  Inspired by Chern-Simons effective theory description of symmetry protected
topological (SPT) phases in two dimensions, we present a projective
construction for many-body wavefunctions of SPT phases. Using this projective
construction we can systematically write down trial wavefunctions of SPT phases
on a lattice. An explicit example of SPT phase with $U(1)$ symmetry is
constructed for two types of bosons with filling $\nu_{b_1}=\nu_{b_2}=\frac12$
per site on square lattice. We study continuous phase transitions between
different $U(1)$-SPT phases based on projective construction. The effective
theory around the critical point is emergent $QED_3$ with fermion number
$N_f=2$. Such a continuous phase transition however needs fine tuning, and in
general there are intermediate phases between different $U(1)$-SPT phases. We
show that such an intermediate phase has the same response as an anyon
superconductor, and hence dub it "anyon superfluid". A schematic phase diagram
of interacting bosons with $U(1)$ symmetry is depicted.
