A Semantic Framework for PEGs

Parsing Expression Grammars (PEGs) are a recognition-based formalism which allows to describe the syntactical and the lexical elements of a language. The main difference between Context-Free Grammars (CFGs) and PEGs relies on the interpretation of the choice operator: while the CFGs' unordered choice e | e' is interpreted as the union of the languages recognized by e and e, the PEGs' prioritized choice e/e' discards e' if e succeeds. Such subtle, but important difference, changes the language recognized and yields more efficient parsing algorithms. This paper proposes a rewriting logic semantics for PEGs. We start with a rewrite theory giving meaning to the usual constructs in PEGs. Later, we show that cuts, a mechanism for controlling backtracks in PEGs, finds also a natural representation in our framework. We generalize such mechanism, allowing for both local and global cuts with a precise, unified and formal semantics. Hence, our work strives at better understanding and controlling backtracks in parsers for PEGs. The semantics we propose is executable and, besides being a parser with modest efficiency, it can be used as a playground to test different optimization ideas. More importantly, it is a mathematical tool that can be used for different analyses.