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Extending the Calculus of Constructions with Tarski's fix-point theorem

Yves Bertot 1
1 MARELLE - Mathematical, Reasoning and Software
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : We propose to use Tarski's least fixpoint theorem as a basis to define recursive functions in the calculus of inductive constructions. This widens the class of functions that can be modeled in type-theory based theorem proving tool to potentially non-terminating functions. This is only possible if we extend the logical framework by adding the axioms that correspond to classical logic. We claim that the extended framework makes it possible to reason about terminating and non-terminating computations and we show that common facilities of the calculus of inductive construction, like program extraction can be extended to also handle the new functions.
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Contributor : Yves Bertot <>
Submitted on : Wednesday, October 11, 2006 - 2:43:53 PM
Last modification on : Thursday, January 7, 2021 - 3:40:05 PM
Long-term archiving on: : Tuesday, April 6, 2010 - 7:21:54 PM



  • HAL Id : inria-00105529, version 1
  • ARXIV : cs/0610055



Yves Bertot. Extending the Calculus of Constructions with Tarski's fix-point theorem. [Research Report] 2006, pp.15. ⟨inria-00105529⟩



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