Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-10-31T11:41:50.464Z Has data issue: false hasContentIssue false
  • English
  • Français

A note on recursive functions†

Published online by Cambridge University Press:  04 March 2009

Nicoletta Sabadini ,
Sebastiano Vigna  and
Robert F. C. Walters
Nicoletta Sabadini
Affiliation:
Dipartimento di Scienze dell’Informazione, Università di Milano, Italy.
Sebastiano Vigna
Affiliation:
Dipartimento di Scienze dell’Informazione, Università di Milano, Italy.
Robert F. C. Walters
Affiliation:
School of Mathematics and Statistics, University of Sydney, Australia.
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper, we propose a new and elegant definition of the class of recursive functions, which is analogous to Kleene's definition but differs in the primitives taken, thus demonstrating the computational power of the concurrent programming language introduced in Walters (1991), Walters (1992) and Khalil and Walters (1993).

The definition can be immediately rephrased for any distributive graph in a countably extensive category with products, thus allowing a wide, natural generalization of computable functions.

Type
Research Article
Information
Mathematical Structures in Computer Science , Volume 6 , Issue 2 , April 1996 , pp. 127 - 139
Copyright
Copyright © Cambridge University Press 1996

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Backus, J. (1978) Can programming be liberated from the von Neumann style? A functional style and its algebra of programs. Communications of the ACM 21 (8) 613.CrossRefGoogle Scholar
Carboni, A., Lack, S. and Walters, R. F. C. (1993) Introduction to extensive and distributive categories. Journal of Pure and Applied Algebra 84 145–158.CrossRefGoogle Scholar
Heller, A. (1990) An existence theorem for recursion categories. Journal of Symbolic Logic 55 (3) 1252–1268.CrossRefGoogle Scholar
Katis, P., Sabadini, N. and Walters, R. F. C. (1994) The bicategory of circuits. School of Mathematics and Statistics Report 94–22, Sydney University.Google Scholar
Khalil, W. and Walters, R. F. C. (1993) An imperative language based on distributive categories II. Informatique Théorique et Applications 27 (6) 503–522.CrossRefGoogle Scholar
Manin, Yu. I. (1977) A Course in Mathematical Logic, Springer-Verlag.CrossRefGoogle Scholar
Sabadini, N., Walters, R. F. C. and Weld, H. (1993) Distributive automata and asynchronous circuits. CTCS ‘93, Amsterdam. Available by anonymous ftp at maths.su.oz.au in the directory sydcat/papers/walters.Google Scholar
Walters, R. F. C. (1991) Categories and Computer Science, Carslaw Publications (also Cambridge University Press (1992)).Google Scholar
Walters, R. F. C. (1992) An imperative language based on distributive categories. Mathematical Structures in Computer Science 2 249–256.CrossRefGoogle Scholar