Abstract
In this paper I use the notion of trace defined in (Theoret. Comput. Sci. 266 (2001) 159) to extend Coquand's constructive proof (C. R. Acad. Sci. Ser. I 314 (1992)) of the ultimate obstination theorem of Colson to the case when mutual recursion is allowed. As a by-product I get an algorithm that computes the value of a primitive recursive combinator applied to lazy integers (infinite or partially undefined arguments may appear). I also get, as Coquand got from his proof, that, even when mutual recursion is allowed, there is no primitive recursive definition f such that f( S n (⊥))= S n 2 (⊥).
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