  We present a discrete analogue of the so-called symmetry reduced or
`constrained' KP hierarchy. As a result we obtain integrable discretisations,
in both space and time, of some well-known continuous integrable systems such
as the nonlinear Schroedinger equation, the Broer-Kaup equation and the
Yajima-Oikawa system, together with their Lax pairs. It will be shown that
these discretisations also give rise to a discrete description of the entire
hierarchy of associated integrable systems. The discretisations of the
Broer-Kaup equation and of the Yajima-Oikawa system are thought to be new.
