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Narrowing and rewriting logic: from foundations to applications. (English) Zbl 1279.68205
López Fraguas, Francisco J. (ed.), Proceedings of the 15th workshop on functional and (constraint) logic programming (WFLP 2006), Madrid, Spain, November 16–17, 2006. Amsterdam: Elsevier. Electronic Notes in Theoretical Computer Science 177, 5-33 (2007).
Summary: Narrowing was originally introduced to solve equational \(E\)-unification problems. It has also been recognized as a key mechanism to unify functional and logic programming. In both cases, narrowing supports equational reasoning and assumes confluent equations. The main goal of this work is to show that narrowing can be greatly generalized, so as to support a much wider range of applications, when it is performed with rewrite theories \((\Sigma, E, R)\), where \((\Sigma, E)\) is an equational theory, and \(R\) is a collection of rewrite rules with no restrictions. Such theories axiomatize concurrent systems, whose states are equivalence classes of terms modulo \(E\), and whose transitions are specified by \(R\). In this context, narrowing is generalized from an equational reasoning technique to a symbolic model checking technique for reachability analysis of a, typically infinite, concurrent system. We survey the foundations of this approach, suitable narrowing strategies, and various applications to security protocol verification, theorem proving, and programming languages.
For the entire collection see [Zbl 1275.68023].

68Q60 Specification and verification (program logics, model checking, etc.)
03B70 Logic in computer science
68Q42 Grammars and rewriting systems
Full Text: DOI
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