boost_1_45_0/libs/fusion/doc/algorithm.qbk

[/==============================================================================
    Copyright (C) 2001-2007 Joel de Guzman, Dan Marsden, Tobias Schwinger
    Copyright (C) 2010 Christopher Schmidt

    Use, modification and distribution is subject to the Boost Software
    License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
    http://www.boost.org/LICENSE_1_0.txt)
===============================================================================/]
[section Algorithm]

[heading Lazy Evaluation]

Unlike __mpl__, Fusion algorithms are lazy and non sequence-type
preserving. What does that mean? It means that when you operate on a
sequence through a Fusion algorithm that returns a sequence, the sequence
returned may not be of the same class as the original. This is by design.
Runtime efficiency is given a high priority. Like __mpl__, and unlike
__stl__, fusion algorithms are functional in nature such that algorithms
are non mutating (no side effects). However, due to the high cost of
returning full sequences such as vectors and lists, /Views/ are returned
from Fusion algorithms instead. For example, the __transform__ algorithm
does not actually return a transformed version of the original sequence.
__transform__ returns a __transform_view__. This view holds a reference to
the original sequence plus the transform function. Iteration over the
__transform_view__ will apply the transform function over the sequence
elements on demand. This /lazy/ evaluation scheme allows us to chain as
many algorithms as we want without incurring a high runtime penalty.

[heading Sequence Extension]

The /lazy/ evaluation scheme where __algorithms__ return __views__ also
allows operations such as __push_back__ to be totally generic. In Fusion,
__push_back__ is actually a generic algorithm that works on all sequences.
Given an input sequence `s` and a value `x`, Fusion's __push_back__
algorithm simply returns a __joint_view__: a view that holds a reference to
the original sequence `s` and the value `x`. Functions that were once
sequence specific and need to be implemented N times over N different
sequences are now implemented only once. That is to say that Fusion
sequences are cheaply extensible.
To regain the original sequence, __conversion__ functions are provided. You
may use one of the __conversion__ functions to convert back to the original
sequence type.

[heading Header]

    #include <boost/fusion/algorithm.hpp>
    #include <boost/fusion/include/algorithm.hpp>

[section Iteration]

The iteration algorithms provide the fundamental algorithms for traversing
a sequence repeatedly applying an operation to its elements.

[heading Header]

    #include <boost/fusion/algorithm/iteration.hpp>
    #include <boost/fusion/include/iteration.hpp>

[section Functions]

[template fold_desc[name result_of_name arg_desc seq_concept arg_id arg_type_id invoke_desc semantics_elements_desc example_arg_transform example_result I0 I1 IN]
[heading Description]
For a sequence `seq`, initial state `initial_state`, and binary function object
or function pointer `f`, [^[name]] returns the result of the repeated application of
binary `f` to the result of the previous `f` invocation (`inital_state` if it is
the first call) and [arg_desc] of `seq`.

[def name_macro [name]]
[def result_of_name_macro [result_of_name]]
[heading Synopsis]
    template<
        typename Sequence,
        typename State,
        typename F
        >
    typename result_of_name_macro<Sequence, State const, F>::type name_macro(
        Sequence& seq, State const& initial_state, F f);
        
    template<
        typename Sequence,
        typename State,
        typename F
        >
    typename result_of_name_macro<Sequence const, State const, F>::type name_macro(
        Sequence const& seq, State const& initial_state, F f);

[def seq_concept_macro [seq_concept]]
[def arg_type_id_macro [arg_type_id]]
[def arg_id_macro [arg_id]]
[def invoke_desc_macro [invoke_desc]]
[table Parameters
    [[Parameter][Requirement][Description]]
    [[`seq`][A model of seq_concept_macro][Operation's argument]]
    [[`initial_state`][Any type][Initial state]]
    [[`f`][`f(s,arg_id_macro)` with return type `__boost_result_of_call__<F(S,arg_type_id_macro)>::type` for current state `s` of type `S`, and for each invoke_desc_macro][Operation's argument]]
]

[heading Expression Semantics]
    name_macro(seq, initial_state, f);

[*Return type]: Any type

[*Semantics]: Equivalent to [^f(... f(f(initial_state,[arg_id][I0]),[arg_id][I1]) ...[arg_id][IN])] where [^[arg_id]1 ...[arg_id]N] are [semantics_elements_desc].

[heading Complexity]
Linear, exactly `__result_of_size__<Sequence>::value` applications of `f`.

[heading Header]

    #include <boost/fusion/algorithm/iteration/name_macro.hpp>
    #include <boost/fusion/include/name_macro.hpp>

[def example_result_macro [example_result]]
[def example_arg_transform_macro [example_arg_transform]]
[heading Example]
    struct make_string
    {
        typedef std::string result_type;

        template<typename T>
        std::string operator()(const std::string& str, const T& t) const
        {
            return str + boost::lexical_cast<std::string>(example_arg_transform_macro);
        }
    };
    ...
    const __vector__<int,int> vec(1,2);
    assert(name_macro(vec,std::string(""), make_string()) == example_result_macro);
]

[section fold]
[fold_desc fold..__result_of_fold__..each element..__forward_sequence__..e..E..element `e` of type `E` in `seq`..the consecutive elements of `seq`..t.."12"..1..2..N]
[endsect]

[section reverse_fold]
[fold_desc reverse_fold..__result_of_reverse_fold__..each element..__bidirectional_sequence__..e..E..element `e` of type `E` in `seq`..the consecutive elements of `seq`..t.."21"..N..N-1..1]
[endsect]

[section iter_fold]
[fold_desc iter_fold..__result_of_iter_fold__..iterators on each element..__forward_sequence__..it..It..iterator `it` of type `It` on an element of `seq`..consecutive iterators on the elements of `seq`..__deref__(t).."12"..1..2..N]
[endsect]

[section reverse_iter_fold]
[fold_desc reverse_iter_fold..__result_of_reverse_iter_fold__..iterators on each element..__bidirectional_sequence__..it..It..iterator `it` of type `It` on an element of `seq`..consecutive iterators on the elements of `seq`..__deref__(t).."21"..N..N-1..1]
[endsect]

[section accumulate]
[fold_desc accumulate..__result_of_accumulate__..each element..__forward_sequence__..e..E..element `e` of type `E` in `seq`..the consecutive elements of `seq`..t.."12"..1..2..N]
[endsect]

[section for_each]

[heading Description]
Applies a unary function object to each element of a sequence.

[heading Synopsis]
    template<
        typename Sequence,
        typename F
        >
    typename __result_of_for_each__<Sequence, F>::type for_each(
        Sequence& seq, F f);

[table Parameters
    [[Parameter][Requirement][Description]]
    [[`seq`][A model of __forward_sequence__, `f(e)` must be a valid expression for each element `e` in `seq`][Operation's argument]]
    [[`f`][A unary __reg_callable_obj__][Operation's argument]]
]

[heading Expression Semantics]
    __for_each__(seq, f);

[*Return type]: `void`

[*Semantics]: Calls `f(e)` for each element `e` in `seq`.

[heading Complexity]
Linear, exactly `__result_of_size__<Sequence>::value` applications of `f`.

[heading Header]

    #include <boost/fusion/algorithm/iteration/for_each.hpp>
    #include <boost/fusion/include/for_each.hpp>

[heading Example]
    struct increment
    {
        template<typename T>
        void operator()(T& t) const
        {
            ++t;
        }
    };
    ...
    __vector__<int,int> vec(1,2);
    __for_each__(vec, increment());
    assert(vec == __make_vector__(2,3));

[endsect]

[endsect]

[section Metafunctions]

[template meta_fold_desc[name name_func seq_concept arg_id arg_type_id invoke_meta_desc]
[heading Description]
Returns the result type of [name_func].

[def name_macro [name]]
[heading Synopsis]
    template<
        typename Sequence,
        typename State,
        typename F>
    struct name_macro
    {
        typedef __unspecified__ type;
    };

[def seq_concept_macro [seq_concept]]
[def arg_type_id_macro [arg_type_id]]
[def arg_id_macro [arg_id]]
[def invoke_meta_desc_macro [invoke_meta_desc]]
[table Parameters
    [[Parameter]  [Requirement] [Description]]
    [[`Sequence`] [A model of seq_concept_macro]    [The sequence to iterate]]
    [[`State`]    [Any type]                        [The initial state for the first application of `F`]]
    [[`F`]        [`__boost_result_of_call__<F(S,arg_type_id_macro)>::type` is the return type of `f(s,arg_id_macro)` with current state `s` of type `S`, and an invoke_meta_desc_macro][The operation to be applied on traversal]]
]

[heading Expression Semantics]
    name_macro<Sequence, State, F>::type

[*Return type]: Any type

[*Semantics]: Returns the result of applying [name_func] to a sequence of type
`Sequence`, with an initial state of type `State` and binary function object or
function pointer of type `F`.

[heading Complexity]
Linear, exactly `__result_of_size__<Sequence>::value` applications of `F`.

