[Haskell-cafe] Odd lack of laziness

[Stefan O'Rear]

On Fri, Jun 22, 2007 at 07:14:39PM +0100, Andrew Coppin wrote:
> Chaddaï Fouché wrote:
> >You should be using BS.null f rather than BS.length f > 0.
> >
> While we're on the subject... anybody know a neat way to check, say, 
> whether a list contains exactly 1 element? (Obviously pattern matching 
> can do it, but that requires big case-expressions...)

data LazyNat = Zero | Succ LazyNat  deriving(Eq,Ord)

instance Enum LazyNat where
    succ = Succ
    pred (Succ x) = x

    toEnum 0 = Zero
    toEnum (x+1) = succ (toEnum x)

    fromEnum Zero = 0
    fromEnum (Succ x) = fromEnum x + 1

instance Num LazyNat where -- this is a lie, the lifted naturals only
                           -- form a *semi*ring.  Sigh.
    fromIntegral = toEnum

    Zero + y = y
    Succ x + y = Succ (x + y)

    Zero * y = 0
    Succ x * y = y + x * y

    abs = id
    signum 0 = 0
    signum _ = 1

    x - Zero = x
    Succ x - Succ y = x - y


length' [] = Zero
length' (x:xs) = Succ (length xs)

null x = length' x == 0

one x = length' x == 1

atLeastFive x = length' x >= 5

Stefan