haskell - A monad is just a monoid in the category of endofunctors . . . A Monad f is a fixed endofunctor, not a subset of endofunctors closed under composition A common construction is to use f to generate a monoid by taking the set of all k -fold compositions f^k = f(f( )) of f with itself, including k=0 that corresponds to the identity f^0 = id
What is it that Leibniz calls a “Monad”? Monads capable of this are called "vernünftige Seelen" or "Geister" (intelligent souls or spirits, "animae") Now, there is a hierarchy of monads with regard to their apperceptions: From "schlummernden" (slumbering) up to the omniscient monad, the "monas monadum" (monad of monads) – God Somewhere in between are animal and spirit monads
Relationship between Functor, Applicative Functor, and Monad Changing the definition of Monad at this point, would have broken a lot of existing code (any piece of code that defines a Monad instance) to be worthwhile Breaking backwards-compatibility like that is only worthwhile if there is a large practical benefit to the change
How to extract value from monadic action - Stack Overflow (See also my previous thoughts on magicMonadUnwrap :: Monad m => m a -> a) Suppose I tell you I have a value which has the type [Int] Since we know that [] is a monad, this is similar to telling you I have a value which has the type Monad m => m Int So let's suppose you want to get the Int out of that [Int] Well, which Int do you want? The
c# 3. 0 - In C#, What is a monad? - Stack Overflow A monad is essentially deferred processing If you are trying to write code that has side effects (e g I O) in a language that does not permit them, and only allows pure computation, one dodge is to say, "Ok, I know you won't do side effects for me, but can you please compute what would happen if you did?"
What is a monad in FP, in categorical terms? - Stack Overflow As a compliment to Carl's answer, a Monad in Haskell is (theoretically) this: class Monad m where join :: m (m a) -> m a return :: a -> m a fmap :: (a -> b) -> m a -> m b Note that "bind" (>>=) can be defined as x >>= f = join (fmap f x) According to the Haskell Wiki A monad in a category C is a triple (F: C → C, η : Id → F, μ : F ∘ F
haskell - What are free monads? - Stack Overflow I stand by my terminology For example, using my index-core package you can define "free monad comprehensions", which behave just like the list monad, except that you bind functors instead of values A free monad is a list of functors in the sense that if you translate all Haskell concepts up the category of functors, then lists become free monads