Boost.Hana: Searchable

| Boost.Hana 1.0.0 Your standard library for metaprogramming |

Variables
Searchable
Concepts

## Description

The `Searchable` concept represents structures that can be searched.

Intuitively, a `Searchable` is any structure, finite or infinite, containing elements that can be searched using a predicate. Sometimes, `Searchable`s will associate keys to values; one can search for a key with a predicate, and the value associated to it is returned. This gives rise to map-like data structures. Other times, the elements of the structure that are searched (i.e. those to which the predicate is applied) are the same that are returned, which gives rise to set-like data structures. In general, we will refer to the keys of a `Searchable` structure as those elements that are used for searching, and to the values of a `Searchable` as those elements that are returned when a search is successful. As was explained, there is no requirement that both notions differ, and it is often useful to have keys and values coincide (think about `std::set`).

Some methods like `any_of`, `all_of` and `none_of` allow simple queries to be performed on the keys of the structure, while other methods like `find` and `find_if` make it possible to find the value associated to a key. The most specific method should always be used if one cares about performance, because it is usually the case that heavy optimizations can be performed in more specific methods. For example, an associative data structure implemented as a hash table will be much faster to access using `find` than `find_if`, because in the second case it will have to do a linear search through all the entries. Similarly, using `contains` will likely be much faster than `any_of` with an equivalent predicate.

> Insight
> In a lazy evaluation context, any `Foldable` can also become a model of `Searchable` because we can search lazily through the structure with `fold_right`. However, in the context of C++, some `Searchable`s can not be folded; think for example of an infinite set.

## Minimal complete definition

`find_if` and `any_of`

When `find_if` and `any_of` are provided, the other functions are implemented according to the laws explained below.

Note
  We could implement `any_of(xs, pred)` by checking whether `find_if(xs, pred)` is an empty `optional` or not, and then reduce the minimal complete definition to `find_if`. However, this is not done because that implementation requires the predicate of `any_of` to return a compile-time `Logical`, which is more restrictive than what we have right now.

## Laws

In order for the semantics of the methods to be consistent, some properties must be satisfied by any model of the `Searchable` concept. Rigorously, for any `Searchable`s `xs` and `ys` and any predicate `p`, the following laws should be satisfied:

any_of(xs, p) <=> !all_of(xs, negated p)
<=> !none_of(xs, p)
contains(xs, x) <=> any_of(xs, equal.to(x))
find(xs, x) == find_if(xs, equal.to(x))
find_if(xs, always(false_)) == nothing
is_subset(xs, ys) <=> all_of(xs, [](auto x) { return contains(ys, x); })
is_disjoint(xs, ys) <=> none_of(xs, [](auto x) { return contains(ys, x); })

Additionally, if all the keys of the `Searchable` are `Logical`s, the following laws should be satisfied:

any(xs) <=> any_of(xs, id)
all(xs) <=> all_of(xs, id)
none(xs) <=> none_of(xs, id)

## Concrete models

`hana::map`, `hana::optional`, `hana::range`, `hana::set`, `hana::string`, `hana::tuple`

## Free model for builtin arrays

Builtin arrays whose size is known can be searched as-if they were homogeneous tuples. However, since arrays can only hold objects of a single type and the predicate to `find_if` must return a compile-time `Logical`, the `find_if` method is fairly useless. For similar reasons, the `find` method is also fairly useless. This model is provided mainly because of the `any_of` method & friends, which are both useful and compile-time efficient.

## Structure preserving functions

Given two `Searchables` `S1` and `S2`, a function \( f : S_1(X) \to S_2(X) \) is said to preserve the `Searchable` structure if for all `xs` of data type `S1(X)` and predicates \( \mathtt{pred} : X \to Bool \) (for a `Logical` `Bool`),

any_of(xs, pred) if and only if any_of(f(xs), pred)
find_if(xs, pred) == find_if(f(xs), pred)

This is really just a generalization of the following, more intuitive requirements. For all `xs` of data type `S1(X)` and `x` of data type `X`,

x ^in^ xs if and only if x ^in^ f(xs)
find(xs, x) == find(f(xs), x)

These requirements can be understood as saying that `f` does not change the content of `xs`, although it may reorder elements. As usual, such a structure-preserving transformation is said to be an embedding if it is also injective, i.e. if it is a lossless transformation.

