First-Order Theory of Rewriting

The first-order theory of rewriting (FORT) is a decidable theory for linear variable-separated rewrite systems. The decision procedure is based on tree automata technique and an inference system presented in "Certifying Proofs in the First-Order Theory of Rewriting". This AFP entry provides a formalization of the underlying decision procedure. Moreover it allows to generate a function that can verify each inference step via the code generation facility of Isabelle/HOL. Additionally it contains the specification of a certificate language (that allows to state proofs in FORT) and a formalized function that allows to verify the validity of the proof. This gives software tool authors, that implement the decision procedure, the possibility to verify their output.