Abstract
We describe an implementation of general (abstract) lattice theory in the HOL system and its use in transformational reasoning within concrete instances of lattices, using the window inference of HOL. The implementation is extensible; users can add new instances of lattices and all the existing transformation rules are then available for the added structures. As a particularly promising application we briefly describe how our system can be used as part of a tool for transformational reasoning about programs (program refinement).
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
R.J.R. Back. A calculus of refinements for program derivations. Acta Informatica, 25:593–624, 1988.
R.J.R. Back and J. von Wright. Duality in specification languages: a latticetheoretical approach. Acta Informatica, 27:583–625, 1990.
R.J.R. Back and J. von Wright. Refinement concepts formalised in higher-order logic. Formal Aspects of Computing, 2:247–272, 1990.
M.J.C. Gordon. HOL: A proof generating system for higher-order logic. In VLSI Specification, Verification and Synthesis. Kluwer Academic Publishers, 1988.
M.J.C. Gordon, R. Milner and C. Wadsworth. Edinburgh LCF: A mechanised logic of computation. In LNCS 78. Springer-Verlag, 1979.
J. Grundy. Window Inference in the HOL System. In Proc. of the Int. Workshop on the HOL Theorem Proving System and Its Applications, Aug. 1991. IEEE Computer Society Press.
E. Gunter. Doing algebra in higher order logic. In the HOL system documentation, Cambridge, 1990.
E. Gunter. The Implementation and Use of Abstract Theories in HOL In Proc. of the Third HOL Users Meeting, Aarhus, Denmark, October 1990. Technical Report DAIMI PB — 340, 1990.
T. Långbacka, R. Rukšėnas and J. von Wright. TkWinHOL: A tool for doing window inference in HOL. In LNCS 971, 245–260. Springer-Verlag, 1995.
F. Regensburger. HOLCF: Higher Order Logic of Computable Functions. In LNCS 971, 293–307. Springer-Verlag, 1995.
P.J. Robinson and J. Staples. Formalising the hierarchical structure of practical mathematical reasoning. Logic and Computation, 1:47–61, 1993.
P.J. Windley. Abstract Theories in HOL. In Proc. of the Int. Workshop on the HOL Theorem Proving System and Its Applications, September 1992. IFIP Transactions A-20, 197–210.
J. von Wright. Doing Lattice Theory in Higher Order Logic. In Technical Report 136, Reports on Computer Science and Mathematics, Series A. Åbo Akademi, Turku, 1992.
J. von Wright. Program refinement by theorem prover. In Proc. 6th Refinement Workshop, London, January 1994. Springer-Verlag.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Laibinis, L. (1996). Using lattice theory in higher order logic. In: Goos, G., Hartmanis, J., van Leeuwen, J., von Wright, J., Grundy, J., Harrison, J. (eds) Theorem Proving in Higher Order Logics. TPHOLs 1996. Lecture Notes in Computer Science, vol 1125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0105413
Download citation
DOI: https://doi.org/10.1007/BFb0105413
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-61587-3
Online ISBN: 978-3-540-70641-0
eBook Packages: Springer Book Archive