Add type_util meta-programming utilities.

common/BUILD.bazel

@@ -45,6 +45,7 @@ drake_cc_library(
         ":symbolic",
         ":symbolic_decompose",
         ":type_safe_index",
+        ":type_util",
         ":unused",
     ],
     # Intentionally excluded items:
@@ -347,6 +348,11 @@ drake_cc_library(
     ],
 )
 
+drake_cc_library(
+    name = "type_util",
+    hdrs = ["type_util.h"],
+)
+
 drake_cc_library(
     name = "unused",
     hdrs = ["unused.h"],
@@ -882,6 +888,14 @@ drake_cc_googletest(
     ],
 )
 
+drake_cc_googletest(
+    name = "type_util_test",
+    deps = [
+        ":nice_type_name",
+        ":type_util",
+    ],
+)
+
 drake_cc_googletest(
     name = "eigen_autodiff_types_test",
     deps = [":autodiff"],

common/test/type_util_test.cc

@@ -0,0 +1,120 @@
+#include "drake/common/type_util.h"
+
+#include <string>
+#include <vector>
+
+#include <gtest/gtest.h>
+
+#include "drake/common/nice_type_name.h"
+
+using std::string;
+using std::vector;
+
+namespace drake {
+namespace {
+
+template <typename... Ts>
+struct SimpleTemplate {};
+
+using Pack = type_pack<int, double, char, void>;
+
+// Mostly, this just checks for compilation failures.
+GTEST_TEST(TypeUtilTest, TypeAt) {
+  using T_0 = type_at<0, int, double, char, void>::type;
+  EXPECT_TRUE((std::is_same<T_0, int>::value));
+  using T_1 = type_at<1, int, double, char, void>::type;
+  EXPECT_TRUE((std::is_same<T_1, double>::value));
+  using T_2 = type_at<2, int, double, char, void>::type;
+  EXPECT_TRUE((std::is_same<T_2, char>::value));
+  using T_3 = type_at<3, int, double, char, void>::type;
+  EXPECT_TRUE((std::is_same<T_3, void>::value));
+
+  EXPECT_TRUE((std::is_same<Pack::type_at<0>, int>::value));
+  EXPECT_TRUE((std::is_same<Pack::type_at<1>, double>::value));
+  EXPECT_TRUE((std::is_same<Pack::type_at<2>, char>::value));
+  EXPECT_TRUE((std::is_same<Pack::type_at<3>, void>::value));
+}
+
+GTEST_TEST(TypeUtilTest, TypeTags) {
+  // Ensure that we can default-construct tags for types that are not
+  // default-constructible.
+  auto tag_check = type_tag<void>{};
+  EXPECT_TRUE((std::is_same<
+      decltype(tag_check), type_tag<void>>::value));
+  auto pack_check_empty = type_pack<>{};
+  EXPECT_TRUE((std::is_same<
+      decltype(pack_check_empty), type_pack<>>::value));
+  auto pack_check = type_pack<void, void>{};
+  EXPECT_TRUE((std::is_same<
+      decltype(pack_check), type_pack<void, void>>::value));
+}
+
+GTEST_TEST(TypeUtilTest, Bind) {
+  using T_0 = Pack::bind<SimpleTemplate>;
+  EXPECT_TRUE((std::is_same<
+      T_0, SimpleTemplate<int, double, char, void>>::value));
+  Pack pack;
+  using T_1 = decltype(type_bind<SimpleTemplate>(pack));
+  EXPECT_TRUE((std::is_same<
+      T_1, SimpleTemplate<int, double, char, void>>::value));
+}
+
+GTEST_TEST(TypeUtilTest, Extract) {
+  using T = SimpleTemplate<int, double, char, void>;
+  using TPack = type_pack_extract<T>;
+  EXPECT_TRUE((std::is_same<TPack, Pack>::value));
+}
+
+GTEST_TEST(TypeUtilTest, Visit) {
+  using PackTags = type_pack<
+      type_tag<int>, type_tag<double>, type_tag<char>, type_tag<void>>;
+  vector<string> names;
+  const vector<string> names_expected = {"int", "double", "char", "void"};
+
+  auto visitor = [&names](auto tag) {
+    using T = typename decltype(tag)::type;
+    names.push_back(NiceTypeName::Get<T>());
+  };
+  names.clear();
+  type_visit(visitor, PackTags{});
+  EXPECT_EQ(names, names_expected);
+
+  names.clear();
+  type_visit<visit_with_tag<>>(visitor, Pack{});
+  EXPECT_EQ(names, names_expected);
+
+  // N.B. `Check` will operate types contained within the pack as dictated by
+  // the `VisitWith` parameter in `type_visit`.
+  // As an example, see below that the two visit calls will be visiting the
+  // same types (with the same results), but `Check` will operate on
+  // (a) the direct types with `visit_with_tag<>` and (b) the tag types with
+  // `visit_with_default` (the default parameter).
+  const vector<string> names_expected_sub = {"int", "char", "void"};
+
+  names.clear();
+  type_visit<visit_with_tag<>>(
+      visitor, Pack{}, check_different_from<double>{});
+  EXPECT_EQ(names, names_expected_sub);
+
+  names.clear();
+  type_visit(visitor, PackTags{}, check_different_from<type_tag<double>>{});
+  EXPECT_EQ(names, names_expected_sub);
+};
+
+GTEST_TEST(TypeUtilTest, Transform) {
+  auto seq = sequence_transform(
+      constant_add<int, 5>{}, std::make_integer_sequence<int, 5>{});
+  EXPECT_TRUE((std::is_same<
+      decltype(seq), std::integer_sequence<int, 5, 6, 7, 8, 9>>::value));
+}
+
+GTEST_TEST(TypeUtilTest, Hash) {
+  using T = int;
+  using U = int;
+  using V = double;
+  EXPECT_EQ(type_hash<T>(), type_hash<U>());
+  EXPECT_NE(type_hash<T>(), type_hash<V>());
+}
+
+}  // namespace
+}  // namespace drake

