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.
