State and its relative ST both produce `monolithic’ stateful computations which may be run as units. They basically treat the mutable state as intermediate data, which is needed to produce a result, but should not, in and of itself, be of interest to the rest of the programme. On the other hand, what one puts … Read more
The type of the main function should be IO t (where t is a type variable). The type of map putStrLn ls is [IO ()]. This why you are getting this error message. You can verify this yourself by running the following in ghci: Prelude> :type map putStrLn ls map putStrLn ls :: [IO ()] … Read more
Could someone explain the reasoning behind this choice of definition for bind? Sure, and it’s almost exactly the same reasoning you have. It’s just… we wanted a more general application operator, not a more general composition operator. If you’ve done much (any) point-free programming, you’ll immediately recognize why: point-free programs are hard to write, and … Read more
My favorite example is the “purely applicative Either”. We’ll start by analyzing the base Monad instance for Either instance Monad (Either e) where return = Right Left e >>= _ = Left e Right a >>= f = f a This instance embeds a very natural short-circuiting notion: we proceed from left to right and … 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
Without plumbing the depths of metaphor, might I suggest to read a typical monad m as “strategy to produce a”, so the type m value is a first class “strategy to produce a value”. Different notions of computation or external interaction require different types of strategy, but the general notion requires some regular structure to … 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
There are two excellent papers by Lindley, Wadler & Yallop (discussed at LTU here). The most important thing to understand is that there are more things which are arrows than there are things which are monads. Conversely, monads are strictly more powerful than arrows (the second paper above specifies precisely in which fashion). In particular, … Read more
The main difference between monadic and applicative parsing is in how sequential composition is handled. In the case of an applicative parser, we use (<*>), whereas with a monad we use (>>=). (<*>) :: Parser (a -> b) -> Parser a -> Parser b (>>=) :: Parser a -> (a -> Parser b) -> Parser … Read more
First: The term monad is a bit vacuous if you are not a mathematician. An alternative term is computation builder which is a bit more descriptive of what they are actually useful for. They are a pattern for chaining operations. It looks a bit like method chaining in object-oriented languages, but the mechanism is slightly … Read more