Termination of Programs using Term Rewriting and SAT Solving

Abstract

There are many powerful techniques for automated termination analysis of
term rewrite systems (TRSs). However, up to now they have hardly been used 
for real programming languages. In this talk, we describe recent results 
which permit the application of existing techniques from term rewriting 
in order to prove termination of programs. We discuss two possible approaches:

1. One could translate programs into TRSs and then use existing tools to 
   verify termination of the resulting TRSs.

2. One could adapt TRS-techniques to the respective programming languages
   in order to analyze programs directly. 

We present such approaches for the functional language Haskell and the logic
language Prolog. Our results have been implemented in the termination provers
AProVE and Polytool. In order to handle termination problems resulting 
from real programs, these provers had to be coupled with modern SAT solvers,
since the automation of the TRS-termination techniques had to
improve significantly. Our resulting termination analyzers are currently
the most powerful ones for Haskell and Prolog.