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 Grammars
       (short:  CFG),  languages, and associated terms like LL(k), LR(k), terminal and nonterminal symbols, etc.
       We do not intend to recapitulate 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  nonterminal  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 alternatives 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 backtracking of failed choices, the  latter
       of  which  amounts  to  unlimited  lookahead.   By  additionally  recording  the  success  or  failure of
       nonterminals 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 references 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 backtracking. 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 applicabilities, including error recovery techniques.

       [4]    Compilers and  Compiler  Generators  [http://scifac.ru.ac.za/compilers/],  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  Trackers  [http://core.tcl.tk/tcllib/reportlist].   Please
       also report any ideas for enhancements you may have for either package and/or documentation.

       When proposing code changes, please provide unified diffs, i.e the output of diff -u.

       Note  further  that  attachments  are strongly preferred over inlined patches. Attachments can be made by
       going to the Edit form of the ticket immediately after its creation, and then using the left-most  button
       in the secondary navigation bar.

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>