diff --git a/aten/src/ATen/core/union_type.cpp b/aten/src/ATen/core/union_type.cpp
index f763879b77b9f..5d4edc70d8a73 100644
--- a/aten/src/ATen/core/union_type.cpp
+++ b/aten/src/ATen/core/union_type.cpp
@@ -111,10 +111,8 @@ void filterDuplicateSubtypes(std::vector<TypePtr>* types) {
   size_t end_idx = types->size()-1;
   for (size_t i = types->size()-1; i > 0; --i) {
     for (size_t j = std::min(i-1, end_idx); ; --j) {
-      c10::optional<TypePtr> unified;
-      unified = get_supertype((*types)[i], (*types)[j]);
-      if (unified) {
-        (*types)[j] = *unified;
+      if (auto unified = get_supertype((*types)[i], (*types)[j])) {
+        (*types)[j] = std::move(*unified);
         (*types)[i] = (*types)[end_idx];
         --end_idx;
         break;
@@ -160,13 +158,13 @@ void standardizeVectorForUnion(std::vector<TypePtr>* to_flatten) {
                         "passed a `nullptr`");
   std::vector<TypePtr> to_fill;
   standardizeVectorForUnion(*to_flatten, &to_fill);
-  *to_flatten = to_fill;
+  *to_flatten = std::move(to_fill);
 }
 
 OptionalType::OptionalType(TypePtr contained)
                            : UnionType({contained, NoneType::get()}, TypeKind::OptionalType) {
   bool is_numbertype = false;
-  if (auto as_union = contained->cast<UnionType>()) {
+  if (auto as_union = contained->castRaw<UnionType>()) {
     is_numbertype = as_union->containedTypes().size() == 3 &&
                     as_union->canHoldType(*NumberType::get());
   }
@@ -195,20 +193,17 @@ UnionType::UnionType(std::vector<TypePtr> reference, TypeKind kind) : SharedType
   // Gate the assert in a regular conditional so that we don't create
   // this long error message unnecessarily
   if (types_.size() == 1) {
-    std::stringstream msg;
-    msg << "After type unification was performed, the Union with the "
-        << "original types {";
+    std::string msg = "After type unification was performed, the Union with the original types {";
     for (const auto i : c10::irange(reference.size())) {
-      msg << reference[i]->repr_str();
+      msg += reference[i]->repr_str();
       if (i > 0) {
-        msg << ",";
+        msg += ",";
       }
-      msg << " ";
+      msg += " ";
     }
-    msg << "} has the single type " << types_[0]->repr_str()
-         << ". Use the common supertype instead of creating a Union"
-         << "type";
-    TORCH_INTERNAL_ASSERT(false, msg.str());
+    msg += "} has the single type " + types_[0]->repr_str()
+         + ". Use the common supertype instead of creating a Union type";
+    TORCH_INTERNAL_ASSERT(false, msg);
   }
 
   can_hold_none_ = false;
@@ -357,7 +352,7 @@ bool UnionType::isSubtypeOfExt(const Type& rhs, std::ostream* why_not) const {
 
 std::string UnionType::unionStr(TypePrinter printer, bool is_annotation_str)
     const {
-  std::stringstream ss;
+  std::string ss;
 
   bool can_hold_numbertype = this->canHoldType(*NumberType::get());
 
@@ -375,33 +370,33 @@ std::string UnionType::unionStr(TypePrinter printer, bool is_annotation_str)
   std::string open_delimeter = is_annotation_str ? "[" : "(";
   std::string close_delimeter = is_annotation_str ? "]" : ")";
 
-  ss << "Union" + open_delimeter;
+  ss = "Union" + open_delimeter;
   bool printed = false;
   for (size_t i = 0; i < types_.size(); ++i) {
     if (!can_hold_numbertype || !is_numbertype(types_[i])) {
       if (i > 0) {
-        ss << ", ";
+        ss += ", ";
         printed = true;
       }
       if (is_annotation_str) {
-        ss << this->containedTypes()[i]->annotation_str(printer);
+        ss += this->containedTypes()[i]->annotation_str(printer);
       } else {
-        ss << this->containedTypes()[i]->str();
+        ss += this->containedTypes()[i]->str();
       }
     }
   }
   if (can_hold_numbertype) {
     if (printed) {
-      ss << ", ";
+      ss += ", ";
     }
     if (is_annotation_str) {
-      ss << NumberType::get()->annotation_str(printer);
+      ss += NumberType::get()->annotation_str(printer);
     } else {
-      ss << NumberType::get()->str();
+      ss += NumberType::get()->str();
     }
   }
-  ss << close_delimeter;
-  return ss.str();
+  ss += close_delimeter;
+  return ss;
 }
 
 std::string UnionType::str() const {
diff --git a/torch/csrc/jit/frontend/schema_type_parser.cpp b/torch/csrc/jit/frontend/schema_type_parser.cpp
index f09aa60ba72a9..9d51220d90b79 100644
--- a/torch/csrc/jit/frontend/schema_type_parser.cpp
+++ b/torch/csrc/jit/frontend/schema_type_parser.cpp
@@ -289,96 +289,104 @@ TypePtr SchemaTypeParser::parseRefinedTensor() {
 }
 
