[Haskell-beginners] stream of monadic calculations

[Patrick Redmond]

Wouldn't the applicative style be applicable here? I just read the
chapter in LYAH on it, and I feel like it could be used somehow..?


On Tue, Oct 2, 2012 at 3:14 PM, Nick Vanderweit
<nick.vanderweit at gmail.com> wrote:
> Let's look at the analogous case:
>
> let a'  = f a
>       a'' = g a'
>      a''' = h a''
>   in <something to do with a'''>
>
> 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?)
>
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