pt::pegrammar(n) Parser Tools pt::pegrammar(n)______________________________________________________________________________NAME
pt::pegrammar - Introduction to Parsing Expression Grammars
SYNOPSIS
package require Tcl 8.5
_________________________________________________________________DESCRIPTION
Are you lost ? Do you have trouble understanding this document ? In
that case please read the overview provided by the Introduction to
Parser Tools. This document is the entrypoint to the whole system the
current package is a part of.
Welcome to the introduction to Parsing Expression Grammars (short:
PEG), the formalism used by the Parser Tools. It is assumed that the
reader has a basic knowledge of parsing theory, i.e. Context-Free Gram‐
mars (short: CFG), languages, and associated terms like LL(k), LR(k),
terminal and nonterminal symbols, etc. We do not intend to recapitu‐
late such basic definitions or terms like useful, reachable,
(left/right) recursive, nullable, first/last/follow sets, etc. Please
see the References at the end instead if you are in need of places and
books which provide such background information.
PEGs are formally very similar to CFGs, with terminal and nonterminal
symbols, start symbol, and rules defining the structure of each nonter‐
minal symbol. The main difference lies in the choice(sic!) of choice
operators. Where CFGs use an unordered choice to represent alternatives
PEGs use prioritized choice. Which is fancy way of saying that a parser
has to try the first alternative first and can try the other alterna‐
tives if only if it fails for the first, and so on.
On the CFG side this gives rise to LL(k) and LR(k) for making the
choice deterministic with a bounded lookahead of k terminal symbols,
where LL is in essence topdown aka recursive descent parsing, and LR
bottomup aka shift reduce parsing.
On the PEG side we can parse input with recursive descent and back‐
tracking of failed choices, the latter of which amounts to unlimited
lookahead. By additionally recording the success or failure of nonter‐
minals at the specific locations they were tried at and reusing this
information after backtracking we can avoid the exponential blowup of
running time usually associated with backtracking and keep the parsing
linear. The memory requirements are of course higher due to this cache,
as we are trading space for time.
This is the basic concept behind packrat parsers.
A limitation pure PEGs share with LL(k) CFGs is that left-recursive
grammars cannot be parsed, with the associated recursive descent parser
entering an infinite recursion. This limitation is usually overcome by
extending pure PEGs with explicit operators to specify repetition, zero
or more, and one or more, or, formally spoken, for the kleene closure
and positive kleene closure. This is what the Parser Tools are doing.
Another extension, specific to Parser Tools, is a set of operators
which map more or less directly to various character classes built into
Tcl, i.e. the classes reachable via string is.
The remainder of this document consists of the formal definition of
PEGs for the mathematically inclined, and an appendix listing refer‐
ences to places with more information on PEGs specifically, and parsing
in general.
FORMAL DEFINITION
For the mathematically inclined, a Parsing Expression Grammar is a
4-tuple (VN,VT,R,eS) where
· VN is a set of nonterminal symbols,
· VT is a set of terminal symbols,
· R is a finite set of rules, where each rule is a pair (A,e), A
in VN, and e a parsing expression.
· eS is a parsing expression, the start expression.
Further constraints are
· The intersection of VN and VT is empty.
· For all A in VT exists exactly one pair (A,e) in R. In other
words, R is a function from nonterminal symbols to parsing
expressions.
Parsing expressions are inductively defined via
· The empty string (epsilon) is a parsing expression.
· A terminal symbol a is a parsing expression.
· A nonterminal symbol A is a parsing expression.
· e1e2 is a parsing expression for parsing expressions e1 and 2.
This is called sequence.
· e1/e2 is a parsing expression for parsing expressions e1 and 2.
This is called ordered choice.
· e* is a parsing expression for parsing expression e. This is
called zero-or-more repetitions, also known as kleene closure.
· e+ is a parsing expression for parsing expression e. This is
called one-or-more repetitions, also known as positive kleene
closure.
· !e is a parsing expression for parsing expression e1. This is
called a not lookahead predicate.
· &e is a parsing expression for parsing expression e1. This is
called an and lookahead predicate.
PEGs are used to define a grammatical structure for streams of symbols
over VT. They are a modern phrasing of older formalisms invented by
Alexander Birham. These formalisms were called TS (TMG recognition
scheme), and gTS (generalized TS). Later they were renamed to TPDL
(Top-Down Parsing Languages) and gTPDL (generalized TPDL).
They can be easily implemented by recursive descent parsers with back‐
tracking. This makes them relatives of LL(k) Context-Free Grammars.
REFERENCES
[1] The Packrat Parsing and Parsing Expression Grammars Page
[http://www.pdos.lcs.mit.edu/~baford/packrat/], by Bryan Ford,
Massachusetts Institute of Technology. This is the main entry
page to PEGs, and their realization through Packrat Parsers.
[2] http://en.wikipedia.org/wiki/Parsing_expression_grammar
Wikipedia's entry about Parsing Expression Grammars.
[3] Parsing Techniques - A Practical Guide
[http://www.cs.vu.nl/~dick/PTAPG.html], an online book offering
a clear, accessible, and thorough discussion of many different
parsing techniques with their interrelations and applicabili‐
ties, including error recovery techniques.
[4] Compilers and Compiler Generators [http://scifac.ru.ac.za/com‐
pilers/], an online book using CoCo/R, a generator for recursive
descent parsers.
BUGS, IDEAS, FEEDBACK
This document, and the package it describes, will undoubtedly contain
bugs and other problems. Please report such in the category pt of the
Tcllib SF Trackers [http://sourceforge.net/tracker/?group_id=12883].
Please also report any ideas for enhancements you may have for either
package and/or documentation.
KEYWORDS
EBNF, LL(k), PEG, TDPL, context-free languages, expression, grammar,
matching, parser, parsing expression, parsing expression grammar, push
down automaton, recursive descent, state, top-down parsing languages,
transducer
CATEGORY
Parsing and Grammars
COPYRIGHT
Copyright (c) 2009 Andreas Kupries <andreas_kupries@users.sourceforge.net>
pt 1 pt::pegrammar(n)
