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

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 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

_______________________________________________ Haskell-Cafe mailing list To (un)subscribe, modify options or view archives go to: http://mail.haskell.org/cgi-bin/mailman/listinfo/haskell-cafe Only members subscribed via the mailman list are allowed to post.

-------------------------------------------------------------------- Andrew Butterfield Tel: +353-1-896-2517 Fax: +353-1-677-2204 Lero@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/ --------------------------------------------------------------------