Parallel and efficient implementation of the compartmentalized connection graph proof procedure: Resolution to unification

Abstract

This paper documents aspects of the development of a logic programming paradigm with implicit control, based in a compartmentalized connection graph theorem prover. Whilst the research has as it main goal the development of a language in which programs can be written with much less explicit control than PROLOG and its existing successors, a secondary goal is to exploit the immense parallelism inherent in the connection graph. This is what is in focus in this presentation.

We focus initially on analysis of the extent of the parallelism inherent in the proof procedure. We characterize six different forms of parallelism These various forms of parallelism can be further classified into two classes: those associated with the performance of resolution steps, and those which are more concerned with unification.

Unification is thus also a major topic of this report, and is identified as a major source of the cost of executing a logic program or proving a theorem. It turns out that deferring unification is the one of the best ways of dealing with it: hashing to perform it, and indexing to avoid it.

Indexing and hashing, therefore, are our third topic.

The work reported here was in the main undertaken while the author was at Macquarie University NSW 2009 AUSTRALIA, and was supported in part by IMPACT Ltd, PETERSHAM NSW 2049 AUSTRALIA, the Australian Telecommunications and Electronics Research Board, and the Australian Research Council (Grant No. A48615954). The author is currently supported under ESPRIT BRA 3012: COMPULOG.