InforLorV4, Main, Exploration, bibRecord, 000318

A Rewriting Approach to the Combination of Data Structures with Bridging Theories

Identifieur interne : 000318 ( Main/Exploration ); précédent : 000317; suivant : 000319

A Rewriting Approach to the Combination of Data Structures with Bridging Theories

Auteurs : Paula Chocron [France] ; Pascal Fontaine [France] ; Christophe Ringeissen [France]

Source :

RBID : Hal:hal-01206187

Abstract

We introduce a combination method à la Nelson-Oppen to solve the satisfiability problem modulo a non-disjoint union of theories connected with bridging functions. The combination method is particularly useful to handle verification conditions involving functions defined over inductive data structures. We investigate the problem of determining the data structure theories for which this combination method is sound and complete. Our completeness proof is based on a rewriting approach where the bridging function is defined as a term rewrite system, and the data structure theory is given by a basic congruence relation. Our contribution is to introduce a class of data structure theories that are combinable with a disjoint target theory via an inductively defined bridging function. This class includes the theory of equality, the theory of absolutely free data structures, and all the theories in between. Hence, our non-disjoint combination method applies to many classical data structure theories admitting a rewrite-based satisfiability procedure.

Url:

https://hal.inria.fr/hal-01206187

DOI: 10.1007/978-3-319-24246-0_17

Affiliations:

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Le document en format XML

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<country>France</country>
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<settlement type="city">Metz</settlement>
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</placeName>
<orgName type="university">Université de Lorraine</orgName>
<placeName><settlement type="city" wicri:auto="siege">Besançon</settlement>
<region type="region" nuts="2">Franche-Comté</region>
</placeName>
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<front><div type="abstract" xml:lang="en">We introduce a combination method à la Nelson-Oppen to solve the  satisfiability problem modulo a non-disjoint union of theories  connected with bridging functions. The combination method is  particularly useful to handle verification conditions involving  functions defined over inductive data structures. We investigate the  problem of determining the data structure theories for which this  combination method is sound and complete. Our completeness proof is  based on a rewriting approach where the bridging function is defined  as a term rewrite system, and the data structure theory is given by  a basic congruence relation.  Our contribution is to introduce a  class of data structure theories that are combinable with a disjoint  target theory via an inductively defined bridging function. This  class includes the theory of equality, the theory of absolutely free  data structures, and all the theories in between.  Hence, our  non-disjoint combination method applies to many classical data  structure theories admitting a rewrite-based satisfiability  procedure.</div>
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<li>Université de Franche-Comté</li>
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<name sortKey="Ringeissen, Christophe" sort="Ringeissen, Christophe" uniqKey="Ringeissen C" first="Christophe" last="Ringeissen">Christophe Ringeissen</name>
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A Rewriting Approach to the Combination of Data Structures with Bridging Theories

A Rewriting Approach to the Combination of Data Structures with Bridging Theories

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