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1// Copyright Louis Dionne 2013-2016
2// Distributed under the Boost Software License, Version 1.0.
3// (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)
4
5#include <boost/hana/all_of.hpp>
6#include <boost/hana/assert.hpp>
7#include <boost/hana/contains.hpp>
8#include <boost/hana/core/to.hpp>
9#include <boost/hana/equal.hpp>
10#include <boost/hana/functional/demux.hpp>
11#include <boost/hana/integral_constant.hpp>
12#include <boost/hana/minus.hpp>
13#include <boost/hana/not_equal.hpp>
14#include <boost/hana/plus.hpp>
15#include <boost/hana/set.hpp>
16#include <boost/hana/transform.hpp>
17#include <boost/hana/tuple.hpp>
18namespace hana = boost::hana;
19using namespace hana::literals;
20
21
22struct Function { };
23
24template <typename Domain, typename Codomain, typename F>
25struct function_type {
26 using hana_tag = Function;
27
28 Domain domain_;
29 Codomain codomain_;
30 F f_;
31
32 template <typename X>
33 constexpr auto operator()(X x) const {
34 BOOST_HANA_ASSERT(boost::hana::contains(domain_, x));
35 return f_(x);
36 }
37};
38
39template <typename ...F, typename ...G>
40constexpr auto operator==(function_type<F...> f, function_type<G...> g)
41{ return hana::equal(f, g); }
42
43template <typename ...F, typename ...G>
44constexpr auto operator!=(function_type<F...> f, function_type<G...> g)
45{ return hana::not_equal(f, g); }
46
47
48auto function = [](auto domain, auto codomain) {
49 return [=](auto definition) {
50 return function_type<decltype(domain), decltype(codomain), decltype(definition)>{
51 domain, codomain, definition
52 };
53 };
54};
55
56template <typename Function>
57constexpr auto domain(Function f)
58{ return f.domain_; }
59
60template <typename Function>
61constexpr auto codomain(Function f)
62{ return f.codomain_; }
63
64template <typename Function>
65constexpr auto range(Function f) {
66 // We must convert to hana::tuple first because hana::set is not a Functor
67 return hana::to_set(hana::transform(hana::to_tuple(domain(f)), f));
68}
69
70namespace boost { namespace hana {
71 template <>
72 struct equal_impl<Function, Function> {
73 template <typename F, typename G>
74 static constexpr auto apply(F f, G g) {
75 return domain(f) == domain(g) &&
76 hana::all_of(domain(f), hana::demux(hana::equal)(f, g));
77 }
78 };
79}} // end namespace boost::hana
80
81
82// BOOST_HANA_CONSTEXPR_LAMBDA auto is_injective = [](auto f) {
83// auto check = [](auto x, auto y) {
84// return (x != y) ^implies^ (f(x) != f(y));
85// };
86// return all_of(product(domain(f), domain(f)), check);
87// };
88
89// BOOST_HANA_CONSTEXPR_LAMBDA auto is_onto = [](auto f) {
90// return codomain(f) == range(g);
91// };
92
93//////////////////////////////////////////////////////////////////////////////
94
95int main() {
96 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))(
97 [](auto x) { return x + 1_c; }
98 );
99
100 auto g = function(hana::make_set(1_c, 2_c, 3_c), hana::make_set(2_c, 3_c, 4_c))(
101 [](auto x) { return x + 1_c; }
102 );
103
104 auto h = function(hana::make_set(1_c, 2_c, 3_c), hana::make_set(0_c, 1_c, 2_c))(
105 [](auto x) { return x - 1_c; }
106 );
107
108 BOOST_HANA_CONSTANT_CHECK(f == g);
109 BOOST_HANA_CONSTANT_CHECK(f != h);
110 BOOST_HANA_CONSTANT_CHECK(f(1_c) == 2_c);
111
112 BOOST_HANA_CONSTANT_CHECK(range(f) == hana::make_set(4_c, 3_c, 2_c));
113}