In this paper, we describe a methodology for proving termination of logic programs. First, we introduce U-graphs as an abstraction of logic programs and establish that SLDNFderivations can be realized by instances of paths in the U-graphs. Such a relation enables us to use U-graphs for establishing the universal termination of logic programs. In our method, we associate pre- and post-assertions to the nodes of the graph and ordered assertions to selected edges of the graph. With this as the basis, we develop a simple method for establishing the termination of logic programs. The simplicity/practicality of the method is illustrated through examples. 1 Introduction One of the most important features of logic programming is its declarative semantics. That is, one can consider the programs to be self-specifying as they are non-procedural, and hence do not need elaborate correctness proofs. There can be a debate about whether it is meaningful to talk about verifying logic programs. It wil...

Relational program derivation has gathered momentum over the last decade with the development of many specification logics. However, before such relational specifications can be executed in existing programming languages, they must be carefully phrased to respect the evaluation order of the language. In turn, this requirement inhibits the rapid prototyping of specifications in a relational notation. The aim of this thesis is to bridge the gap between the methodology and practice of relational program derivation by realising a compositional style of logic programming that permits specifications to be phrased naturally and executed declaratively.

We present a slicing approach for analyzing logic programs with respect to non-termination. The notion of a failure-slice is presented which is an executable reduced fragment of the program. Each failureslice represents a necessary termination condition for the program. If a failure-slice does not terminate it can be used as an explanation for the non-termination of the whole program. To effectively determine useful failure-slices we combine a constraint based static analysis with the dynamic execution of actual slices. The current approach has been integrated into a programming environment for beginners. Further, we show how our approach can be combined with traditional techniques of termination analysis.