Fixed point semantics and partial recursion in Coq

Yves Bertot 1, * Vladimir Komendantsky 1, *
* Corresponding author
1 MARELLE - Mathematical, Reasoning and Software
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : We propose to use the Knaster-Tarski least fixed point theorem as a basis to define recursive functions in the Calculus of Inductive Constructions. This widens the class of functions that can be modelled in type-theory based theorem proving tools to potentially non-terminating functions. This is only possible if we extend the logical framework by adding some axioms of classical logic. We claim that the extended framework makes it possible to reason about terminating or non-terminating computations and we show that extraction can also be extended to handle the new functions.
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Submitted on : Thursday, July 24, 2008 - 4:10:40 PM
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Yves Bertot, Vladimir Komendantsky. Fixed point semantics and partial recursion in Coq. PPDP 2008, Jul 2008, Valencia, Spain. ⟨inria-00190975v11⟩

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