[heading Header]

    #include <boost/fusion/algorithm/iteration/name_macro.hpp>
    #include <boost/fusion/include/name_macro.hpp>
]

[section fold]
[meta_fold_desc fold..__fold__..__forward_sequence__..e..E..element `e` of type `E` in `seq`]
[endsect]

[section reverse_fold]
[meta_fold_desc reverse_fold..__reverse_fold__..__bidirectional_sequence__..e..E..element `e` of type `E` in `seq`]
[endsect]

[section iter_fold]
[meta_fold_desc iter_fold..__iter_fold__..__forward_sequence__..it..It..iterator `it` of type `It` on an element of `seq`]
[endsect]

[section reverse_iter_fold]
[meta_fold_desc reverse_iter_fold..__reverse_iter_fold__..__bidirectional_sequence__..it..It..iterator `it` of type `It` on an element of `seq`]
[endsect]

[section accumulate]
[meta_fold_desc accumulate..__accumulate__..__forward_sequence__..e..E..element `e` of type `E` in `seq`]
[endsect]

[section for_each]
A metafunction returning the result type of applying __for_each__ to a sequence. The
return type of __for_each__ is always `void`.

[heading Description]

[heading Synopsis]
    template<
        typename Sequence,
        typename F
    >
    struct for_each
    {
        typedef void type;
    };

[table Parameters
    [[Parameter] [Requirement] [Description]]
    [[`Sequence`] [A model of __forward_sequence__] [Operation's argument]]
    [[`F`]    [Any type] [Operation's argument]]
]

[heading Expression Semantics]
    __result_of_for_each__<Sequence, F>::type

[*Return type]: `void`.

[*Semantics]: Returns the return type of __for_each__ for a sequence of type `Sequence` and a unary function object `F`.
The return type is always `void`.

[heading Complexity]
Constant.

[heading Header]

    #include <boost/fusion/algorithm/iteration/for_each.hpp>
    #include <boost/fusion/include/for_each.hpp>

[endsect]

[endsect]

[endsect]

[section Query]
The query algorithms provide support for searching and analyzing sequences.

[heading Header]

    #include <boost/fusion/algorithm/query.hpp>
    #include <boost/fusion/include/query.hpp>

[section Functions]

[section any]

[heading Description]
For a sequence `seq` and unary function object `f`, `any` returns true if `f` returns true for at least one element of `seq`.

[heading Synopsis]
    template<
        typename Sequence,
        typename F
        >
    typename __result_of_any__<Sequence,F>::type any(
        Sequence const& seq, F f);

[table Parameters
    [[Parameter][Requirement][Description]]
    [[`seq`][A model of __forward_sequence__, `f(e)` must be a valid expression, convertible to `bool`, for each element `e` in `seq`][The sequence to search]]
    [[`f`][A unary function object][The search predicate]]
]

[heading Expression semantics]
    __any__(seq, f);

[*Return type]: `bool`

[*Semantics]: Returns true if and only if `f(e)` evaluates to `true` for some element `e` in `seq`.

[heading Complexity]
Linear. At most `__result_of_size__<Sequence>::value` comparisons.

[heading Header]

    #include <boost/fusion/algorithm/query/any.hpp>
    #include <boost/fusion/include/any.hpp>

[heading Example]
    struct odd
    {
        template<typename T>
        bool operator()(T t) const
        {
            return t % 2;
        }
    };
    ...
    assert(__any__(__make_vector__(1,2), odd()));
    assert(!__any__(__make_vector__(2,4), odd()));

[endsect]

[section all]

[heading Description]
For a sequence `seq` and unary function object `f`, `all` returns true if `f` returns true for every element of `seq`.

[heading Synopsis]
    template<
        typename Sequence,
        typename F
        >
    typename __result_of_all__<Sequence,F>::type all(
        Sequence const& seq, F f);

[table Parameters
    [[Parameter][Requirement][Description]]
    [[`seq`][A model of __forward_sequence__, `f(e)` is a valid expression, convertible to `bool`, for every element `e` in `seq`][The sequence to search]]
    [[`f`][A unary function object][The search predicate]]
]

[heading Expression Semantics]
    __all__(seq, f);

[*Return type]: `bool`

[*Semantics]: Returns true if and only if `f(e)` evaluates to `true` for every element `e` in `seq`.

[heading Complexity]
Linear. At most `__result_of_size__<Sequence>::value` comparisons.

[heading Header]

    #include <boost/fusion/algorithm/query/all.hpp>
    #include <boost/fusion/include/all.hpp>

[heading Example]
    struct odd
    {
        template<typename T>
        bool operator()(T t) const
        {
            return t % 2;
        }
    };
    ...
    assert(__all__(__make_vector__(1,3), odd()));
    assert(!__all__(__make_vector__(1,2), odd()));

[endsect]

[section none]

[heading Description]
For a sequence `seq` and unary function object `f`, `none` returns true if `f` returns false for every element of `seq`.

[heading Synopsis]
    template<
        typename Sequence,
        typename F
        >
    typename __result_of_none__<Sequence,F>::type none(
        Sequence const& seq, F f);

[table Parameters
    [[Parameter][Requirement][Description]]
    [[`seq`][A model of __forward_sequence__, `f(e)` is a valid expression, convertible to `bool`, for every element `e` in `seq`][The sequence to search]]
    [[`f`][A unary function object][The search predicate]]
]

[heading Expression Semantics]
    __none__(seq, f);

[*Return type]: `bool`

[*Semantics]: Returns true if and only if `f(e)` evaluates to `false` for every element `e` in `seq`. Result equivalent to `!any(seq, f)`.

[heading Complexity]
Linear. At most `__result_of_size__<Sequence>::value` comparisons.

[heading Header]

    #include <boost/fusion/algorithm/query/none.hpp>
    #include <boost/fusion/include/none.hpp>

[heading Example]
    struct odd
    {
        template<typename T>
        bool operator()(T t) const
        {
            return t % 2;
        }
    };
    ...
    assert(__none__(__make_vector__(2,4), odd()));
    assert(!__none__(__make_vector__(1,2), odd()));

[endsect]

[section find]

[heading Description]
Finds the first element of a given type within a sequence.

[heading Synopsis]
    template<
        typename T,
        typename Sequence
        >
    __unspecified__ find(Sequence const& seq);

    template<
        typename T,
        typename Sequence
        >
    __unspecified__ find(Sequence& seq);

[table Parameters
    [[Parameter][Requirement][Description]]
    [[`seq`][A model of __forward_sequence__][The sequence to search]]
    [[`T`][Any type][The type to search for]]
]

[heading Expression Semantics]
    __find__<T>(seq)

[*Return type]: A model of the same iterator category as the iterators of `seq`.

[*Semantics]: Returns an iterator to the first element of `seq` of type `T`, or `__end__(seq)` if there is no such element.
Equivalent to `__find_if__<boost::is_same<_, T> >(seq)`

[heading Complexity]
Linear. At most `__result_of_size__<Sequence>::value` comparisons.

[heading Header]

    #include <boost/fusion/algorithm/query/find.hpp>
    #include <boost/fusion/include/find.hpp>

[heading Example]
    const __vector__<char,int> vec('a','0');
    assert(*__find__<int>(vec) == '0');
    assert(__find__<double>(vec) == __end__(vec));

[endsect]

[section find_if]
Finds the first element within a sequence with a type for which a given __mpl_lambda_expression__ evaluates to
`boost::mpl::true_`.

[heading Description]

[heading Synopsis]
    template<
        typename F,
        typename Sequence
        >
    __unspecified__ find_if(Sequence const& seq);

    template<
        typename F,
        typename Sequence
        >
    __unspecified__ find_if(Sequence& seq);

[table Parameters
    [[Parameter][Requirement][Description]]
    [[`seq`][A model of __forward_sequence__][The sequence to search]]
    [[`F`][A unary __mpl_lambda_expression__][The search predicate]]
]

[heading Expression Semantics]
    __find_if__<F>(seq)

[*Return type]: An iterator of the same iterator category as the iterators of `seq`.

[*Semantics]: Returns the first element of `seq` for which __mpl_lambda_expression__ `F` evaluates to `boost::mpl::true_`,
or `__end__(seq)` if there is no such element.

[heading Complexity]
Linear. At most `__result_of_size__<Sequence>::value` comparisons.

#include <boost/fusion/algorithm/query/find_if.hpp>
#include <boost/fusion/include/find_if.hpp>

[heading Example]
    const __vector__<double,int> vec(1.0,2);
    assert(*__find_if__<is_integral<mpl::_> >(vec) == 2);
    assert(__find_if__<is_class<mpl::_> >(vec) == __end__(vec));

[endsect]

[section count]

[heading Description]
Returns the number of elements of a given type within a sequence.

