Parsing Expression Grammar (PEG) is a recognition-based foundation for describing syntax that renewed interest in top-down parsing approaches. Generally, the implementation of PEGs is based on a recursive-descent parser, or uses a memoization algorithm.We present a new approach for implementing PEGs, based on a virtual parsing machine, which is more suitable for pattern matching. Each PEG has a corresponding program that is executed by the parsing machine, and new programs are dynamically created and composed. The virtual machine is embedded in a scripting language and used by a patternmatching tool.We give an operational semantics of PEGs used for pattern matching, then describe our parsing machine and its semantics. We show how to transform PEGs to parsing machine programs, and give a correctness proof of our transformation.

Context-Free Grammars (CFGs) and Parsing Expression Grammars (PEGs) have several similarities and a few differences in both their syntax and semantics, but they are usually presented through formalisms that hinder a proper comparison. In this paper we present a new formalism for CFGs that highlights the similarities and differences between them. The new formalism borrows from PEGs the use of parsing expressions and the recognition-based semantics. We show how one way of removing non-determinism from this formalism yields a formalism with the semantics of PEGs. We also prove, based on these new formalisms, how LL(1) grammars define the same language whether interpreted as CFGs or as PEGs, and also show how strong-LL(k), right-linear, and LLregular grammars have simple language-preserving translations from CFGs to PEGs. Once these classes of CFGs can be automatically translated to equivalent PEGs, we can reuse classic top-down grammars in PEG-based tools.

Parsing Expression Grammars (PEGs) describe top-down parsers. Unfortunately, the errorreporting techniques used in conventional top-down parsers do not directly apply to parsers based on Parsing Expression Grammars (PEGs), so they have to be somehow simulated. While the PEG formalism has no account of semantic actions, actual PEG implementations add them, and we show how to simulate an error-reporting heuristic through these semantic actions.We also propose a complementary error reporting strategy that may lead to better error messages: labeled failures. This approach is inspired by exception handling of programming languages, and lets a PEG define different kinds of failure, with each ordered choice operator specifying which kinds it catches. Labeled failures give a way to annotate grammars for better error reporting, to express some of the error reporting strategies used by deterministic parser combinators, and to encode predictive top-down parsing in a PEG.

Abstract. 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.

Most scripting languages nowadays use regex pattern-matching libraries. These regex libraries borrow the syntax of regular expressions, but have an informal semantics that is different from the semantics of regular expressions, removing the commutativity of alternation and adding ad-hoc extensions that cannot be expressed by formalisms for efficient recognition of regular languages, such as deterministic finite automata.Parsing Expression Grammars are a formalism that can describe all deterministic context-free languages and has a simple computational model. In this paper, we present a formalization of regexes via transformation to Parsing Expression Grammars. The proposed transformation easily accommodates several of the common regex extensions, giving a formal meaning to them. It also provides a clear computational model that helps to estimate the efficiency of regex-based matchers, and a basis for specifying provably correct optimizations for them.