[Haskell-cafe] I think I discovered my first Monoid instance

[Andrew Butterfield]

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 at 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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