  In order 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.
