Closed combination of context-embedding iterative strategies
Identifieur interne : 000065 ( Main/Exploration ); précédent : 000064; suivant : 000066Closed combination of context-embedding iterative strategies
Auteurs : Walid Belkhir [France] ; Nicolas Ratier [France] ; Duy Duc Nguyen [France] ; Michel Lenczner [France]Source :
English descriptors
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Abstract
This work is motivated by the challenging problem of the computer-aided generation of approximations (viewed as a series of transformations) of partial derivative equations. In this framework, the approximations posed over complex settings are incrementally constructed by extending an approximation posed on a simple setting and combining these extensions. In order to formalize these extensions and their combination, we introduce a class of rewriting strategies, called context-embedding iterative strategies (CE-strategies, for short). Roughly speaking, the class of CE-strategies is constructed by means of adding contexts and an iteration operator allowing the definition of recursive strategies. We show that the class of CE-strategies is closed under combination with respect to a correctness-completeness criterion. It turns out that the class CE-strategies enjoy nice algebraic properties, namely, the combination is associative, has a neutral element, and all the elements are idempotents.
Url:
Affiliations:
- France
- Franche-Comté
- Belfort, Besançon
- Université de Bourgogne Franche-Comté, Université de Franche-Comté, Université de technologie de Belfort-Montbéliard
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Le document en format XML
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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><tutelles><tutelle active="#struct-242365" type="direct"><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="direct"><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="direct"><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="direct"><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></tutelles></hal:affiliation><country>France</country><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>Fixed-point</term><term>Strategies</term><term>Unification</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">This work is motivated by the challenging problem of the computer-aided generation of approximations (viewed as a series of transformations) of partial derivative equations. In this framework, the approximations posed over complex settings are incrementally constructed by extending an approximation posed on a simple setting and combining these extensions. In order to formalize these extensions and their combination, we introduce a class of rewriting strategies, called context-embedding iterative strategies (CE-strategies, for short). Roughly speaking, the class of CE-strategies is constructed by means of adding contexts and an iteration operator allowing the definition of recursive strategies. We show that the class of CE-strategies is closed under combination with respect to a correctness-completeness criterion. It turns out that the class CE-strategies enjoy nice algebraic properties, namely, the combination is associative, has a neutral element, and all the elements are idempotents.</div></front></TEI><affiliations><list><country><li>France</li></country><region><li>Franche-Comté</li></region><settlement><li>Belfort</li><li>Besançon</li></settlement><orgName><li>Université de Bourgogne Franche-Comté</li><li>Université de Franche-Comté</li><li>Université de technologie de Belfort-Montbéliard</li></orgName></list><tree><country name="France"><region name="Franche-Comté"><name sortKey="Belkhir, Walid" sort="Belkhir, Walid" uniqKey="Belkhir W" first="Walid" last="Belkhir">Walid Belkhir</name></region><name sortKey="Lenczner, Michel" sort="Lenczner, Michel" uniqKey="Lenczner M" first="Michel" last="Lenczner">Michel Lenczner</name><name sortKey="Nguyen, Duy Duc" sort="Nguyen, Duy Duc" uniqKey="Nguyen D" first="Duy Duc" last="Nguyen">Duy Duc Nguyen</name><name sortKey="Ratier, Nicolas" sort="Ratier, Nicolas" uniqKey="Ratier N" first="Nicolas" last="Ratier">Nicolas Ratier</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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