Combining Lists with Non-Stably Infinite Theories
Identifieur interne : 005A75 ( Main/Exploration ); précédent : 005A74; suivant : 005A76Combining Lists with Non-Stably Infinite Theories
Auteurs : Pascal Fontaine [France] ; Silvio Ranise [France] ; Calogero Zarba [France]Source :
English descriptors
- mix :
Abstract
In program verification one has often to reason about lists over elements of a given nature. Thus, it becomes important to be able to combine the theory of lists with a generic theory $T$ modeling the elements. This combination can be achieved using the Nelson-Oppen method only if $T$ is stably infinite. The goal of this paper is to relax the stable-infiniteness requirement. More specifically, we provide a new method that is able to combine the theory of lists with any theory $T$ of the elements, regardless of whether $T$ is stably infinite or not. The crux of our combination method is to guess an arrangement over a set of variables that is larger than the one considered by Nelson and Oppen. Furthermore, our results entail that it is also possible to combine $T$ with the more general theory of lists with a length function.
Url:
DOI: 10.1007/b106931
Affiliations:
- France
- Franche-Comté, Grand Est, Lorraine (région)
- Belfort, Besançon, Nancy
- Institut national polytechnique de Lorraine, Université Nancy 2, Université de Bourgogne Franche-Comté, Université de Franche-Comté, Université de Lorraine, Université de technologie de Belfort-Montbéliard
Links toward previous steps (curation, corpus...)
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- to stream Hal, to step Curation: 001583
- to stream Hal, to step Checkpoint: 004713
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- to stream Main, to step Curation: 005A75
Le document en format XML
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xml:id="struct-441569" status="VALID"><idno type="ISNI">0000000122597504</idno><idno type="IdRef">02636817X</idno><orgName>Centre National de la Recherche Scientifique</orgName><orgName type="acronym">CNRS</orgName><date type="start">1939-10-19</date><desc><address><country key="FR"></country></address><ref type="url">http://www.cnrs.fr/</ref></desc></org></tutelle><tutelle active="#struct-2496" type="direct"><org type="laboratory" xml:id="struct-2496" status="OLD"><orgName>INRIA Lorraine</orgName><desc><address><addrLine>615 rue du Jardin Botanique 54600 Villers-lès-Nancy</addrLine><country key="FR"></country></address><ref type="url">http://www.inria.fr/centre-de-recherche-inria/nancy-grand-est</ref></desc><listRelation><relation active="#struct-300009" type="direct"></relation></listRelation></org></tutelle></tutelles></hal:affiliation><country>France</country><placeName><settlement type="city">Nancy</settlement><region type="region" nuts="2">Grand Est</region><region type="old region" nuts="2">Lorraine (région)</region></placeName><orgName type="university">Université Nancy 2</orgName><orgName type="institution" wicri:auto="newGroup">Université de Lorraine</orgName><placeName><settlement type="city">Nancy</settlement><region type="region" nuts="2">Grand Est</region><region type="old region" nuts="2">Lorraine (région)</region></placeName><orgName type="university">Institut national polytechnique de Lorraine</orgName><orgName type="institution" wicri:auto="newGroup">Université de Lorraine</orgName><placeName><settlement type="city" wicri:auto="siege">Besançon</settlement><region type="region" nuts="2">Franche-Comté</region></placeName><orgName type="university">Université de Franche-Comté</orgName><orgName type="institution" wicri:auto="newGroup">Université de Bourgogne Franche-Comté</orgName><placeName><settlement type="city" wicri:auto="siege">Belfort</settlement><region type="region" nuts="2">Franche-Comté</region></placeName><orgName type="university">Université de technologie de Belfort-Montbéliard</orgName></affiliation></author></analytic><idno type="DOI">10.1007/b106931</idno></biblStruct></sourceDesc></fileDesc><profileDesc><textClass><keywords scheme="mix" xml:lang="en"><term>arithmetic</term><term>combination</term><term>decision procedure</term><term>lists</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">In program verification one has often to reason about lists over elements of a given nature. Thus, it becomes important to be able to combine the theory of lists with a generic theory $T$ modeling the elements. This combination can be achieved using the Nelson-Oppen method only if $T$ is stably infinite. The goal of this paper is to relax the stable-infiniteness requirement. More specifically, we provide a new method that is able to combine the theory of lists with any theory $T$ of the elements, regardless of whether $T$ is stably infinite or not. The crux of our combination method is to guess an arrangement over a set of variables that is larger than the one considered by Nelson and Oppen. Furthermore, our results entail that it is also possible to combine $T$ with the more general theory of lists with a length function.</div></front></TEI><affiliations><list><country><li>France</li></country><region><li>Franche-Comté</li><li>Grand Est</li><li>Lorraine (région)</li></region><settlement><li>Belfort</li><li>Besançon</li><li>Nancy</li></settlement><orgName><li>Institut national polytechnique de Lorraine</li><li>Université Nancy 2</li><li>Université de Bourgogne Franche-Comté</li><li>Université de Franche-Comté</li><li>Université de Lorraine</li><li>Université de technologie de Belfort-Montbéliard</li></orgName></list><tree><country name="France"><region name="Grand Est"><name sortKey="Fontaine, Pascal" sort="Fontaine, Pascal" uniqKey="Fontaine P" first="Pascal" last="Fontaine">Pascal Fontaine</name></region><name sortKey="Ranise, Silvio" sort="Ranise, Silvio" uniqKey="Ranise S" first="Silvio" last="Ranise">Silvio Ranise</name><name sortKey="Zarba, Calogero" sort="Zarba, Calogero" uniqKey="Zarba C" first="Calogero" last="Zarba">Calogero Zarba</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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