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Size-based termination: Semantics and generalizations

Cody Roux 1
1 PAREO - Formal islands: foundations and applications
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : The present manuscript is a reflection on termination of higher-order rewrite systems. We concentrate our efforts on a particular approach, size-based termination. This method uses typing to give a syntactic approximation to the size of an element of the language. Our contribution is twofold: first we give a structured approach to proving the correctness of size-based termination. To do this, we show that it is possible to apply a certain version of semantic labelling. This technique uses annotations on terms computed using the semantics of subterms in a certain equational premodel. We show correctness of our labelling framework and of the criterion that allows us to prove termination of the labelled system, and we build a premodel of the rewrite system that intuitively corresponds to the rewrite system. We show that the system labelled using these semantics passes the termination criterion. Furthermore we show that a modification of the classical size-types approach allows us to perform a fine control-flow analysis in a higher-order language. This allows us to build an approximated dependency graph, and show that if a certain syntactic criterion is satisfied by the graph, then all well-typed terms are terminating.
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https://tel.archives-ouvertes.fr/tel-01746182
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Submitted on : Wednesday, July 6, 2011 - 12:58:34 PM
Last modification on : Thursday, June 14, 2018 - 1:19:56 AM
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Cody Roux. Size-based termination: Semantics and generalizations. Other [cs.OH]. Université Henri Poincaré - Nancy 1, 2011. English. ⟨NNT : 2011NAN10034⟩. ⟨tel-01746182v2⟩

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