# [Haskell-cafe] Odd lack of laziness

Stefan O'Rear stefanor at cox.net
Fri Jun 22 14:26:48 EDT 2007

```On Fri, Jun 22, 2007 at 07:14:39PM +0100, Andrew Coppin 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)

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
```