[/==============================================================================
    Copyright (C) 2001-2010 Joel de Guzman
    Copyright (C) 2001-2010 Hartmut Kaiser

    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 Syntax Diagram]

In the next section, we will deal with Parsing Expression Grammars
(PEG) [footnote Bryan Ford: Parsing Expression Grammars: A Recognition-Based 
Syntactic Foundation, [@http://pdos.csail.mit.edu/~baford/packrat/popl04/]], 
a variant of Extended Backus-Naur Form (EBNF) [footnote Richard E. Pattis: EBNF: 
A Notation to Describe Syntax, [@http://www.cs.cmu.edu/~pattis/misc/ebnf.pdf]]
with a different interpretation. It is easier to understand PEG using Syntax 
Diagrams. Syntax diagrams represent a grammar graphically. It was used extensively
by Niklaus Wirth [footnote Niklaus Wirth: The Programming Language
Pascal. (July 1973)] in the "Pascal User Manual". Syntax Diagrams are
easily understandable by programmers due to their similarity to flow
charts. The isomorphism of the diagrams and functions make them ideal for
representing __rd__ parsers which are essentially mutually recursive
functions.

Historically, Parsing Expression Grammars have been used for describing grammars
for parsers only (hence the name). In __spirit__ we use a very similar notation 
for output generation as well. Almost all the concepts described here are 
equally applicable both to __qi__ parsers and to __karma__ generators.

[heading Elements]

All diagrams have one entry and one exit point. Arrows connect all possible
paths through the grammar from the entry point to the exit point.

[:__sd_start_stop__]

Terminals are represented by round boxes. Terminals are atomic and
usually represent plain characters, strings or tokens.

[:__sd_terminals__]

Non-terminals are represented by boxes. Diagrams are modularized using
named non-terminals. A complex diagram can be broken down into a set of
non-terminals. Non-terminals also allow recursion (i.e. a non-terminal
can call itself).

[:__sd_non_terminals__]

[heading Constructs]

The most basic composition is the Sequence. B follows A:

[:__sd_sequence__]

The ordered choice henceforth we will call /alternatives/. In PEG,
ordered choice and alternatives are not quite the same. PEG allows
ambiguity of choice where one or more branches can succeed. In PEG, in
case of ambiguity, the first one always wins.

[:__sd_choice__]

The optional (zero-or-one):

[:__sd_optional__]

Now, the loops. We have the zero-or-more and one-or-more:

[:__sd_kleene__]
[:__sd_plus__]

Take note that, as in PEG, these loops behave greedily. If there is
another 'A' just before the end-point, it will always fail because the
preceding loop has already exhausted all 'A's and there is nothing more
left. This is a crucial difference between PEG and general Context Free
Grammars (CFGs). This behavior is quite obvious with syntax diagrams as
they resemble flow-charts.

[heading Predicates]

Now, the following are Syntax Diagram versions of PEG predicates. These
are not traditionally found in Syntax Diagrams. These are special
extensions we invented to closely follow PEGs.

First, we introduce a new element, the Predicate:

[:__sd_predicate__]

This is similar to the conditionals in flow charts where the 'No' branch
is absent and always signals a failed parse.

We have two versions of the predicate, the /And-Predicate/ and the
/Not-Predicate/:

[:__sd_and_predicate__]
[:__sd_not_predicate__]

The /And-Predicate/ tries the predicate, P, and succeeds if P succeeds,
or otherwise fail. The opposite is true with the /Not-Predicate/. It
tries the predicate, P, and fails if P succeeds, or otherwise succeeds.
Both versions do a look-ahead but do not consume any input regardless if
P succeeds or not.

[endsect]