[/==============================================================================
    Copyright (C) 2001-2015 Joel de Guzman
    Copyright (C) 2001-2011 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.

[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]
