Parser combinators are well-known in functional programming languages such as Haskell. In this paper, we describe how they are implemented as a library in Scala, a functional object-oriented language. Thanks to Scala’s flexible syntax, we are able to closely approximate the EBNF notation supported by dedicated parser generators. For the uninitiated, we first explain the concept of parser combinators by developing a minimal library from scratch. We then turn to the existing Scala library, and discuss its features using various examples.

Abstract. An LR(1) parser is a finite-state automaton, equipped with a stack, which uses a combination of its current state and one lookahead symbol in order to determine which action to perform next. We present a validator which, when applied to a context-free grammar G and an automaton A, checks that A and G agree. Validating the parser provides the correctness guarantees required by verified compilers and other high-assurance software that involves parsing. The validation process is independent of which technique was used to construct A. The validator is implemented and proved correct using the Coq proof assistant. As an application, we build a formally-verified parser for the C99 language. 1

We present a functional approach to parsing unrestricted contextfree grammars based on Brzozowski’s derivative of regular expressions. If we consider context-free grammars as recursive regular expressions, Brzozowski’s equational theory extends without modification to context-free grammars (and it generalizes to parser combinators). The supporting actors in this story are three concepts familiar to functional programmers—laziness, memoization and fixed points; these allow Brzozowski’s original equations to be transliterated into purely functional code in about 30 lines spread over three functions. Yet, this almost impossibly brief implementation has a drawback: its performance is sour—in both theory and practice. The culprit? Each derivative can double the size of a grammar, and with it, the cost of the next derivative. Fortunately, much of the new structure inflicted by the derivative is either dead on arrival, or it dies after the very next derivative. To eliminate it, we once again exploit laziness and memoization to transliterate an equational theory that prunes such debris into working code. Thanks to this compaction, parsing times become reasonable in practice. We equip the functional programmer with two equational theories that, when combined, make for an abbreviated understanding and implementation of a system for parsing context-free languages.

Grammars for programming languages are traditionally specified statically. They are hard to compose and reuse due to ambiguities that inevitably arise. PetitParser combines ideas from scannerless parsing, parser combinators, parsing expression grammars and packrat parsers to model grammars and parsers as objects that can be reconfigured dynamically. Through examples and benchmarks we demonstrate that dynamic grammars are not only flexible but highly practical.

Parsing Expression Grammars (PEGs) are specifications of unambiguous recursive-descent style parsers. PEGs incorporate both lexing and parsing phases and have valuable properties, such as being closed under composition. In common with most recursive-descent systems, raw PEGs cannot handle left-recursion; traditional approaches to leftrecursion elimination lead to incorrect parses. In this paper, I show how the approach proposed for direct left-recursive Packrat parsing by Warth et al. can be adapted for ‘pure ’ PEGs. I then demonstrate that this approach results in incorrect parses for some PEGs, before outlining a restrictive subset of left-recursive PEGs which can safely work with this algorithm. Finally I suggest an alteration to Warth et al.’s algorithm that can correctly parse a less restrictive subset of directly recursive PEGs.