Abstract Reduction Systems and Idea of Knuth-Bendix Completion Algorithm
نویسنده
چکیده
Reduction Systems and Idea of Knuth-Bendix Completion Algorithm Grzegorz Bancerek Association of Mizar Users Białystok, Poland Summary. Educational content for abstract reduction systems concerning reduction, convertibility, normal forms, divergence and convergence, ChurchRosser property, term rewriting systems, and the idea of the Knuth-Bendix Completion Algorithm. The theory is based on [1].
منابع مشابه
Automated Reasoning I∗
Preliminaries abstract reduction systems well-founded orderings Propositional logic syntax, semantics calculi: DPLL-procedure, . . . implementation: 2-watched literals, clause learning First-order predicate logic syntax, semantics, model theory, . . . calculi: resolution, tableaux, . . . implementation: sharing, indexing First-order predicate logic with equality term rewriting systems calculi: ...
متن کاملTerm Rewriting
Contents 1 Abstract Reduction Systems Abstract Term Rewriting Systems play an important role in various areas, such as abstract data type speciications, implementations of functional programming languages and automated deduction. In this chapter we introduce several of the basic concepts and facts for TRS's. Speciically, we discuss Abstract Reduction Systems; general Term Rewriting Systems incl...
متن کاملReduction Relations
The goal of the article is to start the formalization of Knuth-Bendix completion method (see [2], [10] or [1]; see also [11],[9]), i.e. to formalize the concept of the completion of a reduction relation. The completion of a reduction relation R is a complete reduction relation equivalent to R such that convertible elements have the same normal forms. The theory formalized in the article include...
متن کاملKnuth-Bendix Completion with a Termination Checker
Knuth-Bendix completion takes as input a set of universal equations and attempts to generate a convergent rewriting system with the same equational theory. An essential parameter is a reduction order used at runtime to ensure termination of intermediate rewriting systems. Any reduction order can be used in principle, but modern completion tools typically implement only a few classes of such ord...
متن کاملSlothrop: Knuth-Bendix Completion with a Modern Termination Checker
A Knuth-Bendix completion procedure is parametrized by a reduction ordering used to ensure termination of intermediate and resulting rewriting systems. While in principle any reduction ordering can be used, modern completion tools typically implement only Knuth-Bendix and path orderings. Consequently, the theories for which completion can possibly yield a decision procedure are limited to those...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Formalized Mathematics
دوره 22 شماره
صفحات -
تاریخ انتشار 2014