Termination of Isabelle functions via termination of rewriting


We show how to automate termination proofs for recursive functions in (a first-order subset of) Isabelle/HOL by encoding them as term rewrite systems and invoking an external termination prover. Our link to the external prover includes full proof reconstruction, where all necessary properties are derived inside Isabelle/HOL without oracles. Apart from the certification of the imported proof, the main challenge is the formal reduction of the proof obligation produced by Isabelle/HOL to the termination of the corresponding term rewrite system. We automate this reduction via suitable tactics which we added to the IsaFoR library.

In Marko van Eekelen, Herman Geuvers, Julien Schmaltz, and Freek Wiedijk, editors, Interactive Theorem Proving (ITP 2011), volume 6898 of Lecture Notes in Computer Science. Springer Verlag, 2011.