On abstract unification for variable aliasing

We face the problem of devising optimal unification operators for domains of abstract substitutions. In particular, we are interested in abstract domains for sharing and linerity properties, which are widely used in logic program analysis. We propose a new (infinite) domain ShLin which can be thought of as a general framework from which other domains can be easily derived by abstraction. The advantage is that abstract unification in ShLin is simple and elegant, and it is based on a new concept of sharing graph which plays the same role of alternating paths for pair sharing analysis. We also provide an alternative, purely algebraic description of sharing graphs. Starting from the results for ShLin, we derive optimal abstract operators for two well-known domains which combine sharing and linearity: a domain proposed by Andy King and the classic Sharing X Lin