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- 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
- Why are monad transformers different to stacking monads?
A monad transformer is simply a type t for which t m is a Monad for any Monad m However, it is not true, in general, that the composition of two monads is a monad - because of this, there aren't many abstract operations (if any at all) that can be defined in terms of the composition of two monads (and without abstraction, programming in Haskell with monads would be very tedious)
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