common/type_util.h

@@ -0,0 +1,189 @@
+#pragma once
+
+/// @file
+/// Basic meta-programming utilities for types, focused on template parameter
+/// packs.
+
+#include <cstddef>
+#include <type_traits>
+#include <typeindex>
+#include <typeinfo>
+#include <utility>
+
+namespace drake {
+
+template <typename ... Ts>
+struct type_pack;
+
+namespace detail {
+
+// Provides type at given index.
+template <size_t N, size_t K, typename T, typename ... Ts>
+struct type_at_impl {
+  using type = typename type_at_impl<N, K + 1, Ts...>::type;
+};
+
+// Base case.
+template <size_t N, typename T, typename ... Ts>
+struct type_at_impl<N, N, T, Ts...> {
+  using type = T;
+};
+
+// Visits a type given a VisitWith mechanism, templated to permit
+// conditional execution.
+template <typename VisitWith, typename Visitor>
+struct type_visit_impl {
+  template <typename T, bool execute>
+  struct runner {
+    inline static void run(Visitor&& visitor) {
+      VisitWith::template run<T>(std::forward<Visitor>(visitor));
+    }
+  };
+  template <typename T>
+  struct runner<T, false> {
+    inline static void run(Visitor&&) {}
+  };
+};
+
+// Catches non-template types explicitly.
+template <typename T>
+struct type_pack_extract_impl {
+  // Defer to show that this is a bad instantiation.
+  static_assert(!std::is_same<T, T>::value, "Wrong template");
+};
+
+template <template <typename ... Ts> class Tpl, typename ... Ts>
+struct type_pack_extract_impl<Tpl<Ts...>> {
+  using type = type_pack<Ts...>;
+};
+
+// Provides type for pack expansion into an initializer list for
+// deterministic execution order.
+using DummyList = bool[];
+
+}  // namespace detail
+
+
+/// Extracts the Ith type from a sequence of types.
+template <size_t I, typename ... Ts>
+struct type_at {
+  static_assert(I >= 0 && I < sizeof...(Ts), "Invalid type index");
+  using type = typename detail::type_at_impl<I, 0, Ts...>::type;
+};
+
+/// Provides a tag to pass a type for ease of inference.
+template <typename T>
+struct type_tag {
+  using type = T;
+};
+
+/// Provides a tag to pass a parameter packs for ease of inference.
+template <typename ... Ts>
+struct type_pack {
+  /// Number of template parameters.
+  static constexpr int size = sizeof...(Ts);
+
+  /// Rebinds parameter pack to a given template.
+  template <template <typename...> class Tpl>
+  using bind = Tpl<Ts...>;
+
+  /// Extracts the Ith type from this sequence.
+  template <size_t I>
+  using type_at = typename drake::type_at<I, Ts...>::type;
+};
+
+/// Returns an expression (only to be used in `decltype`) for inferring
+/// and binding a parameter pack to a template.
+template <template <typename...> class Tpl, typename ... Ts>
+Tpl<Ts...> type_bind(type_pack<Ts...>);
+
+/// Extracts the inner template arguments (typename only) for a typename which
+/// is a template instantiation.
+template <typename T>
