On the Formulae-as-Types Correspondence for Classical Logic

Doctoral thesis of Charles Stewart, which investigates foundational aspects of the application of the formulae-as-types correspondence to classical logic, and extends the treatment to include intensional equality and induction.

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A Notion of Classical Pure Type System (1997)

Article by Gilles Barthes.

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A Curry-Howard Foundation for Functional Computation with Control (1997)

Article by C.-H. L. Ong and C. A. Stewart which presents a call-by-name variant of Parigot's lambda-mu calculus. The calculus is proposed as a foundation for first-class continuations and statically scoped exceptions in functional programming languages.

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Extracting Constructive Content from Classical Logic via Control-like Reductions

Article by F. Barbanera and S. Berardi showing how computational content may be extracted from proofs in Peano Arithmetic by a variant of a method proposed by William Tait.

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On the computational content of the Axiom of Choice (1995)

Article by S. Berardi, M. Bezem and T. Coquand presenting a possible computational content of the negative translation of classical analysis with the Axiom of Choice.

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Computational Content of Classical Logic (1996)

Lecture notes from a research seminar series by Thierry Coquand covering double-negation translations, game semantics of classical logic and point-free topology.

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A Semantic View of Classical Proofs (1996)

Article by C.-H. Luke Ong presenting the semantics of classical proof theory from three prespectives: a formulae-as-types characterisation in a variant of Parigot's lambda-mu calculus, a denotational characterisation in game semantics, and a categorical semantics as a fibred CCC.

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Computational Isomorphisms in Classical Logic

Article by V. Danos, J. B. Joinet and H. Schellinx examining the categorical semantics of classical logic from a persepctive inspired by linear logic.

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CPS Translations and Applications: the Cube and Beyond (1996)

Article by G. Barthe, J. Hatcliff, and M.H. Sørensen which presents a CPS translation to Barenderegt's `cube' of pure type systems, and applies this to provide a formulae-as-types correspondence for higher-order classical predicate logic.

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