On Automating Inductive and Non-inductive Termination Methods

The Coq and ProPre systems show the automated termination of a recursive function by rst constructing a tree associated with the speciication of the function which satisses a notion of terminal property and then verifying that this construction process is formally correct. However, those two steps strongly depend on inductive principles and hence Coq and ProPre can only deal with the termination proofs that are inductive. There are however many functions for which the termination proofs are non-inductive. In this article, we attempt to extend the class of functions whose proofs can be done automatically a la Coq and ProPre to a larger class including functions whose termination proofs are not inductive. We do this by extending the terminal property notion and replacing the veriication step above by one that searches for a decreasing measure which can be used to establish the termination of the function.