diff --git a/clang/include/clang/Tooling/Transformer/Stencil.h b/clang/include/clang/Tooling/Transformer/Stencil.h
--- a/clang/include/clang/Tooling/Transformer/Stencil.h
+++ b/clang/include/clang/Tooling/Transformer/Stencil.h
@@ -48,26 +48,18 @@
   virtual llvm::Error eval(const ast_matchers::MatchFinder::MatchResult &Match,
                            std::string *Result) const = 0;
 
-  virtual bool isEqual(const StencilPartInterface &other) const = 0;
-
   /// Constructs a string representation of the StencilPart. StencilParts
   /// generated by the `selection` and `run` functions do not have a unique
   /// string representation.
   virtual std::string toString() const = 0;
 
-  const void *typeId() const { return TypeId; }
-
 protected:
-  StencilPartInterface(const void *DerivedId) : TypeId(DerivedId) {}
+  StencilPartInterface() = default;
 
   // Since this is an abstract class, copying/assigning only make sense for
   // derived classes implementing `clone()`.
   StencilPartInterface(const StencilPartInterface &) = default;
   StencilPartInterface &operator=(const StencilPartInterface &) = default;
-
-  /// Unique identifier of the concrete type of this instance.  Supports safe
-  /// downcasting.
-  const void *TypeId;
 };
 
 /// A copyable facade for a std::unique_ptr<StencilPartInterface>. Copies result
@@ -88,7 +80,7 @@
       return true;
     if (Impl == nullptr || Other.Impl == nullptr)
       return false;
-    return Impl->isEqual(*Other.Impl);
+    return Impl->toString() == Other.Impl->toString();
   }
 
   std::string toString() const {
diff --git a/clang/lib/Tooling/Transformer/Stencil.cpp b/clang/lib/Tooling/Transformer/Stencil.cpp
--- a/clang/lib/Tooling/Transformer/Stencil.cpp
+++ b/clang/lib/Tooling/Transformer/Stencil.cpp
@@ -31,14 +31,6 @@
 using llvm::Expected;
 using llvm::StringError;
 
-// A down_cast function to safely down cast a StencilPartInterface to a subclass
-// D. Returns nullptr if P is not an instance of D.
-template <typename D> const D *down_cast(const StencilPartInterface *P) {
-  if (P == nullptr || D::typeId() != P->typeId())
-    return nullptr;
-  return static_cast<const D *>(P);
-}
-
 static llvm::Expected<DynTypedNode>
 getNode(const ast_matchers::BoundNodes &Nodes, StringRef Id) {
   auto &NodesMap = Nodes.getMap();
@@ -100,35 +92,6 @@
   StencilPart FalsePart;
 };
 
-bool isEqualData(const RawTextData &A, const RawTextData &B) {
-  return A.Text == B.Text;
-}
-
-bool isEqualData(const DebugPrintNodeData &A, const DebugPrintNodeData &B) {
-  return A.Id == B.Id;
-}
-
-bool isEqualData(const UnaryOperationData &A, const UnaryOperationData &B) {
-  return A.Op == B.Op && A.Id == B.Id;
-}
-
-// Equality is not (yet) defined for \c RangeSelector.
-bool isEqualData(const SelectorData &, const SelectorData &) { return false; }
-
-bool isEqualData(const AccessData &A, const AccessData &B) {
-  return A.BaseId == B.BaseId && A.Member == B.Member;
-}
-
-bool isEqualData(const IfBoundData &A, const IfBoundData &B) {
-  return A.Id == B.Id && A.TruePart == B.TruePart && A.FalsePart == B.FalsePart;
-}
-
-// Equality is not defined over MatchConsumers, which are opaque.
-bool isEqualData(const MatchConsumer<std::string> &A,
-                 const MatchConsumer<std::string> &B) {
-  return false;
-}
-
 std::string toStringData(const RawTextData &Data) {
   std::string Result;
   llvm::raw_string_ostream OS(Result);
@@ -275,28 +238,13 @@
 
 public:
   template <typename... Ps>
-  explicit StencilPartImpl(Ps &&... Args)
-      : StencilPartInterface(StencilPartImpl::typeId()),
-        Data(std::forward<Ps>(Args)...) {}
-
-  // Generates a unique identifier for this class (specifically, one per
-  // instantiation of the template).
-  static const void* typeId() {
-    static bool b;
-    return &b;
-  }
+  explicit StencilPartImpl(Ps &&... Args) : Data(std::forward<Ps>(Args)...) {}
 
   Error eval(const MatchFinder::MatchResult &Match,
              std::string *Result) const override {
     return evalData(Data, Match, Result);
   }
 
-  bool isEqual(const StencilPartInterface &Other) const override {
-    if (const auto *OtherPtr = down_cast<StencilPartImpl>(&Other))
-      return isEqualData(Data, OtherPtr->Data);
-    return false;
-  }
-
   std::string toString() const override { return toStringData(Data); }
 };
 } // namespace
diff --git a/clang/unittests/Tooling/StencilTest.cpp b/clang/unittests/Tooling/StencilTest.cpp
--- a/clang/unittests/Tooling/StencilTest.cpp
+++ b/clang/unittests/Tooling/StencilTest.cpp
@@ -375,19 +375,30 @@
   EXPECT_NE(Lhs, Rhs);
 }
 
-// node is opaque and therefore cannot be examined for equality.
-TEST(StencilEqualityTest, InEqualitySelection) {
-  auto S1 = cat(node("node"));
-  auto S2 = cat(node("node"));
-  EXPECT_NE(S1, S2);
-}
-
-// `run` is opaque.
-TEST(StencilEqualityTest, InEqualityRun) {
-  auto F = [](const MatchResult &R) { return "foo"; };
-  auto S1 = cat(run(F));
-  auto S2 = cat(run(F));
-  EXPECT_NE(S1, S2);
+// For stencils generated by `selection`, equality returns true by default
+// even if different selectors are used in the stencils.
+TEST(StencilEqualityTest, EqualitySelection) {
+  auto S1 = cat(node("node1"));
+  auto S1Dup = cat(node("node1"));
+  auto S2 = cat(node("node2"));
+  auto T = cat("foo");
+  EXPECT_EQ(S1, S1Dup);
+  EXPECT_EQ(S1, S2);
+  EXPECT_NE(S1, T);
+}
+
+// For stencils generated by `run`, equality returns true by default even if
+// different functions are used in the stencils.
+TEST(StencilEqualityTest, EqualityRun) {
+  auto F1 = [](const MatchResult &R) { return "foo"; };
+  auto F2 = [](const MatchResult &R) { return "bar"; };
+  auto S1 = cat(run(F1));
+  auto S1Dup = cat(run(F1));
+  auto S2 = cat(run(F2));
+  auto T = cat("foo");
+  EXPECT_EQ(S1, S1Dup);
+  EXPECT_EQ(S1, S2);
+  EXPECT_NE(S1, T);
 }
 
 TEST(StencilToStringTest, RawTextOp) {