diff --git a/include/swift/AST/Module.h b/include/swift/AST/Module.h
index 126a0e9e401..133a2dc1ed2 100644
--- a/include/swift/AST/Module.h
+++ b/include/swift/AST/Module.h
@@ -28,6 +28,7 @@
 #include "llvm/ADT/SmallSet.h"
 #include "llvm/ADT/SmallVector.h"
 #include "llvm/ADT/StringMap.h"
+#include "llvm/ADT/STLExtras.h"
 #include "llvm/ADT/TinyPtrVector.h"
 #include "llvm/Support/ErrorHandling.h"
 
@@ -369,11 +370,11 @@ public:
   ///         due to the callback.
   bool forAllVisibleModules(AccessPathTy topLevelAccessPath,
                             bool includePrivateTopLevelImports,
-                            std::function<bool(ImportedModule)> fn);
+                            llvm::function_ref<bool(ImportedModule)> fn);
 
   bool forAllVisibleModules(AccessPathTy topLevelAccessPath,
                             bool includePrivateTopLevelImports,
-                            std::function<void(ImportedModule)> fn) {
+                            llvm::function_ref<void(ImportedModule)> fn) {
     return forAllVisibleModules(topLevelAccessPath,
                                 includePrivateTopLevelImports,
                                 [=](const ImportedModule &import) -> bool {
@@ -385,38 +386,28 @@ public:
   template <typename Fn>
   bool forAllVisibleModules(AccessPathTy topLevelAccessPath,
                             bool includePrivateTopLevelImports,
-                            const Fn &fn) {
-    using RetTy = typename as_function<Fn>::type::result_type;
-    std::function<RetTy(ImportedModule)> wrapped = std::cref(fn);
+                            Fn &&fn) {
+    using RetTy = typename std::result_of<Fn(ImportedModule)>::type;
+    llvm::function_ref<RetTy(ImportedModule)> wrapped{std::forward<Fn>(fn)};
     return forAllVisibleModules(topLevelAccessPath,
                                 includePrivateTopLevelImports,
                                 wrapped);
   }
 
   template <typename Fn>
-  bool forAllVisibleModules(AccessPathTy topLevelAccessPath,
-                            const Fn &fn) {
-    return forAllVisibleModules(topLevelAccessPath, false, fn);
+  bool forAllVisibleModules(AccessPathTy topLevelAccessPath, Fn &&fn) {
+    return forAllVisibleModules(topLevelAccessPath, false,
+                                std::forward<Fn>(fn));
   }
 
   /// @}
 
-  using LinkLibraryCallback = std::function<void(LinkLibrary)>;
-
-  /// @{
+  using LinkLibraryCallback = llvm::function_ref<void(LinkLibrary)>;
 
   /// Generate the list of libraries needed to link this module, based on its
   /// imports.
   void collectLinkLibraries(LinkLibraryCallback callback);
 
-  template <typename Fn>
-  void collectLinkLibraries(const Fn &fn) {
-    LinkLibraryCallback wrapped = std::cref(fn);
-    collectLinkLibraries(wrapped);
-  }
-
-  /// @}
-
   /// Returns true if the two access paths contain the same chain of
   /// identifiers.
   ///
@@ -578,20 +569,23 @@ public:
   ///
   /// \return True if the traversal ran to completion, false if it ended early
   ///         due to the callback.
-  bool forAllVisibleModules(std::function<bool(Module::ImportedModule)> fn);
+  bool
+  forAllVisibleModules(llvm::function_ref<bool(Module::ImportedModule)> fn);
 
-  bool forAllVisibleModules(std::function<void(Module::ImportedModule)> fn) {
-    forAllVisibleModules([=](const Module::ImportedModule &import) -> bool {
+  bool
+  forAllVisibleModules(llvm::function_ref<void(Module::ImportedModule)> fn) {
+    return forAllVisibleModules([=](Module::ImportedModule import) -> bool {
       fn(import);
       return true;
     });
-    return true;
   }
   
