Equational reasoning and combination methods: from programs to proofs
Identifieur interne : 003317 ( Main/Exploration ); précédent : 003316; suivant : 003318Equational reasoning and combination methods: from programs to proofs
Auteurs : Christophe Ringeissen [France]Source :
Descripteurs français
- mix :
English descriptors
Abstract
In this document, we present decision procedures and solvers which are useful in verification. We consider first order logic with equality. This logic is undecidable in general, but the study of interesting fragments leads to automatic (push-button) tools. The notion of equality is particularly interesting for programming via oriented equalities (rule-based programming) or for deriving proofs thanks to the principle of replacement of equal by equal. In a modelisation using first order logic with equality, we easily have to deal with a problem involving different theories. For instance, these theories may be used to modelise the functions, the arithmetic operations and the memory of a program. Hence, we have to face a problem expressed in a combination of theories, which is interesting to solve in a modular way by using the decision procedures known for individual theories. This problem is the bulk of my research interests. The originality of my approach consists in developing combination methods which are useful in the domain of verification. All the given decision procedures are designed by using a rule-based formalism to ease their proofs.
Url:
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...)
- to stream Hal, to step Corpus: 002002
- to stream Hal, to step Curation: 002002
- to stream Hal, to step Checkpoint: 002946
- to stream Main, to step Merge: 003398
- to stream Main, to step Curation: 003317
Le document en format XML
<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en">Equational reasoning and combination methods: from programs to proofs</title><title xml:lang="fr">Raisonnement équationnel et méthodes de combinaison: de la programmation à la preuve</title><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 type="url">http://www.inria.fr/equipes/cassis</ref></desc><listRelation><relation active="#struct-160" type="direct"></relation><relation name="UMR7503" active="#struct-441569" type="indirect"></relation><relation active="#struct-300009" type="indirect"></relation><relation active="#struct-300291" type="indirect"></relation><relation active="#struct-300292" type="indirect"></relation><relation active="#struct-300293" type="indirect"></relation><relation active="#struct-866" type="direct"></relation><relation active="#struct-242365" type="indirect"></relation><relation active="#struct-300261" type="indirect"></relation><relation active="#struct-300360" type="indirect"></relation><relation name="UMR6174" active="#struct-441569" type="indirect"></relation><relation active="#struct-2496" type="direct"></relation></listRelation><tutelles><tutelle active="#struct-160" type="direct"><org type="laboratory" xml:id="struct-160" status="OLD"><orgName>Laboratoire Lorrain de Recherche en Informatique et ses Applications</orgName><orgName type="acronym">LORIA</orgName><desc><address><addrLine>Campus Scientifique BP 239 54506 Vandoeuvre-lès-Nancy Cedex</addrLine><country key="FR"></country></address><ref type="url">http://www.loria.fr</ref></desc><listRelation><relation name="UMR7503" active="#struct-441569" type="direct"></relation><relation active="#struct-300009" type="direct"></relation><relation active="#struct-300291" type="direct"></relation><relation active="#struct-300292" type="direct"></relation><relation active="#struct-300293" type="direct"></relation></listRelation></org></tutelle><tutelle name="UMR7503" active="#struct-441569" type="indirect"><org type="institution" 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-300009" type="indirect"><org type="institution" xml:id="struct-300009" status="VALID"><orgName>Institut National de Recherche en Informatique et en Automatique</orgName><orgName type="acronym">Inria</orgName><desc><address><addrLine>Domaine de VoluceauRocquencourt - BP 10578153 Le Chesnay Cedex</addrLine><country key="FR"></country></address><ref type="url">http://www.inria.fr/en/</ref></desc></org></tutelle><tutelle active="#struct-300291" type="indirect"><org type="institution" xml:id="struct-300291" status="OLD"><orgName>Université Henri Poincaré - Nancy 1</orgName><orgName type="acronym">UHP</orgName><date type="end">2011-12-31</date><desc><address><addrLine>24-30 rue Lionnois, BP 60120, 54 003 NANCY cedex, France</addrLine><country key="FR"></country></address></desc></org></tutelle><tutelle active="#struct-300292" type="indirect"><org type="institution" xml:id="struct-300292" status="OLD"><orgName>Université Nancy 2</orgName><date type="end">2011-12-31</date><desc><address><addrLine>91 avenue de la Libération, BP 454, 54001 Nancy cedex</addrLine><country key="FR"></country></address></desc></org></tutelle><tutelle active="#struct-300293" type="indirect"><org type="institution" xml:id="struct-300293" status="OLD"><orgName>Institut National Polytechnique de Lorraine</orgName><orgName type="acronym">INPL</orgName><date type="end">2011-12-31</date><desc><address><country