  {
-    TypeBuilder builder(1);
-    builder[0] = Struct();
-    auto result = builder.build();
-    ASSERT_TRUE(result);
-    auto built = *result;
-    A = Type(built[0], Nullable);
-  }
-
-  // Build a type B <: A using a new builder
-  Type B;
-  {
-    TypeBuilder builder(1);
-    builder[0] = Struct();
-    builder.setSubType(0, A.getHeapType());
-    auto result = builder.build();
-    ASSERT_TRUE(result);
-    auto built = *result;
-    B = Type(built[0], Nullable);
-  }
-
-  // Test that B <: A where A is the initial type A
-  auto superOfB = B.getHeapType().getSuperType();
-  ASSERT_TRUE(superOfB);
-  EXPECT_EQ(*superOfB, A.getHeapType());
-  EXPECT_NE(B.getHeapType(), A.getHeapType());
-}
-
-// Test reuse of a previously built type as supertype, where in isorecursive
-// mode canonicalization is performed.
-TEST_F(IsorecursiveTest, TestExistingSuperType) {
+TEST_F(TypeTest, TestExistingSuperType) {
   // Build an initial type A1
   Type A1;
   {
@@ -993,7 +939,7 @@ TEST_F(IsorecursiveTest, TestExistingSuperType) {
 }
 
 // Test .getMaxDepths() helper.
-TEST_F(NominalTest, TestMaxStructDepths) {
+TEST_F(TypeTest, TestMaxStructDepths) {
   /*
       A
       |
@@ -1022,7 +968,7 @@ TEST_F(NominalTest, TestMaxStructDepths) {
   EXPECT_EQ(maxDepths[HeapType::any], Index(4));
 }
 
-TEST_F(NominalTest, TestMaxArrayDepths) {
+TEST_F(TypeTest, TestMaxArrayDepths) {
   HeapType A;
   {
     TypeBuilder builder(1);
@@ -1043,7 +989,7 @@ TEST_F(NominalTest, TestMaxArrayDepths) {
 }
 
 // Test .depth() helper.
-TEST_F(NominalTest, TestDepth) {
+TEST_F(TypeTest, TestDepth) {
   HeapType A, B, C;
   {
     TypeBuilder builder(3);
@@ -1086,7 +1032,7 @@ TEST_F(NominalTest, TestDepth) {
 }
 
 // Test .iterSubTypes() helper.
-TEST_F(NominalTest, TestIterSubTypes) {
+TEST_F(TypeTest, TestIterSubTypes) {
   /*
         A
        / \
diff --git a/test/gtest/type-test.h b/test/gtest/type-test.h
index 49c6381fa..f029b8027 100644
--- a/test/gtest/type-test.h
+++ b/test/gtest/type-test.h
@@ -5,19 +5,10 @@
 #define wasm_test_gtest_type_test_h
 
 // Helper test fixture for managing the global type system state.
-template<wasm::TypeSystem system>
-class TypeSystemTest : public ::testing::Test {
-  wasm::TypeSystem originalSystem;
+class TypeTest : public ::testing::Test {
 
 protected:
-  void SetUp() override {
-    originalSystem = wasm::getTypeSystem();
-    wasm::setTypeSystem(system);
-  }
-  void TearDown() override {
-    wasm::destroyAllTypesForTestingPurposesOnly();
-    wasm::setTypeSystem(originalSystem);
-  }
+  void TearDown() override { wasm::destroyAllTypesForTestingPurposesOnly(); }
 
   // Utilities
   wasm::Struct makeStruct(wasm::TypeBuilder& builder,
@@ -32,8 +23,4 @@ protected:
   }
 };
 
-using TypeTest = TypeSystemTest<wasm::TypeSystem::Isorecursive>;
-using NominalTest = TypeSystemTest<wasm::TypeSystem::Nominal>;
-using IsorecursiveTest = TypeSystemTest<wasm::TypeSystem::Isorecursive>;
-
 #endif // wasm_test_gtest_type_test_h