Hi,
I was wondering what the best way to implement Natural number would be. Is
there a package which already does this?
Here are some options:
1. Don’t bother. Just use Integer.
2. Use the type
data Natural = Zero | Succ !Natural
3. Use the following definition taken from the Gentle Introduction to
Haskell 98
newtype Natural = MakeNatural Integer
toNatural ::Integer-> Integer
toNatural x | x < 0 = error “Can’t create negative naturals!”
| otherwise = MakeNatural x
fromNatural :: Natural -> Integer
fromNatural (MakeNatural i) = i
and then...
instance Num Natural where
fromInteger = toNAtural
x + y = toNatural (fromNatural x + fromNatural y)
x – y = etc..
x * y = etc...
Which method is best? So far, I’ve been picking option #1 – just leaving
things as they are and using Integer to keep things simple.
I’ve got that feeling that [2] would be fast and [3] would be slow. Comment
appreciated on the merits of each.
Cheers,
Mark Spezzano
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