## Variables

constexpr auto | boost::hana::all
| Returns whether all the keys of the structure are true-valued.The keys of the structure must be `Logical`s. If the structure is not finite, a false-valued key must appear at a finite "index" in order for this method to finish. More...
constexpr auto | boost::hana::all_of
| Returns whether all the keys of the structure satisfy the `predicate`.If the structure is not finite, `predicate` has to return a false- valued `Logical` after looking at a finite number of keys for this method to finish. More...
constexpr auto | boost::hana::any
| Returns whether any key of the structure is true-valued.The keys of the structure must be `Logical`s. If the structure is not finite, a true-valued key must appear at a finite "index" in order for this method to finish. More...
constexpr auto | boost::hana::any_of
| Returns whether any key of the structure satisfies the `predicate`.If the structure is not finite, `predicate` has to be satisfied after looking at a finite number of keys for this method to finish. More...
constexpr auto | boost::hana::at_key

Returns the value associated to the given key in a structure, or fail.Given a `key` and a `Searchable` structure, `at_key` returns the first value whose key is equal to the given `key`, and fails at compile-time if no such key exists. This requires the `key` to be compile-time `Comparable`, exactly like for `find`. `at_key` satisfies the following: More...

constexpr auto | boost::hana::contains

Returns whether the key occurs in the structure.Given a `Searchable` structure `xs` and a `key`, `contains` returns whether any of the keys of the structure is equal to the given `key`. If the structure is not finite, an equal key has to appear at a finite position in the structure for this method to finish. For convenience, `contains` can also be applied in infix notation. More...

constexpr auto | boost::hana::in = hana::infix(hana::flip(hana::contains))

Return whether the key occurs in the structure.Specifically, this is equivalent to `contains`, except `in` takes its arguments in reverse order. Like `contains`, `in` can also be applied in infix notation for increased expressiveness. This function is not a method that can be overriden; it is just a convenience function provided with the concept. More...

constexpr auto | boost::hana::find

Finds the value associated to the given key in a structure.Given a `key` and a `Searchable` structure, `find` returns the `just` the first value whose key is equal to the given `key`, or `nothing` if there is no such key. Comparison is done with `equal`. `find` satisfies the following: More...

constexpr auto | boost::hana::find_if

Finds the value associated to the first key satisfying a predicate.Given a `Searchable` structure `xs` and a predicate `pred`, `find_if(xs, pred)` returns `just` the first element whose key satisfies the predicate, or `nothing` if there is no such element. More...

constexpr auto | boost::hana::is_disjoint

Returns whether two `Searchable`s are disjoint.Given two `Searchable`s `xs` and `ys`, `is_disjoint` returns a `Logical` representing whether the keys in `xs` are disjoint from the keys in `ys`, i.e. whether both structures have no keys in common. More...

constexpr auto | boost::hana::is_subset

Returns whether a structure contains a subset of the keys of another structure.Given two `Searchable`s `xs` and `ys`, `is_subset` returns a `Logical` representing whether `xs` is a subset of `ys`. In other words, it returns whether all the keys of `xs` are also present in `ys`. This method does not return whether `xs` is a strict subset of `ys`; if `xs` and `ys` are equal, all the keys of `xs` are also present in `ys`, and `is_subset` returns true. More...

constexpr auto | boost::hana::none
| Returns whether all of the keys of the structure are false-valued.The keys of the structure must be `Logical`s. If the structure is not finite, a true-valued key must appear at a finite "index" in order for this method to finish. More...
constexpr auto | boost::hana::none_of
| Returns whether none of the keys of the structure satisfy the `predicate`.If the structure is not finite, `predicate` has to return a true- valued `Logical` after looking at a finite number of keys for this method to finish. More...

## Variable Documentation

constexpr auto boost::hana::all

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

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

Returns whether all the keys of the structure are true-valued.The keys of the structure must be `Logical`s. If the structure is not finite, a false-valued key must appear at a finite "index" in order for this method to finish.

## 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/all.hpp>
#include <boost/hana/assert.hpp>
#include <boost/hana/bool.hpp>
#include <boost/hana/not.hpp>
#include <boost/hana/tuple.hpp>
namespace hana = boost::hana;
static_assert(hana::all(hana::make_tuple(hana::true_c, true, hana::true_c)), "");
BOOST_HANA_CONSTANT_CHECK(!hana::all(hana::make_tuple(true, hana::false_c, hana::true_c)));
int main() { }

constexpr auto boost::hana::all_of

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

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

Returns whether all the keys of the structure satisfy the `predicate`.If the structure is not finite, `predicate` has to return a false- valued `Logical` after looking at a finite number of keys for this method to finish.

