[Haskell-cafe] Why is Bool no instance of Num and Bits?

[Deniz Dogan]

2009/5/8 Stephan Friedrichs <deduktionstheorem at web.de>:
> Hi!
>
> When looking for an xor function, I found one in Data.Bits but couldn't
> use it for Bool, because Bool is no instance of Bits and of Num (which
> would be necessary, because it's "class (Num b) => Bits b"). My question
> is: Why not?
>
> We could declare
>
> instance Num Bool where
>    (+) False = id
>    (+) True  = not
>
>    (*) True  True = True
>    (*) _     _    = False
>
>    (-) = (+)
>
>    negate      = id
>    abs         = id
>    signum      = const True
>    fromInteger = not . even
>
> which basically implements the field with 2 elements and
>
> instance Bits Bool where
>    bitSize  = const 1
>    isSigned = const False
>
>    (.&.) = (&&)
>    (.|.) = (||)
>    xor   = (+)
>
>    complement = not
>
>    shift  = const
>    shiftL = const
>    shiftR = const
>
>    rotate  = const
>    rotateL = const
>    rotateR = const
>
>    bit = (==0)
>
>    setBit _ 0 = True
>    setBit b _ = b
>
>    clearBit _ 0 = False
>    clearBit b _ = b
>
>    complementBit b 0 = not b
>    complementBit b _ = b
>
>    testBit b 0 = b
>    testBit _ _ = False
>
> quite trivial... Why is this not part of base? Or am I missing something?
>
> //Stephan

Isn't "XOR" for booleans (/=)?

Deniz Dogan