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