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Using Linear Positional Grammars for the LR Parsing of 2-D Symbolic Languages

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Grammars

Abstract

In this paper we present a grammar formalism for the generation and parsing of two-dimensional symbolic languages. Linear Positional Grammars (or LPGs for short) are an immediate generalization of the context-free string grammars. Through the use of general spatial relations they allow the definition of pictures whose symbols span on a two-dimensional space. Due to their analogy to context-free string grammars, LPGs can be used to construct an LR-based parser which uses the spatial relations to navigate the input. We study ambiguous grammars and present several ways to solve them. Moreover we provide an algorithm to translate a linear positional grammar into a context-free grammar with actions and suggest a general methodology to parse two-dimensional symbolic languages by making use of the well-known tool YACC (Yet Another Compiler-Compiler [25]). As an example, we construct a parser for a subset of the two-dimensional arithmetical expression language.

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Authors and Affiliations

  1. Dipartimento di Matematica ed Informatica, Università di Salerno, 84081, Baronissi (SA), Italy. E-mail

    Gennaro Costagliola

  2. Department of Computer Science, University of Pittsburgh, Pittsburgh, PA, 15260, U.S.A. E-mail

    Shi-Kuo Chang

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  1. Gennaro Costagliola
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  2. Shi-Kuo Chang
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Costagliola, G., Chang, SK. Using Linear Positional Grammars for the LR Parsing of 2-D Symbolic Languages. Grammars 2, 1–34 (1999). https://doi.org/10.1023/A:1006926614934

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