   template <typename Fn>
-  bool forAllVisibleModules(const Fn &fn) {
-    using RetTy = typename as_function<Fn>::type::result_type;
-    std::function<RetTy(Module::ImportedModule)> wrapped = std::cref(fn);
+  bool forAllVisibleModules(Fn &&fn) {
+    using RetTy = typename std::result_of<Fn(Module::ImportedModule)>::type;
+    llvm::function_ref<RetTy(Module::ImportedModule)> wrapped{
+      std::forward<Fn>(fn)
+    };
     return forAllVisibleModules(wrapped);
   }
 
diff --git a/include/swift/Basic/STLExtras.h b/include/swift/Basic/STLExtras.h
index 2e5ab425116..c14d3cd52f5 100644
--- a/include/swift/Basic/STLExtras.h
+++ b/include/swift/Basic/STLExtras.h
@@ -102,28 +102,6 @@ inline void for_each3(const Container1 &c1, const Container2 &c2,
 
 /// @}
 
-/// @{
-
-/// Declares a member \c type that is a std::function compatible with the given
-/// callable type.
-///
-/// \tparam T A callable type, such as a lambda.
-template <typename T>
-struct as_function : public as_function<decltype(&T::operator())> {};
-
-template <typename L, typename R, typename... Args>
-struct as_function<R(L::*)(Args...) const> {
-  using type = std::function<R(Args...)>;
-};
-
-/// @}
-
-/// Returns a std::function that can call a lambda without copying it.
-template <typename L>
-static typename as_function<L>::type makeStackLambda(const L &theLambda) {
-  return std::cref(theLambda);
-}
-
 /// A range of iterators.
 template<typename Iterator>
 class IteratorRange {
diff --git a/lib/AST/Module.cpp b/lib/AST/Module.cpp
index be6060fdd0e..ce1c5441045 100644
--- a/lib/AST/Module.cpp
+++ b/lib/AST/Module.cpp
@@ -1328,13 +1328,13 @@ static bool forAllImportedModules(Module *topLevel,
 
 bool Module::forAllVisibleModules(AccessPathTy thisPath,
                                   bool includePrivateTopLevelImports,
-                                  std::function<bool(ImportedModule)> fn) {
+                                  llvm::function_ref<bool(ImportedModule)> fn) {
   return forAllImportedModules<true>(this, thisPath,
                                      includePrivateTopLevelImports, fn);
 }
 
-bool
-FileUnit::forAllVisibleModules(std::function<bool(Module::ImportedModule)> fn) {
+bool FileUnit::forAllVisibleModules(
+    llvm::function_ref<bool(Module::ImportedModule)> fn) {
   if (!getParentModule()->forAllVisibleModules(Module::AccessPathTy(), fn))
     return false;
 
diff --git a/lib/ClangImporter/ClangDiagnosticConsumer.cpp b/lib/ClangImporter/ClangDiagnosticConsumer.cpp
index c6d4ed686c3..e4e1d19b313 100644
--- a/lib/ClangImporter/ClangDiagnosticConsumer.cpp
+++ b/lib/ClangImporter/ClangDiagnosticConsumer.cpp
@@ -18,18 +18,18 @@
 #include "clang/AST/ASTContext.h"
 #include "clang/Frontend/DiagnosticRenderer.h"
 #include "clang/Lex/LexDiagnostic.h"
+#include "llvm/ADT/STLExtras.h"
 
 using namespace swift;
 
 namespace {
   class ClangDiagRenderer final : public clang::DiagnosticNoteRenderer {
-    const std::function<void(clang::FullSourceLoc,
-                             clang::DiagnosticsEngine::Level,
-                             StringRef)> callback;
+    const llvm::function_ref<void(clang::FullSourceLoc,
+                                  clang::DiagnosticsEngine::Level,
+                                  StringRef)> callback;
 
   public:
-    template <typename Fn>
-    ClangDiagRenderer(const clang::ASTContext &ctx, const Fn &fn)
+    ClangDiagRenderer(const clang::ASTContext &ctx, decltype(callback) fn)
        : DiagnosticNoteRenderer(ctx.getLangOpts(),
                                 &ctx.getDiagnostics().getDiagnosticOptions()),
          callback(fn) {}
@@ -219,8 +219,7 @@ void ClangDiagnosticConsumer::HandleDiagnostic(
 
