[AutoDiff upstream] Add the _Differentiation module.

The `_Differentiation` module is the experimental support library for
differentiable programming. It is built when the build-script flag
`--enable-experimental-differentiable-programming` is enabled.

The `Differentiable` protocol generalizes all types that work with
differentiation. It is a core piece of the differentiable programming
project. Other parts depending on the `Differentiable` protocol will
be upstreamed piece by piece.

The `Differentiable` protocol is compiler-known and will be used during
type-checking, SILGen, and the SIL differentiation transform.

Author: dan-zheng

include/swift/AST/KnownIdentifiers.def

@@ -53,6 +53,7 @@ IDENTIFIER(decode)
 IDENTIFIER(decodeIfPresent)
 IDENTIFIER(Decoder)
 IDENTIFIER(decoder)
+IDENTIFIER_WITH_NAME(Differentiation, "_Differentiation")
 IDENTIFIER(dynamicallyCall)
 IDENTIFIER(dynamicMember)
 IDENTIFIER(Element)

include/swift/AST/KnownProtocols.def

@@ -83,6 +83,8 @@ PROTOCOL_(DestructorSafeContainer)
 
 PROTOCOL(StringInterpolationProtocol)
 
+PROTOCOL(Differentiable)
+
 EXPRESSIBLE_BY_LITERAL_PROTOCOL(ExpressibleByArrayLiteral, "Array", false)
 EXPRESSIBLE_BY_LITERAL_PROTOCOL(ExpressibleByBooleanLiteral, "BooleanLiteralType", true)
 EXPRESSIBLE_BY_LITERAL_PROTOCOL(ExpressibleByDictionaryLiteral, "Dictionary", false)

lib/AST/ASTContext.cpp

@@ -899,6 +899,9 @@ ProtocolDecl *ASTContext::getProtocol(KnownProtocolKind kind) const {
   case KnownProtocolKind::CFObject:
     M = getLoadedModule(Id_CoreFoundation);
     break;
+  case KnownProtocolKind::Differentiable:
+    M = getLoadedModule(Id_Differentiation);
+    break;
   default:
     M = getStdlibModule();
     break;

lib/IRGen/GenMeta.cpp

@@ -4217,6 +4217,7 @@ SpecialProtocol irgen::getSpecialProtocolID(ProtocolDecl *P) {
   case KnownProtocolKind::Encodable:
   case KnownProtocolKind::Decodable:
   case KnownProtocolKind::StringInterpolationProtocol:
+  case KnownProtocolKind::Differentiable:
     return SpecialProtocol::None;
   }
 

stdlib/public/CMakeLists.txt

@@ -63,6 +63,12 @@ if(SWIFT_BUILD_STDLIB)
   add_subdirectory(SwiftOnoneSupport)
 endif()
 
+# Build differentiable programming support library only if enabled.
+if(SWIFT_ENABLE_EXPERIMENTAL_DIFFERENTIABLE_PROGRAMMING AND SWIFT_BUILD_STDLIB)
+  message(STATUS "Building Swift differentiable programming support library.")
+  add_subdirectory(Differentiation)
+endif()
+
 if(SWIFT_BUILD_STDLIB OR SWIFT_BUILD_REMOTE_MIRROR)
   add_subdirectory(Reflection)
   add_subdirectory(SwiftRemoteMirror)

stdlib/public/Differentiation/CMakeLists.txt

@@ -0,0 +1,18 @@
+#===--- CMakeLists.txt - Differentiable programming support library ------===#
+#
+# This source file is part of the Swift.org open source project
+#
+# Copyright (c) 2014 - 2019 Apple Inc. and the Swift project authors
+# Licensed under Apache License v2.0 with Runtime Library Exception
+#
+# See https://swift.org/LICENSE.txt for license information
+# See https://swift.org/CONTRIBUTORS.txt for the list of Swift project authors
+#
+#===----------------------------------------------------------------------===#
+
+add_swift_target_library(swift_Differentiation ${SWIFT_STDLIB_LIBRARY_BUILD_TYPES} IS_STDLIB
+  Differentiable.swift
+
+  SWIFT_COMPILE_FLAGS ${SWIFT_STANDARD_LIBRARY_SWIFT_FLAGS}
+  LINK_FLAGS "${SWIFT_RUNTIME_SWIFT_LINK_FLAGS}"
+  INSTALL_IN_COMPONENT stdlib)

