Abstract
A notation for expressing the control algorithms (subgoaling strategies) of natural deduction theorem provers is presented. The language provides tools for building widely known, fundamental theorem proving strategies and is independent of the problem area and inference rule system chosen, facilitating formulation of high level algorithms that can be compared, analyzed, and even ported across theorem proving systems. The notation is a simplification and generalization of the tactic language of Edinburgh LCF. Examples using a natural deduction system for propositional logic are given.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Andrews, P.B. Transformaing matings into natural deduction proofs. 5th Conference on Automated Deduction, Les Arcs, France, 1980, LNCS 87, pp. 281–292.
Bledsoe, W.W., and Tyson, M. The UT interactive theorem prover. Memo ATP-17, Mathematics Dept., University of Texas, Austin, 1975.
Boyer, R.S., and Moore, J.S. A Computational Logic. Academic Press, New York, 1979.
Chang, C., and Lee, R.E. Symbolic Logic and Mechanical Theorem Proving. Academic Press, New York, 1973.
Cohen, P.R., and Feigenbaum, E.A., eds. The Handbook of Artificial Intelligence, Vol. 3. Pittman, New York, Ch. 12.
Cohn, A. The equivalence of two semantic definitions: a case study in LCF. Report CSR-76-81, Computer Science Dept., University of Edinburgh, Scotland, 1981.
Cohn, A., and Milner, R. On using Edinburgh LCF to prove the correctness of a parsing algorithm. Report CSR-113-82, Computer Science Dept., University of Edinburgh, Scotland, 1982.
Constable, R.L. Proofs as programs: a synopsis. Information Proc. Letters 16-3 (1983) 105–112.
Gordon, M., Milner, R., and Wadsworth, C. Edinburgh LCF. LNCS 78, Springer-Verlag, Berlin, 1979.
Guttag, J. Notes on type abstraction. IEEE Trans. on Software Engg. SE-6-1 (1980) 13–23.
Hoare, C.A.R. An axiomatic basis for computer programming. Comm. ACM 12 (1969) 576–580, 583.
Lemmon, E.J. Beginning Logic. Nelson, London, 1965.
Leszczyłowski, J. An experiment with Edinburgh LCF. 5th Conference on Automated Deduction, Les Arcs, France, 1980, LNCS 87, pp. 170–181.
Monahan, B. Ph.D. thesis, University of Edinburgh, forthcoming.
Nordström, B. Programming in constructive set theory: some examples. ACM Conf. on Functional Programming Languages and Computer Architecture, Portsmouth, N.H., 1981, pp. 141–153.
Plotkin, G. A structural approach to operational semantics. Report DAIMI FN-19, Computer Science Dept., University of Aarhus, Denmark, 1981.
Prawitz, D. Natural Deduction. Almquist and Wiksel, Stockholm, 1965.
Robinson, J.A. Logic:Form and Function. Edinburgh Univ. Press, Edinburgh, 1979.
Suppes, P. Introduction to Logic. Van Nostrand, Princeton, 1957.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1984 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Schmidt, D.A. (1984). A Programming Notation for Tactical Reasoning. In: Shostak, R.E. (eds) 7th International Conference on Automated Deduction. CADE 1984. Lecture Notes in Computer Science, vol 170. Springer, New York, NY. https://doi.org/10.1007/978-0-387-34768-4_26
Download citation
DOI: https://doi.org/10.1007/978-0-387-34768-4_26
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-96022-7
Online ISBN: 978-0-387-34768-4
eBook Packages: Springer Book Archive