diff --git a/libcxx/include/concepts b/libcxx/include/concepts
--- a/libcxx/include/concepts
+++ b/libcxx/include/concepts
@@ -398,7 +398,25 @@
 template<class _Fn, class... _Args>
 concept regular_invocable = invocable<_Fn, _Args...>;
 
-#endif // _LIBCPP_STD_VER > 17 && !defined(_LIBCPP_HAS_NO_CONCEPTS)
+// [concept.predicate]
+template<class _Fn, class... _Args>
+concept predicate =
+  regular_invocable<_Fn, _Args...> && __boolean_testable<invoke_result_t<_Fn, _Args...>>;
+
+// [concept.relation]
+template<class _Rp, class _Tp, class _Up>
+concept relation =
+  predicate<_Rp, _Tp, _Tp> && predicate<_Rp, _Up, _Up> &&
+  predicate<_Rp, _Tp, _Up> && predicate<_Rp, _Up, _Tp>;
+
+// [concept.equiv]
+template<class _Rp, class _Tp, class _Up>
+concept equivalence_relation = relation<_Rp, _Tp, _Up>;
+
+// [concept.strictweakorder]
+template<class _Rp, class _Tp, class _Up>
+concept strict_weak_order = relation<_Rp, _Tp, _Up>;
+#endif //_LIBCPP_STD_VER > 17 && !defined(_LIBCPP_HAS_NO_CONCEPTS)
 
 _LIBCPP_END_NAMESPACE_STD
 
diff --git a/libcxx/test/std/concepts/concepts.callable/concepts.equiv/equivalence_relation.pass.cpp b/libcxx/test/std/concepts/concepts.callable/concepts.equiv/equivalence_relation.pass.cpp
new file mode 100644
--- /dev/null
+++ b/libcxx/test/std/concepts/concepts.callable/concepts.equiv/equivalence_relation.pass.cpp
@@ -0,0 +1,60 @@
+//===----------------------------------------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+// UNSUPPORTED: c++03, c++11, c++14, c++17
+// UNSUPPORTED: libcpp-no-concepts
+
+// template<class F, class... Args>
+// concept equivalence_relation;
+
+#include <concepts>
+
+static_assert(std::equivalence_relation<bool(int, int), int, int>);
+static_assert(std::equivalence_relation<bool(int, int), double, double>);
+static_assert(std::equivalence_relation<bool(int, double), double, double>);
+
+static_assert(!std::equivalence_relation<bool (*)(), int, double>);
+static_assert(!std::equivalence_relation<bool (*)(int), int, double>);
+static_assert(!std::equivalence_relation<bool (*)(double), int, double>);
+
+static_assert(
+    !std::equivalence_relation<bool(double, double*), double, double*>);
+static_assert(!std::equivalence_relation<bool(int&, int&), double&, double&>);
+
+struct S1 {};
+static_assert(!std::equivalence_relation<int S1::*, S1*, std::nullptr_t>);
+
+struct S2 {};
+
+struct P1 {
+  bool operator()(S1, S1) const;
+};
+static_assert(std::equivalence_relation<P1, S1, S1>);
+
+struct P2 {
+  bool operator()(S1, S1) const;
+  bool operator()(S1, S2) const;
+};
+static_assert(!std::equivalence_relation<P2, S1, S2>);
+
+struct P3 {
+  bool operator()(S1, S1) const;
+  bool operator()(S1, S2) const;
+  bool operator()(S2, S1) const;
+};
+static_assert(!std::equivalence_relation<P3, S1, S2>);
+
+struct P4 {
+  bool operator()(S1, S1) const;
+  bool operator()(S1, S2) const;
+  bool operator()(S2, S1) const;
+  bool operator()(S2, S2) const;
+};
+static_assert(std::equivalence_relation<P4, S1, S2>);
+
+int main(int, char**) { return 0; }
diff --git a/libcxx/test/std/concepts/concepts.callable/concepts.equiv/equivalence_relation.subsumption.pass.cpp b/libcxx/test/std/concepts/concepts.callable/concepts.equiv/equivalence_relation.subsumption.pass.cpp
new file mode 100644
--- /dev/null
+++ b/libcxx/test/std/concepts/concepts.callable/concepts.equiv/equivalence_relation.subsumption.pass.cpp
@@ -0,0 +1,40 @@