stdlib/public/Differentiation/Differentiable.swift

@@ -0,0 +1,44 @@
+//===--- Differentiable.swift ---------------------------------*- swift -*-===//
+//
+// This source file is part of the Swift.org open source project
+//
+// Copyright (c) 2014 - 2019 Apple Inc. and the Swift project authors
+// Licensed under Apache License v2.0 with Runtime Library Exception
+//
+// See https://swift.org/LICENSE.txt for license information
+// See https://swift.org/CONTRIBUTORS.txt for the list of Swift project authors
+//
+//===----------------------------------------------------------------------===//
+//
+// This file defines the Differentiable protocol, used by the experimental
+// differentiable programming project. This API is not stable and subject to
+// change.
+//
+// Please see forum discussion for more information about the differentiable
+// programming project:
+// https://forums.swift.org/t/differentiable-programming-mega-proposal/28547
+//
+//===----------------------------------------------------------------------===//
+
+/// A type that mathematically represents a differentiable manifold whose
+/// tangent spaces are finite-dimensional.
+public protocol Differentiable {
+  /// A type representing a differentiable value's derivatives.
+  ///
+  /// Mathematically, this is equivalent to the tangent bundle of the
+  /// differentiable manifold represented by the differentiable type.
+  associatedtype TangentVector: Differentiable & AdditiveArithmetic
+    where TangentVector.TangentVector == TangentVector
+
+  /// Moves `self` along the given direction. In Riemannian geometry, this is
+  /// equivalent to exponential map, which moves `self` on the geodesic surface
+  /// along the given tangent vector.
+  mutating func move(along direction: TangentVector)
+}
+
+public extension Differentiable where TangentVector == Self {
+  @_alwaysEmitIntoClient
+  mutating func move(along direction: TangentVector) {
+    self += direction
+  }
+}

stdlib/public/core/CMakeLists.txt

@@ -196,13 +196,6 @@ set(SWIFTLIB_ESSENTIAL_GYB_SOURCES
   UnsafeRawBufferPointer.swift.gyb
   )
 
-# Compile differentiable programming sources only if enabled.
-set(SWIFTLIB_DIFFERENTIABLE_PROGRAMMING_SOURCES)
-if(SWIFT_ENABLE_EXPERIMENTAL_DIFFERENTIABLE_PROGRAMMING)
-  # TODO: Add `_Differentiable` protocol.
-  message(STATUS "Differentiable programming standard library additions enabled.")
-endif()
-
 # The complete list of sources in the core standard library.  Includes
 # all the essential sources listed above.
 set(SWIFTLIB_SOURCES
@@ -221,7 +214,6 @@ set(SWIFTLIB_SOURCES
   VarArgs.swift
   Zip.swift
   "${SWIFT_SOURCE_DIR}/stdlib/linker-support/magic-symbols-for-install-name.c"
-  ${SWIFTLIB_DIFFERENTIABLE_PROGRAMMING_SOURCES}
   )
 
 set(SWIFTLIB_GYB_SOURCES

test/Differentiation/differentiable_protocol.swift

@@ -0,0 +1,33 @@
+// RUN: %target-typecheck-verify-swift
+
+import _Differentiation
+
+// Test conformances.
+
+struct Wrapper<T> {
+  var value: T
+}
+extension Wrapper: Equatable where T: Equatable {}
+extension Wrapper: AdditiveArithmetic where T: AdditiveArithmetic {
+  static var zero: Self {
+    Wrapper(value: T.zero)
+  }
+  static func + (lhs: Self, rhs: Self) -> Self {
+    return Wrapper(value: lhs.value + rhs.value)
+  }
+  static func - (lhs: Self, rhs: Self) -> Self {
+    return Wrapper(value: lhs.value + rhs.value)
+  }
+}
+extension Wrapper: Differentiable where T: Differentiable {
+  typealias TangentVector = Wrapper<T.TangentVector>
+  mutating func move(along direction: TangentVector) {
+    value.move(along: direction.value)
+  }
+}
+
+// Test conformances for standard library types.
+
+extension Float: Differentiable {
+  public typealias TangentVector = Self
+}