Semantics and Termination of Simply-Moded Logic Programs with Dynamic Scheduling

TL;DR

This paper formalizes the relationship between delay declarations and input-consuming derivations in simply-moded logic programs with dynamic scheduling, providing a semantic framework and a criterion for termination.

Contribution

It introduces a formal model-theoretic semantics for input-consuming derivations and establishes a necessary and sufficient condition for termination in simply-moded programs.

Findings

One-to-one correspondence between delay declarations and input-consuming derivations in many cases.

A semantic framework for analyzing input-consuming derivations.

A criterion for termination of simply-moded logic programs with dynamic scheduling.

Abstract

In logic programming, dynamic scheduling refers to a situation where the selection of the atom in each resolution (computation) step is determined at runtime, as opposed to a fixed selection rule such as the left-to-right one of Prolog. This has applications e.g. in parallel programming. A mechanism to control dynamic scheduling is provided in existing languages in the form of delay declarations. Input-consuming derivations were introduced to describe dynamic scheduling while abstracting from the technical details. In this paper, we first formalise the relationship between delay declarations and input-consuming derivations, showing in many cases a one-to-one correspondence. Then, we define a model-theoretic semantics for input-consuming derivations of simply-moded programs. Finally, for this class of programs, we provide a necessary and sufficient criterion for termination.