[heading Synopsis]
    template<
        typename Sequence,
        typename T
        >
    typename __result_of_count__<Sequence, T>::type count(
        Sequence const& seq, T const& t);

[table Parameters
    [[Parameter][Requirement][Description]]
    [[`seq`][A model of __forward_sequence__, `e == t` must be a valid expression, convertible to `bool`, for each element `e` in `seq`][The sequence to search]]
    [[`T`][Any type][The type to count]]
]

[heading Expression Semantics]
    __count__(seq, t);

[*Return type]: `int`

[*Semantics]: Returns the number of elements of type `T` and equal to `t` in `seq`.

[heading Complexity]
Linear. At most `__result_of_size__<Sequence>::value` comparisons.

[heading Header]

    #include <boost/fusion/algorithm/query/count.hpp>
    #include <boost/fusion/include/count.hpp>

[heading Example]
    const __vector__<double,int,int> vec(1.0,2,3);
    assert(__count__(vec,2) == 1);

[endsect]

[section count_if]

[heading Description]
Returns the number of elements within a sequence with a type for which a given unary function object evaluates to
`true`.

[heading Synopsis]
    template<
        typename Sequence,
        typename F
        >
    typename __result_of_count_if__<Sequence, F>::type count_if(
        Sequence const& seq, F f);

[table Parameters
    [[Parameter][Requirement][Description]]
    [[`seq`][A model of __forward_sequence__, `f(e)` is a valid expression, convertible to `bool`, for each element `e` in `seq`][The sequence to search]]
    [[`f`][A unary function object][The search predicate]]
]

[heading Expression Semantics]
    __count_if__(seq, f)

[*Return type]: `int`

[*Semantics]: Returns the number of elements in `seq` where `f` evaluates to `true`.

[heading Complexity]
Linear. At most `__result_of_size__<Sequence>::value` comparisons.

[heading Header]

    #include <boost/fusion/algorithm/query/count_if.hpp>
    #include <boost/fusion/include/count_if.hpp>

[heading Example]
    const __vector__<int,int,int> vec(1,2,3);
    assert(__count_if__(vec,odd()) == 2);

[endsect]

[endsect]

[section Metafunctions]

[section any]

[heading Description]
A metafunction returning the result type of __any__.

[heading Synopsis]
    template<
        typename Sequence,
        typename F
        >
    struct any
    {
        typedef bool type;
    };

[table Parameters
    [[Parameter] [Requirement] [Description]]
    [[`Sequence`] [A model of __forward_sequence__] [Operation's argument]]
    [[`F`]       [A model of unary __poly_func_obj__] [Operation's argument]]
]

[heading Expression Semantics]
    __result_of_any__<Sequence, F>::type

[*Return type]: `bool`.

[*Semantics]: Returns the return type of __any__ given a sequence of type `Sequence` and a unary __poly_func_obj__ of type `F`. The return type is always `bool`.

[heading Complexity]
Constant.

[heading Header]

    #include <boost/fusion/algorithm/query/any.hpp>
    #include <boost/fusion/include/any.hpp>

[endsect]

[section all]

[heading Description]
A metafunction returning the result type of __all__.

[heading Synopsis]
    template<
        typename Sequence,
        typename F
        >
    struct all
    {
        typedef bool type;
    };

[table Parameters
    [[Parameter] [Requirement] [Description]]
    [[`Sequence`] [A model of __forward_sequence__] [Operation's argument]]
    [[`F`]        [A model of unary __poly_func_obj__] [Operation's argument]]
]

[heading Expression Semantics]
    __result_of_all__<Sequence, F>::type

[*Return type]: `bool`.

[*Semantics]: Returns the return type of __all__ given a sequence of type `Sequence` and a unary __poly_func_obj__ of type `F`. The return type is always `bool`.

[heading Complexity]
Constant.

[heading Header]

    #include <boost/fusion/algorithm/query/all.hpp>
    #include <boost/fusion/include/all.hpp>

[endsect]

[section none]

[heading Description]
A metafunction returning the result type of __none__.

[heading Synopsis]
    template<
        typename Sequence,
        typename F
        >
    struct none
    {
        typedef bool type;
    };

[table Parameters
    [[Parameter] [Requirement] [Description]]
    [[`Sequence`] [A model of __forward_sequence__] [Operation's argument]]
    [[`F`]        [A model of unary __poly_func_obj__] [Operation's argument]]
]

[heading Expression Semantics]
    __result_of_none__<Sequence, F>::type

[*Return type]: `bool`.

[*Semantics]: Returns the return type of __none__ given a sequence of type `Sequence` and a unary __poly_func_obj__ of type `F`. The return type is always `bool`.

[heading Complexity]
Constant.

[heading Header]

    #include <boost/fusion/algorithm/query/none.hpp>
    #include <boost/fusion/include/none.hpp>

[endsect]

[section find]

[heading Description]
Returns the result type of __find__, given the sequence and search types.

[heading Synopsis]
    template<
        typename Sequence,
        typename T
        >
    struct find
    {
        typedef __unspecified__ type;
    };

[table Parameters
    [[Parameter] [Requirement] [Description]]
    [[`Sequence`] [Model of __forward_sequence__] [Operation's argument]]
    [[`T`]        [Any type] [Operation's argument]]
]

[heading Expression Semantics]
    __result_of_find__<Sequence, T>::type

[*Return type]: A model of the same iterator category as the iterators of `Sequence`.

[*Semantics]: Returns an iterator to the first element of type `T` in `Sequence`, or `__result_of_end__<Sequence>::type` if there is no such element.

[heading Complexity]
Linear, at most `__result_of_size__<Sequence>::value` comparisons.

[heading Header]

    #include <boost/fusion/algorithm/query/find.hpp>
    #include <boost/fusion/include/find.hpp>

[endsect]

[section find_if]

[heading Description]
Returns the result type of __find_if__ given the sequence and predicate types.

[heading Synopsis]
    template<
        typename Sequence,
        typename Pred
        >
    struct find_if
    {
        typedef __unspecified__ type;
    };

[table Parameters
    [[Parameter] [Requirement] [Description]]
    [[`Sequence`] [A model of __forward_sequence__] [Operation's argument]]
    [[`Pred`]     [A model of __mpl_lambda_expression__] [Operation's arguments]]
]

[heading Expression Semantics]
    __result_of_find_if__<Sequence, Pred>::type

[*Return type]: A model of the same iterator category as the iterators of `Sequence`.

[*Semantics]: Returns an iterator to the first element in `Sequence` for which `Pred` evaluates to true. Returns `__result_of_end__<Sequence>::type` if there is no such element.

[heading Complexity]
Linear. At most `__result_of_size__<Sequence>::value` comparisons.

[heading Header]

    #include <boost/fusion/algorithm/query/find_if.hpp>
    #include <boost/fusion/include/find_if.hpp>

[endsect]

[section count]

[heading Description]
A metafunction that returns the result type of `count` given the sequence and search types.

[heading Synopsis]
    template<
        typename Sequence,
        typename T
        >
    struct count
    {
        typedef int type;
    };

[table Parameters
    [[Parameter] [Requirement] [heading Description]]
    [[`Sequence`] [A model of __forward_sequence__] [Operation's argument]]
    [[`T`] [Any type] [Operation's argument]]
]

[heading Expression Semantics]
    __result_of_count__<T>::type

[*Return type]: `int`.

[*Semantics]: Returns the return type of __count__. The return type is always `int`.

[heading Complexity]
Constant.

[heading Header]

    #include <boost/fusion/algorithm/query/count.hpp>
    #include <boost/fusion/include/count.hpp>

[endsect]

[section count_if]

[heading Description]
A metafunction that returns the result type of `count_if` given the sequence and predicate types.

[heading Synopsis]
    template<
        typename Sequence,
        typename Pred
        >
    struct count_if
    {
        typedef int type;
    };

[table Parameters
    [[Parameter] [Requirement] [Description]]
    [[`Sequence`] [A model of __forward_sequence__] [Operation's argument]]
    [[`Pred`]     [A unary function object] [Operation's argument]]
]

[heading Expression Semantics]
    __result_of_count_if__<Sequence, Pred>::type

[*Return type]: `int`.

[*Semantics]: Returns the return type of __count_if__. The return type is always `int`.

[heading Complexity]
Constant.

[heading Header]

    #include <boost/fusion/algorithm/query/count_if.hpp>
    #include <boost/fusion/include/count_if.hpp>

[endsect]

[endsect]

[endsect]

[section Transformation]
The transformation algorithms create new sequences out of existing sequences by performing some sort of transformation. In reality the new sequences are views onto the data in the original sequences.

[note As the transformation algorithms return views onto their input arguments,
it is important that the lifetime of the input arguments is greater than the
period during which you wish to use the results.]

[heading Header]

    #include <boost/fusion/algorithm/transformation.hpp>
    #include <boost/fusion/include/transformation.hpp>

[section Functions]

[section filter]

[heading Description]
For a given sequence, filter returns a new sequences containing only the elements of a specified type.

