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

Parse Forest Diagnostics with Dr. Ambiguity

In this paper we propose and evaluate a method for locating causes of ambiguity in context-free grammars by automatic analysis of parse forests. A parse forest is the set of parse trees of an ambiguous sentence. % an output of a static ambiguity detection tool that has detected ambiguity in a context-free grammar or of a general parser that has accidentally parsed an ambiguous sentence. Deducing causes of ambiguity from observing parse forests is hard for grammar engineers because of (a) the size of the parse forests, (b) the complex shape of parse forests, and (c) the diversity of causes of ambiguity. We first analyze the diversity of ambiguities in grammars for programming languages and the diversity of solutions to these ambiguities. Then we introduce \drambiguity: a parse forest diagnostics tools that explains the causes of ambiguity by analyzing differences between parse trees and proposes solutions. We demonstrate its effectiveness using a small experiment with a grammar for Java 5

Purely functional GLL parsing

Generalised parsing has become increasingly important in the context of software language design and several compiler generators and language workbenches have adopted generalised parsing algorithms such as GLR and GLL. The original GLL parsing algorithms are described in low-level pseudo-code as the output of a parser generator. This paper explains GLL parsing differently, defining the FUN-GLL algorithm as a collection of pure, mathematical functions and focussing on the logic of the algorithm by omitting implementation details. In particular, the data structures are modelled by abstract sets and relations rather than specialised implementations. The description is further simplified by omitting lookahead and adopting the binary subtree representation of derivations to avoid the clerical overhead of graph construction. Conventional parser combinators inherit the drawbacks from the recursive descent algorithms they implement. Based on FUN-GLL, this paper defines generalised parser combinators that overcome these problems. Th