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Left Recursion in Parsing Expression Grammars
Parsing Expression Grammars (PEGs) are a formalism that can describe all
deterministic context-free languages through a set of rules that specify a
top-down parser for some language. PEGs are easy to use, and there are
efficient implementations of PEG libraries in several programming languages.
A frequently missed feature of PEGs is left recursion, which is commonly used
in Context-Free Grammars (CFGs) to encode left-associative operations. We
present a simple conservative extension to the semantics of PEGs that gives
useful meaning to direct and indirect left-recursive rules, and show that our
extensions make it easy to express left-recursive idioms from CFGs in PEGs,
with similar results. We prove the conservativeness of these extensions, and
also prove that they work with any left-recursive PEG.
PEGs can also be compiled to programs in a low-level parsing machine. We
present an extension to the semantics of the operations of this parsing machine
that let it interpret left-recursive PEGs, and prove that this extension is
correct with regards to our semantics for left-recursive PEGs.Comment: Extended version of the paper "Left Recursion in Parsing Expression
Grammars", that was published on 2012 Brazilian Symposium on Programming
Language
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