A symmetric lambda calculus for “classical” program extraction

  • Franco Barbanera
  • Stefano Berardi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 789)


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 2 0 formulas, i.e. the ones corresponding to program specifications.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Franco Barbanera
    • 1
  • Stefano Berardi
    • 1
  1. 1.Dipartimento di InformaticaUniversita' di TorinoTorinoItaly

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