  We derive a series of quantitative bulk-boundary correspondences for 3D
bosonic and fermionic symmetry-protected topological (SPT) phases under the
assumption that the surface is gapped, symmetric and topologically ordered,
i.e., a symmetry-enriched topological (SET) state. We consider those SPT phases
that are protected by the mirror symmetry and continuous symmetries that form a
group of $U(1)$, $SU(2)$ or $SO(3)$. In particular, the fermionic cases
correspond to a crystalline version of 3D topological insulators and
topological superconductors in the famous ten-fold-way classification, with the
time-reversal symmetry replaced by the mirror symmetry and with strong
interaction taken into account. For surface SETs, the most general interplay
between symmetries and anyon excitations is considered. Based on the previously
proposed dimension reduction and folding approaches, we re-derive the
classification of bulk SPT phases and define a \emph{complete} set of bulk
topological invariants for every symmetry group under consideration, and then
derive explicit expressions of the bulk invariants in terms of surface
topological properties (such as topological spin, quantum dimension) and
symmetry properties (such as mirror fractionalization, fractional charge or
spin). These expressions are our quantitative bulk-boundary correspondences.
Meanwhile, the bulk topological invariants can be interpreted as \emph{anomaly
indicators} for the surface SETs which carry 't Hooft anomalies of the
associated symmetries whenever the bulk is topologically non-trivial. Hence,
the quantitative bulk-boundary correspondences provide an easy way to compute
the 't Hooft anomalies of the surface SETs. Moreover, our anomaly indicators
are complete. Our derivations of the bulk-boundary correspondences and anomaly
indicators are explicit and physically transparent.
