Modularity of Termination Using Dependency pairs
نویسندگان
چکیده
The framework of dependency pairs allows automated termination and innermost termination proofs for many TRSs where such proofs were not possible before. In this paper we present a reenement of this framework in order to prove termination in a modular way. Our mod-ularity results signiicantly increase the class of term rewriting systems where termination resp. innermost termination can be proved automatically. Moreover, the modular approach to dependency pairs yields new modularity criteria which extend previous results in this area. In particular , existing results for modularity of innermost termination can easily be obtained as direct consequences of our new criteria.
منابع مشابه
Modular Termination Proofs for Rewriting Using Dependency Pairs
Recently, Arts and Giesl developed the dependency pair approach which allows automated termination and innermost termination proofs for many term rewriting systems (TRSs) for which such proofs were not possible before. The motivation for this approach was that virtually all previous techniques for automated termination proofs of TRSs were based on simplification orderings. In practice, however,...
متن کاملTermination of Narrowing: Automated Proofs and Modularity Properties
In 1936, Alan Turing proved that the halting problem, that is, deciding whether a program terminates, is an undecidable problem for most practical programming languages. Even so, termination is so relevant that a vast number of techniques for proving the termination of programs have been researched in the recent decades. Term rewriting systems provide an abstract theoretical framework ideally s...
متن کاملThe Dependency Pair Framework: Combining Techniques for Automated Termination Proofs
The dependency pair approach is one of the most powerful techniques for automated termination proofs of term rewrite systems. Up to now, it was regarded as one of several possible methods to prove termination. In this paper, we show that dependency pairs can instead be used as a general concept to integrate arbitrary techniques for termination analysis. In this way, the benefits of different te...
متن کاملProving and Disproving Termination in the Dependency Pair Framework
The dependency pair approach is one of the most powerful techniques for automated termination proofs of term rewrite systems. Up to now, it was regarded as one of several possible methods to prove termination. We show that dependency pairs can instead be used as a general concept to integrate arbitrary techniques for termination analysis. In this way, the benefits of different techniques can be...
متن کاملProving and Disproving Termination of Higher-Order Functions
The dependency pair technique is a powerful modular method for automated termination proofs of term rewrite systems (TRSs). We present two important extensions of this technique: First, we show how to prove termination of higher-order functions using dependency pairs. To this end, the dependency pair technique is extended to handle (untyped) applicative TRSs. Second, we introduce a method to pr...
متن کامل