Download PDF by Colin Stirling (auth.), Frank Pfenning (eds.): Automated Deduction – CADE-21: 21st International Conference

By Colin Stirling (auth.), Frank Pfenning (eds.)

ISBN-10: 3540735941

ISBN-13: 9783540735946

This ebook constitutes the refereed lawsuits of the twenty first foreign convention on computerized Deduction, CADE-21, held in Bremen, Germany, in July 2007.

The 28 revised complete papers and six method descriptions provided have been rigorously reviewed and chosen from sixty four submissions. All present points of computerized deduction are addressed, starting from theoretical and methodological matters to presentation and overview of theorem provers and logical reasoning platforms. The papers are prepared in topical sections on higher-order common sense, description common sense, intuitionistic common sense, satisfiability modulo theories, induction, rewriting, and polymorphism, first-order common sense, version checking and verification, termination, in addition to tableaux and first-order systems.

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Extra info for Automated Deduction – CADE-21: 21st International Conference on Automated Deduction Bremen, Germany, July 17-20, 2007 Proceedings

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For instance, Liang [13] implements a compiler for a simple imperative language using a higher-order abstract syntax implementation in λ-Prolog. Boyle, Resler and Winter [8], propose using rewrites that model code transformation to build trusted compilers. They also introduce a transformation grammar to guide the application of rewrites [25]. Similarly, Sampaio [21] uses term rewriting to convert source programs to their normal forms representing object code. However, these works do not not address the issue of validation of the compiler.

The features of this new approach include: (1) The automation provided by the host logic logical framework are fully utilized; (2) All intermediate languages except for the one at the last step can be reasoned directly using ordinary mathematics provided by the logical framework; (3) Program transformations are cleanly isolated and specified as certified rewrite rules. This approach overlaps only a little with the implementations in our previous work [5,12]. In fact, less than 5% of the code is shared between our previous work and the work presented here.

This invariance under renamings does, however, not hold in general, not even under renamings with fresh variables. For example if we assume that variables are linearly ordered, then the relation v = min{v0 , . . , vn } ({v0 , . . , vn }, v) that associates finite subsets of these variables to the smallest variable occurring in it, is not invariant (apply the renaming [v := v ] where v is a variable that is bigger than every variable in {v0 , . . , vn }). Other examples are rules that involve a substitution for concrete variables or a substitution with concrete terms.

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Automated Deduction – CADE-21: 21st International Conference on Automated Deduction Bremen, Germany, July 17-20, 2007 Proceedings by Colin Stirling (auth.), Frank Pfenning (eds.)

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