   } else {
     assert(clangDiag.hasSourceManager());
-    ClangDiagRenderer renderer(ImporterImpl.getClangASTContext(),
-                               std::cref(emitDiag));
+    ClangDiagRenderer renderer(ImporterImpl.getClangASTContext(), emitDiag);
     renderer.emitDiagnostic(clangDiag.getLocation(), clangDiagLevel, message,
                             clangDiag.getRanges(), clangDiag.getFixItHints(),
                             &clangDiag.getSourceManager());
diff --git a/lib/Driver/DependencyGraph.cpp b/lib/Driver/DependencyGraph.cpp
index d5c5f0214f3..6b344492f20 100644
--- a/lib/Driver/DependencyGraph.cpp
+++ b/lib/Driver/DependencyGraph.cpp
@@ -13,6 +13,7 @@
 #include "swift/Driver/DependencyGraph.h"
 #include "llvm/ADT/SmallVector.h"
 #include "llvm/ADT/StringSwitch.h"
+#include "llvm/ADT/STLExtras.h"
 #include "llvm/Support/raw_ostream.h"
 #include "llvm/Support/MemoryBuffer.h"
 #include "llvm/Support/SourceMgr.h"
@@ -34,9 +35,9 @@ namespace {
 } // end anonymous namespace
 
 static bool
-parseDependencyFileImpl(llvm::MemoryBuffer &buffer, bool providesOnly,
-                        std::function<void(StringRef, DependencyKind,
-                                           DependencyDirection)> callback) {
+parseDependencyFile(llvm::MemoryBuffer &buffer, bool providesOnly,
+                    llvm::function_ref<void(StringRef, DependencyKind,
+                                            DependencyDirection)> callback) {
   using namespace llvm;
 
   // FIXME: Switch to a format other than YAML.
@@ -81,12 +82,6 @@ parseDependencyFileImpl(llvm::MemoryBuffer &buffer, bool providesOnly,
   return false;
 }
 
-template <typename Fn>
-static bool parseDependencyFile(llvm::MemoryBuffer &buffer, bool providesOnly,
-                                Fn fn) {
-  return parseDependencyFileImpl(buffer, providesOnly, std::cref(fn));
-}
-
 bool DependencyGraphImpl::loadFromPath(const void *node, StringRef path) {
   auto buffer = llvm::MemoryBuffer::getFile(path);
   if (!buffer)
diff --git a/lib/PrintAsObjC/PrintAsObjC.cpp b/lib/PrintAsObjC/PrintAsObjC.cpp
index 0a4b9365095..d565391aa7c 100644
--- a/lib/PrintAsObjC/PrintAsObjC.cpp
+++ b/lib/PrintAsObjC/PrintAsObjC.cpp
@@ -25,8 +25,9 @@
 #include "clang/AST/DeclObjC.h"
 #include "clang/Basic/Module.h"
 #include "llvm/ADT/SetVector.h"
-#include "llvm/Support/Path.h"
 #include "llvm/ADT/StringSwitch.h"
+#include "llvm/ADT/STLExtras.h"
+#include "llvm/Support/Path.h"
 #include "llvm/Support/raw_ostream.h"
 
 using namespace swift;
@@ -723,9 +724,9 @@ private:
 class ReferencedTypeFinder : private TypeVisitor<ReferencedTypeFinder> {
   friend TypeVisitor;
 
-  std::function<void(ReferencedTypeFinder &, const TypeDecl *)> Callback;
+  llvm::function_ref<void(ReferencedTypeFinder &, const TypeDecl *)> Callback;
 
-  ReferencedTypeFinder(decltype(Callback) &&callback) : Callback(callback) {}
+  ReferencedTypeFinder(decltype(Callback) callback) : Callback(callback) {}
 
   void visitType(TypeBase *base) {
     assert(base->getDesugaredType() == base && "unhandled sugared type");
@@ -795,9 +796,8 @@ class ReferencedTypeFinder : private TypeVisitor<ReferencedTypeFinder> {
 public:
   using TypeVisitor::visit;
 
-  template<typename Fn>
-  static void walk(Type ty, const Fn &callback) {
-    ReferencedTypeFinder(std::cref(callback)).visit(ty);
+  static void walk(Type ty, decltype(Callback) callback) {
+    ReferencedTypeFinder(callback).visit(ty);
   }
 };