<html><head><meta http-equiv="Content-Type" content="text/html; charset=us-ascii"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class="">Not only that, `xor` has inverses so it forms an abelian group<br class=""><div class=""><br class=""><div class="">Regards, Andrew</div></div><div><br class=""><blockquote type="cite" class=""><div class="">On 29 Sep 2020, at 10:41, Andrew Butterfield <<a href="mailto:Andrew.Butterfield@scss.tcd.ie" class="">Andrew.Butterfield@scss.tcd.ie</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><meta http-equiv="Content-Type" content="text/html; charset=us-ascii" class=""><div style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class="">Hmmm - I thought so at first<div class=""><br class=""></div><div class="">A B A `xor` B</div><div class="">0 0 0</div><div class="">0 1 1</div><div class="">1 0 1</div><div class="">1 1 0</div><div class=""><br class=""></div><div class="">0 `xor` b = b</div><div class="">a `xor` 0 = a</div><div class=""><br class=""></div><div class="">Looks like 0 is the identity to me.</div><div class=""><br class=""><div class="">Regards, Andrew</div></div><div class=""><br class=""><blockquote type="cite" class=""><div class="">On 29 Sep 2020, at 10:33, Ben Franksen <<a href="mailto:ben.franksen@online.de" class="">ben.franksen@online.de</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><div class="">Am 29.09.20 um 10:27 schrieb Mario Lang:<br class=""><blockquote type="cite" class="">instance Monoid QuadBitboard where<br class=""> mempty = QBB 0 0 0 0<br class=""><br class="">-- | bitwise XOR<br class="">instance Semigroup QuadBitboard where<br class=""> QBB b0 b1 b2 b3 <> QBB b0' b1' b2' b3' =<br class=""> QBB (b0 `xor` b0') (b1 `xor` b1') (b2 `xor` b2') (b3 `xor` b3')<br class=""><br class="">But maybe I am violating some laws<br class=""></blockquote><br class="">The Semigroup is okay, since 'xor' is indeed associative, and your<br class="">instance basically lifts it to 4-tuples.<br class=""><br class="">The Monoid instance is wrong, though. There is no unit for 'xor'!<br class=""><br class="">Cheers<br class="">Ben<br class=""><br class="">_______________________________________________<br class="">Haskell-Cafe mailing list<br class="">To (un)subscribe, modify options or view archives go to:<br class=""><a href="http://mail.haskell.org/cgi-bin/mailman/listinfo/haskell-cafe" class="">http://mail.haskell.org/cgi-bin/mailman/listinfo/haskell-cafe</a><br class="">Only members subscribed via the mailman list are allowed to post.</div></div></blockquote></div><br class=""><div class="">
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