[heading Synopsis]
    template<
        typename T,
        typename Sequence
        >
    typename __result_of_filter__<Sequence const, T>::type filter(Sequence const& seq);

[table Parameters
    [[Parameter][Requirement][Description]]
    [[`seq`][A model of __forward_sequence__][Operation's argument]]
    [[`T`][Any type][The type to retain]]
]

[heading Expression Semantics]
    __filter__<T>(seq);

[*Return type]:

* A model of __forward_sequence__.
* A model of __associative_sequence__ if `seq` implements the __associative_sequence__ model.

[*Semantics]: Returns a sequence containing all the elements of `seq` of type `T`.
Equivalent to `__filter_if__<boost::same_type<_, T> >(seq)`.

[heading Complexity]
Constant. Returns a view which is lazily evaluated.

[heading Header]

    #include <boost/fusion/algorithm/transformation/filter.hpp>
    #include <boost/fusion/include/filter.hpp>

[heading Example]
    const __vector__<int,int,long,long> vec(1,2,3,4);
    assert(__filter__<int>(vec) == __make_vector__(1,2));

[endsect]

[section filter_if]

[heading Description]
For a given sequence, __filter_if__ returns a new sequences containing
only the elements with types for which a given __mpl_lambda_expression__ evaluates to `boost::mpl::true_`.

[heading Synopsis]
    template<
        typename Pred,
        typename Sequence
        >
    typename __result_of_filter_if__<Sequence const, Pred>::type filter_if(Sequence const& seq);

[table Parameters
    [[Parameter][Requirement][Description]]
    [[`seq`][A model of __forward_sequence__][Operation's argument]]
    [[`Pred`][A unary __mpl_lambda_expression__][The predicate to filter by]]
]

[heading Expression Semantics]
    __filter_if__<Pred>(seq);

[*Return type]:

* A model of __forward_sequence__.
* A model of __associative_sequence__ if `seq` implements the __associative_sequence__ model.

[*Semantics]: Returns a sequence containing all the elements of `seq` with types for which `Pred` evaluates
to `boost::mpl::true_`. The order of the retained elements is the same as in the original sequence.

[heading Complexity]
Constant. Returns a view which is lazily evaluated.

[heading Header]

    #include <boost/fusion/algorithm/transformation/filter_if.hpp>
    #include <boost/fusion/include/filter_if.hpp>

[heading Example]
    const __vector__<int,int,double,double> vec(1,2,3.0,4.0);
    assert(__filter_if__<is_integral<mpl::_> >(vec) == __make_vector__(1,2));

[endsect]

[section transform]

[heading Description]
For a sequence `seq` and function object or function pointer `f`, `transform` returns a new sequence
with elements created by applying `f(e)` to each element of `e` of `seq`.

[heading Unary version synopsis]
    template<
        typename Sequence,
        typename F
        >
    typename __result_of_transform__<Sequence const, F>::type transform(
        Sequence const& seq, F f);

[table Parameters
    [[Parameter][Requirement][Description]]
    [[`seq`][A model of __forward_sequence__][Operation's argument]]
    [[`f`][`f(e)` is a valid expression for each element `e` of `seq`. `__boost_result_of_call__<F(E)>::type` is the return type of `f` when called with a value of each element type `E`.][Transformation function]]
]

[heading Expression Semantics]
    __transform__(seq, f);

[*Return type]: A model of __forward_sequence__

[*Semantics]: Returns a new sequence, containing the return values of `f(e)` for each element `e` within `seq`.

[heading Binary version synopsis]
    template<
        typename Sequence1,
        typename Sequence2,
        typename F
        >
    typename __result_of_transform__<Sequence1 const, Sequence2 const, F>::type transform(
        Sequence1 const& seq1, Sequence2 const& seq2, F f);

[table Parameters
    [[Parameter][Requirement][Description]]
    [[`seq1`][A model of __forward_sequence__][Operation's argument]]
    [[`seq2`][A model of __forward_sequence__][Operation's argument]]
    [[`f`][`f(e1,e2)` is a valid expression for each pair of elements `e1` of `seq1` and `e2` of `seq2`. `__boost_result_of_call__<F(E1,E2)>::type` is the return type of `f` when called with elements of type `E1` and `E2`][Transformation function]]
]

[*Return type]: A model of __forward_sequence__.

[*Semantics]: Returns a new sequence, containing the return values of `f(e1, e2)` for each pair of elements `e1` and `e2` within `seq1` and `seq2` respectively.

[heading Complexity]
Constant. Returns a view which is lazily evaluated.

[heading Header]

    #include <boost/fusion/algorithm/transformation/transform.hpp>
    #include <boost/fusion/include/transform.hpp>

[heading Example]
    struct triple
    {
        typedef int result_type;

        int operator()(int t) const
        {
            return t * 3;
        };
    };
    ...
    assert(__transform__(__make_vector__(1,2,3), triple()) == __make_vector__(3,6,9));

[endsect]

[section replace]

[heading Description]
Replaces each value within a sequence of a given type and value with a new value.

[heading Synopsis]
    template<
        typename Sequence,
        typename T
        >
    typename __result_of_replace__<Sequence const, T>::type replace(
        Sequence const& seq, T const& old_value, T const& new_value);

[table Parameters
    [[Parameter][Requirement][Description]]
    [[`seq`][A model of __forward_sequence__, `e == old_value` is a valid expression, convertible to `bool`, for each element `e` in `seq` with type convertible to `T`][Operation's argument]]
    [[`old_value`][Any type][Value to replace]]
    [[`new_value`][Any type][Replacement value]]
]

[heading Expression Semantics]
    __replace__(seq, old_value, new_value);

[*Return type]: A model of __forward_sequence__.

[*Semantics]: Returns a new sequence with all the values of `seq` with `new_value` assigned to elements with the same type and equal to `old_value`.

[heading Complexity]
Constant. Returns a view which is lazily evaluated.

[heading Header]

    #include <boost/fusion/algorithm/transformation/replace.hpp>
    #include <boost/fusion/include/replace.hpp>

[heading Example]
    assert(__replace__(__make_vector__(1,2), 2, 3) == __make_vector__(1,3));

[endsect]

[section replace_if]

[heading Description]
Replaces each element of a given sequence for which an unary function object evaluates to `true` replaced with
a new value.

[heading Synopsis]
    template<
        typename Sequence,
        typename F,
        typename T>
    typename __result_of_replace_if__<Sequence const, F, T>::type replace_if(
        Sequence const& seq, F f, T const& new_value);

[table Parameters
    [[Parameter][Requirement][Description]]
    [[`seq`][A model of __forward_sequence__][Operation's argument]]
    [[`f`][A function object for which `f(e)` is a valid expression, convertible to `bool`, for each element `e` in `seq`][Operation's argument]]
    [[`new_value`][Any type][Replacement value]]
]

[heading Expression Semantics]
    __replace_if__(seq, f, new_value);

[*Return type]: A model of __forward_sequence__.

[*Semantics]: Returns a new sequence with all the elements of `seq`,
with `new_value` assigned to each element for which `f` evaluates to `true`.

[heading Complexity]
Constant. Returns a view which is lazily evaluated.

[heading Header]

    #include <boost/fusion/algorithm/transformation/replace_if.hpp>
    #include <boost/fusion/include/replace_if.hpp>

[heading Example]
    struct odd
    {
        template<typename T>
        bool operator()(T t) const
        {
            return t % 2;
        }
    };
    ...
    assert(__replace_if__(__make_vector__(1,2), odd(), 3) == __make_vector__(3,2));

[endsect]

[section remove]

[heading Description]
Returns a new sequence, with all the elements of the original sequence, except those of a given type.

[heading Synopsis]
    template<
        typename T,
        typename Sequence
        >
    typename __result_of_remove__<Sequence const, T>::type replace(Sequence const& seq);

[table Parameters
    [[Parameter][Requirement][Description]]
    [[`seq`][A model of __forward_sequence__][Operation's argument]]
    [[`T`][Any type][Type to remove]]
]

[heading Expression Semantics]
    __remove__<T>(seq);

[*Return type]:

* A model of __forward_sequence__.
* A model of __associative_sequence__ if `Sequence` implements the __associative_sequence__ model.

[*Semantics]: Returns a new sequence, containing all the elements of `seq`, in their original order, except
those of type `T`. Equivalent to `__remove_if__<boost::is_same<_,T> >(seq)`.

[heading Complexity]
Constant. Returns a view which is lazily evaluated.

[heading Header]

    #include <boost/fusion/algorithm/transformation/remove.hpp>
    #include <boost/fusion/include/remove.hpp>

[heading Example]
    const __vector__<int,double> vec(1,2.0);
    assert(__remove__<double>(vec) == __make_vector__(1));

[endsect]

[section remove_if]

[heading Description]
Returns a new sequence, containing all the elements of the original except those where a given unary
function object evaluates to `true`.