 std::pair<TypePtr, c10::optional<AliasInfo>> SchemaTypeParser::parseType() {
-  TypePtr value;
   c10::optional<AliasInfo> alias_info;
   // Tuple type
-  if (L.cur().kind == '(') {
-    std::vector<TypePtr> types;
-    parseList('(', ',', ')', [&] {
-      auto r = parseType();
-      types.push_back(std::move(r.first));
-      if (alias_info && r.second) {
-        alias_info->addContainedType(std::move(*r.second));
-      }
-    });
-    value = TupleType::create(std::move(types));
-  } else if (L.cur().kind == TK_IDENT && L.cur().text() == "Future") {
-    L.next(); // Future
-    L.expect('(');
-    auto p = parseType();
-    auto subtype = std::move(p.first);
-    auto subalias = std::move(p.second);
-    L.expect(')');
-    value = FutureType::create(subtype);
-  } else if (L.cur().kind == TK_IDENT && L.cur().text() == "RRef") {
-    L.next(); // RRef
-    L.expect('(');
-    auto p = parseType();
-    auto subtype = std::move(p.first);
-    auto subalias = std::move(p.second);
-    L.expect(')');
-    value = RRefType::create(subtype);
-  } else if (L.cur().kind == TK_IDENT && L.cur().text() == "Tensor") {
-    L.next();
-    value = TensorType::get();
-    alias_info = parseAliasAnnotation();
-  } else if (L.cur().kind == TK_IDENT && L.cur().text() == "Dict") {
-    L.next();
-    L.expect('(');
-    auto key_type = parseType().first;
-    L.expect(',');
-    auto value_type = parseType().first;
-    L.expect(')');
-    alias_info = parseAliasAnnotation();
-    value = DictType::create(key_type, value_type);
-  } else if (L.cur().kind == TK_IDENT && L.cur().text() == "Union") {
-    L.next();
-    L.expect('(');
-    std::vector<TypePtr> types;
-    types.emplace_back(parseType().first);
-    while (L.cur().kind != ')') {
+  auto parseHead = [&]() -> TypePtr {
+    if (L.cur().kind == '(') {
+      std::vector<TypePtr> types;
+      parseList('(', ',', ')', [&] {
+        auto r = parseType();
+        types.push_back(std::move(r.first));
+        if (alias_info && r.second) {
+          alias_info->addContainedType(std::move(*r.second));
+        }
+      });
+      return TupleType::create(std::move(types));
+    } else if (L.cur().kind == TK_IDENT && L.cur().text() == "Future") {
+      L.next(); // Future
+      L.expect('(');
+      auto p = parseType();
+      auto subtype = std::move(p.first);
+      auto subalias = std::move(p.second);
+      L.expect(')');
+      return FutureType::create(subtype);
+    } else if (L.cur().kind == TK_IDENT && L.cur().text() == "RRef") {
+      L.next(); // RRef
+      L.expect('(');
+      auto p = parseType();
+      auto subtype = std::move(p.first);
+      auto subalias = std::move(p.second);
+      L.expect(')');
+      return RRefType::create(subtype);
+    } else if (L.cur().kind == TK_IDENT && L.cur().text() == "Tensor") {
+      L.next();
+      auto value = TensorType::get();
+      alias_info = parseAliasAnnotation();
+      return value;
+    } else if (L.cur().kind == TK_IDENT && L.cur().text() == "Dict") {
+      L.next();
+      L.expect('(');
+      auto key_type = parseType().first;
       L.expect(',');
+      auto value_type = parseType().first;
+      L.expect(')');
+      alias_info = parseAliasAnnotation();
+      return DictType::create(key_type, value_type);
+    } else if (L.cur().kind == TK_IDENT && L.cur().text() == "Union") {
+      L.next();
+      L.expect('(');
+      std::vector<TypePtr> types;
       types.emplace_back(parseType().first);
+      while (L.cur().kind != ')') {
+        L.expect(',');
+        types.emplace_back(parseType().first);
+      }
+      L.expect(')');
+      alias_info = parseAliasAnnotation();
+      return UnionType::create(types);
+    } else if (
+        complete_tensor_types && L.cur().kind == TK_IDENT &&
+        parseTensorDType(L.cur().text())) {
+      auto value = parseRefinedTensor();
+      alias_info = parseAliasAnnotation();
+      return value;
+    } else if (L.cur().kind == TK_IDENT && L.cur().text() == "__torch__") {
+      L.next();
+      L.expect('.');
+      auto torch_tok = L.expect(TK_IDENT);
+      if (torch_tok.text() != "torch") {
+        throw ErrorReport(torch_tok.range)
+            << "Expected classes namespace but got " << torch_tok.text();
+      }
+      L.expect('.');
+      auto classes_tok = L.expect(TK_IDENT);
+      if (classes_tok.text() != "classes") {
+        throw ErrorReport(classes_tok.range)
+            << "Expected classes namespace but got " << classes_tok.text();
+      }
+      L.expect('.');
+      auto ns_tok = L.expect(TK_IDENT);
+      L.expect('.');
+      auto class_tok = L.expect(TK_IDENT);
+      auto value = getCustomClass(
+          std::string("__torch__.torch.classes.") + ns_tok.text() + "." +
+          class_tok.text());
+      if (!value) {
+        throw ErrorReport(class_tok.range)
+            << "Unknown custom class type "
+            << ns_tok.text() + "." + class_tok.text()
+            << ". Please ensure it is registered.";
+      }
+      return value;
+    } else {
+      auto value = parseBaseType();
+      alias_info = parseAliasAnnotation();
+      return value;
     }
-    L.expect(')');
-    alias_info = parseAliasAnnotation();
-    value = UnionType::create(types);
-  } else if (
-      complete_tensor_types && L.cur().kind == TK_IDENT &&
-      parseTensorDType(L.cur().text())) {
-    value = parseRefinedTensor();
-    alias_info = parseAliasAnnotation();
-  } else if (L.cur().kind == TK_IDENT && L.cur().text() == "__torch__") {
-    L.next();
-    L.expect('.');
-    auto torch_tok = L.expect(TK_IDENT);
-    if (torch_tok.text() != "torch") {
-      throw ErrorReport(torch_tok.range)
-          << "Expected classes namespace but got " << torch_tok.text();
-    }
-    L.expect('.');
-    auto classes_tok = L.expect(TK_IDENT);
-    if (classes_tok.text() != "classes") {
-      throw ErrorReport(classes_tok.range)
-          << "Expected classes namespace but got " << classes_tok.text();
-    }
-    L.expect('.');
-    auto ns_tok = L.expect(TK_IDENT);
-    L.expect('.');
-    auto class_tok = L.expect(TK_IDENT);
-    value = getCustomClass(
-        std::string("__torch__.torch.classes.") + ns_tok.text() + "." +
-        class_tok.text());
-    if (!value) {
-      throw ErrorReport(class_tok.range)
-          << "Unknown custom class type "
-          << ns_tok.text() + "." + class_tok.text()
-          << ". Please ensure it is registered.";
-    }
-  } else {
-    value = parseBaseType();
-    alias_info = parseAliasAnnotation();
-  }
+  };
+
+  TypePtr value = parseHead();
+
   while (true) {
     if (L.cur().kind == '[' && L.lookahead().kind == ']') {
       L.next(); // [
diff --git a/torch/csrc/jit/mobile/model_compatibility.cpp b/torch/csrc/jit/mobile/model_compatibility.cpp
index 6dd2aeab88ad2..f2a9d82f62e8c 100644
--- a/torch/csrc/jit/mobile/model_compatibility.cpp
+++ b/torch/csrc/jit/mobile/model_compatibility.cpp
@@ -335,7 +335,7 @@ ModelCompatCheckResult is_compatible(
     result.errors.emplace_back(s.str());
   }
 
