{-# LANGUAGE NPlusKPatterns #-}

-- The factorial function: fac n = 1 * 2 * .... * n
-- fac n = 1 * 2 * .... * (n-1) * n
-- fac n = fac (n-1) * n  (if n>0)
-- fac 0 = 1

--fac :: Integer -> Integer
fac n = if n==0 then 1
                else n * fac (n-1)

facg n | n==0 = 1
       | n>0  = n * facg (n-1)

facp 0     = 1
facp (n+1) = (n+1) * facp n

-- Boolean conjunction:
and1 True  True  = True
and1 True  False = False
and1 False True  = False
and1 False False = False

and2 True  x = x
and2 False x = False

and3 x y = if x==True then y else False

f True  = 0
f False = 1
f True  = 2