104 lines
3.9 KiB
C++
104 lines
3.9 KiB
C++
/*!
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@file
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Forward declares `boost::hana::Product`.
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@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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*/
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#ifndef BOOST_HANA_FWD_CONCEPT_PRODUCT_HPP
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#define BOOST_HANA_FWD_CONCEPT_PRODUCT_HPP
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#include <boost/hana/config.hpp>
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namespace boost { namespace hana {
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//! @ingroup group-concepts
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//! @defgroup group-Product Product
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//! Represents types that are generic containers of two elements.
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//!
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//! This concept basically represents types that are like `std::pair`.
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//! The motivation for making such a precise concept is similar to the
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//! motivation behind the `Sequence` concept; there are many different
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//! implementations of `std::pair` in different libraries, and we would
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//! like to manipulate any of them generically.
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//!
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//! Since a `Product` is basically a pair, it is unsurprising that the
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//! operations provided by this concept are getting the first and second
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//! element of a pair, creating a pair from two elements and other
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//! simmilar operations.
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//!
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//! @note
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//! Mathematically, this concept represents types that are category
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//! theoretical [products][1]. This is also where the name comes
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//! from.
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//!
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//!
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//! Minimal complete definition
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//! ---------------------------
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//! `first`, `second` and `make`
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//!
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//! `first` and `second` must obviously return the first and the second
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//! element of the pair, respectively. `make` must take two arguments `x`
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//! and `y` representing the first and the second element of the pair,
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//! and return a pair `p` such that `first(p) == x` and `second(p) == y`.
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//! @include example/product/make.cpp
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//!
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//!
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//! Laws
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//! ----
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//! For a model `P` of `Product`, the following laws must be satisfied.
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//! For every data types `X` and `Y`, there must be a unique function
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//! @f$ \mathtt{make} : X \times Y \to P @f$ such that for every `x`, `y`,
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//! @code
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//! x == first(make<P>(x, y))
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//! y == second(make<P>(x, y))
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//! @endcode
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//!
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//! @note
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//! This law is less general than the universal property typically used to
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//! define category theoretical products, but it is vastly enough for what
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//! we need.
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//!
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//! This is basically saying that a `Product` must be the most general
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//! object able to contain a pair of objects `(P1, P2)`, but nothing
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//! more. Since the categorical product is defined by a universal
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//! property, all the models of this concept are isomorphic, and
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//! the isomorphism is unique. In other words, there is one and only
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//! one way to convert one `Product` to another.
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//!
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//! Another property that must be satisfied by `first` and `second` is
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//! that of @ref move-independence, which ensures that we can optimally
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//! decompose a `Product` into its two members without making redundant
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//! copies.
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//!
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//!
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//! Refined concepts
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//! ----------------
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//! 1. `Comparable` (free model)\n
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//! Two products `x` and `y` are equal iff they are equal element-wise,
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//! by comparing the first element before the second element.
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//! @include example/product/comparable.cpp
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//!
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//! 2. `Orderable` (free model)\n
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//! Products are ordered using a lexicographical ordering as-if they
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//! were 2-element tuples.
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//!
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//! 3. `Foldable` (free model)\n
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//! Folding a `Product` `p` is equivalent to folding a list containing
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//! `first(p)` and `second(p)`, in that order.
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//!
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//!
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//! Concrete models
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//! ---------------
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//! `hana::pair`
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//!
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//!
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//! [1]: http://en.wikipedia.org/wiki/Product_(category_theory)
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template <typename P>
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struct Product;
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}} // end namespace boost::hana
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#endif // !BOOST_HANA_FWD_CONCEPT_PRODUCT_HPP
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