-  std::unordered_set<std::string> supported_type = runtime_info.supported_types;
+  const auto& supported_type = runtime_info.supported_types;
 
   // Check type table
   for (const auto& type_name : model_info.type_table) {
@@ -349,8 +349,7 @@ ModelCompatCheckResult is_compatible(
   }
 
   // Check operators
-  std::unordered_map<std::string, OperatorInfo> operator_info =
-      model_info.operator_info;
+  const auto& operator_info = model_info.operator_info;
   for (auto const& op : operator_info) {
     std::string op_name = op.first;
     OperatorInfo model_op_info = op.second;
diff --git a/torch/csrc/jit/mobile/type_parser.cpp b/torch/csrc/jit/mobile/type_parser.cpp
index 2863fcf6d5b5c..9a40d1200acd6 100644
--- a/torch/csrc/jit/mobile/type_parser.cpp
+++ b/torch/csrc/jit/mobile/type_parser.cpp
@@ -89,7 +89,7 @@ const std::unordered_set<std::string>& TypeParser::getCustomType() {
 // compatibility check between model and runtime. For example:
 // PyThon string: "Dict[int, Tuple[Tensor, Tensor, Tensor]]"
 // contained type is: [Dict, int, Tuple, Tensor]
-std::unordered_set<std::string> TypeParser::getContainedTypes() {
+const std::unordered_set<std::string>& TypeParser::getContainedTypes() {
   return contained_types_;
 }
 
diff --git a/torch/csrc/jit/mobile/type_parser.h b/torch/csrc/jit/mobile/type_parser.h
index e215b17a73a57..4a8a274c69605 100644
--- a/torch/csrc/jit/mobile/type_parser.h
+++ b/torch/csrc/jit/mobile/type_parser.h
@@ -14,7 +14,7 @@ class TORCH_API TypeParser {
   std::vector<TypePtr> parseList();
   static const std::unordered_set<std::string>& getNonSimpleType();
   static const std::unordered_set<std::string>& getCustomType();
-  std::unordered_set<std::string> getContainedTypes();
+  const std::unordered_set<std::string>& getContainedTypes();
 
  private:
   TypePtr parseNamedTuple(const std::string& qualified_name);