Stylistically this is very nice. In the real world, I would expect a 60% chance of this notation instead of the one you gave: C x c >>= f = C (value $ f x) (c + 1) But that is so minor it is hardly worth mentioning. On a more serious note, not stylistic … Read more
Let me explain my understanding without going into category theory: Functors and monads both provide some tool to wrapped input, returning a wrapped output. Functor = unit + map (i.e. the tool) where, unit = something which takes raw input and wraps it inside a small context. map = the tool which takes a function … Read more
As I understand it, the function “executes” each element in the list which must be an “action” (IO monad). That’s true for IO, but in your code example you don’t use the IO monad, you use the list monad (the function you give to mapM returns a list ([x]), not an IO). mapM is defined … Read more
Most APIs do not satisify the monad laws. jQuery is a large API, so statistically, it is unlikely to be “accidentally” monadic. As a result I am pretty skeptical that the jQuery API as a whole could satisfy the monad laws (i.e. that “jQuery is a monad”). This doesn’t mean that a given (very restricted) … Read more
Let’s start with a simple, superficial difference between your approach and the Reader approach, which is that you no longer need to hang onto config anywhere at all. Let’s say you define the following vaguely clever type synonym: type Configured[A] = ConfigSource => A Now, if I ever need a ConfigSource for some function, say … Read more
Yes, there are several things outside programming that can be said to be like monads. No, none of them will help you understand monads. Please read Abstraction, intuition, and the “monad tutorial fallacy”: Joe Haskeller is trying to learn about monads. After struggling to understand them for a week, looking at examples, writing code, reading … Read more
This problem can be broken into two pieces, how you represent the data type and how you compose them together. Data types The styles you listed use only 2 styles of data types, the “normal” style and the continuation passing style. They differ in which objects are chosen as the primitives of the language. In … Read more
A monad in category theory is an endofunctor, i.e. a functor where the domain and codomain is the same category. But a Bifunctor is a functor from the product category Hask x Hask to Hask. But we could try to find out what a monad in the Hask x Hask category looks like. It is … Read more
Actually, in a way, join is where all the magic really happens–(>>=) is used mostly for convenience. All Functor-based type classes describe additional structure using some type. With Functor this extra structure is often thought of as a “container”, while with Monad it tends to be thought of as “side effects”, but those are just … Read more
Here’s an example based on coin tossing. The problem is as follows: You have two coins, labeled Biased and Fair. The Biased coin has two heads, and the Fair coin has one head and one tail. Pick one of these coins at random, toss it and observe the result. If the result is a head, … Read more