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Journal Articles Theoretical Computer Science Year : 2003

Decidability results for primitive recursive algorithms

René David
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Abstract

In this paper I use the notion of trace to extend T.Coquand's constructive proof of the ultimate obstination theorem of L. 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 T. Coquand got from his proof, that, even when mutual recursion is allowed, there is no primitive recursive definition f such that $f(S^{n}(\bot ))=S^{n^{2}}(\bot )$.
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Dates and versions

hal-00384668 , version 1 (15-05-2009)

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  • HAL Id : hal-00384668 , version 1

Cite

René David. Decidability results for primitive recursive algorithms. Theoretical Computer Science, 2003, 300 (1-3), pp.477-504. ⟨hal-00384668⟩
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