FM / concept

/usr/include/boost/hana/fwd/concept

Name	Size	Mode	Actions
applicative.hpp	4209	0644	edit dl rm
comonad.hpp	3746	0644	edit dl rm
comparable.hpp	7585	0644	edit dl rm
constant.hpp	10197	0644	edit dl rm
euclidean_ring.hpp	4711	0644	edit dl rm
foldable.hpp	6531	0644	edit dl rm
functor.hpp	6097	0644	edit dl rm
group.hpp	3744	0644	edit dl rm
hashable.hpp	2551	0644	edit dl rm
integral_constant.hpp	2634	0644	edit dl rm
iterable.hpp	6495	0644	edit dl rm
logical.hpp	7173	0644	edit dl rm
metafunction.hpp	4618	0644	edit dl rm
monad.hpp	9312	0644	edit dl rm
monad_plus.hpp	3404	0644	edit dl rm
monoid.hpp	4062	0644	edit dl rm
orderable.hpp	7687	0644	edit dl rm
product.hpp	3951	0644	edit dl rm
ring.hpp	3886	0644	edit dl rm
searchable.hpp	6460	0644	edit dl rm
sequence.hpp	7412	0644	edit dl rm
struct.hpp	7534	0644	edit dl rm

Edit: /usr/include/boost/hana/fwd/concept/functor.hpp (6097B)

/*!
@file
Forward declares `boost::hana::Functor`.

@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)
 */

#ifndef BOOST_HANA_FWD_CONCEPT_FUNCTOR_HPP
#define BOOST_HANA_FWD_CONCEPT_FUNCTOR_HPP

#include <boost/hana/config.hpp>

BOOST_HANA_NAMESPACE_BEGIN
    //! @ingroup group-concepts
    //! @defgroup group-Functor Functor
    //! The `Functor` concept represents types that can be mapped over.
    //!
    //! Intuitively, a [Functor][1] is some kind of box that can hold generic
    //! data and map a function over this data to create a new, transformed
    //! box. Because we are only interested in mapping a function over the
    //! contents of a black box, the only real requirement for being a functor
    //! is to provide a function which can do the mapping, along with a couple
    //! of guarantees that the mapping is well-behaved. Those requirements are
    //! made precise in the laws below. The pattern captured by `Functor` is
    //! very general, which makes it widely useful. A lot of objects can be
    //! made `Functor`s in one way or another, the most obvious example being
    //! sequences with the usual mapping of the function on each element.
    //! While this documentation will not go into much more details about
    //! the nature of functors, the [Typeclassopedia][2] is a nice
    //! Haskell-oriented resource for such information.
    //!
    //! Functors are parametric data types which are parameterized over the
    //! data type of the objects they contain. Like everywhere else in Hana,
    //! this parametricity is only at the documentation level and it is not
    //! enforced.
    //!
    //! In this library, the mapping function is called `transform` after the
    //! `std::transform` algorithm, but other programming languages have given
    //! it different names (usually `map`).
    //!
    //! @note
    //! The word _functor_ comes from functional programming, where the
    //! concept has been used for a while, notably in the Haskell programming
    //! language. Haskell people borrowed the term from [category theory][3],
    //! which, broadly speaking, is a field of mathematics dealing with
    //! abstract structures and transformations between those structures.
    //!
    //!
    //! Minimal complete definitions
    //! ----------------------------
    //! 1. `transform`\n
    //! When `transform` is specified, `adjust_if` is defined analogously to
    //! @code
    //!     adjust_if(xs, pred, f) = transform(xs, [](x){
    //!         if pred(x) then f(x) else x
    //!     })
    //! @endcode
    //!
    //! 2. `adjust_if`\n
    //! When `adjust_if` is specified, `transform` is defined analogously to
    //! @code
    //!     transform(xs, f) = adjust_if(xs, always(true), f)
    //! @endcode
    //!
    //!
    //! Laws
    //! ----
    //! Let `xs` be a Functor with tag `F(A)`,
    //!     \f$ f : A \to B \f$ and
    //!     \f$ g : B \to C \f$.
    //! The following laws must be satisfied:
    //! @code
    //!     transform(xs, id) == xs
    //!     transform(xs, compose(g, f)) == transform(transform(xs, f), g)
    //! @endcode
    //! The first line says that mapping the identity function should not do
    //! anything, which precludes the functor from doing something nasty
    //! behind the scenes. The second line states that mapping the composition
    //! of two functions is the same as mapping the first function, and then
    //! the second on the result. While the usual functor laws are usually
    //! restricted to the above, this library includes other convenience
    //! methods and they should satisfy the following equations.
    //! Let `xs` be a Functor with tag `F(A)`,
    //!     \f$ f : A \to A \f$,
    //!     \f$ \mathrm{pred} : A \to \mathrm{Bool} \f$
    //! for some `Logical` `Bool`, and `oldval`, `newval`, `value` objects
    //! of tag `A`. Then,
    //! @code
    //!     adjust(xs, value, f) == adjust_if(xs, equal.to(value), f)
    //!     adjust_if(xs, pred, f) == transform(xs, [](x){
    //!         if pred(x) then f(x) else x
    //!     })
    //!     replace_if(xs, pred, value) == adjust_if(xs, pred, always(value))
    //!     replace(xs, oldval, newval) == replace_if(xs, equal.to(oldval), newval)
    //!     fill(xs, value)             == replace_if(xs, always(true), value)
    //! @endcode
    //! The default definition of the methods will satisfy these equations.
    //!
    //!
    //! Concrete models
    //! ---------------
    //! `hana::lazy`, `hana::optional`, `hana::tuple`
    //!
    //!
    //! Structure-preserving functions for Functors
    //! -------------------------------------------
    //! A mapping between two functors which also preserves the functor
    //! laws is called a natural transformation (the term comes from
    //! category theory). A natural transformation is a function `f`
    //! from a functor `F` to a functor `G` such that for every other
    //! function `g` with an appropriate signature and for every object
    //! `xs` of tag `F(X)`,
    //! @code
    //!     f(transform(xs, g)) == transform(f(xs), g)
    //! @endcode
    //!
    //! There are several examples of such transformations, like `to<tuple_tag>`
    //! when applied to an optional value. Indeed, for any function `g` and
    //! `hana::optional` `opt`,
    //! @code
    //!     to<tuple_tag>(transform(opt, g)) == transform(to<tuple_tag>(opt), g)
    //! @endcode
    //!
    //! Of course, natural transformations are not limited to the `to<...>`
    //! functions. However, note that any conversion function between Functors
    //! should be natural for the behavior of the conversion to be intuitive.
    //!
    //!
    //! [1]: http://en.wikipedia.org/wiki/Functor
    //! [2]: https://wiki.haskell.org/Typeclassopedia#Functor
    //! [3]: http://en.wikipedia.org/wiki/Category_theory
    template <typename F>
    struct Functor;
BOOST_HANA_NAMESPACE_END

#endif // !BOOST_HANA_FWD_CONCEPT_FUNCTOR_HPP

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