[heading Synopsis]
    template<
        typename Pred,
        typename Sequence
        >
    typename __result_of_remove_if__<Sequence const, Pred>::type remove_if(Sequence const& seq);

[table Parameters
    [[Parameter][Requirement][Description]]
    [[`seq`][A model of __forward_sequence__][Operation's argument]]
    [[`Pred`][A model of unary __mpl_lambda_expression__][Removal predicate]]
]

[heading Expression Semantics]
    __remove_if__<Pred>(seq);

[*Return type]:

* A model of __forward_sequence__.
* A model of __associative_sequence__ if `seq` implements the __associative_sequence__ model.

[*Semantics]: Returns a new sequence, containing all the elements of `seq`, in their original order, except
those elements with types for which `Pred` evaluates to `boost::mpl::true_`.
Equivalent to `__filter__<boost::mpl::not_<Pred> >(seq)`.

[heading Complexity]
Constant. Returns a view which is lazily evaluated.

[heading Header]

    #include <boost/fusion/algorithm/transformation/remove_if.hpp>
    #include <boost/fusion/include/remove_if.hpp>

[heading Example]
    const __vector__<int,double> vec(1,2.0);
    assert(__remove_if__<is_floating_point<mpl::_> >(vec) == __make_vector__(1));

[endsect]

[section reverse]

[heading Description]
Returns a new sequence with the elements of the original in reverse order.

[heading Synposis]
    template<
        typename Sequence
        >
    typename __result_of_reverse__<Sequence const>::type reverse(Sequence const& seq);

[table Parameters
    [[Parameter][Requirement][Description]]
    [[`seq`][A model of __bidirectional_sequence__][Operation's argument]]
]

[heading Expression Semantics]
    __reverse__(seq);

[*Return type]:

* A model of __bidirectional_sequence__ if `seq` is a __bidirectional_sequence__
else, __random_access_sequence__ if `seq` is a __random_access_sequence__.
* A model of __associative_sequence__ if `seq` implements the __associative_sequence__ model.

[*Semantics]: Returns a new sequence containing all the elements of `seq` in reverse order.

[heading Complexity]
Constant. Returns a view which is lazily evaluated.

[heading Header]

    #include <boost/fusion/algorithm/transformation/reverse.hpp>
    #include <boost/fusion/include/reverse.hpp>

[heading Example]
    assert(__reverse__(__make_vector__(1,2,3)) == __make_vector__(3,2,1));

[endsect]

[section clear]

[heading Description]
__clear__ returns an empty sequence.

[heading Synposis]
    template<
        typename Sequence
        >
    typename __result_of_clear__<Sequence const>::type clear(Sequence const& seq);

[table Parameters
    [[Parameter][Requirement][Description]]
    [[`seq`][A model of __forward_sequence__][Operation's argument]]
]

[heading Expression Semantics]
    __clear__(seq);

[*Return type]: A model of __forward_sequence__.

[*Expression Semantics]: Returns a sequence with no elements.

[heading Complexity]
Constant.

[heading Header]

    #include <boost/fusion/algorithm/transformation/clear.hpp>
    #include <boost/fusion/include/clear.hpp>

[heading Example]
    assert(__clear__(__make_vector__(1,2,3)) == __make_vector__());

[endsect]

[section erase]

[heading Description]
Returns a new sequence, containing all the elements of the original except those at a specified iterator, or
between two iterators.

[heading Synposis]
    template<
        typename Sequence,
        typename First
        >
    typename __result_of_erase__<Sequence const, First>::type erase(
        Sequence const& seq, First const& it1);

    template<
        typename Sequence,
        typename First,
        typename Last
        >
    typename __result_of_erase__<Sequence const, First, Last>::type erase(
        Sequence const& seq, First const& it1, Last const& it2);

[table Parameters
    [[Parameters][Requirement][Description]]
    [[`seq`][A model of __forward_sequence__][Operation's argument]]
    [[`it1`][A model of __forward_iterator__][Iterator into `seq`]]
    [[`it2`][A model of __forward_iterator__][Iterator into `seq` after `it1`]]
]

[heading Expression Semantics]
    __erase__(seq, pos);

[*Return type]:

* A model of __forward_sequence__.
* A model of __associative_sequence__ if `seq` implements the __associative_sequence__ model.

[*Semantics]: Returns a new sequence, containing all the elements of `seq` except the element at `pos`.

    __erase__(seq, first, last);

[*Return type]:

* A model of __forward_sequence__.
* A model of __associative_sequence__ if `seq` implements the __associative_sequence__ model.

[*Semantics]: Returns a new sequence, with all the elements of `seq`, in their original order, except those
in the range [`first`,`last`).

[heading Complexity]
Constant. Returns a view which is lazily evaluated.

[heading Header]

    #include <boost/fusion/algorithm/transformation/erase.hpp>
    #include <boost/fusion/include/erase.hpp>

[heading Example]
    const __vector__<int, double, char> vec(1, 2.0, 'c');
    assert(__erase__(vec, __next__(__begin__(vec))) == __make_vector__(1, 'c'));
    assert(__erase__(vec, __next__(__begin__(vec)), __end__(vec)) == __make_vector__(1));

[endsect]

[section erase_key]

[heading Description]
For an [link fusion.sequence.concepts.associative_sequence associative]] __forward_sequence__ `seq`,
returns a [link fusion.sequence.concepts.associative_sequence associative]] __forward_sequence__ containing
all the elements of the original except those with a given key.

[heading Synposis]
    template<
        typename Key,
        typename Sequence
        >
    typename __result_of_erase_key__<Sequence const, Key>::type erase_key(Sequence const& seq);

[table Parameters
    [[Parameter][Requirement][Description]]
    [[`seq`][A model of __forward_sequence__ and __associative_sequence__][Operation's argument]]
    [[`Key`][Any type][Key to erase]]
]

[heading Expression Semantics]
    __erase_key__<Key>(seq);

[*Return type]: A model of __forward_sequence__ and __associative_sequence__.

[*Semantics]: Returns a new sequence, containing all the elements of `seq`, except those with key `Key`.

[heading Complexity]
Constant. Returns a view which is lazily evaluated.

[heading Header]

    #include <boost/fusion/algorithm/transformation/erase_key.hpp>
    #include <boost/fusion/include/erase_key.hpp>

[heading Example]
    assert(__erase_key__<int>(__make_map__<int, long>('a', 'b')) == __make_map__<long>('b'));

[endsect]

[section insert]

[heading Description]
Returns a new sequence with all the elements of the original, an a new element inserted the
position described by a given iterator.

[heading Synposis]
    template<
        typename Sequence,
        typename Pos,
        typename T
        >
    typename __result_of_insert__<Sequence const, Pos, T>::type insert(
        Sequence const& seq, Pos const& pos, T const& t);

[table Parameters
    [[Parameter][Requirement][Description]]
    [[`seq`][A model of __forward_sequence__][Operation's argument]]
    [[`pos`][A model of __forward_iterator__][The position to insert at]]
    [[`t`][Any type][The value to insert]]
]

[heading Expression Semantics]
    __insert__(seq, p, t);

[*Return type]:

* A model of __forward_sequence__.

[*Semantics]: Returns a new sequence, containing all the elements of `seq`, in their original order, and a new element with the
type and value of `t` inserted at iterator `pos`.

[heading Complexity]
Constant. Returns a view which is lazily evaluated.

[heading Header]

    #include <boost/fusion/algorithm/transformation/insert.hpp>
    #include <boost/fusion/include/insert.hpp>

[heading Example]
    const __vector__<int,int> vec(1,2);
    assert(__insert__(vec, __next__(__begin__(vec)), 3) == __make_vector__(1,3,2));

[endsect]

[section insert_range]

[heading Description]
Returns a new sequence with another sequence inserted at a specified iterator.

[heading Synposis]
    template<
        typename Sequence,
        typename Pos,
        typename Range
        >
    typename __result_of_insert_range__<Sequence const, Pos, Range>::type insert_range(
        Sequence const& seq, Pos const& pos, Range const& range);

[table Parameters
    [[Parameter][Requirement][Description]]
    [[`seq`][A model of __forward_sequence__][Operation's argument]]
    [[`pos`][A model of __forward_iterator__][The position to insert at]]
    [[`range`][A model of __forward_sequence__][Range to insert]]
]

[heading Expression Semantics]
    __insert_range__(seq, pos, range);

[*Return type]:

* A model of __forward_sequence__.
* A model of __associative_sequence__ if `seq` implements the __associative_sequence__ model.

[*Semantics]: Returns a new sequence, containing all the elements of `seq`, and the elements of
`range` inserted at iterator `pos`. All elements retaining their ordering from the orignal sequences.

[heading Complexity]
Constant. Returns a view which is lazily evaluated.

[heading Header]

    #include <boost/fusion/algorithm/transformation/insert_range.hpp>
    #include <boost/fusion/include/insert_range.hpp>

[heading Example]
    const __vector__<int,int> vec(1,2);
    assert(__insert_range__(vec, __next__(__begin__(vec)), __make_vector__(3,4)) == __make_vector__(1,3,4,2));

[endsect]

[section join]

[heading Description]
Takes 2 sequences and returns a sequence containing the elements of the first followed by the elements of the second.

