[Haskell-beginners] Adding 1 to Just 9

[Alex Belanger]

Applicative is taking one step further, where the transformation itself
is also in such container/context.
<*> :: Functor => f (a -> b) -> f a -> f b
<*> ~ Maybe (a -> b) -> Maybe a -> Maybe b
<*> ~ Num n => Maybe (n -> n) -> Maybe n -> Maybe n

And the implementation:

(<*>) (Just f) (Just n) = Just (f n)
(<*>) Nothing (Just n) = Just n
(<*>) (Just f) Nothing = Nothing
(<*>) Nothing Nothing = Nothing

Thus, with everything we've learned, we should be able to deal with any
situation thrown at use, using Functor or Applicative.
Given (+1) and 42, I can basic function application with ($) or writing
it (+1) 42.Given (+1) and Just 42, I can use fmap to apply my transformation on
that functor, fmap (+1) (Just 42).Given Just (+1) and Just 42, I can use <*> to apply my transformation
inside a functor (applicative functor) to another functor, Just (+1)
<*> Just 42.Given Just (+1) and 42, I can wrap 42 with Just and again use <*> as
earlier, Just (+1) <*> Just 42.
Hope this helps.

nitrix

On Mon, May 14, 2018, at 9:17 AM, Alex Belanger wrote:
> A first approximative intuition is to think of Functors as containers
> (or more like a context) and of fmap as a way to apply a
> transformation function of your choice on the contained value,
> respecting the signification of that context.> 
> For example, Maybe represents the possibility of having or not having
> a value, therefore, fmap will apply your transformation on that value
> if it exists, otherwise you're still left with nothing.> 
> This example might seem straight forward but it had to be defined
> somewhere, thus, made possible by the Functor instance implementation
> for the type Maybe.> 
> Let's have a look at it:
> 
> fmap :: Functor f => (a -> b) -> f a -> f b
> 
> Specialized:
> 
> fmap ~ (a -> b) -> Maybe a -> Maybe b
> 
> And concretize further:
> 
> fmap ~ Num n => (n -> n) -> Maybe n -> Maybe n
> 
> As you can see, given a transformation function and maybe some
> numeral, you'll get maybe another numeral.> 
> The implementation lools like this:
> 
> fmap f (Just n) = Just (f n)
> fmap f Nothing = Nothing
> 
> Thus, starting with Nothing, we cannot apply our tranformation so you
> stay with Nothing. Similarly, with Just n, we're able to pattern match
> to obtain that n, apply our transformation f on that n, and then
> rewrap everything back into Just.> 
> You can see how the value cannot escape its container / context.
> 
> Of course there are more complex such containers / context.
> 
> Either represents a choice between two values. [] contains multiple
> values, IO contains (side-)effects, and so on.> 
> Hope this helps.
> 
> nitrix
> 
> On Mon, May 14, 2018, 08:18 David McBride <toad3k at gmail.com> wrote:
>> let foo = \x -> Just (x + 1)
>> fmap foo (Just 9)
>> 
>> Just (Just 10)
>> 
>> 
>> On Mon, May 14, 2018 at 8:15 AM, Olumide <50295 at web.de> wrote:
>>> Dear List,
>>> 
>>>  Chapter 14 of LYH appears to suggest that a Just value can be added
>>>  to an Int. Quote from
>>>  http://learnyouahaskell.com/for-a-few-monads-more#useful-monadic-functions>>> 
>>>  "For instance, say we have Just 9 and the function \x -> Just
>>>  (x+1). If we map this function over Just 9, we're left with Just
>>>  (Just 10).">>> 
>>>  I've tried the following in ghci but got the error:
>>> 
>>>  <interactive>:12:1: error:
>>>      • Non type-variable argument in the constraint: Num (Maybe a)
>>>        (Use FlexibleContexts to permit this)
>>>      • When checking the inferred type
>>>          it :: forall a. (Num (Maybe a), Num a) => Maybe a
>>> 
>>> 
>>>  Am I reading the quote wrong? Is Just (Just 10) a hypothetical?
>>> 
>>>  Regards,
>>> 
>>>  - Olumide
>>>  _______________________________________________
>>>  Beginners mailing list
>>> Beginners at haskell.org
>>> http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners
>> 
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