  Analysis of (partial) groundness is an important application of abstract
interpretation. There are several proposals for improving the precision of such
an analysis by exploiting type information, icluding our own work with Hill and
King, where we had shown how the information present in the type declarations
of a program can be used to characterise the degree of instantiation of a term
in a precise and yet inherently finite way. This approach worked for
polymorphically typed programs as in Goedel or HAL. Here, we recast this
approach following works by Codish, Lagoon and Stuckey. To formalise which
properties of terms we want to characterise, we use labelling functions, which
are functions that extract subterms from a term along certain paths. An
abstract term collects the results of all labelling functions of a term. For
the analysis, programs are executed on abstract terms instead of the concrete
ones, and usual unification is replaced by unification modulo an equality
theory which includes the well-known ACI-theory. Thus we generalise the works
by Codish, Lagoon and Stuckey w.r.t. the type systems considered and relate the
works among each other.
