123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143 |
- // Copyright Louis Dionne 2013-2017
- // Distributed under the Boost Software License, Version 1.0.
- // (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)
- #include <boost/hana/all_of.hpp>
- #include <boost/hana/assert.hpp>
- #include <boost/hana/cartesian_product.hpp>
- #include <boost/hana/contains.hpp>
- #include <boost/hana/core/to.hpp>
- #include <boost/hana/equal.hpp>
- #include <boost/hana/functional/demux.hpp>
- #include <boost/hana/fuse.hpp>
- #include <boost/hana/integral_constant.hpp>
- #include <boost/hana/minus.hpp>
- #include <boost/hana/mod.hpp>
- #include <boost/hana/not.hpp>
- #include <boost/hana/not_equal.hpp>
- #include <boost/hana/or.hpp>
- #include <boost/hana/plus.hpp>
- #include <boost/hana/set.hpp>
- #include <boost/hana/transform.hpp>
- #include <boost/hana/tuple.hpp>
- namespace hana = boost::hana;
- using namespace hana::literals;
- // A function that can have an arbitrary compile-time set of values as a domain
- // and co-domain. This is most likely purely of theoretical interest, but it
- // allows creating functions with very complex domains and co-domains that are
- // computed at compile-time.
- struct Function { };
- template <typename Domain, typename Codomain, typename F>
- struct function_type {
- using hana_tag = Function;
- Domain domain_;
- Codomain codomain_;
- F f_;
- template <typename X>
- constexpr auto operator()(X x) const {
- BOOST_HANA_CONSTANT_ASSERT(boost::hana::contains(domain_, x));
- return f_(x);
- }
- };
- template <typename ...F, typename ...G>
- constexpr auto operator==(function_type<F...> f, function_type<G...> g)
- { return hana::equal(f, g); }
- template <typename ...F, typename ...G>
- constexpr auto operator!=(function_type<F...> f, function_type<G...> g)
- { return hana::not_equal(f, g); }
- auto function = [](auto domain, auto codomain) {
- return [=](auto definition) {
- return function_type<decltype(domain), decltype(codomain), decltype(definition)>{
- domain, codomain, definition
- };
- };
- };
- template <typename Function>
- constexpr auto domain(Function f)
- { return f.domain_; }
- template <typename Function>
- constexpr auto codomain(Function f)
- { return f.codomain_; }
- template <typename Function>
- constexpr auto range(Function f) {
- // We must convert to hana::tuple first because hana::set is not a Functor
- return hana::to_set(hana::transform(hana::to_tuple(domain(f)), f));
- }
- template <typename P, typename Q>
- constexpr auto implies(P p, Q q) {
- return hana::or_(hana::not_(p), q);
- }
- template <typename F>
- constexpr auto is_injective(F f) {
- auto dom = hana::to_tuple(domain(f));
- auto pairs = hana::cartesian_product(hana::make_tuple(dom, dom));
- return hana::all_of(pairs, hana::fuse([&](auto x, auto y) {
- return implies(hana::not_equal(x, y), hana::not_equal(f(x), f(y)));
- }));
- }
- template <typename F>
- constexpr auto is_onto(F f) {
- return codomain(f) == range(f);
- }
- namespace boost { namespace hana {
- template <>
- struct equal_impl<Function, Function> {
- template <typename F, typename G>
- static constexpr auto apply(F f, G g) {
- return domain(f) == domain(g) &&
- hana::all_of(domain(f), hana::demux(hana::equal)(f, g));
- }
- };
- }} // end namespace boost::hana
- int main() {
- auto f = function(hana::make_set(1_c, 2_c, 3_c), hana::make_set(1_c, 2_c, 3_c, 4_c, 5_c, 6_c))(
- [](auto x) { return x + 1_c; }
- );
- auto g = function(hana::make_set(1_c, 2_c, 3_c), hana::make_set(2_c, 3_c, 4_c))(
- [](auto x) { return x + 1_c; }
- );
- auto h = function(hana::make_set(1_c, 2_c, 3_c), hana::make_set(0_c, 1_c, 2_c))(
- [](auto x) { return x - 1_c; }
- );
- BOOST_HANA_CONSTANT_CHECK(f == g);
- BOOST_HANA_CONSTANT_CHECK(f != h);
- BOOST_HANA_CONSTANT_CHECK(f(1_c) == 2_c);
- BOOST_HANA_CONSTANT_CHECK(range(f) == hana::make_set(4_c, 3_c, 2_c));
- BOOST_HANA_CONSTANT_CHECK(range(g) == hana::make_set(2_c, 3_c, 4_c));
- BOOST_HANA_CONSTANT_CHECK(range(h) == hana::make_set(0_c, 1_c, 2_c));
- BOOST_HANA_CONSTANT_CHECK(hana::not_(is_onto(f)));
- BOOST_HANA_CONSTANT_CHECK(is_onto(g));
- BOOST_HANA_CONSTANT_CHECK(is_onto(h));
- auto even = function(hana::make_set(1_c, 2_c, 3_c), hana::make_set(hana::true_c, hana::false_c))(
- [](auto x) { return x % 2_c == 0_c; }
- );
- BOOST_HANA_CONSTANT_CHECK(is_injective(f));
- BOOST_HANA_CONSTANT_CHECK(is_injective(g));
- BOOST_HANA_CONSTANT_CHECK(is_injective(h));
- BOOST_HANA_CONSTANT_CHECK(hana::not_(is_injective(even)));
- }
|