key="FR"></country></address></desc></org></tutelle><tutelle active="#struct-866" type="direct"><org type="laboratory" xml:id="struct-866" status="VALID"><idno type="IdRef">152639071</idno><idno type="RNSR">200412232H</idno><orgName>Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies</orgName><orgName type="acronym">FEMTO-ST</orgName><desc><address><addrLine>32 avenue de l'Observatoire 25044 BESANCON CEDEX</addrLine><country key="FR"></country></address><ref type="url">http://www.femto-st.fr</ref></desc><listRelation><relation active="#struct-242365" type="direct"></relation><relation active="#struct-300261" type="direct"></relation><relation active="#struct-300360" type="direct"></relation><relation name="UMR6174" active="#struct-441569" type="direct"></relation></listRelation></org></tutelle><tutelle active="#struct-242365" type="indirect"><org type="institution" xml:id="struct-242365" status="VALID"><idno type="IdRef">026403188</idno><idno type="ISNI">0000 0001 2188 3779 </idno><orgName>Université de Franche-Comté</orgName><orgName type="acronym">UFC</orgName><desc><address><country key="FR"></country></address><ref type="url">http://www.univ-fcomte.fr</ref></desc></org></tutelle><tutelle active="#struct-300261" type="indirect"><org type="institution" xml:id="struct-300261" status="VALID"><orgName>Université de Technologie de Belfort-Montbeliard</orgName><orgName type="acronym">UTBM</orgName><desc><address><country key="FR"></country></address></desc></org></tutelle><tutelle active="#struct-300360" type="indirect"><org type="institution" xml:id="struct-300360" status="VALID"><orgName>Ecole Nationale Supérieure de Mécanique et des Microtechniques</orgName><orgName type="acronym">ENSMM</orgName><desc><address><country key="FR"></country></address></desc></org></tutelle><tutelle name="UMR6174" active="#struct-441569" type="indirect"><org type="institution" 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></titleStmt><publicationStmt><idno type="wicri:source">HAL</idno><idno type="RBID">Hal:tel-00578600</idno><idno type="halId">tel-00578600</idno><idno type="halUri">https://tel.archives-ouvertes.fr/tel-00578600</idno><idno type="url">https://tel.archives-ouvertes.fr/tel-00578600</idno><date when="2009-11-27">2009-11-27</date><idno type="wicri:Area/Hal/Corpus">002002</idno><idno type="wicri:Area/Hal/Curation">002002</idno><idno type="wicri:Area/Hal/Checkpoint">002946</idno><idno type="wicri:explorRef" wicri:stream="Hal" wicri:step="Checkpoint">002946</idno><idno type="wicri:Area/Main/Merge">003398</idno><idno type="wicri:Area/Main/Curation">003317</idno><idno type="wicri:Area/Main/Exploration">003317</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en">Equational reasoning and combination methods: from programs to proofs</title><title xml:lang="fr">Raisonnement équationnel et méthodes de combinaison: de la programmation à la preuve</title><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 type="url">http://www.inria.fr/equipes/cassis</ref></desc><listRelation><relation active="#struct-160" type="direct"></relation><relation name="UMR7503" active="#struct-441569" type="indirect"></relation><relation active="#struct-300009" type="indirect"></relation><relation active="#struct-300291" type="indirect"></relation><relation active="#struct-300292" type="indirect"></relation><relation active="#struct-300293" type="indirect"></relation><relation active="#struct-866" type="direct"></relation><relation active="#struct-242365" type="indirect"></relation><relation active="#struct-300261" type="indirect"></relation><relation active="#struct-300360" type="indirect"></relation><relation name="UMR6174" active="#struct-441569" type="indirect"></relation><relation active="#struct-2496" type="direct"></relation></listRelation><tutelles><tutelle active="#struct-160" type="direct"><org type="laboratory" xml:id="struct-160" status="OLD"><orgName>Laboratoire Lorrain de Recherche en Informatique et ses Applications</orgName><orgName type="acronym">LORIA</orgName><desc><address><addrLine>Campus Scientifique BP 239 54506 Vandoeuvre-lès-Nancy Cedex</addrLine><country key="FR"></country></address><ref type="url">http://www.loria.fr</ref></desc><listRelation><relation name="UMR7503" active="#struct-441569" type="direct"></relation><relation active="#struct-300009" type="direct"></relation><relation active="#struct-300291" type="direct"></relation><relation active="#struct-300292" type="direct"></relation><relation active="#struct-300293" type="direct"></relation></listRelation></org></tutelle><tutelle name="UMR7503" active="#struct-441569" type="indirect"><org type="institution" 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-300009" type="indirect"><org type="institution" xml:id="struct-300009" status="VALID"><orgName>Institut National de Recherche en Informatique et en Automatique</orgName><orgName type="acronym">Inria</orgName><desc><address><addrLine>Domaine de VoluceauRocquencourt - BP 10578153 Le Chesnay Cedex</addrLine><country key="FR"></country></address><ref type="url">http://www.inria.fr/en/</ref></desc></org></tutelle><tutelle active="#struct-300291" type="indirect"><org type="institution" xml:id="struct-300291" status="OLD"><orgName>Université