[Haskell-cafe] need help making sense of the type ...

Daryoush Mehrtash dmehrtash at gmail.com
Wed Sep 24 22:51:07 EDT 2008

I am having hard time making sense of the types in the following example
from the Applicative Programming paper:

ap :: Monad m ⇒ m (a → b ) → m a → m b
ap mf mx = do
    f ← mf
    x ← mx
    return (f x )
Using this function we could rewrite sequence as:

sequence :: [ IO a ] → IO [ a ]
sequence [ ] = return [ ]
sequence (c : cs ) =* return (:) 'ap' c *'ap' sequence cs

I am specifically confused over the type of "m" in:

     return (:) 'ap' c

"c" is obviously an  instance of IO a monad.   "return (:)"  on the other
hand (at least as I would expect it) is an instance of " ->" monad.

a) are the above statements correct?
b) if so, does it make sense for the "ap"  function to have two different
instances of the "m"?

thanks for you help

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