Boost.Hana: Functor

| Boost.Hana 1.0.0 Your standard library for metaprogramming |

Variables
Functor
Concepts

## Description

The `Functor` concept represents types that can be mapped over.

Intuitively, a Functor 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 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, which, broadly speaking, is a field of mathematics dealing with abstract structures and transformations between those structures.

## Minimal complete definitions

1. `transform`
   When `transform` is specified, `adjust_if` is defined analogously to
   adjust_if(xs, pred, f) = transform(xs, [](x){
   if pred(x) then f(x) else x
   })
2. `adjust_if`
   When `adjust_if` is specified, `transform` is defined analogously to
   transform(xs, f) = adjust_if(xs, always(true), f)

## Laws

Let `xs` be a Functor with tag `F(A)`, \( f : A \to B \) and \( g : B \to C \). The following laws must be satisfied:

transform(xs, id) == xs
transform(xs, compose(g, f)) == transform(transform(xs, f), g)

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)`, \( f : A \to A \), \( \mathrm{pred} : A \to \mathrm{Bool} \) for some `Logical` `Bool`, and `oldval`, `newval`, `value` objects of tag `A`. Then,

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)

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)`,

f(transform(xs, g)) == transform(f(xs), g)

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`,

to<tuple_tag>(transform(opt, g)) == transform(to<tuple_tag>(opt), g)

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.

## Variables

constexpr auto | boost::hana::adjust
| Apply a function on all the elements of a structure that compare equal to some value. More...
constexpr auto | boost::hana::adjust_if

Apply a function on all the elements of a structure satisfying a predicate.Given a Functor, a predicate `pred` and a function `f`, `adjust_if` will adjust the elements of the Functor that satisfy the predicate with the function `f`. In other words, `adjust_if` will return a new Functor equal to the original one, except that the elements satisfying the predicate will be transformed with the given function. Elements for which the predicate is not satisfied are left untouched, and they are kept as-is in the resulting Functor. More...

constexpr auto | boost::hana::fill
| Replace all the elements of a structure with a fixed value. More...
constexpr auto | boost::hana::replace
| Replace all the elements of a structure that compare equal to some `value` with some new fixed value. More...
constexpr auto | boost::hana::replace_if
| Replace all the elements of a structure satisfying a `predicate` with a fixed value. More...
constexpr auto | boost::hana::transform
| Map a function over a `Functor`. More...

## Variable Documentation

constexpr auto boost::hana::adjust

`#include <boost/hana/fwd/adjust.hpp>`

Initial value:
= [](auto&& xs, auto&& value, auto&& f) {
return tag-dispatched;
}
boost::hana::value
constexpr auto value
Return the compile-time value associated to a constant.This function returns the value associated to ...
Definition: value.hpp:54

Apply a function on all the elements of a structure that compare equal to some value.

## Signature

Given `F` a Functor and `U` a type that can be compared with `T`'s, the signature is \( \mathtt{adjust} : F(T) \times U \times (T \to T) \to F(T) \)

Parameters

  xs | The structure to adjust with `f`.
  value | An object that is compared with each element `x` of the structure. Elements of the structure that compare equal to `value` are adjusted with the `f` function.
  f | A function called as `f(x)` on the element(s) of the structure that compare equal to `value`.

## Example

// Copyright Louis Dionne 2013-2016
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)
#include <boost/hana/adjust.hpp>
#include <boost/hana/assert.hpp>
#include <boost/hana/config.hpp>
#include <boost/hana/equal.hpp>
#include <boost/hana/tuple.hpp>
namespace hana = boost::hana;
BOOST_HANA_CONSTEXPR_LAMBDA auto negate = [](auto x) {
return -x;
};
int main() {
BOOST_HANA_CONSTEXPR_CHECK(
hana::adjust(hana::make_tuple(1, 4, 9, 2, 3, 4), 4, negate)
==
hana::make_tuple(1, -4, 9, 2, 3, -4)
);
}

constexpr auto boost::hana::adjust_if

`#include <boost/hana/fwd/adjust_if.hpp>`

Initial value:
= [](auto&& xs, auto const& pred, auto const& f) {
return tag-dispatched;
}