Parameters

  xs | The structure to search.
  predicate | A function called as `predicate(k)`, where `k` is a key of the structure, and returning a `Logical`.

## 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/all_of.hpp>
#include <boost/hana/assert.hpp>
#include <boost/hana/config.hpp>
#include <boost/hana/ext/std/integral_constant.hpp>
#include <boost/hana/integral_constant.hpp>
#include <boost/hana/mod.hpp>
#include <boost/hana/not.hpp>
#include <boost/hana/not_equal.hpp>
#include <boost/hana/tuple.hpp>
#include <boost/hana/type.hpp>
#include <type_traits>
namespace hana = boost::hana;
using namespace hana::literals;
BOOST_HANA_CONSTEXPR_LAMBDA auto is_odd = [](auto x) {
return x % 2_c != 0_c;
};
int main() {
BOOST_HANA_CONSTEXPR_CHECK(hana::all_of(hana::make_tuple(1, 3), is_odd));
BOOST_HANA_CONSTANT_CHECK(!hana::all_of(hana::make_tuple(3_c, 4_c), is_odd));
BOOST_HANA_CONSTANT_CHECK(!hana::all_of(
hana::make_tuple(hana::type_c<void>, hana::type_c<char&>), hana::trait<std::is_void>
));
BOOST_HANA_CONSTANT_CHECK(hana::all_of(
hana::make_tuple(hana::type_c<int>, hana::type_c<char>), hana::trait<std::is_integral>
));
}

constexpr auto boost::hana::any

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

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

Returns whether any key of the structure is true-valued.The keys of the structure must be `Logical`s. If the structure is not finite, a true-valued key must appear at a finite "index" in order for this method to finish.

## 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/any.hpp>
#include <boost/hana/assert.hpp>
#include <boost/hana/bool.hpp>
#include <boost/hana/tuple.hpp>
namespace hana = boost::hana;
BOOST_HANA_CONSTANT_CHECK(hana::any(hana::make_tuple(false, hana::false_c, hana::true_c)));
static_assert(hana::any(hana::make_tuple(false, hana::false_c, true)), "");
static_assert(!hana::any(hana::make_tuple(false, hana::false_c, hana::false_c)), "");
int main() { }

constexpr auto boost::hana::any_of

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

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

Returns whether any key of the structure satisfies the `predicate`.If the structure is not finite, `predicate` has to be satisfied after looking at a finite number of keys for this method to finish.

Parameters

  xs | The structure to search.
  predicate | A function called as `predicate(k)`, where `k` is a key of the structure, and returning a `Logical`.

## 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/any_of.hpp>
#include <boost/hana/assert.hpp>
#include <boost/hana/config.hpp>
#include <boost/hana/ext/std/integral_constant.hpp>
#include <boost/hana/integral_constant.hpp>
#include <boost/hana/mod.hpp>
#include <boost/hana/not.hpp>
#include <boost/hana/not_equal.hpp>
#include <boost/hana/tuple.hpp>
#include <boost/hana/type.hpp>
#include <type_traits>
namespace hana = boost::hana;
using namespace hana::literals;
BOOST_HANA_CONSTEXPR_LAMBDA auto is_odd = [](auto x) {
return x % 2_c != 0_c;
};
int main() {
BOOST_HANA_CONSTEXPR_CHECK(hana::any_of(hana::make_tuple(1, 2), is_odd));
BOOST_HANA_CONSTANT_CHECK(!hana::any_of(hana::make_tuple(2_c, 4_c), is_odd));
BOOST_HANA_CONSTANT_CHECK(hana::any_of(
hana::make_tuple(hana::type_c<void>, hana::type_c<char&>), hana::trait<std::is_void>
));
BOOST_HANA_CONSTANT_CHECK(!hana::any_of(
hana::make_tuple(hana::type_c<void>, hana::type_c<char&>), hana::trait<std::is_integral>
));
}

constexpr auto boost::hana::at_key

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

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

Returns the value associated to the given key in a structure, or fail.Given a `key` and a `Searchable` structure, `at_key` returns the first value whose key is equal to the given `key`, and fails at compile-time if no such key exists. This requires the `key` to be compile-time `Comparable`, exactly like for `find`. `at_key` satisfies the following:

at_key(xs, key) == find(xs, key).value()

If the `Searchable` actually stores the elements it contains, `at_key` is required to return a lvalue reference, a lvalue reference to const or a rvalue reference to the found value, where the type of reference must match that of the structure passed to `at_key`. If the `Searchable` does not store the elements it contains (i.e. it generates them on demand), this requirement is dropped.

