Strong normalization of lambda-Sym-Prop and lambda bare-mu-mu tilde*-calculi

Péter Battyányi (1) , Karim Nour (2)

1 Department of computer science, Faculty of informatics
2 LAMA - Laboratoire de Mathématiques

In this paper we give an arithmetical proof of the strong normalization of λ Sym Prop of Berardi and Barbanera [1], which can be considered as a formulae-as-types translation of classical propositional logic in natural deduction style. Then we give a translation between the lambda-Sym-Prop-calculus and the lambda bare-mu-mu tilde*-calculus, which is the implicational part of the lambda bare-mu-mu tilde-calculus invented by Curien and Herbelin [3] extended with negation. In this paper we adapt the method of [4] for proving strong normalization. The novelty in our proof is the notion of zoom-in sequences of redexes, which leads us directly to the proofs of the main theorems.

Mots clés: classical propositional logic; strong normalization; lambda-Sym-Prop-calculus; lambda bare-mu-mu tilde-calculus; zoom-in sequence

Domaines: Logique [math.LO]

Péter Battyányi, Karim Nour. Strong normalization of lambda-Sym-Prop and lambda bare-mu-mu tilde*-calculi . 2016. ⟨hal-01421201⟩