Let's look at the analogous case:
let a' = f a
a'' = g a'
a''' = h a''
in
Here, the way we would shorten "apply f, then apply g, then apply h" is using
the function composition operator, (.), whose type signature is:
(.) :: (b -> c) -> (a -> b) -> a -> c
So instead of the above, we could say:
let a''' = h . g . f $ a
Similarly, you have some functions:
f :: a -> m b
g :: b -> m c
for some monad m. And what you'd like to do is, in some sense, to compose
these, to get:
g . f :: a -> m c
But you can't exactly do that with the Prelude composition operator; the types
are wrong. Fortunately, smart people have already thought about how to
generally compose function-like things. The way you do this in a monad-specific
way is to use the (<=<) operator from Control.Monad, whose signature is:
(<=<) :: Monad m => (b -> m c) -> (a -> m b) -> a -> m c
And so that's really what you want: h <=< g <=< f $ a.
More generally, this whole idea of composing things that are similar to
functions is encapsulated by the notion of a category, and this can be viewed
as a specific case of using the composition operator from Control.Category. In
this case, the function-like things (called "arrows" or "morphisms") being
composed are the so-called Kleisli arrows, which are really the functions
you're manipulating here, f :: a -> m b.
Nick
On Tuesday, October 02, 2012 10:12:44 AM Christopher Howard wrote:
Say I've got a stream of monadic calculations, like so:
code:
--------
do a' <- f a
a'' <- g a'
a''' <- h a''
return a'''
--------
There is a cleaner way to do that, yes? (Without using all the tick marks?)
