[Haskell-beginners] Trouble understanding the type of sequence [Just, Just]

[Chas Leichner]

The type of just is (a -> Maybe a) so your list has type [a -> Maybe a]
which means the Monad instance that sequence is using isn't Maybe, it's (a
->), the type constructor for function types with its first parameter
partially applied. This means that the type of sequence specialized to this
context uses [] for t, the Traversable and (a ->) for m, the Monad. That is
to say sequence :: [a -> Maybe a] -> (a -> [Maybe a]). (a ->) is one way of
representing the Reader monad so you can treat its a parameter as a context
that computations can run inside. That means that sequence [Just, Just]
takes two functions that construct a Maybe value from the value in the
context and turns it into a function which constructs a list of Maybe
values each one fed from the same context. That is to say that (sequence
[Just, Just] $ 4) == [Just 4, Just 4].

On Saturday, December 12, 2015, Lim H. <limdauto at gmail.com> wrote:

> Hi everyone,
>
> Sorry if this email disturbs you. I haven't used a developer's mailing
> list before so I'm not sure if I'm violating any etiquette. If I do, please
> excuse me.
>
> I'm trying to understand the type of sequence [Just, Just]. I can
> understand
>  sequence [Just 1, Just 2] :: Num a => Maybe [a]
>
> because when looking at the type of sequence
>
> sequence :: (Monad m, Traversable t) => t (m a) -> m (t a)
>
> it is clear that this function takes a collection of monadic values and
> return a single monadic value of the collection. Thus, when we call sequence
> [Just 1, Just 2] we should get back a Just of [1,2]. Following that train
> of thoughts, shouldn't sequence [Just, Just] return a single Just?
> Here is the corresponding SO question
>
>
> http://stackoverflow.com/questions/34244574/trouble-understanding-the-type-of-sequence-just-just
>
> Lim
>
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