Signed multiset ($m:T\to \mathbb{Z}$)

A finitely supported function $m:T\to \mathbb{Z}$, allowing negative as well as positive multiplicities. Missing keys denote zero. Addition, exact subtraction, pointwise maximum/minimum and pointwise order can be implemented over the union of operand supports. A nonnegative multiset is a refinement, but exact subtraction can leave that refinement while still producing a signed multiset. Fixed-width count implementations must also specify overflow behavior.