Henri Poincaré - Nancy 1</orgName><orgName type="acronym">UHP</orgName><date type="end">2011-12-31</date><desc><address><addrLine>24-30 rue Lionnois, BP 60120, 54 003 NANCY cedex, France</addrLine><country key="FR"></country></address></desc></org></tutelle><tutelle active="#struct-300292" type="indirect"><org type="institution" xml:id="struct-300292" status="OLD"><orgName>Université Nancy 2</orgName><date type="end">2011-12-31</date><desc><address><addrLine>91 avenue de la Libération, BP 454, 54001 Nancy cedex</addrLine><country key="FR"></country></address></desc></org></tutelle><tutelle active="#struct-300293" type="indirect"><org type="institution" xml:id="struct-300293" status="OLD"><orgName>Institut National Polytechnique de Lorraine</orgName><orgName type="acronym">INPL</orgName><date type="end">2011-12-31</date><desc><address><country key="FR"></country></address></desc></org></tutelle><tutelle active="#struct-866" type="direct"><org type="laboratory" xml:id="struct-866" status="VALID"><idno type="IdRef">152639071</idno><idno type="RNSR">200412232H</idno><orgName>Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies</orgName><orgName type="acronym">FEMTO-ST</orgName><desc><address><addrLine>32 avenue de l'Observatoire 25044 BESANCON CEDEX</addrLine><country key="FR"></country></address><ref type="url">http://www.femto-st.fr</ref></desc><listRelation><relation active="#struct-242365" type="direct"></relation><relation active="#struct-300261" type="direct"></relation><relation active="#struct-300360" type="direct"></relation><relation name="UMR6174" active="#struct-441569" type="direct"></relation></listRelation></org></tutelle><tutelle active="#struct-242365" type="indirect"><org type="institution" xml:id="struct-242365" status="VALID"><idno type="IdRef">026403188</idno><idno type="ISNI">0000 0001 2188 3779 </idno><orgName>Université de Franche-Comté</orgName><orgName type="acronym">UFC</orgName><desc><address><country key="FR"></country></address><ref type="url">http://www.univ-fcomte.fr</ref></desc></org></tutelle><tutelle active="#struct-300261" type="indirect"><org type="institution" xml:id="struct-300261" status="VALID"><orgName>Université de Technologie de Belfort-Montbeliard</orgName><orgName type="acronym">UTBM</orgName><desc><address><country key="FR"></country></address></desc></org></tutelle><tutelle active="#struct-300360" type="indirect"><org type="institution" xml:id="struct-300360" status="VALID"><orgName>Ecole Nationale Supérieure de Mécanique et des Microtechniques</orgName><orgName type="acronym">ENSMM</orgName><desc><address><country key="FR"></country></address></desc></org></tutelle><tutelle name="UMR6174" active="#struct-441569" type="indirect"><org type="institution" 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></biblStruct></sourceDesc></fileDesc><profileDesc><textClass><keywords scheme="mix" xml:lang="en"><term>combination</term><term>decision procedure</term><term>equational reasoning</term><term>rewriting</term><term>unions of theories</term></keywords><keywords scheme="mix" xml:lang="fr"><term>combinaison</term><term>mélange de théories</term><term>procédure de décision</term><term>raisonnement équationnel</term><term>réécriture</term><term>unification</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">In this document, we present decision procedures and solvers which are useful in verification. We consider first order logic with equality. This logic is undecidable in general, but the study of interesting fragments leads to automatic (push-button) tools. The notion of equality is particularly interesting for programming via oriented equalities (rule-based programming) or for deriving proofs thanks to the principle of replacement of equal by equal. In a modelisation using first order logic with equality, we easily have to deal with a problem involving different theories. For instance, these theories may be used to modelise the functions, the arithmetic operations and the memory of a program. Hence, we have to face a problem expressed in a combination of theories, which is interesting to solve in a modular way by using the decision procedures known for individual theories. This problem is the bulk of my research interests. The originality of my approach consists in developing combination methods which are useful in the domain of verification. All the given decision procedures are designed by using a rule-based formalism to ease their proofs.</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="Ringeissen, Christophe" sort="Ringeissen, Christophe" uniqKey="Ringeissen C" first="Christophe" last="Ringeissen">Christophe Ringeissen</name></region></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Lorraine/explor/InforLorV4/Data/Main/Exploration
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 003317 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Main/Exploration/biblio.hfd -nk 003317 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien
|wiki= Wicri/Lorraine
|area= InforLorV4
|flux= Main
|étape= Exploration
|type= RBID
|clé= Hal:tel-00578600
|texte= Equational reasoning and combination methods: from programs to proofs
}}
| This area was generated with Dilib version V0.6.33. |  |