Abstract
This system description outlines the λClam system for proof planning in higher-order logic. The usefulness and feasibility of applying higher-order proof planning to a number of types of problem is outlined, in particular the synthesis and verification of software and hardware systems. The use of a higher-order metatheory overcomes problems encountered in Clam because of its inability to reason properly about higher-order objects. λClam is written in λProlog.
The authors gratefully acknowledge the support of EPSRC grant GR/L/11724 and British Council grant ROM/889/95/70 and for the comments of their colleagues in the Mathematical Reasoning Group and of the referees.
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
P. Brisset and O. Ridoux. The architecture of an implementation of LambdaProlog: Prolog/Mali. In Proceedings of the Workshop on Implementation of Logic Programming, ILPS'94, Ithaca, NY. The MIT Press, November 1994.
A. Bundy, A. Stevens, F. van Harmelen, A. Ireland, and A. Smaill. Rippling: A heuristic for guiding inductive proofs. Artificial Intelligence, 62:185–253, 1993. Also available from Edinburgh as DAI Research Paper No. 567.
A. Bundy, F. van Harmelen, C. Horn, and A. Smaill. The Oyster-Clam system. In M. E. Stickel, editor, 10th International Conference on Automated Deduction, pages 647–648. Springer-Verlag, 1990. Lecture Notes in Artificial Intelligence No. 449. Also available from Edinburgh as DAI Research Paper 507.
Alan Bundy. The use of explicit plans to guide inductive proofs. In R. Lusk and R. Overbeek, editors, 9th Conference on Automated Deduction, pages 111–120. Springer-Verlag, 1988. Longer version available as DAI Research Paper No. 349.
A. Felty. A logic programming approach to implementing higher-order term rewriting. In L-H Eriksson et al., editors, Second International Workshop on Extensions to Logic Programming, volume 596 of Lecture Notes in Artificial Intelligence, pages 135–61. Springer-Verlag, 1992.
J. T. Hesketh. Using Middle-Out Reasoning to Guide Inductive Theorem Proving. PhD thesis, University of Edinburgh, 1991.
A. Ireland and A. Bundy. Productive use of failure in inductive proof. Journal of Automated Reasoning, 16(1–2):79–111, 1996. Also available as DAI Research Paper No 716, Dept. of Artificial Intelligence, Edinburgh.
A. Smaill and I. Green. Higher-order annotated terms for proof search. In J. von Wright, J. Grundy, and J Harrison, editors, Theorem Proving in Higher Order Logics, volume 1125 of Lecture Notes in Computer Science, pages 399–414. Springer, 1996. Also available as DAI Research Paper 799.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1998 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Richardson, J., Smaill, A., Green, I. (1998). System description: Proof planning in higher-order logic with λClam. In: Kirchner, C., Kirchner, H. (eds) Automated Deduction — CADE-15. CADE 1998. Lecture Notes in Computer Science, vol 1421. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0054254
Download citation
DOI: https://doi.org/10.1007/BFb0054254
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-64675-4
Online ISBN: 978-3-540-69110-5
eBook Packages: Springer Book Archive