Abstract
An important advantage of using a formal method of developing software is that one can prove that development steps are correct with respect to their specification. Conducting proofs by hand, however, can be time consuming to the extent that designers have to judge whether a proof of a particular obligation is worth conducting. Even if hand proofs are worth conducting, how do we know that they are correct?
One approach to overcoming this problem is to use an automatic theorem proving system to develop and check our proofs. However, in order to enable present day theorem provers to check proofs, one has to conduct them in much more detail than hand proofs. Carrying out more detailed proofs is of course more time consuming.
This paper describes the use of proof by analogy in an attempt to reduce the time spent on proofs. We develop and implement a proof follower based on analogy and present an example to illustrate its characteristics. The example shows that even when the follower fails to complete a proof, it can provide a hint that enables the user to complete a proof.
Similar content being viewed by others
References
Buchanan B. G. et al. Constructing an expert system. In F. Hayes-Roth, D. A. Waterman, and D. B. Lenat, editors,Building Expert Systems, pages 127–167. Addison Wesley, 1983.
Bundy. A.The Computer Modelling of Mathematical Reasoning. Academic Press, 1979.
Bundy. A. 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.
Gick M. and Holyoak K. J. Analogical problem solving.Cognitive Psychology, 12, 1980.
Hall R. P. Computational approaches to analogical reasoning: A comparative analysis.Artificial Intelligence, 39:39–120, 1989.
Jones C. B., Jones K. D., Lindsay P. A. and Moore R. editors, mural;A Formal Development Support System. Springer Verlag, London, 1991.
Jones C. B.Systematic Software Development using VDM. Prentice Hall International, second edition, 1990.
Kling R. E. A paradigm for reasoning by analogy.Artificial Intelligence, 2:147–178, 1971.
McDermott J. Learning to use analogies. InProceedings of the International Joint Conference on Artificial Intelligence, pages 568–576, Tokyo, 1979.
Munyer J. C.Analogy as a means of discovery in problem-solving and learning. PhD thesis, University of California, Santa Cruz, 1981.
Manna Z. and Waldinger R.The Logical Basis for Computer Programming I. Addison Wesley, Reading, Massachusetts, 1985.
Owen S.Analogy for Automated Reasoning. Academic Press, 1990.
Vadera S.Heuristics for Proofs. PhD thesis, University of Manchester, Manchester M13 9PL, UK, 1992.
Vadera S. Proof by analogy in mural — a more detailed account.Formal Aspects of Computing, 7(E): 1–29, 1995.
Author information
Authors and Affiliations
Corresponding author
Electronic supplementary material
Rights and permissions
About this article
Cite this article
Vadera, S. Proof by analogy in mural. Formal Aspects of Computing 7, 183–206 (1995). https://doi.org/10.1007/BF01211605
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF01211605