xor a b = (a + b) mod 2
Many good properties follow. https://en.wikipedia.org/wiki/GF(2)
...
- Oleg
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@scss.tcd.ie> wrote:
Hmmm - I thought so at first_______________________________________________
A B A `xor` B0 0 00 1 11 0 11 1 0
0 `xor` b = ba `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
_______________________________________________
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/
--------------------------------------------------------------------
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/
--------------------------------------------------------------------
_______________________________________________ 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.