Abstract

For decades we have been using Chomsky's generative system of grammars, particularly context-free grammars (CFGs) and regular expressions (REs), to express the syntax of programming languages and protocols. The power of generative grammars to express ambiguity is crucial to their original purpose of modelling natural languages, but this very power makes it unnecessarily difficult both to express and to parse machine-oriented languages using CFGs. Parsing Expression Grammars (PEGs) provide an alternative, recognition-based formal foundation for describing machineoriented syntax, which solves the ambiguity problem by not introducing ambiguity in the first place. Where CFGs express nondeterministic choice between alternatives, PEGs instead use prioritized choice. PEGs address frequently felt expressiveness limitations of CFGs and REs, simplifying syntax definitions and making it unnecessary to separate their lexical and hierarchical components. A linear-time parser can be built for any PEG, avoiding both the complexity and fickleness of LR parsers and the inefficiency of generalized CFG parsing. While PEGs provide a rich set of operators for constructing grammars, they are reducible to two minimal recognition schemas developed around 1970, TS/TDPL and gTS/GTDPL, which are here proven equivalent in effective recognition power.

Citations

1392	The C++ programming language - Stroustrup - 1991
549	Tree-adjoining grammars - Joshi, Schabes - 1997
132	The syntax definition formalism SDF - reference manual, version 6 - Heering, Hendriks, et al. - 1992
68	Disambiguation filters for scannerless generalized LR parsers - Scheerder, Vinju, et al. - 2002
65	What Can We Do about the Unnecessary Diversity of Notation for Syntactic Definitions - Wirth - 1977
48	Conjunctive grammars - Okhotin - 2001
47	Packrat parsing: Simple, powerful, lazy, linear time - Ford
42	Revised report on the algorithmic language ALGOL 68. Acta Informatica, 5:1–236. de la Clergerie1993] Villemonte de la Clergerie - Wijngaarden - 1975
33	Scannerless NSLR(1) parsing of programming languages - Salomon, Cormack - 1989
30	Indexed grammars—an extension of context-free grammars - Aho - 1968
24	Tw<l-lerrel Gr:ammars - Koster, H
23	Adding semantic and syntactic predicates to LL(k)—pred-LL(k - Parr, Quong
21	Modular Grammars for Programming Language Prototyping - Adams - 1991
21	Fast context-free grammar parsing requires fast Boolean matrix multiplication - Lee - 2002
16	Parsing algorithms with backtrack - Birman, Ullman - 1973
16	Lower bounds for matrix product - Shpilka
16	Noncanonical SLR(1) grammars - Tai - 1979
14	The Theory of Parsing, Translation and Compiling Vol. I: Parsing - Aho, Ullman - 1972
14	Packrat parsing: a practical linear-time algorithm with backtracking - Ford - 2002
14	A family of syntax definition formalisms - Visser - 1995
13	The metafront system: Extensible parsing and transformation - Braband, Schwartzbach, et al. - 2003
10	Parsec, a fast combinator parser. http://www.cs.uu.nl/ ~ daan/parsec.html - Leijen - 2000
6	The TMG Recognition Schema - Birman - 1970
6	Derivational minimalism. Logical Aspects of Computational Linguistics - Stabler - 1997
3	C.: Parsing Techniques—A Practical Guide - Grune, Jacobs - 2008