On 29 Sep 2020, at 10:41, Andrew Butterfield <Andrew.Butterfield@scss.tcd.ie> wrote:

Hmmm - I thought so at first

A B A `xor` B

0 0      0

0 1      1

1 0      1

1 1      0

0 `xor` b = b

a `xor` 0 = a

Looks like 0 is the identity to me.

Regards, Andrew

On 29 Sep 2020, at 10:33, Ben Franksen <ben.franksen@online.de> wrote:

Am 29.09.20 um 10:27 schrieb Mario Lang:

instance Monoid QuadBitboard where
 mempty = QBB 0 0 0 0

-- | bitwise XOR
instance Semigroup QuadBitboard where
 QBB b0 b1 b2 b3 <> QBB b0' b1' b2' b3' =
   QBB (b0 `xor` b0') (b1 `xor` b1') (b2 `xor` b2') (b3 `xor` b3')

But maybe I am violating some laws

The Semigroup is okay, since 'xor' is indeed associative, and your
instance basically lifts it to 4-tuples.

The Monoid instance is wrong, though. There is no unit for 'xor'!

Cheers
Ben

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