  We present a general approach to obtain effective field theories for
topological crystalline insulators whose low-energy theories are described by
massive Dirac fermions. We show that these phases are characterized by the
responses to spatially dependent mass parameters with interfaces. These mass
interfaces implement the dimensional reduction procedure such that the state of
interest is smoothly deformed into a topological crystal, which serves as a
representative state of a phase in the general classification. Effective field
theories are obtained by integrating out the massive Dirac fermions, and
various quantized topological terms are uncovered. Our approach can be
generalized to other crystalline symmetry protected topological phases and
provides a general strategy to derive effective field theories for such
crystalline topological phases.
