  We present a discrete analog of the recently introduced Hamilton-Pontryagin
variational principle in Lagrangian mechanics. This unifies two, previously
disparate approaches to discrete Lagrangian mechanics: either using the
discrete Lagrangian to define a finite version of Hamilton's action principle,
or treating it as a symplectic generating function. This is demonstrated for a
discrete Lagrangian defined on an arbitrary Lie groupoid; the often encountered
special case of the pair groupoid (or Cartesian square) is also given as a
worked example.
