Termination of Rewriting under Strategies

Isabelle Gnaedig 1 Hélène Kirchner 2
1 CARTE - Theoretical adverse computations, and safety
Inria Nancy - Grand Est, LORIA - FM - Department of Formal Methods
2 PAREO - Formal islands: foundations and applications
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : A termination proof method for rewriting under strategies, based on an explicit induction on the termination property, is presented and instantiated for the innermost, outermost and local strategies. Rewriting trees are simulated by proof trees generated with an abstraction mechanism, narrowing and constraints representing sets of ground terms. Abstraction introduce variables to represent normal forms without computing them and to control the narrowing mechanism, well-known to easily diverge. The induction ordering is not given a priori, but defined with ordering constraints, incrementally set during the proof. It is established that termination under strategy is equivalent to the construction of finite proof trees schematizing terminating rewriting trees. Sufficient effective conditions to ensure finiteness are studied and the method is illustrated on several examples for each specific strategy.
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Article dans une revue
ACM Transactions on Computational Logic, Association for Computing Machinery, 2009, 10 (2), pp.1-52. 〈10.1145/1462179.1462182〉
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https://hal.inria.fr/inria-00182432
Contributeur : Isabelle Gnaedig <>
Soumis le : jeudi 25 octobre 2007 - 23:08:20
Dernière modification le : mardi 13 mars 2018 - 14:24:05

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Isabelle Gnaedig, Hélène Kirchner. Termination of Rewriting under Strategies. ACM Transactions on Computational Logic, Association for Computing Machinery, 2009, 10 (2), pp.1-52. 〈10.1145/1462179.1462182〉. 〈inria-00182432〉

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