Apply a function on all the elements of a structure satisfying a predicate.Given a Functor, a predicate `pred` and a function `f`, `adjust_if` will adjust the elements of the Functor that satisfy the predicate with the function `f`. In other words, `adjust_if` will return a new Functor equal to the original one, except that the elements satisfying the predicate will be transformed with the given function. Elements for which the predicate is not satisfied are left untouched, and they are kept as-is in the resulting Functor.

## Signature

Given a `Functor` `F` and a `Logical` `Bool`, the signature is \( \mathtt{adjust_if} : F(T) \times (T \to Bool) \times (T \to T) \to F(T) \)

Parameters

  xs | The structure to adjust with `f`.
  pred | A function called as `pred(x)` for each element of the Functor, and returning whether `f` should be applied on that element.
  f | A function called as `f(x)` on the element(s) of the Functor that satisfy the predicate.

## Example

// Copyright Louis Dionne 2013-2016
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)
#include <boost/hana/adjust_if.hpp>
#include <boost/hana/assert.hpp>
#include <boost/hana/config.hpp>
#include <boost/hana/equal.hpp>
#include <boost/hana/tuple.hpp>
namespace hana = boost::hana;
BOOST_HANA_CONSTEXPR_LAMBDA auto negative = [](auto x) {
return x < 0;
};
BOOST_HANA_CONSTEXPR_LAMBDA auto negate = [](auto x) {
return -x;
};
int main() {
BOOST_HANA_CONSTEXPR_CHECK(
hana::adjust_if(hana::make_tuple(-3, -2, -1, 0, 1, 2, 3), negative, negate)
==
hana::make_tuple(3, 2, 1, 0, 1, 2, 3)
);
}

constexpr auto boost::hana::fill

`#include <boost/hana/fwd/fill.hpp>`

Initial value:
= [](auto&& xs, auto&& value) {
return tag-dispatched;
}
boost::hana::value
constexpr auto value
Return the compile-time value associated to a constant.This function returns the value associated to ...
Definition: value.hpp:54

Replace all the elements of a structure with a fixed value.

## Signature

Given `F` a Functor, the signature is \( \mathtt{fill} : F(T) \times U \to F(U) \)

Parameters

  xs | The structure to fill with a `value`.
  value | A value by which every element `x` of the structure is replaced, unconditionally.

## Example

// Copyright Louis Dionne 2013-2016
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)
#include <boost/hana/assert.hpp>
#include <boost/hana/equal.hpp>
#include <boost/hana/fill.hpp>
#include <boost/hana/optional.hpp>
#include <boost/hana/tuple.hpp>
namespace hana = boost::hana;
int main() {
static_assert(
hana::fill(hana::make_tuple(1, '2', 3.3, nullptr), 'x')
==
hana::make_tuple('x', 'x', 'x', 'x')
, "");
BOOST_HANA_CONSTANT_CHECK(hana::fill(hana::nothing, 'x') == hana::nothing);
static_assert(hana::fill(hana::just('y'), 'x') == hana::just('x'), "");
}

constexpr auto boost::hana::replace

`#include <boost/hana/fwd/replace.hpp>`

Initial value:
= [](auto&& xs, auto&& oldval, auto&& newval) {
return tag-dispatched;
}

Replace all the elements of a structure that compare equal to some `value` with some new fixed value.

## Signature

Given `F` a Functor and `U` a type that can be compared with `T`, the signature is \( \mathtt{replace} : F(T) \times U \times T \to F(T) \)

Parameters

  xs | The structure to replace elements of.
  oldval | An object compared with each element of the structure. Elements of the structure that compare equal to `oldval` are replaced by `newval` in the new structure.
  newval | A value by which every element `x` of the structure that compares equal to `oldval` is replaced.

