Abstract Completion, Formalized
نویسندگان
چکیده
Completion is one of the most studied techniques in term rewriting and fundamental to automated reasoning with equalities. In this paper we present new and formalized correctness proofs of abstract completion, both for finite and infinite runs. For the special case of ground completion we present a new proof based on random descent. We moreover extend the results to ordered completion, an important extension of completion that aims to produce ground-complete presentations of the initial equations. We present new proofs concerning the completeness of ordered completion for two settings. Moreover, we revisit and extend results of Metivier concerning canonicity of rewrite systems. All proofs presented in the paper have been formalized in Isabelle/HOL.
منابع مشابه
Abstract Reduction Systems and Idea of Knuth-Bendix Completion Algorithm
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].
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 کاملA New and Formalized Proof of Abstract Completion
Completion is one of the most studied techniques in term rewriting. We present a new proof of the correctness of abstract completion that is based on peak decreasingness, a special case of decreasing diagrams. Peak decreasingness replaces Newman’s Lemma and allows us to avoid proof orders in the correctness proof of completion. As a result, our proof is simpler than the one presented in textboo...
متن کاملCs - R 9633 1996
In this paper we propose a simple framework based on rst-order logic, for the design and decomposition of abstract domains for static analysis. An assertion language is chosen that speciies the properties of interest, and abstract domains are deened to be suitably chosen sets of assertions. Composition and decomposition of abstract domains is facilitated by their logical speciication in rst-ord...
متن کاملReduction Relations Provided the following Requirements Are Met: for Every Natural Number I Such That I 2 Dom a and I + 1 2 Dom a Holds
The goal of the article is to start the formalization of Knuth-Bendix completion method (see 2, ?] or 1]; see also 11, 10]), 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 includes conc...
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:
- CoRR
دوره abs/1802.08437 شماره
صفحات -
تاریخ انتشار 2018