[/
 / Copyright (c) 2008 Eric Niebler
 /
 / 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 Hello Calculator]
[/=======================]

"Hello, world" is nice, but it doesn't get you very far. Let's use Proto to build a 
DSEL (domain-specific embedded language) for a lazily-evaluated calculator. We'll 
see how to define the terminals in your mini-language, how to compose them into 
larger expressions, and how to define an evaluation context so that your 
expressions can do useful work. When we're done, we'll have a mini-language that 
will allow us to declare a lazily-evaluated arithmetic expression, such as 
`(_2 - _1) / _2 * 100`, where `_1` and `_2` are placeholders for values to be 
passed in when the expression is evaluated.

[/=========================]
[heading Defining Terminals]
[/=========================]

The first order of business is to define the placeholders `_1` and `_2`. For that, 
we'll use the _terminal_ metafunction.

    // Define a placeholder type
    template<int I>
    struct placeholder
    {};

    // Define the Protofied placeholder terminals
    proto::terminal<placeholder<0> >::type const _1 = {{}};
    proto::terminal<placeholder<1> >::type const _2 = {{}};

The initialization may look a little odd at first, but there is a good reason
for doing things this way. The objects `_1` and `_2` above do not require
run-time construction -- they are ['statically initialized], which means they
are essentially initialized at compile time. See the
[link boost_proto.appendices.rationale.static_initialization Static
Initialization] section in the [link boost_proto.appendices.rationale Rationale]
appendix for more information.

[/====================================]
[heading Constructing Expression Trees]
[/====================================]

Now that we have terminals, we can use Proto's operator overloads to combine
these terminals into larger expressions. So, for instance, we can immediately
say things like:

    // This builds an expression template
    (_2 - _1) / _2 * 100;

This creates an expression tree with a node for each operator. The type of the
resulting object is large and complex, but we are not terribly interested in it right now.

So far, the object is just a tree representing the expression. It has no
behavior. In particular, it is not yet a calculator. Below we'll see how
to make it a calculator by defining an evaluation context.

[/==================================]
[heading Evaluating Expression Trees]
[/==================================]

No doubt you want your expression templates to actually /do/ something. One
approach is to define an ['evaluation context]. The context is like a function
object that associates behaviors with the node types in your expression tree.
The following example should make it clear. It is explained below.

    struct calculator_context
      : proto::callable_context< calculator_context const >
    {
        // Values to replace the placeholders
        std::vector<double> args;
        
        // Define the result type of the calculator.
        // (This makes the calculator_context "callable".)
        typedef double result_type;

        // Handle the placeholders:
        template<int I>
        double operator()(proto::tag::terminal, placeholder<I>) const
        {
            return this->args[I];
        }
    };

In `calculator_context`, we specify how Proto should evaluate the placeholder
terminals by defining the appropriate overloads of the function call operator.
For any other nodes in the expression tree (e.g., arithmetic operations or
non-placeholder terminals), Proto will evaluate the expression in the "default"
way. For example, a binary plus node is evaluated by first evaluating the left
and right operands and adding the results. Proto's default evaluator uses the
_typeof_ library to compute return types.

Now that we have an evaluation context for our calculator, we can use it to
evaluate our arithmetic expressions, as below:

    calculator_context ctx;
    ctx.args.push_back(45); // the value of _1 is 45
    ctx.args.push_back(50); // the value of _2 is 50

    // Create an arithmetic expression and immediately evaluate it
    double d = proto::eval( (_2 - _1) / _2 * 100, ctx );

    // This prints "10"
    std::cout << d << std::endl;

Later, we'll see how to define more interesting evaluation contexts and
expression transforms that give you total control over how your expressions
are evaluated.

[/===================================]
[heading Customizing Expression Trees]
[/===================================]

Our calculator DSEL is already pretty useful, and for many DSEL scenarios, no more 
would be needed. But let's keep going. Imagine how much nicer it would be if all 
calculator expressions overloaded `operator()` so that they could be used as 
function objects. We can do that by creating a calculator /domain/ and telling 
Proto that all expressions in the calculator domain have extra members. Here is how 
to define a calculator domain:

    // Forward-declare an expression wrapper
    template<typename Expr>
    struct calculator;
    
    // Define a calculator domain. Expression within
    // the calculator domain will be wrapped in the
    // calculator<> expression wrapper.
    struct calculator_domain
      : proto::domain< proto::generator<calculator> >
    {};

The `calculator<>` type will be an expression wrapper. It will behave just like the 
expression that it wraps, but it will have extra member functions that we will 
define. The `calculator_domain` is what informs Proto about our wrapper. It is used 
below in the definition of `calculator<>`. Read on for a description.

    // Define a calculator expression wrapper. It behaves just like
    // the expression it wraps, but with an extra operator() member
    // function that evaluates the expression.    
    template<typename Expr>
    struct calculator
      : proto::extends<Expr, calculator<Expr>, calculator_domain>
    {
        typedef
            proto::extends<Expr, calculator<Expr>, calculator_domain>
        base_type;

        calculator(Expr const &expr = Expr())
          : base_type(expr)
        {}

        typedef double result_type;

        // Overload operator() to invoke proto::eval() with
        // our calculator_context.
        double operator()(double a1 = 0, double a2 = 0) const
        {
            calculator_context ctx;
            ctx.args.push_back(a1);
            ctx.args.push_back(a2);
            
            return proto::eval(*this, ctx);
        }
    };

The `calculator<>` struct is an expression /extension/. It uses `proto::extends<>` to effectively add additional members to an expression type. When composing larger expressions from smaller ones, Proto notes what domain the smaller expressions are in. The larger expression is in the same domain and is automatically wrapped in the domain's extension wrapper.

