Download Rewriting Techniques and Applications: 5th International by Claude Kirchner PDF

By Claude Kirchner

This quantity includes the lawsuits of RTA-93, the 5th overseas convention on Rewriting thoughts and functions, held in Montreal, Canada, in June 1993. the quantity contains 3 invited lectures, "Rewrite recommendations in Theorem Proving" (L. Bachmair); "Proving homes of Typed Lambda phrases: Realizability, Covers, and Sheaves", (J. Gallier); and "On a few Algorithmic difficulties for teams and Monoids", (S.J. Adian). It additionally good points complete types of 29 papers chosen from ninety one submissions, 6 method descriptions, and an inventory of open difficulties within the box. The papers hide many themes: time period rewriting; termination; graph rewriting; constraint fixing; semantic unification, disunification and mix; higher-order logics; and theorem proving, with numerous papers on dispensed theorem proving, theorem proving with constraints and of completion.

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Additional info for Rewriting Techniques and Applications: 5th International Conference, RTA-93 Montreal, Canada, June 16–18, 1993 Proceedings

Example text

The termination of the completion procedure is not guaranteed when the conjecture is invalid. In Table 2, we list some identities which are true in every alternative ring, and in Table 3, we give Herky's proof statistics of these identities (except those of (a13), (c4)-(c8) and (j4), which Herky cannot finish before running out of the space). The time was measured in Sun Common Lisp on a Sun Sparcstation 2 with 16 megabytes of main memory. For each identity listed there, the table gives the computing time, the number of new equations generated by Herky, the number of rewrite rules made from both the input equations and new equations, and the number of equations (including the input equations) in the proof of that identity.

Frequently enough, we must handle three rewrite relations, the terminating relations - "• and - " 2 resulting from the inclusions oriented to the right and to the left respectively, and the non-terminating relation - 1 resulting from the non-oriented inclusions. We name these three relations a (R1 , R 2) hi-rewriting system modulo /. 7 Figure 3 shows an example of them. 1 From Church-Rosser to Local Con8uence The simplest way to have a complete and decidable proof procedure for (R1 , R 2) modulo I is reducing it to the hi-rewriting system {Rt U I, R2 U I) and, like in the previous section, to require of it the following properties ~ U --;-+ 1 5 1 7 and "'ii;+ U -,are quasi-terminating, and (1) If this condition is satisfied tlaen we can make the pair confiuent like in the equational case.

The issue is efficiency. The most significant advantage of building S into a completion procedure is not only that we can have faster rewriting and superposition operations, but also that we can very effectively avoid redundant computations in a completion procedure. An acute problem in every automatic reasoning system is the inability to recognize the unnecessity of a large subset of inferences explosively generated from the input. The techniques for identifying redundant computations in a completion procedure have been developed over the years (see [13] for a survey).

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