PS. Prelude Data.List Data.Number.Natural> genericLength [1..] > (10 :: Natural) True
On 9/24/07, Lennart Augustsson <[EMAIL PROTECTED]> wrote: > > Since natural numbers are trivial to implement (inefficiently) I took 15 > minutes and added them to my numbers package in Hackage. > http://hackage.haskell.org/cgi-bin/hackage-scripts/package/numbers-2007.9.24 > > > -- Lennart > > On 9/24/07, Andrew Coppin <[EMAIL PROTECTED]> wrote: > > > > 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" > > > > _______________________________________________ > > Haskell-Cafe mailing list > > Haskell-Cafe@haskell.org > > http://www.haskell.org/mailman/listinfo/haskell-cafe > > > >
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