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Inductive definitions with decidable atomic formulas

  • Anton Setzer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1258)

Abstract

We introduce a type theory for infinitely branching trees, called the theory of free algebras. In this type theory we define an extensional equality based on decidable atomic formulas only. We show, that equality axioms, which add full extensionality to the theory, yield a conservative extension of the (intensional) type theory for formulas having types of level≤1. Types like nat → nat and well-founded trees with branching over the natural numbers (Kleene's O) have this property. We can therefore extract constructive proofs and programs from classical proofs of II2-sentences with this restriction on the types.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Anton Setzer
    • 1
  1. 1.Department of MathematicsUppsala UniversityUppsalaSweden

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