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Termination of Rewriting under Strategies

Isabelle Gnaedig 1 Hélène Kirchner 2
1 PROTHEO - Constraints, automatic deduction and software properties proofs
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
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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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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