Inductive Definitions with Decidable Atomic Formulas
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by Anton Setzer
http://www.math.uu.se/~setzer/articles/csl96.ps.gz
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Abstract:
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 \Pi 2-sentences with this restriction on the types. 1
Citations
| 44 | Program extraction from classical proofs – Berger, Schwichtenberg - 1994 |
| 6 | Programs from classical proofs – Berger - 1995 |
| 1 | Program extraction from normalization proofs. In: M. Bezem, J.F. Groote (Eds.): Typed Lambda Calculi and Applications – Berger - 1993 |
| 1 | A constructive interpretation of inductive definitions – Berger - 1994 |
