```module Numeric.Natural.Internal
( Natural(..)
, Whole(..)
) where

import Data.Word

newtype Natural = Natural { runNatural :: Integer } deriving (Eq,Ord)

instance Show Natural where
showsPrec d (Natural n) = showsPrec d n

instance Num Natural where
Natural n + Natural m = Natural (n + m)
Natural n * Natural m = Natural (n * m)
Natural n - Natural m | result < 0 = error "Natural.(-): negative result"
| otherwise  = Natural result
where result = n - m
abs (Natural n) = Natural n
signum (Natural n) = Natural (signum n)
fromInteger n
| n >= 0 = Natural n
| otherwise = error "Natural.fromInteger: negative"

instance Real Natural where
toRational (Natural a) = toRational a

instance Enum Natural where
pred (Natural 0) = error "Natural.pred: 0"
pred (Natural n) = Natural (pred n)
succ (Natural n) = Natural (succ n)
toEnum n | n < 0     = error "Natural.toEnum: negative"
| otherwise = Natural (toEnum n)

instance Integral Natural where
quot (Natural a) (Natural b) = Natural (quot a b)
rem (Natural a) (Natural b) = Natural (rem a b)
div (Natural a) (Natural b) = Natural (div a b)
mod (Natural a) (Natural b) = Natural (mod a b)
divMod (Natural a) (Natural b) = (Natural q, Natural r) where (q,r) = divMod a b
quotRem (Natural a) (Natural b) = (Natural q, Natural r) where (q,r) = quotRem a b
toInteger = runNatural

class Integral n => Whole n where
toNatural :: n -> Natural
unsafePred :: n -> n

instance Whole Word where
toNatural = Natural . toInteger
unsafePred n = n - 1

instance Whole Word8 where
toNatural = Natural . toInteger
unsafePred n = n - 1

instance Whole Word16 where
toNatural = Natural . toInteger
unsafePred n = n - 1

instance Whole Word32 where
toNatural = Natural . toInteger
unsafePred n = n - 1

instance Whole Word64 where
toNatural = Natural . toInteger
unsafePred n = n - 1

instance Whole Natural where
toNatural = id
unsafePred (Natural n) = Natural (n - 1)
```