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.
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- A Notion of Classical Pure Type System (1997) Article by Gilles Barthes.
- A Semantic View of Classical Proofs (1996) 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.
- 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.
- 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.
- 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.
- Computational Isomorphisms in Classical Logic Article by V. Danos, J. B. Joinet and H. Schellinx examining the categorical semantics of classical logic from a perspective inspired by linear logic.
- 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.