. This paper proposes a simple computational interpretation of Parigot's ¯-calculus. The ¯-calculus is an extension of the typed -calculus which corresponds via the Curry-Howard correspondence to classical logic. Whereas other work has given computational interpretations by translating the ¯-calculus into other calculi, I wish to propose here a direct computational interpretation. This interpretation is best given as a single-step semantics which, in particular, leads to a relatively simple, but powerful, operational theory. 1 Introduction It is well-known that the typed -calculus can be viewed as a term assignment for natural deduction proofs in intuitionistic logic (IL). Consequently the set of types of all closed -terms enumerates all intuitionistic tautologies. This is known as the CurryHoward correspondence, or the formulae-as-types principle. Thus one can talk of a computational interpretation of IL. A natural question is whether there is such a computational interpretation of c...

This paper proposes a simple computational interpretation of Parigot's -calculus. The -calculus is an extension of the typed -calculus which corresponds via the CurryHoward correspondence to classical logic. Whereas other work has given computational interpretations by translating the -calculus into other calculi, I wish to propose here that the -calculus itself has a simple computational interpretation: it is a typed - calculus which is able to save and restore the runtime environment. This interpretation is best given as a single-step semantics which, in particular, leads to a relatively simple, but powerful, operational theory. This is an expanded version of a paper presented at the 23rd International Symposium on Mathematical Foundations of Computer Science. August 24-- 28, 1998. Brno, Czech Republic. c fl G M B September 2, 1998 i 1 Introduction It is well-known that the typed -calculus can be viewed as a term assignment for natural deduction proofs in intuitionistic logic ...

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Arithmetical proofs of strong normalization results for symmetric λ-calculi