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# reverse_fold

### Synopsis

    template<
          typename Sequence
        , typename State
        , typename BackwardOp
        , typename ForwardOp = _1
        >
    struct reverse_fold
    {
        typedef unspecified type;
    };

### Description

Returns the result of the successive application of binary `BackwardOp` to the result of the previous `BackwardOp` invocation (`State` if it's the first call) and every element in the range [`begin<Sequence>::type`, `end<Sequence>::type`) in reverse order. If `ForwardOp` is provided, then it is applied on forward traversal to form the result that is passed to the first `BackwardOp` call.

### Header

    #include <boost/mpl/reverse_fold.hpp>

### Parameters

Parameter | Requirement | Description
--- | --- | ---
`Sequence` | Forward Sequence | A sequence to iterate.
`State` | Any type | The initial state for the first `BackwardOp` / `ForwardOp` application.
`BackwardOp` | Binary Lambda Expression | The operation to be executed on backward traversal.
`ForwardOp` | Binary Lambda Expression | The operation to be executed on forward traversal.

### Expression semantics

For any Forward Sequence `s`, binary Lambda Expression `backward_op` and `forward_op`, and arbitrary type `state`:

    typedef reverse_fold< s,state,backward_op >::type t;

Return type: | A type
Semantics: | Equivalent to
    typedef lambda<backward_op>::type op;
    typedef reverse_iter_fold<
          s
        , state
        , apply_wrap2< op, _1, deref<_2> >
        >::type t;

    typedef reverse_fold< s,state,backward_op,forward_op >::type t;

Return type: | A type.
Semantics: | Equivalent to
    typedef reverse_fold<
          Sequence
        , fold<s,state,forward_op>::type
        , backward_op
        >::type t;

### Complexity

Linear. Exactly `size<s>::value` applications of `backward_op` and `forward_op`.

### Example

Remove non-negative elements from a sequence [2].

    typedef list_c<int,5,-1,0,-7,-2,0,-5,4> numbers;
    typedef list_c<int,-1,-7,-2,-5> negatives;
    typedef reverse_fold<
          numbers
        , list_c<int>
        , if_< less< _2,int_<0> >, push_front<_1,_2,>, _1 >
        >::type result;

    BOOST_MPL_ASSERT(( equal< negatives,result > ));

[2] | See `remove_if` for a more compact way to do this.

### See also

Algorithms, fold, reverse_iter_fold, iter_fold