On Dec 3, 2007 1:09 PM, Denis Bueno
I don't think I can conclude that there are *no* reasons to teach the do-notation first. I just think that it is more instructive to teach it later.
It's standard in mathematics teaching, when introducing a mathematical structure X, to ensure that students have the knowledge to understand an example of X before they see the definition of X. So students won't study groups before they've met the integers, they won't study fields before they've met the rationals, and they won't study topology until they're familiar with the real line. Not just met them either, usually they've usually completely internalised the examples before moving onto the general structure. The problem with monads is that students have never knowingly met an example of a monad before. If you teach them do-notation for IO without monads, and they get completely familiar with it (which (1) I claim is easy: http://sigfpe.blogspot.com/2007/11/io-monad-for-people-who-simply-dont.html and (2) is inevitable if they want to see the output of their programs) then when they come to learning about monads in general they'll have an example they don't even have to think about. The more adventurous ones may even discover some of the monad laws for themselves if they experiment with nested do's like in Tim Newsham's examples (and think them so obvious they hardly need to be graced with the name "law"). -- Dan