On Tuesday 20 May 2008, ajb@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