Directory of Classical Logic Resources

Home > Science > Math > Logic and Foundations > Computational Logic > Combinatory Logic and Lambda Calculus > Formulae-as-Types Correspondence > Classical Logic

The formulae-as-types correspondence is normally understood as giving a constructive interpretation for a logic, whilst classical logic is normally understood as resisting an interpreatation. Thus results that show that classical logic admits a formulae-as-types correspondence have provoked a lot of interest in the research community.

Resources in This Category

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

  http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.56.2758
  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.

• A Notion of Classical Pure Type System (1997)

  http://citeseer.ist.psu.edu/did/91961
  Article by Gilles Barthes.

• A Semantic View of Classical Proofs (1996)

  http://citeseer.ist.psu.edu/did/231416
  Article by C.-H. Luke Ong presenting the semantics of classical proof theory from three perspectives: 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.

• Computational Content of Classical Logic (1996)

  http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.49.3492
  Lecture notes from a research seminar series by Thierry Coquand covering double-negation translations, game semantics of classical logic and point-free topology.

• Computational Isomorphisms in Classical Logic

  http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.46.7451
  Article by V. Danos, J. B. Joinet and H. Schellinx examining the categorical semantics of classical logic from a perspective inspired by linear logic.

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

  http://citeseer.ist.psu.edu/did/4806
  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.

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

  http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.56.8271
  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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