Recognition is not parsing — SPPF-style parsing from cubic recognisers

AbstractIn their recogniser forms, the Earley and RIGLR algorithms for testing whether a string can be derived from a grammar are worst-case cubic on general context free grammars (CFG). Earley gave an outline of a method for turning his recognisers into parsers, but it turns out that this method is incorrect. Tomita’s GLR parser returns a shared packed parse forest (SPPF) representation of all derivations of a given string from a given CFG but is worst-case unbounded polynomial order. The parser version of the RIGLR algorithm constructs Tomita-style SPPFs and thus is also worst-case unbounded polynomial order. We have given a modified worst-case cubic GLR algorithm, that, for any string and any CFG, returns a binarised SPPF representation of all possible derivations of a given string. In this paper we apply similar techniques to develop worst-case cubic Earley and RIGLR parsing algorithms

Cotransforming Grammars with Shared Packed Parse Forests

SPPF (shared packed parse forest) is the best known graph representation of a parse forest (family of related parse trees) used in parsing with ambiguous/conjunctive grammars. Systematic general purpose transformations of SPPFs have never been investigated and are considered to be an open problem in software language engineering. In this paper, we motivate the necessity of having a transformation operator suite for SPPFs and extend the state of the art grammar transformation operator suite to metamodel/model (grammar/graph) cotransformations

GLL parsing with flexible combinators

At SLE in 2014, Ridge presented the P3 combinator library with which parsers can be developed for left-recursive, non-deterministic and ambiguous grammars. A combinator expression in P3 yields a binarised grammar reflecting the expression's structure. The grammar is given to an underlying, generalised parsing procedure computing all derivations. In this paper we present a combinator library with a similar architecture to P3, adjusting it to avoid grammar binarisation. Avoiding binarisation has a significant positive effect on the running times of the underlying parsing procedure, which we demonstrate using real-world grammars. Binarisation is avoided by restricting the applicability of combinators, resulting in combinator expressions closely resembling BNF fragments. Usability is recovered by defining coercions that automatically convert expressions where necessary. As the underlying parsing procedure, we use a purely functional variant of generalised top-down (GLL) parsing