Termination checking in the λΠ-calculus modulo theory. From a practical and a theoretical viewpoint
Vérification de la terminaison dans le λΠ-calcul modulo théorie. De la pratique à la théorie.
Résumé
Dedukti is a type-checker for the λΠ-calculus modulo theory, which has the
particularity to allow the user to declare rewrite rules, especially in order to
encode the logic he/she wants to use. Thanks to the Curry-Howard-De Bruijn
correspondence, the type checking done by Dedukti can be used to check proofs.
Unfortunately, to decide the type-checking, Dedukti needs the system of
rewrite rules declared by the user, together with β-reduction, to be confluent
and terminating. An external tool already exists to check the confluence, but no
automatic tool exists for the termination, which must be checked independently
by hand, before using Dedukti.
The subject of this report (and more widely of the internship) is to develop
such a tool.
A first part of it is dedicated to an algorithm of termination checking: the
Size-Change Principle. After a brief introduction to Dedukti, the algorithm is
explained and the results obtained by an implementation of it for Dedukti are
presented.
The second and longest part of this report is much more theoretic, since
it presents reducibility candidates for the λΠ-calculus modulo theory. Those
reducibility candidates can then be used together with the Size-Change Principle
detailed in the first part, to check the termination of a rewrite rule system, as
explained in [Wah07].
Domaines
Logique en informatique [cs.LO]Origine | Fichiers produits par l'(les) auteur(s) |
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