Fixed point semantics and partial recursion in Coq

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 nonterminating 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