+//===----------------------------------------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+// UNSUPPORTED: c++03, c++11, c++14, c++17
+// UNSUPPORTED: libcpp-no-concepts
+
+// template<class F, class... Args>
+// concept equivalence_relation;
+
+#include <concepts>
+
+// clang-format off
+template<class F, class T, class U>
+requires std::relation<F&, T, U>
+[[nodiscard]] constexpr bool check_subsumption() { return false; }
+
+template<class F, class T, class U>
+requires std::equivalence_relation<F&, T, U> && true
+[[nodiscard]] constexpr bool check_subsumption() { return true; }
+// clang-format on
+
+static_assert(check_subsumption<int (*)(int, double), int, double>());
+
+struct S1 {};
+struct S2 {};
+
+struct R {
+  bool operator()(S1, S1) const;
+  bool operator()(S1, S2) const;
+  bool operator()(S2, S1) const;
+  bool operator()(S2, S2) const;
+};
+static_assert(check_subsumption<R, S1, S2>());
+
+int main(int, char**) { return 0; }
diff --git a/libcxx/test/std/concepts/concepts.callable/concepts.predicate/predicate.pass.cpp b/libcxx/test/std/concepts/concepts.callable/concepts.predicate/predicate.pass.cpp
new file mode 100644
--- /dev/null
+++ b/libcxx/test/std/concepts/concepts.callable/concepts.predicate/predicate.pass.cpp
@@ -0,0 +1,44 @@
+//===----------------------------------------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+// UNSUPPORTED: c++03, c++11, c++14, c++17
+// UNSUPPORTED: libcpp-no-concepts
+
+// template<class F, class... Args>
+// concept predicate;
+
+#include <concepts>
+
+static_assert(std::predicate<bool()>);
+static_assert(std::predicate<bool (*)()>);
+static_assert(std::predicate<bool (&)()>);
+
+static_assert(!std::predicate<void()>);
+static_assert(!std::predicate<void (*)()>);
+static_assert(!std::predicate<void (&)()>);
+
+struct S {};
+
+static_assert(!std::predicate<S(int), int>);
+static_assert(!std::predicate<S(double), double>);
+static_assert(std::predicate<int S::*, S*>);
+static_assert(std::predicate<int (S::*)(), S*>);
+static_assert(!std::predicate<void (S::*)(), S*>);
+
+static_assert(!std::predicate<bool(S)>);
+static_assert(!std::predicate<bool(S&), S>);
+static_assert(!std::predicate<bool(S&), S const&>);
+static_assert(std::predicate<bool(S&), S&>);
+
+struct Predicate {
+  bool operator()(int, double, char);
+};
+static_assert(std::predicate<Predicate, int, double, char>);
+static_assert(std::predicate<Predicate&, int, double, char>);
+
+int main(int, char**) { return 0; }
diff --git a/libcxx/test/std/concepts/concepts.callable/concepts.predicate/predicate.subsumption.pass.cpp b/libcxx/test/std/concepts/concepts.callable/concepts.predicate/predicate.subsumption.pass.cpp
new file mode 100644
--- /dev/null
+++ b/libcxx/test/std/concepts/concepts.callable/concepts.predicate/predicate.subsumption.pass.cpp
@@ -0,0 +1,45 @@
+//===----------------------------------------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+// UNSUPPORTED: c++03, c++11, c++14, c++17
+// UNSUPPORTED: libcpp-no-concepts
+
+// template<class F, class... Args>
+// concept predicate;
+
+#include <concepts>
+
+[[nodiscard]] constexpr bool check_subsumption(std::regular_invocable auto) {
+  return false;
+}
+
+// clang-format off
+template<class F>
+requires std::predicate<F> && true
+[[nodiscard]] constexpr bool check_subsumption(F)
+{
+  return true;
+}
+// clang-format on
+
+static_assert(!check_subsumption([] {}));
+static_assert(check_subsumption([] { return true; }));
+static_assert(check_subsumption([] { return std::true_type(); }));
