Abstract
Locales are a means to define local scopes for the interactive proving process of the theorem prover Isabelle. They delimit a range in which fixed assumption are made, and theorems are proved that depend on these assumptions. A locale may also contain constants defined locally and associated with pretty printing syntax.
Locales can be seen as a simple form of modules. They are similar to sections as in AUTOMATH or Coq. Locales are used to enhance abstract reasoning and similar applications of theorem provers. This paper motivates the concept of locales by examples from abstract algebraic reasoning. It also discusses some implementation issues.
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References
C. Cornes, J. Courant, J.-C. Filliâtre, G. Huet, P. Manoury, and C. Muñoz. The Coq Proof Assistant User’s Guide, version 6.1. INRIARocquencourt et CNRS-ENS Lyon, 1996.
A. Church. A Formulation of the Simple Theory of Types. Journal of Symbolic Logic, pages 56–68, 1940.
K. Mani Chandi and Jayadev Misra. Parallel Program Design: A Foundation. Addison-Wesley, 1988.
N. G. de Bruijn. A Survey of the Project AUTOMATH. In J.P. Seldin and J.R. Hindley, editors, To H. B. Curry: Essays on Combinatory Logic, Academic Press Limited, pages 579–606. 1980.
G. Dowek. Naming and Scoping in a Mathematical Vernacular. Technical Report 1283, INRIA, Rocquencourt, 1990.
W. M. Farmer, J. D. Guttman, and F. J. Thayer. IMPS: an Interactive Mathematical Proof System. Journal of Automated Reasoning, 11:213–248, 1993.
John V. Guttag and James J. Horning, editors. Larch: Languages and Tools for Formal Specification. Texts and Monographs in Computer Science. Springer-Verlag, 1993. With Stephen J. Garland, Kevin D. Jones, Andrés Modet, and Jeannette M. Wing.
M. J. C. Gordon and T. F. Melham. Introduction to HOL, a Theorem Proving Environment for Higher Order Logic. Cambridge University Press, 1993.
F. Kammüller. Modular Reasoning in Isabelle. PhD thesis, University of Cambridge, 1999. submitted.
F. Kammüller. Modular Structures as Dependent Types in Isabelle. In Types for Proofs and Programs: TYPES’ 98, LNCS. Springer-Verlag, 1999. Selected papers. To appear.
F. Kammüller and L. C. Paulson. A Formal Proof of Sylow’s First Theorem — An Experiment in Abstract Algebra with Isabelle HOL. Journal of Automated Reasoning, 1999. To appear.
W. Naraschewski and M. Wenzel. Object-oriented Verification based on Record Subtyping in Higher-Order Logic. In 11th International Conference on Theorem Proving in Higher Order Logics, volume 1479 of LNCS, ANU, Canberra, Australia, 1998. Springer-Verlag.
[ORR+96]_S. Owre, S. Rajan, J. M. Rushby, N. Shankar, and M. Srivas. PVS: Combining specification, proof checking, and model checking. In R. Alur and T. A. Henzinger, editors, Computer Aided Verification, volume 1102 of LNCS. Springer, 1996.
S. Owre, N. Shankar, J.M. Rushby, and D.W.J. Stringer-Calvert. PVS Language Reference. Part of the PVS Manual. Available on the Web as http://www.csl.sri.com/pvsweb/manuals.html, September 1998.
L. C. Paulson. Isabelle: A Generic Theorem Prover, volume 828 of LNCS. Springer, 1994.
P. J. Windley. Abstract Theories in HOL. In L. Claesen and M. Gordon, editors, Higher Order Logic Theorem Proving and its Applications, IFIP Transactions A-20, pages 197–210. North-Holland, 1993.
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Kammüller, F., Wenzel, M., Paulson, L.C. (1999). Locales A Sectioning Concept for Isabelle. In: Bertot, Y., Dowek, G., Théry, L., Hirschowitz, A., Paulin, C. (eds) Theorem Proving in Higher Order Logics. TPHOLs 1999. Lecture Notes in Computer Science, vol 1690. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48256-3_11
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DOI: https://doi.org/10.1007/3-540-48256-3_11
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