The polarized λ-calculus

• Autor(a) principal: Espírito Santo, José
• Data de Publicação: 2017
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/1822/50672
• topic: Polarized logic; Focusing; Bidirectional natural deduction; General elimination rule; Eta-expansion; Science & Technology

A natural deduction system isomorphic to the focused sequent calculus for polarized intuitionistic logic is proposed. The system comes with a language of proof-terms, named polarized λ-calculus, whose reduction rules express simultaneously a normalization procedure and the isomorphic copy of the cut-elimination procedure pertaining to the focused sequent calculus. Noteworthy features of this natural deduction system are: how the polarity of a connective determines the style of its elimination rule; the existence of a proof-search strategy which is equivalent to focusing in the sequent calculus; the highlydisciplined organization of the syntax - even atoms have introduction, elimination and normalization rules. The polarized λ-calculus is a programming formalism close to call-by-push-value, but justified by its proof-theoretical pedigree.