A Mechanized Proof Reconstruction for SCNP Termination

Ben-Amram and Codish described SCNP [2], a subclass of the size-change termination criterion SCT [8], which permits efficient certificate checking. Termination problems in this class have a global ranking function of a certain form, which can be found using SAT solving. This note describes an automated proof reconstruction for this certificate scheme, implemented in the theorem prover Isabelle/HOL [9]. In previous work [6], we have shown how to use the full size-change principle for termination proofs of recursive function definitions in Isabelle. Although the certificatebased approach is less powerful in theory, it has practical advantages: • The transitive closure computation in [8] is an efficiency bottleneck, and optimizing it is hard since the code must be proved correct and executed within the logical system. • Certificates can be stored, which makes proof checking easier when the proof script is re-run. • Much less logical infrastructure is necessary. In particular, no formalization of Ramsey’s theorem is required, which makes the approach portable to theorem provers with a constructive foundation, such as Coq [3]. Our method is included in the recent release of Isabelle 2009 (http://isabelle.in.tum.de).