Common LISP: the language
Proofs and types
A formulae-as-type notion of control
POPL '90 Proceedings of the 17th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Intuitionistic and classical natural deduction systems with the catch and the throw rules
NSL '94 Proceedings of the first workshop on Non-standard logics and logical aspects of computer science
Lambda-My-Calculus: An Algorithmic Interpretation of Classical Natural Deduction
LPAR '92 Proceedings of the International Conference on Logic Programming and Automated Reasoning
Extracting Constructive Content from Classical Logic via Control-like Reductions
TLCA '93 Proceedings of the International Conference on Typed Lambda Calculi and Applications
A Simple Calculus of Exception Handling
TLCA '95 Proceedings of the Second International Conference on Typed Lambda Calculi and Applications
Classical Brouwer-Heyting-Kolmogorov Interpretation
ALT '97 Proceedings of the 8th International Conference on Algorithmic Learning Theory
A confluent λ-calculus with a catch/throw mechanism
Journal of Functional Programming
A Type-Theoretic Study on Partial Continuations
TCS '00 Proceedings of the International Conference IFIP on Theoretical Computer Science, Exploring New Frontiers of Theoretical Informatics
Disjunctive normal forms and local exceptions
ICFP '03 Proceedings of the eighth ACM SIGPLAN international conference on Functional programming
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The catch/throw mechanism in Common Lisp provides a simple controlmechanism for non-local exits. We study typed calculi by Nakano andSato which formalize the catch/throw mechanism. These calculicorrespond to classical logic through the Curry-Howard isomorphism,and one of their characteristic points is that they havenon-deterministic reduction rules. These calculi can representvarious computational meaning of classical proofs. This paper ismainly concerned with the strong normalizability of these calculi.Namely, we prove the strong normalizability of these calculi, whichwas an open problem. We first formulate a non-deterministic variantof Parigot's λμ-calculus, and show it is stronglynormalizing. We then translate the catch/throw calculi to thisvariant. Since the translation preserves typing and reduction, weobtain the strong normalization of the catch/throw calculi. We alsobriefly consider second-order extension of the catch/throw calculi.Copyright 2002 Elsevier Science B.V