Cyclic proofs, system T, and the power of contraction - INRIA - Institut National de Recherche en Informatique et en Automatique Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2020

Cyclic proofs, system T, and the power of contraction

Résumé

We study a cyclic proof system C over regular expression types, inspired by linear logic and non-wellfounded proof theory. Proofs in C denote total computable functions; we analyse the relative strength of C and Gödel's system T, showing that contraction plays a crucial role. In the general case, we show that the two systems capture the same functions on natural numbers. In the affine case, we manage to give a direct and uniform encoding of C into T, translating cycles into explicit recursions. We also show that for functions on natural numbers, removing contraction reduces the expres-sivity precisely to primitive recursive functions-providing an alternative and more general proof of a result by Dal Lago. The two upper bounds on the expressivity of C w.r.t. functions on natural numbers are obtained by formalising weak normalisation of a small step reduction semantics in subsystems of second-order arithmetic: ACA0 and RCA0. Whether a direct and uniform translation from C to T can be given in the presence of contraction remains open.
Fichier principal
Vignette du fichier
cyclimse.pdf (770.78 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-02487175 , version 1 (21-02-2020)
hal-02487175 , version 2 (24-11-2020)

Identifiants

  • HAL Id : hal-02487175 , version 1

Citer

Denis Kuperberg, Laureline Pinault, Damien Pous. Cyclic proofs, system T, and the power of contraction. 2020. ⟨hal-02487175v1⟩
231 Consultations
802 Téléchargements

Partager

Gmail Mastodon Facebook X LinkedIn More