On 3/17/11 2:50 PM, Luke Palmer wrote:
If you are implementing lazy naturals, I wonder if defining 0 - 1 to
be infinity makes mathematical sense. It's like arithmetic mod
infinity....
Actually, I'm specifically implementing strict naturals :)
There are a number of libraries for lazy naturals out there already, but
for my current project I need the efficiency of Int/Integer--- without
the errors or defensive programming that comes from using them when we
mean Nat/Natural.
So far I haven't actually needed arithmetic operations (Enum, Eq, and
Ord have been enough) but I figure I should square that away before
splitting the code off for a public release. Since the whole thing is
done as newtypes I can always make the Num instances the "right" ones,
since people who obsess over performance can manually unwrap them to
perform raw operations they know/hope will succeed and then revalidate
the invariants when they're done with the arithmetic section. I just
want to make sure the instance I give has the nice mathematical
properties it could/should.
--
Live well,
~wren
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