Automated Deduction — A Basis for Applications: Volume II: by W. Reif, G. Schellhorn, K. Stenzel, M. Balser (auth.),

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

1. easy thoughts OF INTERACTIVE THEOREM PROVING Interactive Theorem Proving eventually goals on the building of robust reasoning instruments that permit us (computer scientists) turn out issues we can't turn out with out the instruments, and the instruments can't end up with no us. interplay typi­ cally is required, for instance, to direct and regulate the reasoning, to invest or generalize strategic lemmas, and occasionally just because the conjec­ ture to be proved doesn't carry. In software program verification, for instance, right types of necessities and courses generally are received simply after a couple of failed facts makes an attempt and next errors corrections. diversified interactive theorem provers may very well glance relatively various: they could aid varied logics (first-or higher-order, logics of courses, sort conception etc.), might be widely used or special-purpose instruments, or can be tar­ geted to diverse functions. 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 innovations, layout ideas, and easy standards of interactive theorem provers, and to discover the band­ width of diversifications. Having a 'person within the loop', strongly affects the layout of the facts software: proofs needs to stay understandable, - evidence ideas has to be high-level and human-oriented, - chronic facts presentation and visualization turns into very important.

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

1. easy thoughts OF INTERACTIVE THEOREM PROVING Interactive Theorem Proving eventually goals on the building of robust reasoning instruments that permit us (computer scientists) turn out issues we can't turn out with out the instruments, and the instruments can't end up with no us. interplay typi­ cally is required, for instance, to direct and regulate the reasoning, to invest or generalize strategic lemmas, and occasionally just because the conjec­ ture to be proved doesn't carry. In software program verification, for instance, right types of necessities and courses generally are received simply after a couple of failed facts makes an attempt and next errors corrections. diversified interactive theorem provers may very well glance relatively various: they could aid varied logics (first-or higher-order, logics of courses, sort conception etc.), might be widely used or special-purpose instruments, or can be tar­ geted to diverse functions. 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 innovations, layout ideas, and easy standards of interactive theorem provers, and to discover the band­ width of diversifications. Having a 'person within the loop', strongly affects the layout of the facts software: proofs needs to stay understandable, - evidence ideas has to be high-level and human-oriented, - chronic facts presentation and visualization turns into very important.

Show description

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Extra resources for Automated Deduction — A Basis for Applications: Volume II: Systems and Implementation Techniques

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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). McMaster University. Farmer, W. , Guttman, J. , and Fabrega, E J. T. (1996). IMPS: an updated description. In 13th International Conference on Automated Deduction, CADE13, SpringerLNCS.

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Edges are drawn from the (export-) specification (the one to be implemented) to the module, and from the module to the (import-) specification (used in the programs). The related theorem base contains automatically generated proof obligations which guarantee the correctness of the module. Thus module verification smoothly fits into the framework described in the previous sections of this chapter. The only additional ingredients are rules and heuristics for program instructions to allow theorem proving with programs.

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