[Haskell-cafe] Are all monads functions?

[Yves Parès]

Thanks for the explanation on free monads, it's interesting.

But still, I maintain my previous view. I could clarify that by saying that
(e.g. for Maybe) we could separate it in two types, Maybe itself and its
monad:

-- The plain Maybe type
data Maybe a = Just a | Nothing

-- The MaybeMonad
newtype MaybeMonad a = MM ( () -> Maybe a )

That's what using Maybe as a monad semantically means, doesn't it?

It's just that as I said before, the function () -> Maybe a is useless,
thus making the whole type MaybeMonad entirely equivalent to Maybe.

So Roman, as I understand it, a free monad can only be a stateless monad.
So *again*, FreeM is equivalent to :

data FreeM f a = Return a
               | Bind (* () ->* f (FreeM f a) )

You cannot express StateT for instance with a functor and FreeM, can you?

But if you change FreeM to be:

data FreeM f s a = Return a
               | Bind (* s ->* f (FreeM f a) )

Then maybe it becomes possible...

2011/12/31 Roman Cheplyaka <roma at ro-che.info>

> * Yves Parès <limestrael+haskell at gmail.com> [2011-12-31 13:09:37+0100]
> > One thought occur to me recently when explaining the concept of Monad to
> > non-haskellers: internally, all standard Monads are newtypes wrapping
> > functions:
> > StateT is, WriterT is, ContT is. Even IO and ST are, both conceptually
> and
> > in their implementation by GHC.
> > ParsecT (not part of mtl, but still) is. And so on...
>
> Writer(T) is not a function, it's just a tuple.
>
> Jerzy already mentioned [] and Maybe.
>
> Another example is a free monad generated by any polynomial functor.
> This subsumes Maybe and (almost) [], as described here:
> http://blog.omega-prime.coRoman.uk/?p=34<http://blog.omega-prime.co.uk/?p=34>
>
> To summarise, since there are only so many ways to form types in Haskell
> (sum, product and exponentiation (functions)), it's no surprise that
> functions do occur often, but that's not something fundamental to monads.
>
> --
> Roman I. Cheplyaka :: http://ro-che.info/
>



-- 
The ⊥ is a lie.
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