Isar — A Generic Interpretative Approach to Readable Formal Proof Documents
- 342 Downloads
We present a generic approach to readable formal proof documents, called Intelligible semi-automated reasoning (Isar). It addresses the major problem of existing interactive theorem proving systems that there is no appropriate notion of proof available that is suitable for human communication, or even just maintenance. Isar’s main aspect is its formal language for natural deduction proofs, which sets out to bridge the semantic gap between internal notions of proof given by state-of-the-art interactive theorem proving systems and an appropriate level of abstraction for user-level work. The Isar language is both human readable and machine-checkable, by virtue of the Isar/VM interpreter.
Compared to existing declarative theorem proving systems, Isar avoids several shortcomings: it is based on a few basic principles only, it is quite independent of the underlying logic, and supports a broad range of automated proof methods. Interactive proof development is supported as well. Most of the Isar concepts have already been implemented within Isabelle. The resulting system already accommodates simple applications.
KeywordsTheorem Prove Operational Semantic Natural Deduction High Order Logic Elimination Rule
Unable to display preview. Download preview PDF.
- K. Arkoudas. Deduction vis-a-vis computation: The need for a formal language for proof engineering. The MIT Express project, http://www.ai.mit.edu/projects/express/, June 1998.
- C. Benzmüller, L. Cheikhrouhou, D. Fehrer, A. Fiedler, X. Huang, M. Kerber, M. Kohlhase, K. Konrad, E. Melis, A. Meier, W. Schaarschmidt, J. Siekmann, and V. Sorge. Mega: Towards a mathematical assistant. In W. McCune, editor, 14th International Conference on Automated Deduction — CADE-14, volume 1249 of LNAI. Springer, 1997.Google Scholar
- Y. Bertot and L. Théry. A generic approach to building user interfaces for theorem provers. Journal of Symbolic Computation, 11, 1996.Google Scholar
- R. Boulton, K. Slind, A. Bundy, and M. Gordon. An interface between CLAM and HOL. In J. Grundy and M. Newey, editors, Proceedings of the 11th International Conference on Theorem Proving in Higher Order Logics, volume 1479 of LNCS. Springer, 1998.Google Scholar
- R. Burstall. Teaching people to write proofs: a tool. In CafeOBJ Symposium, Numazu, Japan, April 1998.Google Scholar
- A. Church. A formulation of the simple theory of types. Journal of Symbolic Logic, pages 56–68, 1940.Google Scholar
- C. Cornes, J. Courant, J.-C. Filliâtre, G. Huet, P. Manoury, and C Muñoz. The Coq Proof Assistant User’s Guide, version 6.1. INRIA-Rocquencourt et CNRSENS Lyon, 1996.Google Scholar
- Y. Coscoy, G. Kahn, and L. Théry. Extracting text from proofs. In Typed Lambda Calculus and Applications, volume 902 of LNCS. Springer, 1995.Google Scholar
- M. J. C. Gordon and T. F. Melham (editors). Introduction to HOL: A theorem proving environment for higher order logic. Cambridge University Press, 1993.Google Scholar
- T. Nipkow. More Church-Rosser proofs (in Isabelle/HOL). In M. McRobbie and J. K. Slaney, editors, 13th International Conference on Automated Deduction–CADE-13, volume 1104 of LNCS, pages 733–747. Springer, 1996.Google Scholar
- T. Nipkow and D. v. Oheimb. Javalight is type-safe — definitely. In Proc. 25th ACM Symp. Principles of Programming Languages, pages 161–170. ACM Press, New York, 1998.Google Scholar
- L. C. Paulson. Generic automatic proof tools. In R. Veroff, editor, Automated Reasoning and its Applications. MIT Press, 1997.Google Scholar
- L. C. Paulson. A generic tableau prover and its integration with Isabelle. In CADE-15 Workshop on Integration of Deductive Systems, 1998.Google Scholar
- P. Rudnicki. An overview of the MIZAR project. In 1992 Workshop on Types for Proofs and Programs. Chalmers University of Technology, Bastad, 1992.Google Scholar
- D. Syme. DECLARE: A prototype declarative proof system for higher order logic. Technical Report 416, University of Cambridge Computer Laboratory, 1997.Google Scholar
- D. Syme. Declarative Theorem Proving for Operational Semantics. PhD thesis, University of Cambridge, 1998. Submitted.Google Scholar
- A. Trybulec. Some features of the Mizar language. Presented at a workshop in Turin, Italy, 1993.Google Scholar