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By W. Reif, G. Schellhorn, K. Stenzel, M. Balser (auth.), Wolfgang Bibel, Peter H. Schmitt (eds.)

1. simple options OF INTERACTIVE THEOREM PROVING Interactive Theorem Proving eventually goals on the building of robust reasoning instruments that allow us (computer scientists) turn out issues we won't end up with no the instruments, and the instruments can't turn out with out us. interplay typi­ cally is required, for instance, to direct and keep an eye on the reasoning, to take a position or generalize strategic lemmas, and infrequently just because the conjec­ ture to be proved doesn't carry. In software program verification, for instance, right models of requirements and courses generally are bought in simple terms after a few failed facts makes an attempt and next mistakes corrections. diversified interactive theorem provers may very well glance particularly varied: they might aid diverse logics (first-or higher-order, logics of courses, sort concept etc.), might be prevalent or special-purpose instruments, or can be tar­ geted to various purposes. however, they percentage universal thoughts and paradigms (e.g. architectural layout, strategies, tactical reasoning etc.). the purpose of this bankruptcy is to explain the typical options, layout rules, and easy necessities of interactive theorem provers, and to discover the band­ width of diversifications. Having a 'person within the loop', strongly impacts the layout of the evidence software: proofs needs to stay understandable, - facts ideas has to be high-level and human-oriented, - power facts presentation and visualization turns into very important.

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Technical Report TUM-19311 and 19312, Technische Universitat Munchen, Fakultat fUr Informatik, TUM, 80290 Munchen, Germany. Constable, R. , Allen, S. E, Bromley, H. , Cleaveland, W. , Cremer, J. E, Harper, R. , Howe, D. , Knoblock, T. , Mendler, N. , Sasaki, J. , and Smith, S. E (1986). Implementing Mathematics with the Nuprl Proof Development System. Prentice Hall. , and Saaltink, M. (1992). The EVES system. In Proceedings of the International Lecture Series on "Functional Programming, Concurrency, Simulation and Automated Reasoning" (FPCSAR).

Automation is attained by an elaborate set of heuristics, efficient simplification, and a user friendly way to customize the prover to the problem. A recent development is the integration of external reasoners such as automated theorem provers. In software verification, proof attempts are more likely to reveal errors than to prove their absence. Therefore, in KIV strong emphasis was put on the tight integration of proving and error correction. Incremental verification by reuse of proofs in KIV goes beyond proof script replay mechanisms in other interactive systems.

Editors, VLSI Specification and Synthesis. Kluwer Academic Publishers. , and Wadsworth, C. (1979). Edinburgh LCF: A Mechanised Logic of Computation. Springer LNCS 78. Graf, P. (1996). Term Indexing. Springer LNCS 1053. Harel, D. (1984). Dynamic logic. In Gabbay, D. and Guenther, E, editors, Handbook ofPhilosophical Logic, volume 2, pages 496-604. Reidel. , and Milner, R. (1986). Standard ML. ECS-LFCS-86-2. Univ. Edinburgh. , and Stephan, W. (1989). A Dynamic Logic for Program Verification. In Meyer, A.

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