On 3/17/11 4:22 PM, Martin Escardo wrote:
On 17/03/11 18:35, wren ng thornton wrote:
(2) Use saturating subtraction, i.e. if the result would drop below zero
then return zero;
This is what people working with quantales do.
Subtraction y-z, when it exists, is the solution in s to the equation
s+z =y.
Truncated subtraction y - z is the supremum of the set of solutions s to
the inequality s+z <= y, when this supremum exists. (In your example,
when z>y, the set of solutions is empty, and the empty set has supremum
zero.)
This amounts to saying that the truncated subtraction function (-) - z
is the right adjoint to the addition function (-) + z.
So (2) is very natural.
Thanks! That's exactly the kind of thing I was looking for. I'd been
needlessly thinking of it as a hack :)
--
Live well,
~wren
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