+using type_pack_extract = typename detail::type_pack_extract_impl<T>::type;
+
+/// Visit a type by constructing its default value.
+/// Useful for iterating over `type_tag`, `type_pack`, `std::integral_constant`,
+/// etc.
+struct visit_with_default {
+  template <typename T, typename Visitor>
+  inline static void run(Visitor&& visitor) {
+    static_assert(std::is_default_constructible<T>::value,
+                  "Type T must be default-constructible");
+    visitor(T{});
+  }
+};
+
+/// Visits a type by construct a template tag's default value.
+template <template <typename> class Tag = type_tag>
+struct visit_with_tag {
+  template <typename T, typename Visitor>
+  inline static void run(Visitor&& visitor) {
+    visitor(Tag<T>{});
+  }
+};
+
+/// Provides a check which will return true for any type.
+struct check_always_true {
+  template <typename T>
+  using check = std::true_type;
+};
+
+/// Provides backport of C++17 `std::negation`.
+// TODO(eric.cousineau): Remove this once C++17 is used.
+template <typename T>
+using negation = std::integral_constant<bool, !T::value>;
+
+/// Provides a check which returns whether `T` is different than `U`.
+template <typename T>
+struct check_different_from {
+  template <typename U>
+  using check = negation<std::is_same<T, U>>;
+};
+
+/// Visits each type in a type pack.
+/// @tparam VisitWith
+///   Visit helper. @see `visit_with_default`, `visit_with_tag.
+/// @tparam Check
+///   Type-checking helper.
+/// @param visitor Lambda or functor for visiting a type.
+/// @param pack Inference argument for Ts...
+/// @param check Inference argument for `Check`.
+template <class VisitWith = visit_with_default,
+          typename Check = check_always_true,
+          typename Visitor = void,
+          typename ... Ts>
+inline void type_visit(
+    Visitor&& visitor, type_pack<Ts...> pack = {}, Check check = {}) {
+  (void)detail::DummyList{(
+      detail::type_visit_impl<VisitWith, Visitor>::
+          template runner<Ts, Check::template check<Ts>::value>::
+              run(std::forward<Visitor>(visitor)),
+      true)...};
+}
+
+/// Transforms an integer sequence.
+/// @tparam TForm
+///   Type with the interface `TForm::template type<T>::value`,
+///   which operates on a constexpr value.
+/// @tparam T Integral type.
+/// @tparam Values... Integral values.
+template <typename TForm, typename T, T... Values>
+auto sequence_transform(TForm = {}, std::integer_sequence<T, Values...> = {}) {
+  return std::integer_sequence<T, TForm::template type<Values>::value...>{};
+}
+
+/// Adds a constant value to a constexpr value.
+template <typename T, T x>
+struct constant_add {
+  template <T y>
+  using type = std::integral_constant<T, x + y>;
+};
+
+/// Provides short-hand for hashing a type.
+template <typename T>
+constexpr size_t type_hash() {
+  return std::type_index(typeid(T)).hash_code();
+}
+
+}  // namespace drake