Introduction to combinators and &lgr;-calculus
Introduction to combinators and &lgr;-calculus
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Cut Elimination for Classical Proofs as Continuation Passing Style Computation
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A First-Order One-Pass CPS Transformation
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Strong Normalization of Second Order Symmetric lambda-Calculus
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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
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The Curry-Howard Correspondence in Set Theory
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Call-by-value is dual to call-by-name
ICFP '03 Proceedings of the eighth ACM SIGPLAN international conference on Functional programming
Disjunctive normal forms and local exceptions
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An environment machine for the λμ-calculus
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Strong normalization proofs by CPS-translations
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Investigations on the Dual Calculus
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Strong Normalisation of Cut-Elimination in Classical Logic
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Specializing continuations a model for dynamic join points
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Alternative Logics: a book review: SIGACT news logic column 18
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A proof theory for machine code
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An approach to call-by-name delimited continuations
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The design and implementation of typed scheme
Proceedings of the 35th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Control reduction theories: The benefit of structural substitution
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Arithmetical Proofs of Strong Normalization Results for Symmetric λ-calculi
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Combining Classical and Intuitionistic Implications
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A Calculus of Realizers for EM1 Arithmetic (Extended Abstract)
CSL '08 Proceedings of the 22nd international workshop on Computer Science Logic
Proofs, tests and continuation passing style
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Denotational Semantics of Call-by-name Normalization in Lambda-mu Calculus
Electronic Notes in Theoretical Computer Science (ENTCS)
Towards Ludics Programming: Interactive Proof Search
ICLP '08 Proceedings of the 24th International Conference on Logic Programming
Sequent calculi and abstract machines
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Intuitionistic Letcc via Labelled Deduction
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Strong normalization of classical natural deduction with disjunction
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Positive arithmetic without exchange is a subclassical logic
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The programming language Scheme contains the control construct call/cc that allows access to the current continuation (the current control context). This, in effect, provides Scheme with first-class labels and jumps. We show that the well-known formulae-as-types correspondence, which relates a constructive proof of a formula &agr; to a program of type &agr;, can be extended to a typed Idealized Scheme. What is surprising about this correspondence is that it relates classical proofs to typed programs. The existence of computationally interesting “classical programs” —programs of type &agr;, where &agr; holds classically, but not constructively — is illustrated by the definition of conjunctively, disjunctive, and existential types using standard classical definitions. We also prove that all evaluations of typed terms in Idealized Scheme are finite.