Knuth-Bendix Completion for Non-Symmetric Transitive Relations

Knuth-Bendix Completion for Non-Symmetri Transitive Relations

Formalizing Knuth-Bendix Orders and Knuth-Bendix Completion

We present extensions of our Isabelle Formalization of Rewriting that cover two historically related concepts: the Knuth-Bendix order and the Knuth-Bendix completion procedure. The former, besides being the first development of its kind in a proof assistant, is based on a generalized version of the Knuth-Bendix order. We compare our version to variants from the literature and show all propertie...

KBCV - Knuth-Bendix Completion Visualizer

This paper describes a tool for Knuth-Bendix completion. In its interactive mode the user only has to select the orientation of equations into rewrite rules; all other computations (including necessary termination checks) are performed internally. Apart from the interactive mode, the tool also provides a fully automatic mode. Moreover, the generation of (dis)proofs in equational logic is suppor...

A user-interface for Knuth-Bendix completion

Knuth-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...