+static_assert(check_subsumption([]() -> int* { return nullptr; }));
+
+struct boolean {
+  operator bool() const noexcept;
+};
+static_assert(check_subsumption([] { return boolean(); }));
+
+struct explicit_bool {
+  explicit operator bool() const noexcept;
+};
+static_assert(!check_subsumption([] { return explicit_bool(); }));
+
+int main(int, char**) { return 0; }
diff --git a/libcxx/test/std/concepts/concepts.callable/concepts.relation/relation.pass.cpp b/libcxx/test/std/concepts/concepts.callable/concepts.relation/relation.pass.cpp
new file mode 100644
--- /dev/null
+++ b/libcxx/test/std/concepts/concepts.callable/concepts.relation/relation.pass.cpp
@@ -0,0 +1,59 @@
+//===----------------------------------------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+// UNSUPPORTED: c++03, c++11, c++14, c++17
+// UNSUPPORTED: libcpp-no-concepts
+
+// template<class F, class... Args>
+// concept relation;
+
+#include <concepts>
+
+static_assert(std::relation<bool(int, int), int, int>);
+static_assert(std::relation<bool(int, int), double, double>);
+static_assert(std::relation<bool(int, double), double, double>);
+
+static_assert(!std::relation<bool (*)(), int, double>);
+static_assert(!std::relation<bool (*)(int), int, double>);
+static_assert(!std::relation<bool (*)(double), int, double>);
+
+static_assert(!std::relation<bool(double, double*), double, double*>);
+static_assert(!std::relation<bool(int&, int&), double&, double&>);
+
+struct S1 {};
+static_assert(!std::relation<int S1::*, S1*, std::nullptr_t>);
+
+struct S2 {};
+
+struct P1 {
+  bool operator()(S1, S1) const;
+};
+static_assert(std::relation<P1, S1, S1>);
+
+struct P2 {
+  bool operator()(S1, S1) const;
+  bool operator()(S1, S2) const;
+};
+static_assert(!std::relation<P2, S1, S2>);
+
+struct P3 {
+  bool operator()(S1, S1) const;
+  bool operator()(S1, S2) const;
+  bool operator()(S2, S1) const;
+};
+static_assert(!std::relation<P3, S1, S2>);
+
+struct P4 {
+  bool operator()(S1, S1) const;
+  bool operator()(S1, S2) const;
+  bool operator()(S2, S1) const;
+  bool operator()(S2, S2) const;
+};
+static_assert(std::relation<P4, S1, S2>);
+
+int main(int, char**) { return 0; }
diff --git a/libcxx/test/std/concepts/concepts.callable/concepts.relation/relation.subsumption.pass.cpp b/libcxx/test/std/concepts/concepts.callable/concepts.relation/relation.subsumption.pass.cpp
new file mode 100644
--- /dev/null
+++ b/libcxx/test/std/concepts/concepts.callable/concepts.relation/relation.subsumption.pass.cpp
@@ -0,0 +1,41 @@
+//===----------------------------------------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+// UNSUPPORTED: c++03, c++11, c++14, c++17
+// UNSUPPORTED: libcpp-no-concepts
+
+// template<class F, class... Args>
+// concept relation;
+
+#include <concepts>
+
+// clang-format off
+template<class F, class T, class U>
+requires std::predicate<F&, T, T> && std::predicate<F&, T, U> &&
+         std::predicate<F&, U, T> && std::predicate<F&, U, U>
+[[nodiscard]] constexpr bool check_subsumption() { return false; }
+
+template<class F, class T, class U>
+requires std::relation<F&, T, U> && true
+[[nodiscard]] constexpr bool check_subsumption() { return true; }
+// clang-format on
+
+static_assert(check_subsumption<int (*)(int, double), int, double>());
+
+struct S1 {};
+struct S2 {};
+
+struct R {
+  bool operator()(S1, S1) const;
+  bool operator()(S1, S2) const;
+  bool operator()(S2, S1) const;
