Subtraction.hs

module Integer.Subtraction
  ( Subtraction (subtractInteger, subtractSigned),
    Subtraction' (subtract),
  )
where

import Integer.Integer (Integer)
import Integer.Natural (Natural)
import Integer.Natural qualified as Natural
import Integer.Positive (Positive)
import Integer.Positive qualified as Positive
import Integer.Signed (Signed)
import Integer.Signed qualified as Signed
import Prelude qualified as Num (Num (..))

-- | Domain of a subtraction operation
class Subtraction a where
  subtractInteger :: a -> a -> Integer
  subtractInteger a b = Signed.toInteger (subtractSigned a b)

  subtractSigned :: a -> a -> Signed
  subtractSigned a b = Signed.fromInteger (subtractInteger a b)

instance Subtraction Integer where
  subtractInteger = (Num.-)

instance Subtraction Signed where
  subtractInteger a b = (Num.-) (Signed.toInteger a) (Signed.toInteger b)
  subtractSigned = (Num.-)

instance Subtraction Natural where
  subtractSigned = Natural.subtract

instance Subtraction Positive where
  subtractSigned = Positive.subtract

-- | Codomain of a subtraction operation
class Subtraction' b where
  subtract :: Subtraction a => a -> a -> b

instance Subtraction' Integer where
  subtract = subtractInteger

instance Subtraction' Signed where
  subtract = subtractSigned