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