[heading Synopsis]
    template<
        typename LhSequence,
        typename RhSequence>
    typename __result_of_join__<LhSequence, RhSequence>::type join(LhSequence const& lhs, RhSequence const& rhs);

[table Parameters
    [[Parameter][Requirement][Description]]
    [[`lhs`][A model of __forward_sequence__][Operation's argument]]
    [[`rhs`][A model of __forward_sequence__][Operation's argument]]
]

[heading Expression Semantics]
    __join__(lhs, rhs);

[*Return type]:

* A model of __forward_sequence__.
* A model of __associative_sequence__ if `lhs` and `rhs` implement the __associative_sequence__ model.

[*Semantics]: Returns a sequence containing all the elements of `lhs` followed by all the elements of `rhs`. The order of the elements is preserved.

[heading Complexity]
Constant. Returns a view which is lazily evaluated.

[heading Header]

    #include <boost/fusion/algorithm/transformation/join.hpp>
    #include <boost/fusion/include/join.hpp>

[heading Example]
    __vector__<int,char> v1(1, 'a');
    __vector__<int,char> v2(2, 'b');
    assert(__join__(v1, v2) == __make_vector__(1,'a',2,'b'));

[endsect]

[section zip]

[heading Description]
Zips sequences together to form a single sequence, whos members are tuples of the members of the component sequences.

[heading Synopsis]
    template<
        typename Sequence1,
        typename Sequence2,
        ...
        typename SequenceN
        >
    typename __result_of_zip__<Sequence1, Sequence2, ... SequenceN>::type
    zip(Sequence1 const& seq1, Sequence2 const& seq2, ... SequenceN const& seqN);

[table Parameters
    [[Parameter][Requirement][Description]]
    [[`seq1` to `seqN`][Each sequence is a model of __forward_sequence__.][Operation's argument]]
]

[heading Expression Semantics]
    __zip__(seq1, seq2, ... seqN);

[*Return type]: A model of __forward_sequence__.

[*Semantics]: Returns a sequence containing tuples of elements from sequences `seq1` to `seqN`. For example, applying zip to tuples `(1, 2, 3)` and `('a', 'b', 'c')` would return `((1, 'a'),(2, 'b'),(3, 'c'))`

[heading Complexity]
Constant. Returns a view which is lazily evaluated.

[heading Header]

    #include <boost/fusion/algorithm/transformation/zip.hpp>
    #include <boost/fusion/include/zip.hpp>

[heading Example]
    __vector__<int,char> v1(1, 'a');
    __vector__<int,char> v2(2, 'b');
    assert(__zip__(v1, v2) == __make_vector__(__make_vector__(1, 2),__make_vector__('a', 'b'));

[endsect]

[section pop_back]

[heading Description]
Returns a new sequence, with the last element of the original removed.

[heading Synopsis]
    template<
        typename Sequence
        >
    typename __result_of_pop_back__<Sequence const>::type pop_back(Sequence const& seq);

[table Parameters
    [[Parameter][Requirement][Description]]
    [[`seq`][A model of __forward_sequence__][Operation's argument]]
]

[heading Expression Semantics]
    __pop_back__(seq);

[*Return type]:

* A model of __forward_sequence__.
* A model of __associative_sequence__ if `seq` implements the __associative_sequence__ model.

[*Semantics]: Returns a new sequence containing all the elements of `seq`, except the last element. The elements in the new sequence are in the same order as they were in `seq`.

[heading Complexity]
Constant. Returns a view which is lazily evaluated.

[heading Header]

    #include <boost/fusion/algorithm/transformation/pop_back.hpp>
    #include <boost/fusion/include/pop_back.hpp>

[heading Example]
    assert(___pop_back__(__make_vector__(1,2,3)) == __make_vector__(1,2));

[endsect]

[section pop_front]

[heading Description]
Returns a new sequence, with the first element of the original removed.

[heading Synopsis]
    template<
        typename Sequence
        >
    typename __result_of_pop_front__<Sequence const>::type pop_front(Sequence const& seq);


[table Parameters
    [[Parameter][Requirement][Description]]
    [[`seq`][A model of __forward_sequence__][Operation's argument]]
]

[heading Expression Semantics]
    __pop_front__(seq);

[*Return type]:

* A model of __forward_sequence__.
* A model of __associative_sequence__ if `seq` implements the __associative_sequence__ model.

[*Semantics]: Returns a new sequence containing all the elements of `seq`, except the first element. The elements in the new sequence are in the same order as they were in `seq`.

[heading Complexity]
Constant. Returns a view which is lazily evaluated.

[heading Header]

    #include <boost/fusion/algorithm/transformation/pop_front.hpp>
    #include <boost/fusion/include/pop_front.hpp>

[heading Example]
    assert(__pop_front__(__make_vector__(1,2,3)) == __make_vector__(2,3));

[endsect]

[section push_back]

[heading Description]
Returns a new sequence with an element added at the end.

[heading Synopsis]
    template<
        typename Sequence,
        typename T
        >
    typename __result_of_push_back__<Sequence, T>::type push_back(
        Sequence const& seq, T const& t);

[table Parameters
    [[Parameter][Requirement][Description]]
    [[`seq`][A model of __forward_sequence__][Operation's argument]]
    [[`t`][Any type][The value to add to the end]]
]

[heading Expression Semantics]
    __push_back__(seq, t);

[*Return type]:

* A model of __forward_sequence__.

[*Semantics]: Returns a new sequence, containing all the elements of `seq`, and new element `t` appended to the end. The elements are in the same order as they were in `seq`.

[heading Complexity]
Constant. Returns a view which is lazily evaluated.

[heading Header]

    #include <boost/fusion/algorithm/transformation/push_back.hpp>
    #include <boost/fusion/include/push_back.hpp>

[heading Example]
    assert(__push_back__(__make_vector__(1,2,3),4) == __make_vector__(1,2,3,4));

[endsect]

[section push_front]

[heading Description]
Returns a new sequence with an element added at the beginning.

[heading Synopsis]
    template<
        typename Sequence,
        typename T
        >
    typename __result_of_push_front__<Sequence, T>::type push_front(
        Sequence const& seq, T const& t);

[table Parameters
    [[Parameter][Requirement][Description]]
    [[`seq`][A model of __forward_sequence__][Operation's argument]]
    [[`t`][Any type][The value to add to the beginning]]
]

[heading Expression Semantics]
    __push_back__(seq, t);

[*Return type]:

* A model of __forward_sequence__.

[*Semantics]: Returns a new sequence, containing all the elements of `seq`, and new element `t` appended to the beginning. The elements are in the same order as they were in `seq`.

[heading Complexity]
Constant. Returns a view which is lazily evaluated.

[heading Header]

    #include <boost/fusion/algorithm/transformation/push_front.hpp>
    #include <boost/fusion/include/push_front.hpp>

[heading Example]
    assert(__push_front__(__make_vector__(1,2,3),0) == __make_vector__(0,1,2,3));

[endsect]

[endsect]

[section Metafunctions]

[section filter]

[heading Description]
Returns the result type of __filter__ given the sequence type and type to retain.

[heading Synopsis]
    template<
        typename Sequence,
        typename T
        >
    struct filter
    {
        typedef __unspecified__ type;
    };

[table Parameter
    [[Parameter] [Requirement] [Description]]
    [[`Sequence`][A model of __forward_sequence__] [Operation's argument]]
    [[`T`][Any type][Type to retain]]
]

[heading Expression Semantics]
    __result_of_filter__<Sequence, T>::type

[*Return type]:

* A model of __forward_sequence__.
* A model of __associative_sequence__ if `Sequence` implements the __associative_sequence__ model.

[*Semantics]: Returns a sequence containing the elements of `Sequence` that are of type `T`. Equivalent to `__result_of_filter_if__<Sequence, boost::is_same<mpl::_, T> >::type`.

[heading Complexity]
Constant.

[heading Header]

    #include <boost/fusion/algorithm/transformation/filter.hpp>
    #include <boost/fusion/include/filter.hpp>

[endsect]

[section filter_if]

[heading Description]
Returns the result type of __filter_if__ given the sequence and unary __mpl_lambda_expression__ predicate type.

[heading Synopsis]
    template<
        typename Sequence,
        typename Pred
        >
    struct filter_if
    {
        typedef __unspecified__ type;
    };

[table Parameter
    [[Parameter] [Requirement] [Description]]
    [[`Sequence`][A model of __forward_sequence__] [Operation's argument]]
    [[`Pred`][A unary __mpl_lambda_expression__][Type to retain]]
]

[heading Expression Semantics]
    __result_of_filter_if__<Sequence, Pred>::type

[*Return type]:

* A model of __forward_sequence__.
* A model of __associative_sequence__ if `Sequence` implements the __associative_sequence__ model.

[*Semantics]: Returns a sequence containing the elements of `Sequence` for which `Pred` evaluates to `boost::mpl::true_`.

