Closed combination of context-embedding iterative strategies
Identifieur interne : 000065 ( Main/Merge ); 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 :
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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.
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<author><name sortKey="Lenczner, Michel" sort="Lenczner, Michel" uniqKey="Lenczner M" first="Michel" last="Lenczner">Michel Lenczner</name>
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<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>
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