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

[Andrew Butterfield]

Not only that, `xor` has inverses so it forms an abelian group

Regards, Andrew

> On 29 Sep 2020, at 10:41, Andrew Butterfield <Andrew.Butterfield at 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 at online.de <mailto: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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> 
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> Lero at TCD, Head of Software Foundations & Verification Research Group
> School of Computer Science and Statistics,
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--------------------------------------------------------------------
Andrew Butterfield     Tel: +353-1-896-2517     Fax: +353-1-677-2204
Lero at TCD, Head of Software Foundations & Verification Research Group
School of Computer Science and Statistics,
Room G.39, O'Reilly Institute, Trinity College, University of Dublin
                         http://www.scss.tcd.ie/Andrew.Butterfield/
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