Decidability results for primitive recursive algorithms

Authors:
R. David
Affiliations:
Laboratoire de Mathématiques, Universite de Chambery, Campus Scientifique, 73376 Le Bourget du Lac Cedex, France
Venue:
Theoretical Computer Science
Year:
2003

Citing 10
Cited 0

Theory of recursive functions and effective computability

Theory of recursive functions and effective computability
About primitive recursive algorithms

Selected papers of the 16th international colloquium on Automata, languages, and programming
On lazy natural numbers with applications to computability theory and functional programming

ACM SIGACT News
The Inf function in the system F

Theoretical Computer Science
Intensional aspects of function definitions

Theoretical Computer Science
Computing minimum with primitive recursion over lists

Theoretical Computer Science
Domains and lambda-calculi

Domains and lambda-calculi
On the asymptotic behaviour of primitive recursive algorithms

Theoretical Computer Science
Intensionality versus Extensionality and Primitive Recursion

ASIAN '96 Proceedings of the Second Asian Computing Science Conference on Concurrency and Parallelism, Programming, Networking, and Security
Proof-techniques for recursive programs.

Proof-techniques for recursive programs.

Quantified Score

Hi-index	5.23

Visualization

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(Sn(⊥)) = Sn2 (⊥).