Disjunctive Axioms and Concurrent $λ$-Calculi: a Curry-Howard Approach

F. Aschieri; A. Ciabattoni; F. A. Genco

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arXiv · 1802.00961

Disjunctive Axioms and Concurrent $λ$-Calculi: a Curry-Howard Approach

F. Aschieri·A. Ciabattoni·F. A. Genco

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Abstract

We add to intuitionistic logic infinitely many classical disjunctive tautologies and use the Curry--Howard correspondence to obtain typed concurrent $λ$-calculi; each of them features a specific communication mechanism, including broadcasting and cyclic message-exchange, and enhanced expressive power with respect to the $λ$-calculus. Moreover they all implement forms of code mobility. Our results provide a first concurrent computational interpretation for many propositional intermediate logics, classical logic included.

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F. Aschieri, A. Ciabattoni, F. A. Genco. 2018-02-13. Disjunctive Axioms and Concurrent $λ$-Calculi: a Curry-Howard Approach. https://arxiv.org/abs/1802.00961

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