Proving termination for logic programs by the query-mapping pairs approach

This paper describes a method for proving termination of queries to logic programs based on abstract interpretation. The method uses query-mapping pairs to abstract the relation between calls in the LD-tree associated with the program and query. Any well founded partial order for terms can be used to prove the termination. The ideas of the query-mapping pairs approach have been implemented in SICStus Prolog in a system called TermiLog, which is available on the web. Given a program and query pattern the system either answers that the query terminates or that there may be non-termination. The advantages of the method are its conceptual simplicity and the fact that it does not impose any restrictions on the programs.