Automated Termination Proofs for Logic Programs by Term Rewriting

There are two kinds of approaches for termination analysis of logic programs: "transformational" and "direct" ones. Direct approaches prove termination directly on the basis of the logic program. Transformational approaches transform a logic program into a term rewrite system (TRS) and then analyze termination of the resulting TRS instead. Thus, transformational approaches make all methods previously developed for TRSs available for logic programs as well. However, the applicability of most existing transformations is quite restricted, as they can only be used for certain subclasses of logic programs. (Most of them are restricted to well-moded programs.) In this paper we improve these transformations such that they become applicable for any definite logic program. To simulate the behavior of logic programs by TRSs, we slightly modify the notion of rewriting by permitting infinite terms. We show that our transformation results in TRSs which are indeed suitable for automated termination analysis. In contrast to most other methods for termination of logic programs, our technique is also sound for logic programming without occur check, which is typically used in practice. We implemented our approach in the termination prover AProVE and successfully evaluated it on a large collection of examples.Comment: 49 page

Proving Termination With Adornments

Proving termination is one of the most intriguing problems of program verification. Recently, the study of termination of numerical programs led to the emerging of the adorning technique. This approach is based on the idea of distinguishing between different subsets of values for variables, and deriving piecewise level mappings based on these subsets. In the current paper we generalise the technique and consider symbolical computations. Our experience suggests that such a generalisation will allow automated tools to verify termination of examples that remain at the moment beyond their abilities

Proving termination with adornments

Termination is well-known to be one of the important aspects of program correctness. Logic programming provides a framework with a strong theoretical basis for tackling this problem. However, due to the declarative formulation of programs, the danger of non-termination may increase. As a result, termination analysis received considerable attention in logic programming. Recently, the study of termination of numerical programs led to the emerging of the adorning technique [7]. This technique implements the well-known divide et impera strategy by distinguishing between different subsets of values for variables, and deriving termination proofs based on these subsets. In this paper we generalise this technique and discuss its applicability to the domain of terms (the Herbrand domain)

Proving termination with adornments

Technical report DSIC-II/15/03status: publishe

Proving termination with adornments

Termination is well-known to be one of the important aspects of program correctness. Logic programming provides a framework with a strong theoretical basis for tackling this problem. However, due to the declarative formulation of programs, the danger of non-termination may increase. As a result, termination analysis received considerable attention in logic programming. Recently, the study of termination of numerical programs led to the emerging of the adorning technique [7]. This technique implements the well-known divide et impera strategy by distinguishing between different subsets of values for variables, and deriving termination proofs based on these subsets. In this paper we generalise this technique and discuss its applicability to the domain of terms (the Herbrand domain)