A Dual-Context Sequent Calculus for S4 Modal Lambda-Term Synthesis



Título del documento: A Dual-Context Sequent Calculus for S4 Modal Lambda-Term Synthesis
Revista: Computación y sistemas
Base de datos:
Número de sistema: 000560694
ISSN: 1405-5546
Autors: 1
2
1
Institucions: 1Universidad Nacional Autónoma de México, Facultad de Ciencias, México
2Universidad Nacional Autónoma de México, Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, México
Any:
Període: Abr-Jun
Volum: 26
Número: 2
Paginació: 787-799
País: México
Idioma: Inglés
Resumen en inglés 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 A, is considered to be fulfilled if we can construct a λ-term M such that M : A, or more precisely if Γ ⊢ M : A holds, that is, if under some suitable assumptions Γ the term M inhabits the type A. In this paper, we tackle this inhabitation/synthesis problem for the case of modal types in the necessity fragment of the constructive logic S 4. 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.
Keyword: Dual-context sequent calculus,
Constructive necessity,
Type inhabitation,
Modal lambda calculus,
Program synthesis
Text complet: Texto completo (Ver HTML) Texto completo (Ver PDF)