  An IDEAL characterization of a particular spacetime metric, $g_0$, consists
of a set of tensorial equations $T[g] = 0$ arising from expressions constructed
from the metric, $g$, its curvature tensor and its covariant derivatives and
which are satisfied if and only if $g$ is locally isometric to the original
metric $g_0$. Earlier applications of the IDEAL classification of spacetimes
relied on the construction of particular scalar polynomial curvature invariants
as an important step in the procedure.
  In this paper we investigate the well-known class of vacuum pp-wave
spacetimes, where all scalar polynomial curvature invariants vanish, and
determine the applicability of an IDEAL classification for these spacetimes. We
consider a modification of the IDEAL approach which permits a corresponding
extension of the Stewart-Walker lemma. With this change, we are able to
construct invariants and IDEAL-ly classify all of the vacuum pp-wave solutions
which admit a two- or higher-dimensional isometry group, with the exception of
one case.
