Deduction, Strategies, and Rewriting

  • Authors:

  • Steven Eker;Narciso Martí-Oliet;José Meseguer;Alberto Verdejo

  • Affiliations:

  • Computer Science Laboratory, SRI International, Menlo Park, CA, USA;Facultad de Informática, Universidad Complutense de Madrid, Spain;Department of Computer Science, University of Illinois at Urbana-Champaign, IL, USA;Facultad de Informática, Universidad Complutense de Madrid, Spain

  • Venue:
  • Electronic Notes in Theoretical Computer Science (ENTCS)
  • Year:
  • 2007

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Abstract

Automated deduction methods should be specified not procedurally, but declaratively, as inference systems which are proved correct regardless of implementation details. Then, different algorithms to implement a given inference system should be specified as strategies to apply the inference rules. The inference rules themselves can be naturally specified as (possibly conditional) rewrite rules. Using a high-performance rewriting language implementation and a strategy language to guide rewriting computations, we can obtain in a modular way implementations of both the inference rules of automated deduction procedures and of algorithms controling their application. This paper presents the design of a strategy language for the Maude rewriting language that supports this modular decomposition: inference systems are specified in system modules, and strategies in strategy modules. We give a set-theoretic semantics for this strategy language, present its different combinators, illustrate its main ideas with several examples, and describe both a reflective prototype in Maude and an ongoing C++ implementation.