Re: [Haskell-cafe] Monad explanation

5 Feb 2009

      On Thu, 2009-02-05 at 15:52 -0800, David Leimbach wrote:
...
On Thu, Feb 5, 2009 at 2:38 PM, Jonathan Cast
 wrote:
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.
All Haskell programs start as

...
main :: IO ()
...
though... so they all get evaluated in the context of another IO ()
don't they?
Well...  Haskell compilers and runhaskell-style interpreters (not
regular Hugs/ghci!) take the value of Main.main as `the program'.  But
that feels (to me --- I could be wrong) like an aspect of a particular
hosted environment.  REPLs can handle programs that aren't wrapped up in
IO at all; and there's no reason why IO has to be the type of
IO-performning-things in REPLs, either.  You could just as well write a
REPL that took, say, tangible values [http://haskell.org/haskellwiki/TV]
as input instead, and displayed them.  So it's more a matter of Haskell
implementations can be given an IO value to run than that combining IO
values together somehow runs them.

jcc