+  bool operator()(S2, S2) const;
+};
+static_assert(check_subsumption<R, S1, S2>());
+
+int main(int, char**) { return 0; }
diff --git a/libcxx/test/std/concepts/concepts.callable/concepts.strictweakorder/strict_weak_order.pass.cpp b/libcxx/test/std/concepts/concepts.callable/concepts.strictweakorder/strict_weak_order.pass.cpp
new file mode 100644
--- /dev/null
+++ b/libcxx/test/std/concepts/concepts.callable/concepts.strictweakorder/strict_weak_order.pass.cpp
@@ -0,0 +1,59 @@
+//===----------------------------------------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+// UNSUPPORTED: c++03, c++11, c++14, c++17
+// UNSUPPORTED: libcpp-no-concepts
+
+// template<class F, class... Args>
+// concept strict_weak_order;
+
+#include <concepts>
+
+static_assert(std::strict_weak_order<bool(int, int), int, int>);
+static_assert(std::strict_weak_order<bool(int, int), double, double>);
+static_assert(std::strict_weak_order<bool(int, double), double, double>);
+
+static_assert(!std::strict_weak_order<bool (*)(), int, double>);
+static_assert(!std::strict_weak_order<bool (*)(int), int, double>);
+static_assert(!std::strict_weak_order<bool (*)(double), int, double>);
+
+static_assert(!std::strict_weak_order<bool(double, double*), double, double*>);
+static_assert(!std::strict_weak_order<bool(int&, int&), double&, double&>);
+
+struct S1 {};
+static_assert(!std::strict_weak_order<int S1::*, S1*, std::nullptr_t>);
+
+struct S2 {};
+
+struct P1 {
+  bool operator()(S1, S1) const;
+};
+static_assert(std::strict_weak_order<P1, S1, S1>);
+
+struct P2 {
+  bool operator()(S1, S1) const;
+  bool operator()(S1, S2) const;
+};
+static_assert(!std::strict_weak_order<P2, S1, S2>);
+
+struct P3 {
+  bool operator()(S1, S1) const;
+  bool operator()(S1, S2) const;
+  bool operator()(S2, S1) const;
+};
+static_assert(!std::strict_weak_order<P3, S1, S2>);
+
+struct P4 {
+  bool operator()(S1, S1) const;
+  bool operator()(S1, S2) const;
+  bool operator()(S2, S1) const;
+  bool operator()(S2, S2) const;
+};
+static_assert(std::strict_weak_order<P4, S1, S2>);
+
+int main(int, char**) { return 0; }
diff --git a/libcxx/test/std/concepts/concepts.callable/concepts.strictweakorder/strict_weak_order.subsumption.pass.cpp b/libcxx/test/std/concepts/concepts.callable/concepts.strictweakorder/strict_weak_order.subsumption.pass.cpp
new file mode 100644
--- /dev/null
+++ b/libcxx/test/std/concepts/concepts.callable/concepts.strictweakorder/strict_weak_order.subsumption.pass.cpp
@@ -0,0 +1,40 @@
+//===----------------------------------------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+// UNSUPPORTED: c++03, c++11, c++14, c++17
+// UNSUPPORTED: libcpp-no-concepts
+
+// template<class F, class... Args>
+// concept strict_weak_order;
+
+#include <concepts>
+
+// clang-format off
+template<class F, class T, class U>
+requires std::relation<F&, T, U>
+[[nodiscard]] constexpr bool check_subsumption() { return false; }
+
+template<class F, class T, class U>
+requires std::strict_weak_order<F&, T, U> && true
+[[nodiscard]] constexpr bool check_subsumption() { return true; }
+// clang-format on
+
+static_assert(check_subsumption<int (*)(int, double), int, double>());
+
+struct S1 {};
+struct S2 {};
+
+struct R {
+  bool operator()(S1, S1) const;
+  bool operator()(S1, S2) const;
+  bool operator()(S2, S1) const;
+  bool operator()(S2, S2) const;
+};
+static_assert(check_subsumption<R, S1, S2>());
+
+int main(int, char**) { return 0; }