It is well known that freeness and linearity information positively interact with aliasing information, allowing both the precision and the efficiency of the sharing analysis of logic programs to be improved. In this paper, we present a novel combination of set-sharing with freeness and linearity information, which is characterized by an improved abstract unification operator. We provide a new abstraction function and prove the correctness of the analysis for both the finite tree and the rational tree cases. Moreover, we show that the same notion of redundant information as identified in Bagnara et al. (2000) and Zaffanella et al. (2002) also applies to this abstract domain combination: this allows for the implementation of an abstract unification operator running in polynomial time and achieving the same precision on all the considered observable properties.

To improve precision and efficiency, sharing analysis should track both freeness and linearity. The abstract unification algorithms for these combined domains are suboptimal, hence there is scope for improving precision. This paper proposes three optimisations for tracing sharing in combination with freeness and linearity. A novel connection between equations and sharing abstractions is used to establish correctness of these optimisations even in the presence of rational trees. A method for pruning intermediate sharing abstractions to improve efficiency is also proposed. The optimisations are lightweight and therefore some, if not all, of these optimisations will be of interest to the implementor.