Thomas Sternagel

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 supported. Finally, the tool outputs proofs in a certifiable format.

Conditional Confluence (System Description)

This paper describes the Conditional Confluence tool, a fully automatic confluence checker for first-order conditional term rewrite systems. The tool implements various confluence criteria that have been proposed in the literature. A simple technique is presented to test conditional critical pairs for infeasibility, which makes conditional confluence criteria more useful. Detailed experimental data is presented.

Certifying Confluence of Almost Orthogonal CTRSs via Exact Tree Automata Completion

Suzuki et al. showed that properly oriented, right-stable, orthogonal, and oriented conditional term rewrite systems with extra variables in right-hand sides are confluent. We present our Isabelle/HOL formalization of this result, including two generalizations. On the one hand, we relax proper orientedness and orthogonality to extended proper orientedness and almost orthogonality modulo infeasibility, as suggested by Suzuki et al. On the other hand, we further loosen the requirements of the latter, enabling more powerful methods for proving infeasibility of conditional critical pairs. Furthermore, we formalized a construction by Jacquemard that employs exact tree automata completion for non-reachability analysis and apply it to certify infeasibility of conditional critical pairs. Combining these two results and extending the conditional confluence checker ConCon accordingly, we are able to automatically prove and certify confluence of an important class of conditional term rewrite systems.

Recording Completion for Certificates in Equational Reasoning

We introduce recording completion, a variant of Knuth-Bendix completion which facilitates the construction of certificates for various equational logic proofs (completion proofs, entailment proofs and dis-proofs). The approach generalizes to more powerful variants of completion such as ordered completion and AC completion. We implemented recording completion in the tools KBCV and MKBTT. Both tools allow to choose among different formats of proof certificates, namely conversions, proof trees, and conversions with history. We report on experimental results in which all generated certificates have been verified by the trustable checker CeTA.

Certifying Confluence of Quasi-Decreasing Strongly Deterministic Conditional Term Rewrite Systems

We formalize a confluence criterion for the class of quasi-decreasing strongly deterministic conditional term rewrite systems in Isabelle/HOL: confluence follows if all conditional critical pairs are joinable. However, quasi-decreasingness, strong determinism, and joinability of conditional critical pairs are all undecidable in general. Therefore, we also formalize sufficient criteria for those properties, which we incorporate into the general purpose certifier CeTA as well as the confluence checker ConCon for conditional term rewrite systems.