Permutability of proofs in intuitionistic sequent calculi
Theoretical Computer Science - Special issue: Gentzen
Terminiation of permutative conversions in intuitionistic Gentzen calculi
Theoretical Computer Science - Special issue: Gentzen
ICFP '00 Proceedings of the fifth ACM SIGPLAN international conference on Functional programming
An Isomorphism between a Fragment of Sequent Calculus and an Extension of Natural Deduction
LPAR '02 Proceedings of the 9th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
Standardization and Confluence for a Lambda Calculus with Generalized Applications
RTA '00 Proceedings of the 11th International Conference on Rewriting Techniques and Applications
A Lambda-Calculus Structure Isomorphic to Gentzen-Style Sequent Calculus Structure
CSL '94 Selected Papers from the 8th International Workshop on Computer Science Logic
Pattern matching as cut elimination
Theoretical Computer Science
Lectures on the Curry-Howard Isomorphism, Volume 149 (Studies in Logic and the Foundations of Mathematics)
Permutative conversions in intuitionistic multiary sequent calculi with cuts
TLCA'03 Proceedings of the 6th international conference on Typed lambda calculi and applications
Continuation-passing style and strong normalisation for intuitionistic sequent calculi
TLCA'07 Proceedings of the 8th international conference on Typed lambda calculi and applications
Structural proof theory as rewriting
RTA'06 Proceedings of the 17th international conference on Term Rewriting and Applications
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Multiary sequent terms were originally introduced as a tool for proving termination of permutative conversions in cut-free sequent calculus. This work develops the language of multiary sequent terms into a term calculus for the computational (Curry-Howard) interpretation of a fragment of sequent calculus with cuts and cut-elimination rules. The system, called generalized multiary λ-calculus, is a rich extension of the λ-calculus where the computational content of the sequent calculus format is explained through an enlarged form of the application constructor. Such constructor exhibits the features of multiarity (the ability to form lists of arguments) and generality (the ability to prescribe a kind of continuation). The system integrates in a modular way the multiary λ-calculus and an isomorphic copy of the λ-calculus with generalized application, Λ J (in particular, natural deduction is captured internally up to isomorphism). In addition, the system: (i) comes with permutative conversion rules, whose role is to eliminate the new features of application; (ii) is equipped with reduction rules — either the μ-rule, typical of the multiary setting, or rules for cut-elimination, which enlarge the ordinary β-rule. This article establishes the metatheory of the system, with emphasis on the role of the μ-rule, and including a study of the interaction of reduction and permutative conversions.