[heading Complexity]
Constant.

[heading Header]

    #include <boost/fusion/algorithm/transformation/filter_if.hpp>
    #include <boost/fusion/include/filter_if.hpp>

[endsect]

[section transform]

[heading Description]
For a sequence `seq` and function object or function pointer `f`, `transform` returns a new sequence
with elements created by applying `f(e)` to each element of `e` of `seq`.

[heading Unary version synopsis]
    template<
        typename Sequence,
        typename F
        >
    typename __result_of_transform__<Sequence const, F>::type transform(
        Sequence const& seq, F f);

[table Parameters
    [[Parameter][Requirement][Description]]
    [[`seq`][A model of __forward_sequence__][Operation's argument]]
    [[`f`][`f(e)` is a valid expression for each element `e` of `seq`. `__boost_result_of_call__<F(E)>::type` is the return type of `f` when called with a value of each element type `E`.][Transformation function]]
]

[heading Expression Semantics]
    __transform__(seq, f);

[*Return type]:

* A model of __forward_sequence__
* A model of __associative_sequence__ if `Sequence` implements the __associative_sequence__ model.

[*Semantics]: Returns a new sequence, containing the return values of `f(e)` for each element `e` within `seq`.

[heading Binary version synopsis]
    template<
        typename Sequence1,
        typename Sequence2,
        typename F
        >
    typename __result_of_transform__<Sequence1 const, Sequence2 const, F>::type transform(
        Sequence1 const& seq1, Sequence2 const& seq2, F f);

[table Parameters
    [[Parameter][Requirement][Description]]
    [[`seq1`][A model of __forward_sequence__][Operation's argument]]
    [[`seq2`][A model of __forward_sequence__][Operation's argument]]
    [[`f`][`f(e1,e2)` is a valid expression for each pair of elements `e1` of `seq1` and `e2` of `seq2`. `__boost_result_of_call__<F(E1,E2)>::type` is the return type of `f` when called with elements of type `E1` and `E2`][Transformation function]]
]

[*Return type]: A model of __forward_sequence__.

[*Semantics]: Returns a new sequence, containing the return values of `f(e1, e2)` for each pair of elements `e1` and `e2` within `seq1` and `seq2` respectively.

[heading Complexity]
Constant. Returns a view which is lazily evaluated.

[heading Header]

    #include <boost/fusion/algorithm/transformation/transform.hpp>
    #include <boost/fusion/include/transform.hpp>

[heading Example]
    struct triple
    {
        typedef int result_type;

        int operator()(int t) const
        {
            return t * 3;
        };
    };
    ...
    assert(__transform__(__make_vector__(1,2,3), triple()) == __make_vector__(3,6,9));

[endsect]

[section replace]

[heading Description]
Returns the result type of __replace__, given the types of the input sequence and element to replace.

[heading Synopsis]
    template<
        typename Sequence,
        typename T
        >
    struct replace
    {
        typedef __unspecified__ type;
    };

[table Parameters
    [[Parameter][Requirement][Description]]
    [[`Sequence`][A model of __forward_sequence__][Operation's argument]]
    [[`T`][Any type][The type of the search and replacement objects]]
]

[heading Expression Semantics]
    __result_of_replace__<Sequence,T>::type

[*Return type]: A model of __forward_sequence__.

[*Semantics]: Returns the return type of __replace__.

[heading Complexity]
Constant.

[heading Header]

    #include <boost/fusion/algorithm/transformation/replace.hpp>
    #include <boost/fusion/include/replace.hpp>

[endsect]

[section replace_if]

[heading Description]
Returns the result type of __replace_if__, given the types of the sequence, __poly_func_obj__ predicate and replacement object.

[heading Synopsis]
    template<
        typename Sequence,
        typename F,
        typename T>
    struct replace_if
    {
        typedef __unspecified__ type;
    };

[table Parameters
    [[Parameter][Requirement][Description]]
    [[`Sequence`][A model of __forward_sequence__][Operation's argument]]
    [[`F`][A model of unary __poly_func_obj__][Replacement predicate]]
    [[`T`][Any type][The type of the replacement object]]
]

[heading Expression Semantics]
    __result_of_replace_if__<Sequence,F,T>::type

[*Return type]: A model of __forward_sequence__.

[*Semantics]: Returns the return type of __replace_if__.

[heading Complexity]
Constant.

[heading Header]

    #include <boost/fusion/algorithm/transformation/replace_if.hpp>
    #include <boost/fusion/include/replace_if.hpp>

[endsect]

[section remove]

[heading Description]
Returns the result type of __remove__, given the sequence and removal types.

[heading Synopsis]
    template<
        typename Sequence,
        typename T
        >
    struct remove
    {
        typedef __unspecified__ type;
    };

[table Parameters
    [[Parameter][Requirement][Description]]
    [[`Sequence`][A model of __forward_sequence__][Operation's argument]]
    [[`T`][Any type][Remove elements of this type]]
]

[heading Expression Semantics]
    __result_of_remove__<Sequence, T>::type

[*Return type]:

* A model of __forward_sequence__.
* A model of __associative_sequence__ if `Sequence` implements the __associative_sequence__ model.

[*Semantics]: Returns a sequence containing the elements of `Sequence` not of type `T`. Equivalent to `__result_of_replace_if__<Sequence, boost::is_same<mpl::_, T> >::type`.

[heading Complexity]
Constant.

[heading Header]

    #include <boost/fusion/algorithm/transformation/remove.hpp>
    #include <boost/fusion/include/remove.hpp>

[endsect]

[section remove_if]

[heading Description]
Returns the result type of __remove_if__, given the input sequence and unary __mpl_lambda_expression__ predicate types.

[heading Synopsis]
    template<
        typename Sequence,
        typename Pred
        >
    struct remove_if
    {
        typedef __unspecified__ type;
    };

[table Parameters
    [[Parameter][Requirement][Description]]
    [[`Sequence`][A model of __forward_sequence__][Operation's argument]]
    [[`Pred`][A model of unary __mpl_lambda_expression__][Remove elements which evaluate to `boost::mpl::true_`]]
]

[heading Expression Semantics]
    __result_of_remove_if__<Sequence, Pred>::type

[*Return type]:

* A model of __forward_sequence__.
* A model of __associative_sequence__ if `Sequence` implements the __associative_sequence__ model.

[*Semantics]: Returns a sequence containing the elements of `Sequence` for which `Pred` evaluates to `boost::mpl::false_`.

[heading Complexity]
Constant.

[heading Header]

    #include <boost/fusion/algorithm/transformation/remove_if.hpp>
    #include <boost/fusion/include/remove_if.hpp>

[endsect]

[section reverse]

[heading Description]
Returns the result type of __reverse__, given the input sequence type.

[heading Synopsis]
    template<
        typename Sequence
        >
    struct reverse
    {
        typedef __unspecified__ type;
    };

[table Parameters
    [[Parameter][Requirement][Description]]
    [[`Sequence`][A model of __bidirectional_sequence__][Operation's argument]]
]

[heading Expression Semantics]
    __result_of_reverse__<Sequence>::type

[*Return type]:

* A model of __bidirectional_sequence__ if `Sequence` is a __bidirectional_sequence__
else, __random_access_sequence__ if `Sequence` is a __random_access_sequence__.
* A model of __associative_sequence__ if `Sequence` implements the __associative_sequence__ model.

[*Semantics]: Returns a sequence with the elements in the reverse order to `Sequence`.

[heading Complexity]
Constant.

[heading Header]

    #include <boost/fusion/algorithm/transformation/reverse.hpp>
    #include <boost/fusion/include/reverse.hpp>

[endsect]

[section clear]

[heading Description]
Returns the result type of __clear__, given the input sequence type.

[heading Synopsis]
    template<
        typename Sequence
        >
    struct clear
    {
        typedef __unspecified__ type;
    };

[table Parameters
    [[Parameter][Requirement][Description]]
    [[`Sequence`][Any type][Operation's argument]]
]

[heading Expression Semantics]
    __result_of_clear__<Sequence>::type

[*Return type]: A model of __forward_sequence__.

[*Semantics]: Returns an empty sequence.

[heading Complexity]
Constant.

[heading Header]

    #include <boost/fusion/algorithm/transformation/clear.hpp>
    #include <boost/fusion/include/clear.hpp>

[endsect]

[section erase]
Returns the result type of __erase__, given the input sequence and range delimiting iterator types.

[heading Description]

[heading Synopsis]
    template<
        typename Sequence,
        typename It1,
        typename It2 = __unspecified__>
    struct erase
    {
        typedef __unspecified__ type;
    };

[table Parameters
    [[Parameter][Requirement][Description]]
    [[`Sequence`][A model of __forward_sequence__][Operation's argument]]
    [[`It1`][A model of __forward_iterator__][Operation's argument]]
    [[`It2`][A model of __forward_iterator__][Operation's argument]]
]

[heading Expression Semantics]
    __result_of_erase__<Sequence, It1>::type

[*Return type]:

* A model of __forward_sequence__.
* A model of __associative_sequence__ if `Sequence` implements the __associative_sequence__ model.