Parameters

  xs | The structure to be searched.
  key | A key to be searched for in the structure. The key has to be `Comparable` with the other keys of the structure. In the current version of the library, the comparison of `key` with any other key of the structure must return a compile-time `Logical`.

## 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/at_key.hpp>
#include <boost/hana/integral_constant.hpp>
#include <boost/hana/map.hpp>
#include <boost/hana/pair.hpp>
#include <boost/hana/type.hpp>
#include <string>
namespace hana = boost::hana;
int main() {
auto m = hana::make_map(
hana::make_pair(hana::type_c<int>, std::string{"int"}),
hana::make_pair(hana::int_c<3>, std::string{"3"})
);
BOOST_HANA_RUNTIME_CHECK(hana::at_key(m, hana::type_c<int>) == "int");
// usage as operator[]
BOOST_HANA_RUNTIME_CHECK(m[hana::type_c<int>] == "int");
BOOST_HANA_RUNTIME_CHECK(m[hana::int_c<3>] == "3");
}

## Benchmarks

constexpr auto boost::hana::contains

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

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

Returns whether the key occurs in the structure.Given a `Searchable` structure `xs` and a `key`, `contains` returns whether any of the keys of the structure is equal to the given `key`. If the structure is not finite, an equal key has to appear at a finite position in the structure for this method to finish. For convenience, `contains` can also be applied in infix notation.

Parameters

  xs | The structure to search.
  key | A key to be searched for in the structure. The key has to be `Comparable` with the other keys of 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/contains.hpp>
#include <boost/hana/integral_constant.hpp>
#include <boost/hana/set.hpp>
#include <boost/hana/tuple.hpp>
#include <boost/hana/type.hpp>
namespace hana = boost::hana;
BOOST_HANA_CONSTANT_CHECK(hana::contains(hana::make_tuple(2, hana::int_c<2>, hana::int_c<3>, 'x'), hana::int_c<3>));
BOOST_HANA_CONSTANT_CHECK(hana::contains(hana::make_set(hana::int_c<3>, hana::type_c<void>), hana::type_c<void>));
// contains can be applied in infix notation
BOOST_HANA_CONSTANT_CHECK(
hana::make_tuple(2, hana::int_c<2>, hana::int_c<3>, 'x') ^hana::contains^ hana::int_c<2>
);
int main() { }

constexpr auto boost::hana::in = hana::infix(hana::flip(hana::contains))

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

Return whether the key occurs in the structure.Specifically, this is equivalent to `contains`, except `in` takes its arguments in reverse order. Like `contains`, `in` can also be applied in infix notation for increased expressiveness. This function is not a method that can be overriden; it is just a convenience function provided with the concept.

## 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/contains.hpp>
#include <boost/hana/integral_constant.hpp>
#include <boost/hana/tuple.hpp>
namespace hana = boost::hana;
BOOST_HANA_CONSTANT_CHECK(hana::int_c<2> ^hana::in^ hana::make_tuple(2, hana::int_c<2>, hana::int_c<3>, 'x'));
int main() { }

constexpr auto boost::hana::find

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

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

Finds the value associated to the given key in a structure.Given a `key` and a `Searchable` structure, `find` returns the `just` the first value whose key is equal to the given `key`, or `nothing` if there is no such key. Comparison is done with `equal`. `find` satisfies the following:

find(xs, key) == find_if(xs, equal.to(key))

Parameters

  xs | The structure to be searched.
  key | A key to be searched for in the structure. The key has to be `Comparable` with the other keys of the structure. In the current version of the library, the comparison of `key` with any other key of the structure must return a compile-time `Logical`.

