23 Apr
2012
23 Apr
'12
8:07 a.m.
Sjoerd,
For a specific example, I haven't the faintest intuition about what 'map' should do. Suppose we have {(k1)x1, (k2)x2} and f x1 == f x2 = y. Should the value of map f {...} be {(k1+k2)y} or {(k1`max`k2)y} or what?
I don't think max would be a good choice, as that would mean that the default multiplicity would have to be negative infinity (the identity element of max) instead of 0, and then using Int as the type for multiplicity would not cut it.
Why would one need such an identity element for map? Note that the monoidal structure isn't defined over the "maximum of multiplicites" but over the "maximum of *nonzero* multiplicites". (For ordinary sets and ordinary multisets these operations happen to coincide.) Cheers, Stefan