[*Semantics]: Returns a new sequence with the element at `It1` removed.

    __result_of_erase__<Sequence, It1, It2>::type

[*Return type]: A model of __forward_sequence__.

[*Semantics]: Returns a new sequence with the elements between `It1` and `It2` removed.

[heading Complexity]
Constant.

[heading Header]

    #include <boost/fusion/algorithm/transformation/erase.hpp>
    #include <boost/fusion/include/erase.hpp>

[endsect]

[section erase_key]

[heading Description]
Returns the result type of __erase_key__, given the sequence and key types.

[heading Synopsis]
    template<
        typename Sequence,
        typename Key
        >
    struct erase_key
    {
        typedef __unspecified__ type;
    };

[table Parameters
    [[Parameter][Requirement][Description]]
    [[`Sequence`][A model of __forward_sequence__ and __associative_sequence__][Operation's argument]]
    [[`Key`][Any type][Key type]]
]

[heading Expression Semantics]
    __result_of_erase_key__<Sequence, Key>::type

[*Return type]: A model of __forward_sequence__ and __associative_sequence__.

[*Semantics]: Returns a sequence with the elements of `Sequence`, except those with key `Key`.

[heading Complexity]
Constant.

[heading Header]

    #include <boost/fusion/algorithm/transformation/erase_key.hpp>
    #include <boost/fusion/include/erase_key.hpp>

[endsect]

[section insert]

[heading Description]
Returns the result type of __insert__, given the sequence, position iterator and insertion types.

[heading Synopsis]
    template<
        typename Sequence,
        typename Position,
        typename T
        >
    struct insert
    {
        typedef __unspecified__ type;
    };

[table Parameters
    [[Parameter][Requirement][Description]]
    [[`Sequence`][A model of __forward_sequence__][Operation's argument]]
    [[`Position`][A model of __forward_iterator__][Operation's argument]]
    [[`T`][Any type][Operation's argument]]
]

[heading Expression Semantics]
    __result_of_insert__<Sequence, Position, T>::type

[*Return type]:

* A model of __forward_sequence__.

[*Semantics]: Returns a sequence with an element of type `T` inserted at position `Position` in `Sequence`.

[heading Complexity]
Constant.

[heading Header]

    #include <boost/fusion/algorithm/transformation/insert.hpp>
    #include <boost/fusion/include/insert.hpp>

[endsect]

[section insert_range]

[heading Description]
Returns the result type of __insert_range__, given the input sequence, position iterator and insertion range types.

[heading Synopsis]
    template<
        typename Sequence,
        typename Position,
        typename Range
        >
    struct insert_range
    {
        typedef __unspecified__ type;
    };

[table Parameters
    [[Parameter][Requirement][Description]]
    [[`Sequence`][A model of __forward_sequence__][Operation's argument]]
    [[`Position`][A model of __forward_iterator__][Operation's argument]]
    [[`Range`][A model of __forward_sequence__][Operation's argument]]
]

[heading Expression Semantics]
    __result_of_insert_range__<Sequence, Position, Range>::type

[*Return type]:

* A model of __forward_sequence__.
* A model of __associative_sequence__ if `Sequence` implements the __associative_sequence__ model.

[*Semantics]: Returns a sequence with the elements of `Range` inserted at position `Position` into `Sequence`.

[heading Complexity]
Constant.

[heading Header]

    #include <boost/fusion/algorithm/transformation/insert_range.hpp>
    #include <boost/fusion/include/insert_range.hpp>

[endsect]

[section join]

[heading Description]
Returns the result of joining 2 sequences, given the sequence types.

[heading Synopsis]
    template<
        typename LhSequence,
        typename RhSequence
        >
    struct join
    {
        typedef __unspecified__ type;
    };

[heading Expression Semantics]
    __result_of_join__<LhSequence, RhSequence>::type

[*Return type]:

* A model of __forward_sequence__.
* A model of __associative_sequence__ if `LhSequence` amd `RhSequence` implement the __associative_sequence__ model.

[*Semantics]: Returns a sequence containing the elements of `LhSequence` followed by the elements of `RhSequence`. The order of the elements in the 2 sequences is preserved.

[heading Complexity]
Constant.

[heading Header]

    #include <boost/fusion/algorithm/transformation/join.hpp>
    #include <boost/fusion/include/join.hpp>

[endsect]

[section zip]

[heading Description]
Zips sequences together to form a single sequence, whos members are tuples of the members of the component sequences.

[heading Synopsis]
    template<
        typename Sequence1,
        typename Sequence2,
        ...
        typename SequenceN
        >
    struct zip
    {
        typedef __unspecified__ type;
    };

[heading Expression Semantics]
    __result_of_zip__<Sequence1, Sequence2, ... SequenceN>::type

[*Return type]: A model of the most restrictive traversal category of sequences `Sequence1` to `SequenceN`.

[*Semantics]: Return a sequence containing tuples of elements from each sequence. For example, applying zip to tuples `(1, 2, 3)` and `('a', 'b', 'c')` would return `((1, 'a'),(2, 'b'),(3, 'c'))`

[heading Complexity]
Constant.

[heading Header]

    #include <boost/fusion/algorithm/transformation/zip.hpp>
    #include <boost/fusion/include/zip.hpp>

[endsect]

[section pop_back]

[heading Description]
Returns the result type of __pop_back__, given the input sequence type.

[heading Synopsis]
    template<
        typename Sequence
        >
    struct pop_back
    {
        typedef __unspecified__ type;
    };

[table Parameters
    [[Parameter][Requirement][Description]]
    [[`Sequence`][A model of __forward_sequence__][Operation's argument]]
]

[heading Expression Semantics]
    __result_of_pop_back__<Sequence>::type

[*Return type]:

* A model of __forward_sequence__.
* A model of __associative_sequence__ if `Sequence` implements the __associative_sequence__ model.

[*Semantics]: Returns a sequence with all the elements of `Sequence` except the last element.

[heading Complexity]
Constant.

[heading Header]

    #include <boost/fusion/algorithm/transformation/pop_back.hpp>
    #include <boost/fusion/include/pop_back.hpp>

[endsect]

[section pop_front]

[heading Description]
Returns the result type of __pop_front__, given the input sequence type.

[heading Synopsis]
    template<
        typename Sequence
        >
    struct pop_front
    {
        typedef __unspecified__ type;
    };

[table Parameters
    [[Parameter][Requirement][Description]]
    [[`Sequence`][A model of __forward_sequence__][Operation's argument]]
]

[heading Expression Semantics]
    __result_of_pop_front__<Sequence>::type

[*Return type]:

* A model of __forward_sequence__.
* A model of __associative_sequence__ if `Sequence` implements the __associative_sequence__ model.

[*Semantics]: Returns a sequence with all the elements of `Sequence` except the first element.

[heading Complexity]
Constant.

[heading Header]

    #include <boost/fusion/algorithm/transformation/pop_front.hpp>
    #include <boost/fusion/include/pop_front.hpp>

[endsect]

[section push_back]

[heading Description]
Returns the result type of __push_back__, given the types of the input sequence and element to push.

[heading Synopsis]
    template<
        typename Sequence,
        typename T
        >
    struct push_back
    {
        typedef __unspecified__ type;
    };

[table Parameters
    [[Parameter][Requirement][Description]]
    [[`Sequence`][A model of __forward_sequence__][Operation's argument]]
    [[`T`][Any type][Operation's argument]]
]

[heading Expression Semantics]
    __result_of_push_back__<Sequence, T>::type

[*Return type]:

* A model of __forward_sequence__.

[*Semantics]: Returns a sequence with the elements of `Sequence` and an element of type `T` added to the end.

[heading Complexity]
Constant.

[heading Header]

    #include <boost/fusion/algorithm/transformation/push_back.hpp>
    #include <boost/fusion/include/push_back.hpp>

[endsect]

[section push_front]

[heading Description]
Returns the result type of __push_front__, given the types of the input sequence and element to push.

[heading Synopsis]
    template<
        typename Sequence,
        typename T
        >
    struct push_front
    {
        typedef __unspecified__ type;
    };

[table Parameters
    [[Parameter][Requirement][Description]]
    [[`Sequence`][A model of __forward_sequence__][Operation's argument]]
    [[`T`][Any type][Operation's argument]]
]

[heading Expression Semantics]
    __result_of_push_front__<Sequence, T>::type

[*Return type]:

* A model of __forward_sequence__.

[*Semantics]: Returns a sequence with the elements of `Sequence` and an element of type `T` added to the beginning.

[heading Complexity]
Constant.

[heading Header]

    #include <boost/fusion/algorithm/transformation/push_front.hpp>
    #include <boost/fusion/include/push_front.hpp>

[endsect]

[endsect]

[endsect]

[endsect]