Roman Numerals

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#### Roman Numerals

This example demonstrates:

- symbol table
- rule
- grammar

###### Symbol Table

The symbol table holds a dictionary of symbols where each symbol is a sequence of characters (a `char`, `wchar_t`, `int`, enumeration etc.) . The template class, parameterized by the character type, can work efficiently with 8, 16, 32 and even 64 bit characters. Mutable data of type T are associated with each symbol.

Traditionally, symbol table management is maintained separately outside the BNF grammar through semantic actions. Contrary to standard practice, the Spirit symbol table class `symbols` is a parser. An object of which may be used anywhere in the EBNF grammar specification. It is an example of a dynamic parser. A dynamic parser is characterized by its ability to modify its behavior at run time. Initially, an empty symbols object matches nothing. At any time, symbols may be added or removed, thus, dynamically altering its behavior.

Each entry in a symbol table has an associated mutable data slot. In this regard, one can view the symbol table as an associative container (or map) of key-value pairs where the keys are strings.

The symbols class expects two template parameters. The first parameter specifies the character type of the symbols. The second specifies the data type associated with each symbol: its attribute.

Here's a parser for roman hundreds (100..900) using the symbol table. Keep in mind that the data associated with each slot is the parser's attribute (which is passed to attached semantic actions).

    struct hundreds_ : qi::symbols<char, unsigned>
    {
        hundreds_()
        {
            add
                ("C"    , 100)
                ("CC"   , 200)
                ("CCC"  , 300)
                ("CD"   , 400)
                ("D"    , 500)
                ("DC"   , 600)
                ("DCC"  , 700)
                ("DCCC" , 800)
                ("CM"   , 900)
            ;
        }

    } hundreds;

Here's a parser for roman tens (10..90):

    struct tens_ : qi::symbols<char, unsigned>
    {
        tens_()
        {
            add
                ("X"    , 10)
                ("XX"   , 20)
                ("XXX"  , 30)
                ("XL"   , 40)
                ("L"    , 50)
                ("LX"   , 60)
                ("LXX"  , 70)
                ("LXXX" , 80)
                ("XC"   , 90)
            ;
        }

    } tens;

and, finally, for ones (1..9):

    struct ones_ : qi::symbols<char, unsigned>
    {
        ones_()
        {
            add
                ("I"    , 1)
                ("II"   , 2)
                ("III"  , 3)
                ("IV"   , 4)
                ("V"    , 5)
                ("VI"   , 6)
                ("VII"  , 7)
                ("VIII" , 8)
                ("IX"   , 9)
            ;
        }

    } ones;

Now we can use `hundreds`, `tens` and `ones` anywhere in our parser expressions. They are all parsers.

###### Rules

Up until now, we've been inlining our parser expressions, passing them directly to the `phrase_parse` function. The expression evaluates into a temporary, unnamed parser which is passed into the `phrase_parse` function, used, and then destroyed. This is fine for small parsers. When the expressions get complicated, you'd want to break the expressions into smaller easier-to-understand pieces, name them, and refer to them from other parser expressions by name.

A parser expression can be assigned to what is called a "rule". There are various ways to declare rules. The simplest form is:

    rule<Iterator> r;

At the very least, the rule needs to know the iterator type it will be working on. This rule cannot be used with `phrase_parse`. It can only be used with the `parse` function -- a version that does not do white space skipping (does not have the skipper argument). If you want to have it skip white spaces, you need to pass in the type skip parser, as in the next form:

    rule<Iterator, Skipper> r;

Example:

    rule<std::string::iterator, space_type> r;

This type of rule can be used for both `phrase_parse` and `parse`.

For our next example, there's one more rule form you should know about:

    rule<Iterator, Signature> r;

or

    rule<Iterator, Signature, Skipper> r;

| Tip
All rule template arguments after Iterator can be supplied in any order.

The Signature specifies the attributes of the rule. You've seen that our parsers can have an attribute. Recall that the `double_` parser has an attribute of `double`. To be precise, these are synthesized attributes. The parser "synthesizes" the attribute value. Think of them as function return values.

There's another type of attribute called "inherited" attribute. We won't need them for now, but it's good that you be aware of such attributes. You can think of them as function arguments. And, rightly so, the rule signature is a function signature of the form:

    result(argN, argN,..., argN)

After having declared a rule, you can now assign any parser expression to it. Example:

    r = double_ >> *(',' >> double_);

###### Grammars

A grammar encapsulates one or more rules. It has the same template parameters as the rule. You declare a grammar by:

1. deriving a struct (or class) from the `grammar` class template
2. declare one or more rules as member variables
3. initialize the base grammar class by giving it the start rule (its the first rule that gets called when the grammar starts parsing)
4. initialize your rules in your constructor

The roman numeral grammar is a very nice and simple example of a grammar:

    template <typename Iterator>
    struct roman : qi::grammar<Iterator, unsigned()>
    {
        roman() : roman::base_type(start)
        {
            using qi::eps;
            using qi::lit;
            using qi::_val;
            using qi::_1;
            using ascii::char_;

            start = eps             [_val = 0] >>
                (
                    +lit('M')       [_val += 1000]
                    ||  hundreds    [_val += _1]
                    ||  tens        [_val += _1]
                    ||  ones        [_val += _1]
                )
            ;
        }

        qi::rule<Iterator, unsigned()> start;
    };

Things to take notice of:

- The grammar and start rule signature is `unsigned()`. It has a synthesized attribute (return value) of type `unsigned` with no inherited attributes (arguments).
- We did not specify a skip-parser. We don't want to skip in between the numerals.
- `roman::base_type` is a typedef for `grammar<Iterator, unsigned()>`. If `roman` was not a template, you could simply write: base_type(start)
- It's best to make your grammar templates such that they can be reused for different iterator types.
- `_val` is another Phoenix placeholder representing the rule's synthesized attribute.
- `eps` is a special spirit parser that consumes no input but is always successful. We use it to initialize `_val`, the rule's synthesized attribute, to zero before anything else. The actual parser starts at `+lit('M')`, parsing roman thousands. Using `eps` this way is good for doing pre and post initializations.
- The expression `a || b` reads: match a or b and in sequence. That is, if both `a` and `b` match, it must be in sequence; this is equivalent to `a >> -b | b`, but more efficient.

###### Let's Parse!

    bool r = parse(iter, end, roman_parser, result);

    if (r && iter == end)
    {
        std::cout << "-------------------------\n";
        std::cout << "Parsing succeeded\n";
        std::cout << "result = " << result << std::endl;
        std::cout << "-------------------------\n";
    }
    else
    {
        std::string rest(iter, end);
        std::cout << "-------------------------\n";
        std::cout << "Parsing failed\n";
        std::cout << "stopped at: \": " << rest << "\"\n";
        std::cout << "-------------------------\n";
    }

`roman_parser` is an object of type `roman`, our roman numeral parser. This time around we are using the no-skipping version of the parse functions. We do not want to skip any spaces! We are also passing in an attribute, `unsigned result`, which will receive the parsed value.

The full cpp file for this example can be found here: ../../example/qi/roman.cpp