The AFFIRM theorem prover: Proof forests and management of large proofs
The AFFIRM theorem prover is an interative, natural-deduction system centered around abstract data types. Since long proofs are often required to verity algorithms, we describe a model (called the "proof forest") which helps the user to visualize and manage the potentially large number of theorems and subgoals that can arise.
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- 1.Burstall, R. M. and Goguen, J. A., "Putting Theories Together to Make Specifications," in Proceedings of the Fifth International Joint Conference on Artificial Intelligence, pp. 1045–1058, IEEE, August 1977.Google Scholar
- 2.Gerhart, S. L. et al., An Overview of AFFIRM: A Specification and Verification System, USC Information Sciences Institute, Technical Report RR-9-81, 1980. Also to appear in Proc. IFIP 80Google Scholar
- 3.Goguen, J. A., Thatcher, J. W., and Wagner, E. G., "Abstract Data Types as Initial Algebras and the Correctness of Data Representations," in Yeh, R. T. (ed.), Current Trends in Programming Methodology, Volume IV, Prentice-Hall, 1978.Google Scholar
- 4.Guttag, J. V., "Abstract Data Types and the Development of Data Structures," CACM 20, June 1977, 397–404.Google Scholar
- 5.Guttag, J. V., Horowitz, E., and Musser, D. R., "Abstract Data Types and Software Validation," CACM 21, December 1978, 1048–1064. (Also USC Information Sciences Institute RR-76/48, August 1976.)Google Scholar
- 6.Guttag, J. V., "Notes on Type Abstraction," IEEE Transactions on Software Engineering SE-6, (1), April 1979, 13–23.Google Scholar
- 7.Huet, G., Confluent Reductions: Abstract Properties and Applications to Term Rewriting Systems, IRIA — LABORIA, Technical Report LABORIA Report No. 250, 1978.Google Scholar
- 8.Knuth, D. E., and Bendix, P. B., "Simple Word Problems in Universal Algebras," in Leech, J. (ed.), Computational Problems in Abstract Algebra, pp. 263–297, Pergamon Press, New York, 1970.Google Scholar
- 9.Lankford, D. S. and Musser, D. R., On Semi-deciding First-Order Validity and Invalidity, 1978. unpublished manuscriptGoogle Scholar
- 10.McCarthy, J., "A Basis for a Mathematical Theory of Computation," in Braffort and Hirschberg (eds.), Computer Programming and Formal Systems, pp. 33–70, North-Holland, 1963.Google Scholar
- 11.Musser, D. R., "Abstract Data Type Specification in the AFFIRM System," IEEE Transactions on Software Engineering SE-6, (1), April 1979, 24–32.Google Scholar
- 12.Spitzen, J., and Wegbreit, B., "The Verification and Synthesis of Data Structures," Acta Informatica 4, 1975, 127–144.Google Scholar
- 13.Thompson, D. H., ed., AFFIRM Reference Manual, USC Information Sciences Institute, 1979.Google Scholar