## 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/find.hpp>
#include <boost/hana/integral_constant.hpp>
#include <boost/hana/map.hpp>
#include <boost/hana/optional.hpp>
#include <boost/hana/pair.hpp>
#include <boost/hana/tuple.hpp>
#include <boost/hana/type.hpp>
namespace hana = boost::hana;
BOOST_HANA_CONSTANT_CHECK(
hana::find(hana::make_tuple(hana::int_c<1>, hana::type_c<int>, '3'), hana::type_c<int>) == hana::just(hana::type_c<int>)
);
BOOST_HANA_CONSTANT_CHECK(
hana::find(hana::make_tuple(hana::int_c<1>, hana::type_c<int>, '3'), hana::type_c<void>) == hana::nothing
);
constexpr auto m = hana::make_map(
hana::make_pair(hana::int_c<2>, 2),
hana::make_pair(hana::type_c<float>, 3.3),
hana::make_pair(hana::type_c<char>, hana::type_c<int>)
);
static_assert(hana::find(m, hana::type_c<float>) == hana::just(3.3), "");
int main() { }

constexpr auto boost::hana::find_if

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

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

Finds the value associated to the first key satisfying a predicate.Given a `Searchable` structure `xs` and a predicate `pred`, `find_if(xs, pred)` returns `just` the first element whose key satisfies the predicate, or `nothing` if there is no such element.

Parameters

  xs | The structure to be searched.
  predicate | A function called as `predicate(k)`, where `k` is a key of the structure, and returning whether `k` is the key of the element being searched for. In the current version of the library, the predicate has to return an `IntegralConstant` holding a value that can be converted to `bool`.

## 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/ext/std/integral_constant.hpp>
#include <boost/hana/find_if.hpp>
#include <boost/hana/functional/compose.hpp>
#include <boost/hana/optional.hpp>
#include <boost/hana/tuple.hpp>
#include <boost/hana/type.hpp>
#include <type_traits>
namespace hana = boost::hana;
// First get the type of the object, and then call the trait on it.
constexpr auto is_integral = hana::compose(hana::trait<std::is_integral>, hana::decltype_);
constexpr auto is_class = hana::compose(hana::trait<std::is_class>, hana::decltype_);
static_assert(
hana::find_if(hana::make_tuple(1.0, 2, '3'), is_integral) == hana::just(2)
, "");
BOOST_HANA_CONSTANT_CHECK(
hana::find_if(hana::make_tuple(1.0, 2, '3'), is_class) == hana::nothing
);
constexpr auto types = hana::tuple_t<char, int, unsigned, long, unsigned long>;
BOOST_HANA_CONSTANT_CHECK(
hana::find_if(types, hana::equal.to(hana::type_c<unsigned>)) == hana::just(hana::type_c<unsigned>)
);
BOOST_HANA_CONSTANT_CHECK(
hana::find_if(types, hana::equal.to(hana::type_c<void>)) == hana::nothing
);
int main() { }

## Benchmarks

constexpr auto boost::hana::is_disjoint

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

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

Returns whether two `Searchable`s are disjoint.Given two `Searchable`s `xs` and `ys`, `is_disjoint` returns a `Logical` representing whether the keys in `xs` are disjoint from the keys in `ys`, i.e. whether both structures have no keys in common.

Parameters

  xs,ys | Two `Searchable`s to test for disjointness.

## 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/is_disjoint.hpp>
#include <boost/hana/map.hpp>
#include <boost/hana/not.hpp>
#include <boost/hana/set.hpp>
#include <boost/hana/tuple.hpp>
#include <boost/hana/type.hpp>
#include <string>
namespace hana = boost::hana;
using namespace std::literals;
int main() {
// Tuples
auto xs = hana::make_tuple(hana::int_c<1>, "alfa"s, hana::type_c<int>);
auto ys = hana::make_tuple(hana::type_c<void>, hana::int_c<3>, "bravo"s);
BOOST_HANA_RUNTIME_CHECK(hana::is_disjoint(xs, ys));
// Sets
auto s1 = hana::make_set(hana::int_c<1>, hana::type_c<void>, hana::int_c<2>);
auto s2 = hana::make_set(hana::type_c<char>, hana::type_c<int>, hana::int_c<1>);
BOOST_HANA_CONSTANT_CHECK(!hana::is_disjoint(s1, s2));
// Maps
auto vowels = hana::make_map(
hana::make_pair(hana::char_c<'a'>, "alfa"s),
hana::make_pair(hana::char_c<'e'>, "echo"s),
hana::make_pair(hana::char_c<'i'>, "india"s)
// ...
);
auto consonants = hana::make_map(
hana::make_pair(hana::char_c<'b'>, "bravo"s),
hana::make_pair(hana::char_c<'c'>, "charlie"s),
hana::make_pair(hana::char_c<'f'>, "foxtrot"s)
// ...
);
BOOST_HANA_CONSTANT_CHECK(hana::is_disjoint(vowels, consonants));
}

