  We propose a set of constraints on the ground-state wavefunctions of fracton
phases, which provide a possible generalization of the string-net equations
used to characterize topological orders in two spatial dimensions. Our
constraint equations arise by exploiting a duality between certain fracton
orders and quantum phases with "subsystem" symmetries, which are defined as
global symmetries on lower-dimensional manifolds, and then studying the
distinct ways in which the defects of a subsystem symmetry group can be
consistently condensed to produce a gapped, symmetric state. We numerically
solve these constraint equations in certain tractable cases to obtain the
following results: in $d=3$ spatial dimensions, the solutions to these
equations yield gapped fracton phases that are distinct as conventional quantum
phases, along with their dual subsystem symmetry-protected topological (SSPT)
states. For an appropriate choice of subsystem symmetry group, we recover known
fracton phases such as Haah's code, along with new, symmetry-enriched versions
of these phases, such as non-stabilizer fracton models which are distinct from
both the X-cube model and the checkerboard model in the presence of global
time-reversal symmetry, as well as a variety of fracton phases enriched by
spatial symmetries. In $d=2$ dimensions, we find solutions that describe new
weak and strong SSPT states, such as ones with both line-like subsystem
symmetries and global time-reversal symmetry. In $d=1$ dimension, we show that
any group cohomology solution for a symmetry-protected topological state
protected by a global symmetry, along with lattice translational symmetry
necessarily satisfies our consistency conditions.
