[/==============================================================================
    Copyright (C) 2001-2010 Joel de Guzman
    Copyright (C) 2001-2005 Dan Marsden
    Copyright (C) 2001-2010 Thomas Heller

    Distributed under 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 Transforming the Expression Tree]

This example will show how to write __phoenix_actions__ that transform the
Phoenix AST.

[:
"/Lisp macros transform the program structure itself, with the full language
available to express such transformations./"

[@http://en.wikipedia.org/wiki/Lisp_macro#Lisp_macros Wikipedia]
]

What we want to do is to invert some arithmetic operators, i.e. plus will be
transformed to minus, minus to plus, multiplication to division and division to
multiplication.

Let's start with defining our default action:

    struct invert_actions
    {
        template <typename Rule>
        struct when
            : proto::_ // the default is proto::_
        {};
    };

By default, we don't want to do anything, well, not exactly nothing, but just
return the expression. This is done by
[@http://www.boost.org/doc/libs/release/doc/html/boost/proto/_.html proto::_]
which, used as a transform, just passes the current expression along. Making this
action an identity transform.

[def __proto_make_expr__     [@http://www.boost.org/doc/libs/release/doc/html/boost/proto/functional/make_expr.html `proto::functional::make_expr`]]

So, after the basics are set up, we can start by writing the transformations we
want to have on our tree:

    // Transform plus to minus
    template <>
    struct invert_actions::when<phoenix::rule::plus>
        : __proto_call__<
            __proto_make_expr__<proto::tag::minus>(
                phoenix::evaluator(proto::_left, phoenix::_context)
              , phoenix::evaluator(proto::_right, phoenix::_context)
            )
        >
    {};

Wow, this looks complicated! Granted you need to know a little bit about __proto__
(For a good introduction read through the 
 [@http://cpp-next.com/archive/2010/08/expressive-c-introduction/ Expressive C++] series).

What is done is the following:

* The left expression is passed to evaluator (with the current context, that contains our invert_actions)
* The right expression is passed to evaluator (with the current context, that contains our invert_actions)
* The result of these two __proto_transforms__ is passed to __proto_make_expr__ which returns the freshly created expression

After you know what is going on, maybe the rest doesn't look so scary anymore:

    // Transform minus to plus
    template <>
    struct invert_actions::when<phoenix::rule::minus>
        : __proto_call__<
            __proto_make_expr__<proto::tag::plus>(
                phoenix::evaluator(proto::_left, phoenix::_context)
              , phoenix::evaluator(proto::_right, phoenix::_context)
            )
        >
    {};

    // Transform multiplies to divides
    template <>
    struct invert_actions::when<phoenix::rule::multiplies>
        : __proto_call__<
            __proto_make_expr__<proto::tag::divides>(
                phoenix::evaluator(proto::_left, phoenix::_context)
              , phoenix::evaluator(proto::_right, phoenix::_context)
            )
        >
    {};

    // Transform divides to multiplies
    template <>
    struct invert_actions::when<phoenix::rule::divides>
        : __proto_call__<
            __proto_make_expr__<proto::tag::multiplies>(
                phoenix::evaluator(proto::_left, phoenix::_context)
              , phoenix::evaluator(proto::_right, phoenix::_context)
            )
        >
    {};

That's it! Now that we have our actions defined, we want to evaluate some of our expressions with them:

    template <typename Expr>
    // Calculate the result type: our transformed AST
    typename boost::result_of<
        phoenix::evaluator(
            Expr const&
          , phoenix::result_of::context<int, invert_actions>::type
        )
    >::type
    invert(Expr const & expr)
    {
        return 
            // Evaluate it with our actions
            phoenix::eval(
                expr
              , phoenix::context(
                    int()
                  , invert_actions()
                )
            );
    }

Run some tests to see if it is working:

    invert(_1);                    // --> _1
    invert(_1 + _2);               // --> _1 - _2
    invert(_1 + _2 - _3);          // --> _1 - _2 + _3
    invert(_1 * _2);               // --> _1 / _2
    invert(_1 * _2 / _3);          // --> _1 / _2 * _3
    invert(_1 * _2 + _3);          // --> _1 / _2 - _3
    invert(_1 * _2 - _3);          // --> _1 / _2 + _2
    invert(if_(_1 * _4)[_2 - _3]); // --> if_(_1 / _4)[_2 + _3]
    _1 * invert(_2 - _3));         // --> _1 * _2 + _3

__note__ The complete example can be found here: [@../../example/invert.cpp example/invert.cpp]

/Pretty simple .../

[endsect]