    module Numeric.Decidable.Zero
      ( DecidableZero(..)
      ) where

    import Numeric.Algebra.Class
    import Data.Int
    import Data.Word
    import Numeric.Natural.Internal

    class Monoidal r => DecidableZero r where
      isZero :: r -> Bool

    instance DecidableZero Bool where isZero = not
    instance DecidableZero Integer where isZero = (0==)
    instance DecidableZero Int where isZero = (0==)
    instance DecidableZero Int8 where isZero = (0==)
    instance DecidableZero Int16 where isZero = (0==)
    instance DecidableZero Int32 where isZero = (0==)
    instance DecidableZero Int64 where isZero = (0==)

    instance DecidableZero Natural where isZero = (0==)
    instance DecidableZero Word where isZero = (0==)
    instance DecidableZero Word8 where isZero = (0==)
    instance DecidableZero Word16 where isZero = (0==)
    instance DecidableZero Word32 where isZero = (0==)
    instance DecidableZero Word64 where isZero = (0==)

    instance DecidableZero () where isZero _ = True

    instance (DecidableZero a, DecidableZero b) => DecidableZero (a, b) where
      isZero (a,b) = isZero a && isZero b

    instance (DecidableZero a, DecidableZero b, DecidableZero c) => DecidableZero (a, b, c) where
      isZero (a,b,c) = isZero a && isZero b && isZero c

    instance (DecidableZero a, DecidableZero b, DecidableZero c, DecidableZero d) => DecidableZero (a, b, c, d) where
      isZero (a,b,c,d) = isZero a && isZero b && isZero c && isZero d

    instance (DecidableZero a, DecidableZero b, DecidableZero c, DecidableZero d, DecidableZero e) => DecidableZero (a, b, c, d, e) where
      isZero (a,b,c,d,e) = isZero a && isZero b && isZero c && isZero d && isZero e