Now, using fucntions unitM and bindM there is possibly to convert arbitrary function (k :: a -> b), which makes from initial value of type a value of type b, into terms of general computation (represented by type M).
Yes, (k :: a -> b) can be converted into a function of type (a -> M b), but I think you have made it more complicated than necessary. All you need to do is (unitM . k).
Hmm, so i was wrong here. Initially, i suppose, that the purpose of bindM is to convert function of type (a -> b) into function of type (a -> M b), but now i see it is wrong. Mentioned above quote from [2] says, that "the purpose of bindM is to evaluate a computation, yielding a value.", which sounds a little unfinished to me. Then may be: the purpose of bindM is to make composition of functions of type (a -> M b) and (b -> M c) possible. Is this right?
Yes! In fact, there is a standard operator
(>=>) :: Monad m => (a -> m b) -> (b -> m c) -> (a -> m c)
which is defined in terms of bind. Implementing it is a good exercise.
By the way, you may be interested in reading the Typeclassopedia:
Thank you very much, Brent! I'll try what you advise and read this link. And then may be ask again.. :) -- Dmitriy Matrosov