On Sat, Jun 28, 2014 at 11:38 PM, Rafael Almeida
No. I'm not trying to say Monad laws are useless or pointless. Rather, I am looking to understand the usefulness of those laws.
My point was more that Ord could *also* be different; it could support partial ordering, for example, or could support non-mathematical ordering which would e.g. enable Data.Map to be used with things that don't have mathematical total ordering, like Complex Double, or possibly to fix its behavior with Double whose Ord instance is actually not a proper total ordering; what matters is not that there is a mathematical total ordering, but that there is *some* kind of reliable ordering that can be used to build a tree. I imagine that, like Ord, a decision was made to implement the proper mathematical abstraction and not merely a convenient one. This seems to be the "Haskell way". (I'm not sure how it explains Double, though the numeric hierarchy has a lot of compromises in the name of convenience or expected behavior. Possibly Monad was in some sense a reaction to this, even: "we got that one wrong, let's do this one correctly".) -- brandon s allbery kf8nh sine nomine associates allbery.b@gmail.com ballbery@sinenomine.net unix, openafs, kerberos, infrastructure, xmonad http://sinenomine.net