Re: [Haskell-cafe] Shouldnt this be lazy too?

PS. Prelude Data.List Data.Number.Natural> genericLength [1..] > (10 :: Natural) True On 9/24/07, Lennart Augustsson 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 wrote:

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Neil Mitchell wrote:

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Hi

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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...)

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and then add some suitable instances. ;-)

Yes. Lots of them. Lots of instances and lots of methods.

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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"

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