  We provide a compact and unified treatment of power spectrum observables for
the effective field theory (EFT) of inflation with the complete set of
operators that lead to second-order equations of motion in metric perturbations
in both space and time derivatives, including Horndeski and GLPV theories. We
relate the EFT operators in ADM form to the four additional free functions of
time in the scalar and tensor equations. Using the generalized slow roll
formalism, we show that each power spectrum can be described by an integral
over a single source that is a function of its respective sound horizon. With
this correspondence, existing model independent constraints on the source
function can be simply reinterpreted in the more general inflationary context.
By expanding these sources around an optimized freeze-out epoch, we also
provide characterizations of these spectra in terms of five slow-roll
hierarchies whose leading order forms are compact and accurate as long as EFT
coefficients vary only on timescales greater than an efold. We also clarify the
relationship between the unitary gauge observables employed in the EFT and the
comoving gauge observables of the post-inflationary universe.
