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module Numeric.Natural (Natural,
mkNatural)
where
data Natural = Natural Integer
mkNatural :: Integer -> Natural
mkNatural n | n < 0 = error "mkNatural: negative number!"
| otherwise = Natural n
instance Enum Natural where
toEnum n = Natural (fromIntegral n)
fromEnum (Natural n) = fromEnum n
succ (Natural n) = Natural (succ n)
pred (Natural n) = mkNatural (pred n)
instance Integral Natural where
toInteger (Natural n) = n
quotRem _ 0 = error "Natural / 0"
quotRem _ _ = error "quotRem @Natural unimplemented"
instance Num Natural where
fromInteger = mkNatural
Natural m + Natural n = Natural (m+n)
Natural m * Natural n = Natural (m*n)
Natural m - Natural n = mkNatural (m-n)
abs = id
signum 0 = 0
signum _ = 1
negate _ = error "negate @Natural"
instance Eq Natural where
(Natural m) == (Natural n) = m == n
instance Ord Natural where
(Natural m) < (Natural n) = n < m
(Natural m) <= (Natural n) = n <= m
(Natural m) > (Natural n) = n > m
(Natural m) >= (Natural n) = n >= m
min (Natural m) (Natural n) = Natural (min m n)
max (Natural m) (Natural n) = Natural (max m n)
instance Real Natural where
toRational = toRational . toInteger
instance Show Natural where
-- showsPrec d (Natural n) = showsPrec d n
show (Natural n) = show n
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