[Haskell-cafe] IO and Cont as monads

Burak Ekici ekcburak at hotmail.com
Tue Apr 12 12:39:12 CEST 2011


Dear List,

I am quite new in Haskell's categorical manner of programming. However I have enough knowledge in Category Theory.
I want to ask a question, maybe very well-known one by some of you, about monads of Haskell.

For
 the type constructors like Maybe and [], I managed to prove that 
together with 2 natural transformations (bind + return), both of these 
triples construct a monad. But when I try to prove that IO and Cont type
 constructors with the same natural transformations (bind + return) are 
monads as well, it was failed.

Here my question is: Is there anyone who knows how to prove that IO and Cont are monads with satisfing following properties:

join . fmap join = join . joinjoin . fmap return = join . return = idreturn . f = fmap f . returnjoin . fmap (fmap f) = fmap f . join
Thanks already now,
Burak Ekici. 		 	   		  
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