I came away from Professor Frisby's Mostly Adequate Guide to Functional Programming with what seems to be a misconception about Maybe.
I believe:
map(add1, Just [1, 2, 3])
// => Just [2, 3, 4]
My feeling coming away from the aforementioned guide is that Maybe.map should try to call Array.map on the array, essentially returning Just(map(add1, [1, 2, 3]).
When I tried this using Sanctuary's Maybe type, and more recently Elm's Maybe type, I was disappointed to discover that neither of them support this (or, perhaps, I don't understand how they support this).
In Sanctuary,
> S.map(S.add(1), S.Just([1, 2, 3]))
! Invalid value
add :: FiniteNumber -> FiniteNumber -> FiniteNumber
^^^^^^^^^^^^
1
1) [1, 2, 3] :: Array Number, Array FiniteNumber, Array NonZeroFiniteNumber, Array Integer, Array ValidNumber
The value at position 1 is not a member of ‘FiniteNumber’.
In Elm,
> Maybe.map sqrt (Just [1, 2, 3])
-- TYPE MISMATCH --------------------------------------------- repl-temp-000.elm
The 2nd argument to function `map` is causing a mismatch.
4| Maybe.map sqrt (Just [1, 2, 3])
^^^^^^^^^^^^^^
Function `map` is expecting the 2nd argument to be:
Maybe Float
But it is:
Maybe (List number)
Similarly, I feel like I should be able to treat a Just(Just(1)) as a Just(1). On the other hand, my intuition about [[1]] is completely the opposite. Clearly, map(add1, [[1]]) should return [NaN] and not [[2]] or any other thing.
In Elm I was able to do the following:
> Maybe.map (List.map (add 1)) (Just [1, 2, 3])
Just [2,3,4] : Maybe.Maybe (List number)
Which is what I want to do, but not how I want to do it.
How should one map over Maybe List?
As Chad mentioned, you want to transform values nested within two functors.
Let's start by mapping over each individually to get comfortable:
> S.map(S.toUpper, ['foo', 'bar', 'baz'])
['FOO', 'BAR', 'BAZ']
> S.map(Math.sqrt, S.Just(64))
Just(8)
Let's consider the general type of map:
map :: Functor f => (a -> b) -> f a -> f b
Now, let's specialize this type for the two uses above:
map :: (String -> String) -> Array String -> Array String
map :: (Number -> Number) -> Maybe Number -> Maybe Number
So far so good. But in your case we want to map over a value of type Maybe (Array Number). We need a function with this type:
:: Maybe (Array Number) -> Maybe (Array Number)
If we map over S.Just([1, 2, 3]) we'll need to provide a function which takes [1, 2, 3]—the inner value—as an argument. So the function we provide to S.map must be a function of type Array (Number) -> Array (Number). S.map(S.add(1)) is such a function. Bringing this all together we arrive at:
> S.map(S.map(S.add(1)), S.Just([1, 2, 3]))
Just([2, 3, 4])