Depth-k Sharing and Freeness

Analyses for variable sharing and freeness are important both in the automatic parallelisation and in the optimisation of sequential logic programs. In this paper, a new analysis is described which can infer sharing and freeness information to an unusually high degree of accuracy. By encoding structural properties of substitutions in a sharing group fashion, a powerful depth-k sharing and freeness analysis is synthesised which exploits the synergy between tracing sharing information and tracking term structure. The analysis propagates groundness with the accuracy of sharing groups and yet can precisely infer sharing and freeness. Correctness is formally proven.