Abstract
In the present paper we introduce a λ-calculus with symmetric reduction rules and “classical” types, i.e. types corresponding to formulas of classical propositional logic. Strong normalization property is proved to hold for such a calculus. We then extend this calculus in order to get a system equivalent to Peano Arithmetic and show, by means of a theorem on the shape of terms in normal form, how to get recursive functions out of proofs of Π 02 formulas, i.e. the ones corresponding to program specifications.
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© 1994 Springer-Verlag Berlin Heidelberg
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Barbanera, F., Berardi, S. (1994). A symmetric lambda calculus for “classical” program extraction. In: Hagiya, M., Mitchell, J.C. (eds) Theoretical Aspects of Computer Software. TACS 1994. Lecture Notes in Computer Science, vol 789. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57887-0_112
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DOI: https://doi.org/10.1007/3-540-57887-0_112
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