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Induction for termination with local strategies

Olivier Fissore 1 Isabelle Gnaedig 1 Hélène Kirchner 1
1 PROTHEO - Constraints, automatic deduction and software properties proofs
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : In this paper, we propose a method for specifically proving termination of rewriting with particular strategies: local strategies on operators. An inductive proof procedure is proposed, based on an explicit induction on the termination property. Given a term, the proof principle relies on alternatively applying the induction hypothesis on its subterms, by abstracting the subterms with induction variables, and narrowing the obtained terms in one step, according to the strategy. The induction relation, an F-stable ordering having the subterm property, is not given a priori, but its existence is checked along the proof, by testing satisfiability of ordering constraints.
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Submitted on : Tuesday, September 26, 2006 - 2:43:20 PM
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Olivier Fissore, Isabelle Gnaedig, Hélène Kirchner. Induction for termination with local strategies. Electronic Notes in Theoretical Computer Science, Elsevier, 2001, 58 (2), pp.155-188. ⟨10.1016/S1571-0661(04)00284-1⟩. ⟨inria-00100418⟩



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