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Computación y Sistemas
versão On-line ISSN 2007-9737versão impressa ISSN 1405-5546
Resumo
MIRANDA-PEREA, Favio E.; OMANA SILVA, Sammantha e GONZALEZ HUESCA, Lourdes del Carmen. A Dual-Context Sequent Calculus for
In type-based program synthesis, the search of inhabitants in typed calculi can be seen as a process where a specification, given by a type , is considered to be fulfilled if we can construct a -term such that , or more precisely if holds, that is, if under some suitable assumptions the term inhabits the type . In this paper, we tackle this inhabitation/synthesis problem for the case of modal types in the necessity fragment of the constructive logic . Our approach is human-driven in the sense of the usual reasoning procedures of modern theorem provers. To this purpose we employ a so-called dual-context sequent calculus, where the sequents have two contexts, originally proposed to capture the notions of global and local truths without resorting to any formal semantics. The use of dual-contexts allows us to define a sequent calculus which, in comparison to other related systems for the same modal logic, exhibits simpler typing inference rules for the operator. In several cases, the task of searching for a term having subterms with modal types is reduced to the quest for a term containing only subterms typed by non modal propositions.
Palavras-chave : Dual-context sequent calculus; constructive necessity; type inhabitation; modal lambda calculus; program synthesis.