All that remains to be done is to put our placeholders in the calculator domain. We do that by wrapping them in our `calculator<>` wrapper, as below:

    // Define the Protofied placeholder terminals, in the
    // calculator domain.
    calculator<proto::terminal<placeholder<0> >::type> const _1;
    calculator<proto::terminal<placeholder<1> >::type> const _2;

Any larger expression that contain these placeholders will automatically be wrapped in the `calculator<>` wrapper and have our `operator()` overload. That means we can use them as function objects as follows.

    double result = ((_2 - _1) / _2 * 100)(45.0, 50.0);
    assert(result == (50.0 - 45.0) / 50.0 * 100));

Since calculator expressions are now valid function objects, we can use them with standard algorithms, as shown below:

    double a1[4] = { 56, 84, 37, 69 };
    double a2[4] = { 65, 120, 60, 70 };
    double a3[4] = { 0 };

    // Use std::transform() and a calculator expression
    // to calculate percentages given two input sequences:
    std::transform(a1, a1+4, a2, a3, (_2 - _1) / _2 * 100);

Now, let's use the calculator example to explore some other useful features of Proto.

[/====================================]
[heading Detecting Invalid Expressions]
[/====================================]

You may have noticed that you didn't have to define an overloaded `operator-()` or 
`operator/()` -- Proto defined them for you. In fact, Proto overloads /all/ the 
operators for you, even though they may not mean anything in your domain-specific 
language. That means it may be possible to create expressions that are invalid in 
your domain. You can detect invalid expressions with Proto by defining the 
/grammar/ of your domain-specific language.

For simplicity, assume that our calculator DSEL should only allow addition, 
subtraction, multiplication and division. Any expression involving any other 
operator is invalid. Using Proto, we can state this requirement by defining the 
grammar of the calculator DSEL. It looks as follows:

    // Define the grammar of calculator expressions
    struct calculator_grammar
      : proto::or_<
            proto::plus< calculator_grammar, calculator_grammar >
          , proto::minus< calculator_grammar, calculator_grammar >
          , proto::multiplies< calculator_grammar, calculator_grammar >
          , proto::divides< calculator_grammar, calculator_grammar >
          , proto::terminal< proto::_ >
        >
    {};

You can read the above grammar as follows: an expression tree conforms to the calculator grammar if it is a binary plus, minus, multiplies or divides node, where both child nodes also conform to the calculator grammar; or if it is a terminal. In a Proto grammar, _wild_ is a wildcard that matches any type, so `proto::terminal< proto::_ >` matches any terminal, whether it is a placeholder or a literal.

[note This grammar is actually a little looser than we would like. Only placeholders and literals that are convertible to doubles are valid terminals. Later on we'll see how to express things like that in Proto grammars.]

Once you have defined the grammar of your DSEL, you can use the _matches_ metafunction to check whether a given expression type conforms to the grammar. For instance, we might add the following to our `calculator::operator()` overload:

    template<typename Expr>
    struct calculator
      : proto::extends< /* ... as before ... */ >
    {
        /* ... */
        double operator()(double a1 = 0, double a2 = 0) const
        {
            // Check here that the expression we are about to
            // evaluate actually conforms to the calculator grammar.
            BOOST_MPL_ASSERT((proto::matches<Expr, calculator_grammar>));
            /* ... */
        }
    };

The addition of the `BOOST_MPL_ASSERT()` line enforces at compile time that we only 
evaluate expressions that conform to the calculator DSEL's grammar. With Proto 
grammars, `proto::matches<>` and `BOOST_MPL_ASSERT()` it is very easy to give the 
users of your DSEL short and readable compile-time errors when they accidentally 
misuse your DSEL.

[note `BOOST_MPL_ASSERT()` is part of the Boost Metaprogramming Library. To use it, 
just `#include <boost/mpl/assert.hpp>`.]

[/=====================================]
[heading Controlling Operator Overloads]
[/=====================================]

Grammars and `proto::matches<>` make it possible to detect when a user has created 
an invalid expression and issue a compile-time error. But what if you want to 
prevent users from creating invalid expressions in the first place? By using 
grammars and domains together, you can disable any of Proto's operator overloads 
that would create an invalid expression. It is as simple as specifying the DSEL's 
grammar when you define the domain, as shown below:

    // Define a calculator domain. Expression within
    // the calculator domain will be wrapped in the
    // calculator<> expression wrapper.
    // NEW: Any operator overloads that would create an
    //      expression that does not conform to the
    //      calculator grammar is automatically disabled.
    struct calculator_domain
      : proto::domain< proto::generator<calculator>, calculator_grammar >
    {};

The only thing we changed is we added `calculator_grammar` as the second template 
parameter to the `proto::domain<>` template when defining `calculator_domain`. With 
this simple addition, we disable any of Proto's operator overloads that would 
create an invalid calculator expression.

[/========================]
[heading ... And Much More]
[/========================]

Hopefully, this gives you an idea of what sorts of things Proto can do for you. But 
this only scratches the surface. The rest of this users' guide will describe all 
these features and others in more detail.

Happy metaprogramming!

[endsect]