[Haskell-beginners] Applicative for State

[mike h]

Thanks again Francesco.
Part of my problem was confusing the data and type constructors.
With your solution and my renaming of the data constructors it all became much clearer!

:)

Mike


> On 6 Feb 2017, at 20:15, Francesco Ariis <fa-ml at ariis.it> wrote:
> 
> On Mon, Feb 06, 2017 at 07:40:12PM +0000, mike h wrote:
>> I have a State by another name, Stat,  just to experiment and learn.
>> [...]
>> I really can’t get what the <*> in the Applicative should be!
>> I just do see how I ‘get the f out of the Stat’ and then apply it.
>> 
>> I’d be really grateful if someone would explain what it should be and
>> the steps/reasoning needed to get there.
> 
> Hello Mike,
> 
>    when writing an instance, you always have to keep in mind: (a) the
> signature of the function you are writing and (b) what the instance
> is designed to do.
> 
> In our case, (<*>) is:
> 
>    (<*>) :: Applicative f => f (a -> b) -> f a -> f b
> 
>    -- which we could 'rewrite' as
>    (<*>) ::  Stat s (a -> b) -> Stat s a -> Stat s b
> 
> so we grab the results, one being a function and the other a value,
> and apply the first to the second.
> 
> (b) is "pass the state around in the background". Good, let's put this
> in action:
> 
>    (Stat f) <*> (Stat g) = Stat $ \s ->
>        let (h, s')  = f s     -- h is a function :: a -> b
>            (a, s'') = g s'    -- state passing
>            b        = h a in  -- the application
>        (b, s'') -- we're not returning just the tuple, we're returning
>                 -- even the bit before the 'let' statement
> 
> And that is that. Was this clear?
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