Combining Data Structures with Nonstably Infinite Theories using Many-Sorted Logic
Identifieur interne : 006544 ( Main/Exploration ); précédent : 006543; suivant : 006545Combining Data Structures with Nonstably Infinite Theories using Many-Sorted Logic
Auteurs : Silvio Ranise [France] ; Christophe Ringeissen [France] ; Calogero ZarbaSource :
English descriptors
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Abstract
Most computer programs store elements of a given nature into container-based data structures such as lists, arrays, sets, and multisets. To verify the correctness of these programs, one needs to combine a theory modeling the data structure with a theory modeling the elements. This combination can be achieved using the classic Nelson-Oppen method only if both theories are stably infinite. The goal of this report is to relax the stable infiniteness requirement. To achieve this goal, we introduce the notion of polite theories, and we show that natural examples of polite theories include those modeling data structures such as lists, arrays, sets, and multisets. Furthemore, we provide a method that is able to combine a polite theory with any theory of the elements, regardless of whether the latter is stably infinite or not. The results of this report generalize to many-sorted logic those recently obtained by Tinelli and Zarba for combining the so-called shiny theories with nonstably infinite theories in one-sorted logic.
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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
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Le document en format XML
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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><author><name sortKey="Ringeissen, Christophe" sort="Ringeissen, Christophe" uniqKey="Ringeissen C" first="Christophe" last="Ringeissen">Christophe Ringeissen</name><affiliation wicri:level="1"><hal:affiliation type="researchteam" xml:id="struct-2366" status="OLD"><idno type="RNSR">200318302K</idno><orgName>Combination of approaches to the security of infinite states systems</orgName><orgName type="acronym">CASSIS</orgName><desc><address><country key="FR"></country></address><ref 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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><author><name sortKey="Zarba, Calogero" sort="Zarba, Calogero" uniqKey="Zarba C" first="Calogero" last="Zarba">Calogero Zarba</name></author></analytic></biblStruct></sourceDesc></fileDesc><profileDesc><textClass><keywords scheme="mix" xml:lang="en"><term>Combination of satisfiability procedures</term><term>automated deduction</term><term>decision problems</term><term>many-sorted logic</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Most computer programs store elements of a given nature into container-based data structures such as lists, arrays, sets, and multisets. To verify the correctness of these programs, one needs to combine a theory modeling the data structure with a theory modeling the elements. This combination can be achieved using the classic Nelson-Oppen method only if both theories are stably infinite. The goal of this report is to relax the stable infiniteness requirement. To achieve this goal, we introduce the notion of polite theories, and we show that natural examples of polite theories include those modeling data structures such as lists, arrays, sets, and multisets. Furthemore, we provide a method that is able to combine a polite theory with any theory of the elements, regardless of whether the latter is stably infinite or not. The results of this report generalize to many-sorted logic those recently obtained by Tinelli and Zarba for combining the so-called shiny theories with nonstably infinite theories in one-sorted logic.</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><noCountry><name sortKey="Zarba, Calogero" sort="Zarba, Calogero" uniqKey="Zarba C" first="Calogero" last="Zarba">Calogero Zarba</name></noCountry><country name="France"><region name="Grand Est"><name sortKey="Ranise, Silvio" sort="Ranise, Silvio" uniqKey="Ranise S" first="Silvio" last="Ranise">Silvio Ranise</name></region><name sortKey="Ringeissen, Christophe" sort="Ringeissen, Christophe" uniqKey="Ringeissen C" first="Christophe" last="Ringeissen">Christophe Ringeissen</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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