[Haskell-cafe] one-way monads

[Dan Doel]

On Tuesday 20 May 2008, ajb at spamcop.net wrote:
> Actually, it's true less than 50% of the time.  In particular, it's
> not true of any monad transformer.

Sure it is. Any particular transformer t typically comes with some particular 
way of writing a function of type t m a -> m a (you may have to throw away 
some t-related stuff, of course).

Since a specific transformed monad is built from a specific monad, and a 
specific transformer, and specific transformers are likely to have a function 
of type t m a -> m a, and specific monads are likely to have functions of 
type m a -> a, you can compose them to get a function of type t m a -> a for 
the specific monad t m. And so on for transformed-transformed monads. :)

That only fails if either of the specific pieces fails to have the right 
function, which happens well under 50% of the time, I think (IO and STM are 
the ones that immediately occur to me (barring a certain evil function), 
although you could make a case for ST by technicality; no failing 
transformers come to mind (except CCT if we're counting ST), but I haven't 
wracked my brain very hard).

-- Dan