Neil Mitchell wrote:
Hi
Pretty much, yes.
So I just need to write
newtype LazyNatural = LazyNatural [()]
or
data Nat = Zero | Succ Nat
it's your choice really.
I'm guessing there's going to be fairly minimal performance difference. (Or maybe there is. My way uses a few additional pointers. But it also allows me to elegantly recycle existing Prelude list functions, so...)
and then add some suitable instances. ;-)
Yes. Lots of them. Lots of instances and lots of methods.
Hey, the "length" function would then just be
ln_length :: [x] -> LazyNatural ln_length = LazyNatural . map (const ())
Ooo, that's hard.
Nope, its really easy. Its just quite a bit of work filling in all the instances. I bet you can't do it and upload the results to hackage within 24 hours :-)
*ALL* the instances? No. A small handful of them? Sure. How about this... module LazyNatural (LazyNatural ()) where import Data.List newtype LazyNatural = LN [()] instance Show LazyNatural where show (LN x) = "LN " ++ show (length x) instance Eq LazyNatural where (LN x) == (LN y) = x == y instance Ord LazyNatural where compare (LN x) (LN y) = raw_compare x y raw_compare ([]) (_:_) = LT raw_compare ([]) ([]) = EQ raw_compare (_:_) ([]) = GT raw_compare (_:x) (_:y) = raw_compare x y instance Num LazyNatural where (LN x) + (LN y) = LN (x ++ y) (LN x) - (LN y) = LN (raw_minus x y) (LN x) * (LN y) = LN (concatMap (const x) y) negate _ = error "negate is not defined for LazyNatural" abs = id signum (LN []) = LN [] signum (LN _) = LN [()] fromInteger = LN . flip genericReplicate () raw_minus (_:a) (_:b) = raw_minus a b raw_minus (a) ([]) = a raw_minus _ _ = error "negative result from subtraction"