Parsing Expression Grammar

In computer science, a parsing expression grammar, or PEG, is a type of analytic formal grammar, i.e. it describes a formal language in terms of a set of rules for recognizing strings in the language. The formalism was introduced by Bryan Ford in 2004 and is closely related to the family of top-down parsing languages introduced in the early 1970s. Syntactically, PEGs also look similar to context-free grammars (CFGs), but they have a different interpretation: the choice operator selects the first match in PEG, while it is ambiguous in CFG. This is closer to how string recognition tends to be done in practice, e.g. by a recursive descent parser.

Unlike CFGs, PEGs cannot be ambiguous; if a string parses, it has exactly one valid parse tree. It is conjectured that there exist context-free languages that cannot be parsed by a PEG, but this is not yet proven. PEGs are well-suited to parsing computer languages (and artificial human languages such as Lojban), but not natural languages where their performance is comparable to general CFG algorithms such as the Earley algorithm.

Formally, a parsing expression grammar consists of:

Each parsing rule in P has the form A ← e, where A is a nonterminal symbol and e is a parsing expression. A parsing expression is a hierarchical expression similar to a regular expression, which is constructed in the following fashion:

The fundamental difference between context-free grammars and parsing expression grammars is that the PEG's choice operator is ordered. If the first alternative succeeds, the second alternative is ignored. Thus ordered choice is not commutative, unlike unordered choice as in context-free grammars. Ordered choice is analogous to soft cut operators available in some logic programming languages.

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