## Example

// Copyright Louis Dionne 2013-2016
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)
#include <boost/hana/equal.hpp>
#include <boost/hana/replace.hpp>
#include <boost/hana/tuple.hpp>
namespace hana = boost::hana;
static_assert(
hana::replace(hana::make_tuple(1, 1, 1, 2, 3, 1, 4, 5), 1, 0)
==
hana::make_tuple(0, 0, 0, 2, 3, 0, 4, 5)
, "");
int main() { }

constexpr auto boost::hana::replace_if

`#include <boost/hana/fwd/replace_if.hpp>`

Initial value:
= [](auto&& xs, auto&& predicate, auto&& value) {
return tag-dispatched;
}
boost::hana::value
constexpr auto value
Return the compile-time value associated to a constant.This function returns the value associated to ...
Definition: value.hpp:54

Replace all the elements of a structure satisfying a `predicate` with a fixed value.

## Signature

Given `F` a Functor and `Bool` a Logical, the signature is \( \mathtt{replace_if} : F(T) \times (T \to Bool) \times T \to F(T) \)

Parameters

  xs | The structure to replace elements of.
  predicate | A function called as `predicate(x)` for element(s) `x` of the structure and returning a `Logical` representing whether `x` should be replaced by `value`.
  value | A value by which every element `x` of the structure for which `predicate` returns a true-valued `Logical` is replaced.

## Example

// Copyright Louis Dionne 2013-2016
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)
#include <boost/hana/assert.hpp>
#include <boost/hana/config.hpp>
#include <boost/hana/equal.hpp>
#include <boost/hana/replace_if.hpp>
#include <boost/hana/tuple.hpp>
namespace hana = boost::hana;
BOOST_HANA_CONSTEXPR_LAMBDA auto negative = [](auto x) {
return x < 0;
};
int main() {
BOOST_HANA_CONSTEXPR_CHECK(
hana::replace_if(hana::make_tuple(-3, -2, -1, 0, 1, 2, 3), negative, 0)
==
hana::make_tuple(0, 0, 0, 0, 1, 2, 3)
);
}

constexpr auto boost::hana::transform

`#include <boost/hana/fwd/transform.hpp>`

Initial value:
= [](auto&& xs, auto&& f) {
return tag-dispatched;
}

Map a function over a `Functor`.

## Signature

Given `F` a Functor, the signature is \( \mathtt{transform} : F(T) \times (T \to U) \to F(U) \)

Parameters

  xs | The structure to map `f` over.
  f | A function called as `f(x)` on element(s) `x` of the structure, and returning a new value to replace `x` in the structure.

## Example

// Copyright Louis Dionne 2013-2016
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)
#include <boost/hana/assert.hpp>
#include <boost/hana/equal.hpp>
#include <boost/hana/optional.hpp>
#include <boost/hana/transform.hpp>
#include <boost/hana/tuple.hpp>
#include <boost/hana/type.hpp>
#include <sstream>
#include <string>
#include <type_traits>
namespace hana = boost::hana;
using namespace std::literals;
auto to_string = [](auto x) {
std::ostringstream ss;
ss << x;
return ss.str();
};
int main() {
BOOST_HANA_RUNTIME_CHECK(
hana::transform(hana::make_tuple(1, '2', "345", std::string{"67"}), to_string)
==
hana::make_tuple("1", "2", "345", "67")
);
BOOST_HANA_CONSTANT_CHECK(hana::transform(hana::nothing, to_string) == hana::nothing);
BOOST_HANA_RUNTIME_CHECK(hana::transform(hana::just(123), to_string) == hana::just("123"s));
BOOST_HANA_CONSTANT_CHECK(
hana::transform(hana::tuple_t<void, int(), char[10]>, hana::template_<std::add_pointer_t>)
==
hana::tuple_t<void*, int(*)(), char(*)[10]>
);
}

## Benchmarks