grammars.qbk

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There is one more way you can perform a fuzzy match on terminals. Consider the
problem of trying to match a `std::complex<>` terminal. You can easily match
a `std::complex<float>` or a `std::complex<double>`, but how would you match
any instantiation of `std::complex<>`? You can use `proto::_` here to solve
this problem. Here is the grammar to match any `std::complex<>` instantiation:

    struct StdComplex
      : terminal< std::complex< _ > >
    {};

When given a grammar like this, Proto will deconstruct the grammar and the
terminal it is being matched against and see if it can match all the
constituents.

[endsect]

[/====================================================]
[section:if_and_not [^if_<>], [^and_<>], and [^not_<>]]
[/====================================================]

We've already seen how to use expression generators like `terminal<>` and
`shift_right<>` as grammars. We've also seen _or_, which we can use to
express a set of alternate grammars. There are a few others of interest; in
particular, _if_, _and_ and _not_.

The _not_ template is the simplest. It takes a grammar as a template parameter
and logically negates it; `not_<Grammar>` will match any expression that
`Grammar` does /not/ match.

The _if_ template is used together with a Proto transform that is evaluated
against expression types to find matches. (Proto transforms will be described
later.)

The _and_ template is like _or_, except that each argument of the _and_ must
match in order for the _and_ to match. As an example, consider the definition
of `CharString` above that uses _exact_. It could have been written without
_exact_ as follows:

    struct CharString
      : and_<
            terminal< _ >
          , if_< is_same< _arg, char const * >() >
        >
    {};

This says that a `CharString` must be a terminal, /and/ its argument must be
the same as `char const *`. Notice the template argument of _if_:
`is_same< _arg, char const * >()`. This is Proto transform that compares the
argument of a terminal to `char const *`.

The _if_ template has a couple of variants. In additon to `if_<Condition>` you
can also say `if_<Condition, ThenGrammar>` and
`if_<Condition, ThenGrammar, ElseGrammar>`. These let you select one sub-grammar
or another based on the `Condition`.

[endsect]

[/==================================]
[section Matching Vararg Expressions]
[/==================================]

Not all of C++'s overloadable operators are unary or binary. There is the
oddball `operator()` -- the function call operator -- which can have any number
of arguments. Likewise, with Proto you may define your own "operators" that
could also take more that two arguments. As a result, there may be nodes in
your Proto expression tree that have an arbitrary number of children (up to
some predefined maximum). How do you write a grammar to match such a node?

For such cases, Proto provides the _vararg_ class template. Its template
argument is a grammar, and the _vararg_ will match the grammar zero or more
times. Consider a Proto lazy function called `fun()` that can take zero or
more characters as arguments, as follows:

    struct fun_tag {};
    struct FunTag : terminal< fun_tag > {};
    FunTag::type const fun = {{}};

    // example usage:
    fun();
    fun('a');
    fun('a', 'b');
    ...

Below is the grammar that matches all the allowable invocations of `fun()`:

    struct FunCall
      : function< FunTag, vararg< terminal< char > > >
    {};

The `FunCall` grammar uses _vararg_ to match zero or more character literals
as arguments of the `fun()` function.

As another example, can you guess what the following grammar matches?

    struct Foo
      : or_<
            terminal< _ >
          , nary_expr< _, vararg< Foo > >
        >
    {};

Here's a hint: the first template parameter to `nary_expr<>` represents the
node type, and any additional template parameters represent children nodes. The
answer is that this is a degenerate grammar that matches every possible
expression tree, from root to leaves.

[endsect]

[/=============================]
[section Defining DSEL Grammars]
[/=============================]

We've already seen how to use small grammars to answer simple questions about
expression trees. Here's a harder question: ["Does this expression conform to the
grammar of my domain-specific embedded language?] In this section we'll see how
to use Proto to define a grammar for your DSEL and use it to validate
expression templates, giving short, readable compile-time errors for invalid
expressions.

[tip You might be thinking that this is a backwards way of doing things.
["If Proto let me select which operators to overload, my users wouldn't be able
to create invalid expressions in the first place, and I wouldn't need a grammar
at all!] That may be true, but there are reasons for preferring to do things
this way.

First, it lets you develop your DSEL rapidly -- all the operators are
there for you already! -- and worry about invalid syntax later.

Second, it
might be the case that some operators are only allowed in certain contexts
within your DSEL. This is easy to express with a grammar, and hard to do with
straight operator overloading. 

Third, using a DSEL grammar to flag invalid
expressions can often yield better errors than manually selecting the
overloaded operators. 

Fourth, the grammar can be used for more than just
validation. As we'll see later, you can use your grammar to define ['tree
transformations] that convert expression templates into other more useful
objects.

If none of the above convinces you, you actually /can/ use Proto to control
which operators are overloaded within your domain. And to do it, you need to 
define a grammar! We'll see how later.
]

In a previous section, we used Proto to define a DSEL for a lazily evaluated
calculator that allowed any combination of placeholders, floating-point
literals, addition, subtraction, multiplaction, division and grouping. If
we were to write the grammar for this DSEL in
[@http://en.wikipedia.org/wiki/Extended_Backus_Naur_Form EBNF], it might look
like this:

[pre
group       ::= '(' expression ')'
factor      ::= double | placeholder1 | placeholder2 | group
term        ::= factor (('*' factor) | ('/' factor))*
expression  ::= term (('+' term) | ('-' term))*
]

This captures the syntax, associativity and precedence rules of a calculator.
Writing the grammar for our calculator DSEL using Proto is /even simpler/.
Since we are using C++ as the host language, we are bound to the associativity
and precedence rules for the C++ operators. Our grammar can assume them. Also,
in C++ grouping is already handled for us with the use of parenthesis, so we
don't have to code that into our grammar.

Let's begin our grammar for forward-declaring it:

    struct CalculatorGrammar;

It's an incomplete type at this point, but we'll still be able to use it to
define the rules of our grammar. Let's define grammar rules for the terminals:

    struct Double
      : terminal< convertible_to< double > >
    {};

    struct Placeholder1
      : terminal< placeholder1 >
    {};

    struct Placeholder2
      : terminal< placeholder2 >
    {};

    struct Terminal
      : or_< Double, Placeholder1, Placeholder2 >
    {};

Now let's define the rules for addition, subtraction, multiplication and
division. Here, we can ignore issues of associativity and precedence -- the C++
compiler will enforce that for us. We only must enforce that the arguments to
the operators must themselves conform to the `CalculatorGrammar` that we
forward-declared above.

    struct Plus
      : plus< CalculatorGrammar, CalculatorGrammar >
    {};

    struct Minus
      : minus< CalculatorGrammar, CalculatorGrammar >
    {};

    struct Multiplies
      : multiplies< CalculatorGrammar, CalculatorGrammar >
    {};

    struct Divides
      : divides< CalculatorGrammar, CalculatorGrammar >
    {};

Now that we've defined all the parts of the grammar, we can define
`CalculatorGrammar`:

    struct CalculatorGrammar
      : or_<
            Terminal
          , Plus
          , Minus
          , Multiplies
          , Divides
        >
    {};

That's it! Now we can use `CalculatorGrammar` to enforce that an expression
template conforms to our grammar. We can use _matches_ and `BOOST_MPL_ASSERT()`
to issue readable compile-time errors for invalid expressions, as below:

    template< typename Expr >
    void evaluate( Expr const & expr )
    {
        BOOST_MPL_ASSERT(( matches< Expr, CalculatorGrammar > ));
        // ...
    }

[endsect]

[endsect]