Re: [Haskell-cafe] Monad explanation

5 Feb 2009

      On Thu, 2009-02-05 at 13:01 -0800, David Leimbach wrote:
...
On Thu, Feb 5, 2009 at 12:27 PM, Jonathan Cast
 wrote:
On Thu, 2009-02-05 at 12:21 -0800, David Leimbach wrote:
        >
        >
        > On Thu, Feb 5, 2009 at 11:25 AM, Andrew Wagner
        >  wrote:
        >                         I think the point of the Monad is
        that it
        >                         works as a container of stuff, that
        still
        >                         allows mathematically pure things to
        happen,
        >                         while possibly having some opaque
        "other
        >                         stuff" going on.
>          This at least sounds, very wrong, even if it's not.
        Monads
        >         are not impure. IO is, but it's only _one_ instance
        of Monad.
        >         All others, as far as I know, are pure. It's just
        that the
        >         bind operation allows you to hide the stuff you
        don't want to
        >         have to worry about, that should happen every time
        you compose
        >         two monadic actions.

...
> Well all I can tell you is that I can have (IO Int) in a
        function as a
        > return, and the function is not idempotent in terms of the
        "stuff"
        > inside IO being the same.
Sure it's the same.
>  cmp /bin/cat /bin/cat
        > cp /bin/cat ~
        > cmp /bin/cat ~/cat
        >
Pretty much the same, anyway.

...
So if IO represents a program that when executed interacts with the
world's state, is it safe to say that when I return (State Int Int),
that I'm returning a "State program"?
I won't object to it.  Othe people might, though.
...
That'd make sense as it really does look like we force the State to be
evaluated with runState, evalState or execState.
...
The only difference with IO then is that to get IO programs to run,
you have to do it inside another IO program.
Meh.  Combining IO sub-programs into larger programs doesn't really `get
them to run'.  Better to say that an IO value is meaningful only to the
computer, and not mathematically (denotationally) useful.

jcc