## Benchmarks

constexpr auto boost::hana::is_subset

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

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

Returns whether a structure contains a subset of the keys of another structure.Given two `Searchable`s `xs` and `ys`, `is_subset` returns a `Logical` representing whether `xs` is a subset of `ys`. In other words, it returns whether all the keys of `xs` are also present in `ys`. This method does not return whether `xs` is a strict subset of `ys`; if `xs` and `ys` are equal, all the keys of `xs` are also present in `ys`, and `is_subset` returns true.

Note
  For convenience, `is_subset` can also be applied in infix notation.

## Cross-type version of the method

This method is tag-dispatched using the tags of both arguments. It can be called with any two `Searchable`s sharing a common `Searchable` embedding, as defined in the main documentation of the `Searchable` concept. When `Searchable`s with two different tags but sharing a common embedding are sent to `is_subset`, they are first converted to this common `Searchable` and the `is_subset` method of the common embedding is then used. Of course, the method can be overriden for custom `Searchable`s for efficieny.

Note
  While cross-type dispatching for `is_subset` is supported, it is not currently used by the library because there are no models of `Searchable` with a common embedding.

Parameters

  xs | The structure to check whether it is a subset of `ys`.
  ys | The structure to check whether it is a superset of `xs`.

## 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/is_subset.hpp>
#include <boost/hana/tuple.hpp>
namespace hana = boost::hana;
static_assert(
hana::is_subset(hana::make_tuple(1, '2', 3.3), hana::make_tuple(3.3, 1, '2', nullptr))
, "");
// is_subset can be applied in infix notation
static_assert(
hana::make_tuple(1, '2', 3.3) ^hana::is_subset^ hana::make_tuple(3.3, 1, '2', nullptr)
, "");
int main() { }

## Benchmarks

constexpr auto boost::hana::none

`#include <boost/hana/fwd/none.hpp>`

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

Returns whether all of the keys of the structure are false-valued.The keys of the structure must be `Logical`s. If the structure is not finite, a true-valued key must appear at a finite "index" in order for this method to finish.

## 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/bool.hpp>
#include <boost/hana/none.hpp>
#include <boost/hana/not.hpp>
#include <boost/hana/tuple.hpp>
namespace hana = boost::hana;
static_assert(hana::none(hana::make_tuple(false, hana::false_c, hana::false_c)), "");
static_assert(!hana::none(hana::make_tuple(false, hana::false_c, true)), "");
BOOST_HANA_CONSTANT_CHECK(!hana::none(hana::make_tuple(false, hana::false_c, hana::true_c)));
int main() { }

constexpr auto boost::hana::none_of

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

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

Returns whether none of the keys of the structure satisfy the `predicate`.If the structure is not finite, `predicate` has to return a true- valued `Logical` after looking at a finite number of keys for this method to finish.

Parameters

  xs | The structure to search.
  predicate | A function called as `predicate(k)`, where `k` is a key of the structure, and returning a `Logical`.

## 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/ext/std/integral_constant.hpp>
#include <boost/hana/integral_constant.hpp>
#include <boost/hana/mod.hpp>
#include <boost/hana/none_of.hpp>
#include <boost/hana/not.hpp>
#include <boost/hana/not_equal.hpp>
#include <boost/hana/tuple.hpp>
#include <boost/hana/type.hpp>
#include <type_traits>
namespace hana = boost::hana;
using namespace hana::literals;
BOOST_HANA_CONSTEXPR_LAMBDA auto is_odd = [](auto x) {
return x % 2_c != 0_c;
};
int main() {
BOOST_HANA_CONSTANT_CHECK(hana::none_of(hana::make_tuple(2_c, 4_c), is_odd));
BOOST_HANA_CONSTEXPR_CHECK(!hana::none_of(hana::make_tuple(1, 2), is_odd));
BOOST_HANA_CONSTANT_CHECK(
!hana::none_of(hana::make_tuple(hana::type_c<void>, hana::type_c<char&>), hana::trait<std::is_void>)
);
BOOST_HANA_CONSTANT_CHECK(
hana::none_of(hana::make_tuple(hana::type_c<void>, hana::type_c<char&>), hana::trait<std::is_integral>)
);
}