Multiplicative type complex calculus as an alternative to the classical calculus
نویسندگان
چکیده
منابع مشابه
Constructive Classical Logic as CPS-Calculus
We establish the Curry-Howard isomorphism between constructive classical logic and CPS-calculus. CPS-calculus exactly means the target language of Continuation Passing Style(CPS) transforms. Constructive classical logic we refer to are LKT and LKQ introduced by Danos et al.(1993).
متن کاملGentzen-style classical logic as CPS calculus
We show that one can encode proof of the Gentzen'sLK as the -terms; and the cut-elimination procedure for LK as -contraction. Precisely, we observe that Strongly Normalizable(SN) and Church-Rosser(CR) cut-elimination procedure for (intuitionistic decoration of) LKQ, as presented in Danos et al.(1993), can be considered as the call-by-value(CBV) Continuation Passing Style(CPS) computation.
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We study the π-calculus, enriched with pairing and non-blocking input, and define a notion of type assignment that uses the type constructor →. We encode the circuits of the calculus X into this variant of π, and show that all reduction (cut-elimination) and assignable types are preserved. Since X enjoys the Curry-Howard isomorphism for Gentzen’s calculus LK, this implies that all proofs in LK ...
متن کاملApproaches to Polymorphism in Classical Sequent Calculus
X is a relatively new, untyped calculus, invented to give a CurryHoward correspondence with Classical Implicative Sequent Calculus. It is already known to provide a very expressive language; embeddings have been defined of the λ-calculus, Bloo and Rose’s λx, Parigot’s λμ and Curien and Herbelin’s λμμ̃. We investigate various notions of polymorphism in the context of the X -calculus. In particula...
متن کاملFrom X to π Representing the Classical Sequent Calculus in the π - calculus
We study the π-calculus, enriched with pairing and non-blocking input, and define a notion of type assignment that uses the type constructor →. We encode the circuits of the calculus X into this variant of π, and show that all reduction (cut-elimination) and assignable types are preserved. Since X enjoys the Curry-Howard isomorphism for Gentzen’s calculus LK, this implies that all proofs in LK ...
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ژورنال
عنوان ژورنال: Computers & Mathematics with Applications
سال: 2010
ISSN: 0898-1221
DOI: 10.1016/j.camwa.2010.08.089