The Haskell Platform specifies mtl and transformers as standard. If you’re unsure, you should just use mtl. However, if you have a specific technical reason to look at the new libraries, they tend to address issues or add new features to mtl. monadLib in particular has some new features.
Monad transformers aren’t exceedingly mathematically pleasant. However, we can get nice (co)products from free monads, and, more generally, ideal monads: See Ghani and Uustalu’s “Coproducts of Ideal Monads”: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.4.2698
Here’s a somewhat informal answer, but hopefully useful. getCC’ returns a continuation to the current point of execution; you can think of it as saving a stack frame. The continuation returned by getCC’ has not only ContT‘s state at the point of the call, but also the state of any monad above ContT on the … Read more
Let’s say that we’re writing a program that needs some configuration information in the following form: data Config = C { logFile :: FileName } One way to write the program is to explicitly pass the configuration around between functions. It would be nice if we only had to pass it to the functions that … Read more
For all the standard mtl monads, you don’t need lift at all. get, put, ask, tell — they all work in any monad with the right transformer somewhere in the stack. The missing piece is IO, and even there liftIO lifts an arbitrary IO action down an arbitrary number of layers. This is done with … Read more
The Haskell community is split on this issue. John Hughes reports that he finds it easier to teach monad transformers than to teach monads, and that his students do better with a “transformers first” approach. The GHC developers generally avoid monad transformers, preferring to roll up their own monads which integrate all the features they … Read more
This is available here as a .lhs file. The MaybeT transformer will allow us to break out of a monad computation much like throwing an exception. I’ll first quickly go over some preliminaries. Skip down to Adding Maybe powers to IO for a worked example. First some imports: import Control.Monad import Control.Monad.Trans import Control.Monad.Trans.Maybe Rules … Read more
Consider the specific example of IOT Maybe. How would you write a Monad instance for that? You could start with something like this: instance Monad (IOT Maybe) where return x = IOT (Just (return x)) IOT Nothing >>= _ = IOT Nothing IOT (Just m) >>= k = IOT $ error “what now?” where m’ … Read more
I’m with @Rhymoid on this one, I believe all Monads have two (!!) transformers. My construction is a bit different, and far less complete. I’d like to be able to take this sketch into a proof, but I think I’m either missing the skills/intuition and/or it may be quite involved. Due to Kleisli, every monad … Read more
Note: that you provided yourself no direct access to the current state s in this monad. Pause s is just a free monad over the mutate and yield operations. Implemented directly you get: data Pause s a = Return a | Mutate (s -> s) (Pause s a) | Yield (Pause s a) instance Monad … Read more