The rho cube : some results, some problems
Identifieur interne : 008467 ( Main/Merge ); précédent : 008466; suivant : 008468The rho cube : some results, some problems
Auteurs : Horatiu Cirstea [France] ; Claude Kirchner [France] ; Luigi Liquori [France] ; Benjamin Wack [France]Source :
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English descriptors
Abstract
The rewriting calculus embeds in a same setting the lambda calculus and the rewriting, by allowing abstraction not only on variables but also on patterns. The higher-order mechanisms of the lambda-calculus and the pattern matching facilities of the rewriting are then both available at the same level. It is worth noticing that the complexity of the calculu breaks the confluence property, so that we need to define appropiate strategies or restrictions, in order to recover it.We choose here to look at the rho-calculus as an extension of the lambda-calculus, and we study the typed aspects. Our study is based upon a generalization of Barendregt's lambda-cube, in which we unify both abstractors lambda and Pi into a single one. We need to deal with the original features of the rho-calculus too: matching power, non-determinism, confluence issues. With proper restrictions, we have proved most of the usual properties for typed calculi: substitution lemma, correctness of types, subject reduction, consistency. Uniqueness of typing is generally no longer valid but we can still prove it for one of the most restrictive systems, rho-> and rho2.
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Hal:inria-00099411Le document en format XML
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key="FR"></country></address></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></affiliation></author></analytic></biblStruct></sourceDesc></fileDesc><profileDesc><textClass><keywords scheme="mix" xml:lang="en"><term>barendregt's cube</term><term>lambda calculus</term><term>rewriting</term><term>rewriting calculus</term><term>type theory</term></keywords><keywords scheme="mix" xml:lang="fr"><term>calcul de réécriture</term><term>cube de barendregt</term><term>lambda calcul</term><term>réécriture</term><term>théorie des types</term><term>unicité du type</term><term>uniqueness of typing</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">The rewriting calculus embeds in a same setting the lambda calculus and the rewriting, by allowing abstraction not only on variables but also on patterns. The higher-order mechanisms of the lambda-calculus and the pattern matching facilities of the rewriting are then both available at the same level. It is worth noticing that the complexity of the calculu breaks the confluence property, so that we need to define appropiate strategies or restrictions, in order to recover it.We choose here to look at the rho-calculus as an extension of the lambda-calculus, and we study the typed aspects. Our study is based upon a generalization of Barendregt's lambda-cube, in which we unify both abstractors lambda and Pi into a single one. We need to deal with the original features of the rho-calculus too: matching power, non-determinism, confluence issues. With proper restrictions, we have proved most of the usual properties for typed calculi: substitution lemma, correctness of types, subject reduction, consistency. Uniqueness of typing is generally no longer valid but we can still prove it for one of the most restrictive systems, rho-> and rho2.</div></front></TEI></record>Pour manipuler ce document sous Unix (Dilib)
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