Abstract
We define Higher Order Recursive Program Schemes (HRPSs) by allowing metasubstitutions (as in the λ-calculus) in right-hand sides of function and quantifier definitions. A study of several kinds of similarity of redexes makes it possible to lift properties of (first order) Recursive Program Schemes to the higher order case. The main result is the decidability of weak normalization in HRPSs, which immediately implies that HRPSs do not have full computational power. We analyze the structural properties of HRPSs and introduce several kinds of persistent expression reduction systems (PERSs) that enjoy similar properties. Finally, we design an optimal evaluation procedure for PERSs.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
Asperti A, Laneve C. Interaction Systems 1. The theory of optimal reductions. INRIA Report 1748, 1992.
Barendregt H. P. The Lambda Calculus, its Syntax and Semantics. North-Holland, 1984.
Courcelle B. Recursive Applicative Program Schemes. In: J. van Leeuwen ed. Handbook of Theoretical Computer Science, Chapter 9, vol.B, 1990, p. 459–492.
Dershowitz N., Jouannaud J.-P. Rewrite Systems. In: J.van Leeuwen ed. Handbook of Theoretical Computer Science, Chapter 6, vol. B, 1990, p. 243–320.
Huet G., Lévy J.-J. Computations in Orthogonal Rewriting Systems. In Computational Logic, Essays in Honour of Alan Robinson, ed. by J.-L. Lassez and G. Plotkin, MIT Press, 1991.
Khasidashvili Z. The Church-Rosser theorem in Orthogonal Combinatory Reduction Systems. INRIA Report 1825, 1992.
Khasidashvili Z. Optimal normalization in orthogonal term rewriting systems. In: Proc. of the fifth International Conference on Rewriting Techniques and Applications, Springer LNCS, vol. 690, C. Kirchner, ed. Montreal, 1993, p. 243–258.
Khasidashvili Z. Perpetuality and strong normalization in orthogonal term rewriting systems. CWI report CS-R9345, 1993. To appear in: Proc. of 11-th Symposium on Theoretical Aspects of Computer Science, Springer LNCS, Caen, 1994.
Khasidashvili Z. Higher order recursive program schemes are Turing incomplete. CWI report CS-R9348, 1993.
Khasidashvili Z. Perpetual reductions in orthogonal combinatory reduction systems. CWI report CS-R9349, 1993.
Klop, J. W. Combinatory Reduction Systems. Mathematical Centre Tracts n.127, CWI, Amsterdam, 1980.
Klop J. W. Term Rewriting Systems. In: S. Abramsky, D. Gabbay, and T. Maibaum eds. Handbook of Logic in Computer Science, vol. II, Oxford University Press, 1992, p. 1–116.
Klop, J. W., van Oostrom, V., van Raamsdonk, F. Combinatory reduction Systems: introduction and survey. In: To Corrado Böhm, J. of Theoretical Computer Science 121, 1993, p. 279–308.
Lévy J.-J. Optimal Reduction in the Lambda-Calculus. In: To H. B. Curry Essays on Combinatory Logic, Lambda Calculus and Formalism, J. P. Seldin and J. R. Hindley eds, Academic Press, 1980.
Maranget L. “La stratégie paresseuse”, These de l'Université' de Paris VII, 1992.
Pkhakadze Sh. Some problems of the Notation Theory (in Russian). Proceedings of I. Vekua Institute of Applied Mathematics of Tbilisi State University, 1977.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1994 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Khasidashvili, Z. (1994). On higher order recursive program schemes. In: Tison, S. (eds) Trees in Algebra and Programming — CAAP'94. CAAP 1994. Lecture Notes in Computer Science, vol 787. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0017481
Download citation
DOI: https://doi.org/10.1007/BFb0017481
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-57879-6
Online ISBN: 978-3-540-48373-1
eBook Packages: Springer Book Archive