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1 | /*! |
2 | @file | |
3 | Forward declares `boost::hana::Product`. | |
4 | ||
5 | @copyright Louis Dionne 2013-2016 | |
6 | Distributed under the Boost Software License, Version 1.0. | |
7 | (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt) | |
8 | */ | |
9 | ||
10 | #ifndef BOOST_HANA_FWD_CONCEPT_PRODUCT_HPP | |
11 | #define BOOST_HANA_FWD_CONCEPT_PRODUCT_HPP | |
12 | ||
13 | #include <boost/hana/config.hpp> | |
14 | ||
15 | ||
16 | BOOST_HANA_NAMESPACE_BEGIN | |
17 | //! @ingroup group-concepts | |
18 | //! @defgroup group-Product Product | |
19 | //! Represents types that are generic containers of two elements. | |
20 | //! | |
21 | //! This concept basically represents types that are like `std::pair`. | |
22 | //! The motivation for making such a precise concept is similar to the | |
23 | //! motivation behind the `Sequence` concept; there are many different | |
24 | //! implementations of `std::pair` in different libraries, and we would | |
25 | //! like to manipulate any of them generically. | |
26 | //! | |
27 | //! Since a `Product` is basically a pair, it is unsurprising that the | |
28 | //! operations provided by this concept are getting the first and second | |
29 | //! element of a pair, creating a pair from two elements and other | |
30 | //! simmilar operations. | |
31 | //! | |
32 | //! @note | |
33 | //! Mathematically, this concept represents types that are category | |
34 | //! theoretical [products][1]. This is also where the name comes | |
35 | //! from. | |
36 | //! | |
37 | //! | |
38 | //! Minimal complete definition | |
39 | //! --------------------------- | |
40 | //! `first`, `second` and `make` | |
41 | //! | |
42 | //! `first` and `second` must obviously return the first and the second | |
43 | //! element of the pair, respectively. `make` must take two arguments `x` | |
44 | //! and `y` representing the first and the second element of the pair, | |
45 | //! and return a pair `p` such that `first(p) == x` and `second(p) == y`. | |
46 | //! @include example/product/make.cpp | |
47 | //! | |
48 | //! | |
49 | //! Laws | |
50 | //! ---- | |
51 | //! For a model `P` of `Product`, the following laws must be satisfied. | |
52 | //! For every data types `X` and `Y`, there must be a unique function | |
53 | //! @f$ \mathtt{make} : X \times Y \to P @f$ such that for every `x`, `y`, | |
54 | //! @code | |
55 | //! x == first(make<P>(x, y)) | |
56 | //! y == second(make<P>(x, y)) | |
57 | //! @endcode | |
58 | //! | |
59 | //! @note | |
60 | //! This law is less general than the universal property typically used to | |
61 | //! define category theoretical products, but it is vastly enough for what | |
62 | //! we need. | |
63 | //! | |
64 | //! This is basically saying that a `Product` must be the most general | |
65 | //! object able to contain a pair of objects `(P1, P2)`, but nothing | |
66 | //! more. Since the categorical product is defined by a universal | |
67 | //! property, all the models of this concept are isomorphic, and | |
68 | //! the isomorphism is unique. In other words, there is one and only | |
69 | //! one way to convert one `Product` to another. | |
70 | //! | |
71 | //! Another property that must be satisfied by `first` and `second` is | |
72 | //! that of @ref move-independence, which ensures that we can optimally | |
73 | //! decompose a `Product` into its two members without making redundant | |
74 | //! copies. | |
75 | //! | |
76 | //! | |
77 | //! Refined concepts | |
78 | //! ---------------- | |
79 | //! 1. `Comparable` (free model)\n | |
80 | //! Two products `x` and `y` are equal iff they are equal element-wise, | |
81 | //! by comparing the first element before the second element. | |
82 | //! @include example/product/comparable.cpp | |
83 | //! | |
84 | //! 2. `Orderable` (free model)\n | |
85 | //! Products are ordered using a lexicographical ordering as-if they | |
86 | //! were 2-element tuples. | |
87 | //! | |
88 | //! 3. `Foldable` (free model)\n | |
89 | //! Folding a `Product` `p` is equivalent to folding a list containing | |
90 | //! `first(p)` and `second(p)`, in that order. | |
91 | //! | |
92 | //! | |
93 | //! Concrete models | |
94 | //! --------------- | |
95 | //! `hana::pair` | |
96 | //! | |
97 | //! | |
98 | //! [1]: http://en.wikipedia.org/wiki/Product_(category_theory) | |
99 | template <typename P> | |
100 | struct Product; | |
101 | BOOST_HANA_NAMESPACE_END | |
102 | ||
103 | #endif // !BOOST_HANA_FWD_CONCEPT_PRODUCT_HPP |