  We formulate a low energy effective theory describing phases of matter that
are both solid and superfluid. These systems simultaneously break translational
symmetry and the phase symmetry associated with particle number. The symmetries
restrict the combinations of terms that can appear in the effective action and
the lowest order terms featuring equal number of derivatives and Goldstone
fields are completely specified by the thermodynamic free energy, or
equivalently by the long-wavelength limit of static correlation functions in
the ground state. We show that the underlying interaction between particles
that constitute the lattice and the superfluid gives rise to entrainment, and
mixing between the Goldstone modes. As a concrete example we discuss the low
energy theory for the inner crust of a neutron star, where a lattice of ionized
nuclei coexists with a neutron superfluid.
