Hey, I've found terrific slides about monoids! http://comonad.com/reader/wp-content/uploads/2009/08/IntroductionToMonoids.pdf Edward Kmett, you rock!
There's more http://comonad.com/reader/2009/iteratees-parsec-and-monoid/ - but the second part was too hard for me to read it fully without special motivation. 2009/11/15 Daniel Schüssler <anotheraddr...@gmx.de>: > On Sunday 15 November 2009 13:05:08 Nicolas Pouillard wrote: >> Excerpts from Daniel Schüssler's message of Sun Nov 15 07:51:35 +0100 2009: >> > Hi, >> >> Hi, > > Hi, > >> >> > -- Invariant 1: There are never two adjacent Lefts or two adjacent Rights >> >> [...] >> >> > normalize (Left a0 : Left a1 : as) = Left (mappend a0 a1) : normalize as >> > normalize (Right a0 : Right a1 : as) = Right (mappend a0 a1) : normalize >> > as >> >> If you want to preserve your invariant, I think you should do : >> >> normalize (Left a0 : Left a1 : as) = normalize (Left (mappend a0 a1) : >> as) normalize (Right a0 : Right a1 : as) = normalize (Right (mappend a0 >> a1) : as) >> >> However, maybe it is correct if you only call normalize on (xs ++ ys) where >> xs and ys are already normalized so that you have only one point where you >> can break this invariant. >> >> Regards, >> > > You are right :) If `normalize' is meant to normalize arbitrary lists, we'd > have to use your version. If OTOH we just want to normalize xs ++ ys, we > shouldn't iterate over the whole list; it'd be better to use Data.Sequence and > just consider the middle, as you said (I was thinking of free groups, where > there can be more collapse, but in that case we'd need the analogue your > version too). > > > Greetings, > Daniel > _______________________________________________ > Haskell-Cafe mailing list > Haskell-Cafe@haskell.org > http://www.haskell.org/mailman/listinfo/haskell-cafe > -- Eugene Kirpichov Web IR developer, market.yandex.ru _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
