[Haskell-cafe] A Reader Monad Tutorial

[Lee Duhem]

On Sun, Jun 28, 2009 at 12:41 AM, Henry Laxen<nadine.and.henry at pobox.com> wrote:
> Dear Group,
>
> If any of you are struggling with understanding monads, I've tried to put
> together a pretty through explanation of what is behind the Reader monad.  If
> you're interested, have a look at:
>
> http://www.maztravel.com/haskell/readerMonad.html
>

Nice post.

I didn't find how to add comments on your blog, so I post them here:

>Areas of Confusion
>
>  1. What is the relationship between the Reader on the left hand side of the equals sign in the newtype definition and the Reader on the right hand side?
>   2. Why is there a Record field on the right hand side?
>   3. What is that r -> a doing there?

1) Reader on the left hand side be called a type constructor, Reader
on the right hand side be called a data constructor,
in Haskell 98 Report. You call them type definition and instance
constructor, respectively, I'm not sure it's a good idea, or
it is right.

bug in the explanation:
    what you use to make something and instance of a Reader (left hand side)
-> what you use to make something an instance of a Reader (left hand side)

2) runReader be called a selector function in Haskell 98 Report.

3) (->) is a type constructor, so r -> a is  a function type.

I used found 'instance Monad ((->) r)' hard to understand, but by
follow the hit given by Brent Yorgey, i.e. the data constructor for
type constructor (->) is called lambda abstraction, I found I can
understand them by type inference. I have written a post about how I
figure
it out, maybe you want take a look:
http://leeduhem.wordpress.com/2009/06/07/understanding-monad-instance-by-type-inference/

bug in the explanation after  (Reader f1) >>= f2  = Reader $ \e ->
runReader (Reader b) e:
    Reader b is a function that takes and e and returns a c,
-> Reader b is a function that takes an e and returns a c,

lee