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.
Supported in part by the Defense Advanced Research Projects Agency under contract #DAHC15-72-C-0308
This is a preview of subscription content, access via your institution.
Unable to display preview. Download preview PDF.
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.
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 80
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.
Guttag, J. V., "Abstract Data Types and the Development of Data Structures," CACM 20, June 1977, 397–404.
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.)
Guttag, J. V., "Notes on Type Abstraction," IEEE Transactions on Software Engineering SE-6, (1), April 1979, 13–23.
Huet, G., Confluent Reductions: Abstract Properties and Applications to Term Rewriting Systems, IRIA — LABORIA, Technical Report LABORIA Report No. 250, 1978.
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.
Lankford, D. S. and Musser, D. R., On Semi-deciding First-Order Validity and Invalidity, 1978. unpublished manuscript
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.
Musser, D. R., "Abstract Data Type Specification in the AFFIRM System," IEEE Transactions on Software Engineering SE-6, (1), April 1979, 24–32.
Spitzen, J., and Wegbreit, B., "The Verification and Synthesis of Data Structures," Acta Informatica 4, 1975, 127–144.
Thompson, D. H., ed., AFFIRM Reference Manual, USC Information Sciences Institute, 1979.
Editors and Affiliations
© 1980 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Erickson, R.W., Musser, D.R. (1980). The AFFIRM theorem prover: Proof forests and management of large proofs. In: Bibel, W., Kowalski, R. (eds) 5th Conference on Automated Deduction Les Arcs, France, July 8–11, 1980. CADE 1980. Lecture Notes in Computer Science, vol 87. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-10009-1_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-10009-6
Online ISBN: 978-3-540-38140-2
eBook Packages: Springer Book Archive