Termination of narrowing via termination of rewriting

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, th...

Termination of narrowing revisited

This paper describes several classes of term rewriting systems (TRS’s) where narrowing has a finite search space and is still (strongly) complete as a mechanism for solving reachability goals. These classes do not assume confluence of the TRS. We also ascertain purely syntactic criteria that suffice to ensure the termination of narrowing and include several subclasses of popular TRS’s such as r...

Termination of Narrowing

Narrowing extends rewriting with logic capabilities by allowing logic variables in terms and replacing matching with unifcationn Narrowing has been widely used in different contexts, ranging from theorem proving to language designn Surprisingly, the termination of narrowing has been mostly overlookedn In this paper, we present a new approach for analyzing the termination of narrowing in left-li...

Termination of Priority Rewriting

Introducing priorities in rewriting increases the expressive power of rules and helps to limit computations. Priority rewriting is used in rule-based programming as well as in functional programming. Termination of priority rewriting is then important to guarantee that programs give a result. We describe an inductive proof method for termination of priority rewriting, relying on an explicit ind...

Termination of Term Rewriting