A Rule-Based Framework for Building Superposition-Based Decision Procedures
Résumé
This paper deals with decision procedures specified as inference systems. Among them we focus on superposition-based decision procedures. The superposition calculus is a refutation-complete inference system at the core of all equational theorem provers. In general this calculus provides a semi-decision procedure that halts on unsatisfiable inputs but may diverge on satisfiable ones. Fortunately, it may also terminate for some theories of interest in verification, and thus it becomes a decision procedure. To reason on the superposition calculus, a schematic superposition calculus has been studied, for instance to automatically prove termination. This paper presents an implementation in Maude of these two inference systems. Thanks to this implementation we automatically derive termination of superposition for a couple of theories of interest in verification.