Abstract
We propose the Mizar system as a theorem prover capable of verifying generic algebraic algorithms on an appropriate abstract level. The main advantage of the Mizar theorem prover is its special proof script language that enables textbook style presentation of proofs, hence allowing proofs in the language of algebra.
Using Mizar we were able to give a rigorous machine assisted correctness proof of a generic version of the Brown/Henrici arithmetic in the field of fractions over arbitrary gcd domains.
This paper is based on the author’s Ph.D thesis [8], supervised by Rüdiger Loos.
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
George E. Collins, Algebraic Algorithms, chapter two: Arithmetics, Lecture manuscript, 1974.
Antoni Diller, Z—An Introduction to Formal Methods, 2nd ed., Wiley, New York, 1994.
D. Knuth, Literate Programming, The Computer Journal 27(2), 97–111, 1984.
Rüdiger Loos and George E. Collins, Revised Report on the Algorithm Description Language ALDES, Technical Report WSI-92-14, Wilhelm-Schickard-Institut für Informatik, 1992.
Udi Manber and Burra Gopal, GLIMPSE—A Tool to Search Entire File Systems, available from http://glimpse.cs.arizona.edu.
Piotr Rudnicki, An Overview of the Mizar Project, available from http://web.cs.ualberta.ca:80/~piotr/Mizar, June 1992.
Sibylle Schupp, Generic Programming—SuchThat One Can Build an Algebraic Library, Ph.D. thesis, University of Tübingen, 1996.
Christoph Schwarzweller, Mizar Verification of Generic Algebraic Algorithms, Ph.D. thesis, University of Tübingen, 1997.
Andrzej Trybulec, Some Features of the Mizar Language, available from http://web.cs.ualberta.ca:80/~piotr/Mizar, July 1993.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Schwarzweller, C. (2000). Mizar Correctness Proofs of Generic Fraction Field Arithmetic. In: Jazayeri, M., Loos, R.G.K., Musser, D.R. (eds) Generic Programming. Lecture Notes in Computer Science, vol 1766. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-39953-4_14
Download citation
DOI: https://doi.org/10.1007/3-540-39953-4_14
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-41090-4
Online ISBN: 978-3-540-39953-7
eBook Packages: Springer Book Archive