We study the termination properties of well-moded programs, and we show thz, t. under suitable conditions, for these programs there exists an algebraic characteriza zion-in the style of Apt and Pedreschi, Studies in pure prolog: termination, in: J.W. Lloyd ted.), Proceedings of the Simposium in Computational Logic, Springer. Berlin. 1990. pp. 150-176-of the property of being terminating. This characterization enjoys the prorberties of being compositional and. to some extent, of being easy to check.
Abstract. In the last fifteen years, several research efforts have been directed towards the representation and the analysis of metabolic pathways by using Petri nets. The goal of this paper is twofold. First, we discuss how the knowledge about metabolic pathways can be represented with Petri nets. We point out the main problems that arise in the construction of a Petri net model of a metabolic pathway and we outline some solutions proposed in the literature. Second, we present a comprehensive review of recent research on this topic, in order to assess the maturity of the field and the availability of a methodology for modelling a metabolic pathway by a corresponding Petri net.
In this paper semi-linear norms, a class of functions to weight the terms occurring in a program, are defined and studied. All the functions in this class have the nice property of allowing a syntactical characterization of rigid terms, that is terms whose weight does not change under substitution.Based on these norms, a general proof method for termination of pure Prolog programs can be adapted to deal with a large class of programs in a simple way. The sin~lified method requires pre/post specifications well-behaved with respect to substitutions, quite a general case in practice, and ordering functions not increasing with respect to substitutions, which can be based on semi-linear norms, to be associated to program predicates. A few examples of this simplified proof method are given.
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