Daniel J. Dougherty, Ugo de'Liguoro, Luigi Liquori, and Claude Stolze.
A realizability interpretation for intersection and union types.
In Programming Languages and Systems - 14th Asian Symposium,
APLAS 2016, Hanoi, Vietnam, November 21-23, 2016, Proceedings, pages
[ bib |
Proof-functional logical connectives allow reasoning about the structure of logical proofs, in this way giving to the latter the status of first-class objects. This is in contrast to classical truth-functional connectives where the meaning of a compound formula is dependent only on the truth value of its subformulas. In this paper we present a typed lambda calculus, enriched with products, coproducts, and a related proof-functional logic. This calculus, directly derived from a typed calculus previously defined by two of the current authors, has been proved isomorphic to the well-known Barbanera-Dezani-Ciancaglini-de'Liguoro type assignment system. We present a logic L featuring two proof-functional connectives, namely strong conjunction and strong disjunction. We prove the typed calculus to be isomorphic to the logic L and we give a realizability semantics using Mints' realizers [?] and a completeness theorem. A prototype implementation is also described.
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