For a given type r, the function of type r -> a can be thought of as a computation delivering an a using an environment typed r. Given two functions r -> a and a -> (r -> b), it’s easy to imagine that one can compose these when given an environment (again, of type … Read more
Consider this monad which is isomorphic to the (Bool ->) monad: data Pair a = P a a instance Functor Pair where fmap f (P x y) = P (f x) (f y) instance Monad Pair where return x = P x x P a b >>= f = P x y where P x … Read more
I’ll take another swing at this. Is this a valid usage? Yes, in the narrow sense that it compiles and produces the results that you’re expecting. Is this intended usage? No. Now, sometimes things find usefulness beyond what they were originally for, and if this works out, great. But for Optional, we have found that … Read more
unsafePerformIO :: IO a -> a in System.IO.Unsafe (base). Use it with caution and read the description in the documentation carefully.
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
This is the Applicative Monad Proposal (AMP). Now whenever you declare something as Monad, you also have to declare it as Applicative (and therefore Functor). Mathematically speaking, every monad is an applicative functor, so this makes sense. You can do the following to remove the error: instance Functor Wrap where fmap f (Wrap x) = … 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
Why do we need monads? We want to program only using functions. (“functional programming (FP)” after all). Then, we have a first big problem. This is a program: f(x) = 2 * x g(x,y) = x / y How can we say what is to be executed first? How can we form an ordered sequence … Read more
Yes, all of them can be converted to bind syntax; in fact, they are converted internally by the compiler. I hope this translation of your example gives you the hint: main = readFile “foo.txt” >>= \f -> (print $ “prefix ” ++ f) >> (print $ f ++ ” postfix”)
edit2: OK, here’s what I should’ve said from the start: Monads are EDSLs, E as in embedded domain-specific languages. Embedded means that the language’s statements are plain values in our language, Haskell. Let’s try to have us an IO-language. Imagine we have print1 :: IO () primitive, describing an action of printing an integer 1 … Read more