[Haskell-beginners] Help with Why Do Monads Matter blog post understanding

[Matt Ford]

On 29 June 2012 19:52, Brent Yorgey <byorgey at seas.upenn.edu> wrote:

>> "For a set A, we will define the set Pref(A) to be the set of functions
>> from application settings to the set A. Now watch closely: a function in
>> context from A to B is just an ordinary function from A to Pref(B). In
>> other words, you give it a value from the set A, and it gives you back
>> another function that maps from application settings to the set B."
>>
>> This is in the "functioning with dependency" section and is talking about a
>> procedure that uses outside info from preferences or application settings.
>>
>> If I set my prefs as follows
>>
>> configvar = 3
>>
>> and define a function as follows
>>
>> add x = configvar + 6
>>
>> So add’s signature is
>>
>> add: int -> int
>>
>> What does prefs(int) look like? Is that even the right thing to ask?
>
> prefs(int) looks like  Config -> Int (in your example perhaps we
> define  type Config = Int), so add should have type
>
>  Int -> (Config -> Int)
>
> The thing that is confusing the issue here is that you just made add
> implicitly use the 'configvar' which is in scope, so it does not need
> to take it as a parameter.

That's what I'm trying to understand, how we switch from "impure"
functions to "pure" functions which don't rely on external state.

And I see that passing in functions that act on the state helps do
this.  But I don't understand how, for a function that looks like
A->B, that has a whole load dependencies on external variables and
functions (of perhaps lot's of different types) all these variables
and functions are captured by the definition of Pref(B).

And by changing the actual type of the result of A->B in this case
from an Int to a function that returns an Int how can this hope to
match the original intention of the impure A->B.  Say for example
Pref(b) is the empty set as no functions map to from the config to B.
Changing the range means we will never get a sensible result??

I feel as though I'm missing something.

Cheers.

> But imagine that you want to be able to
> do multiple runs with different configurations, without recompiling
> your program -- then you will need to have any function that needs the
> configuation take it as an input.  Like this:
>
>  add x config = config + 6
>
>> By substituting the B for Prefs(B) and returning now only functions from
>> Pref(B) don't we lose the rest of the mapping for add i.e., " + 6"?
>
> I don't think I understand this question.
>
> -Brent
>
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