That operation is called fmap, and it's characteristic of a functor. In Haskell, it's called liftM for monads, but they're really the same thing (and I think recent proposals are going to iron out this redundancy). fmap…
No, plain functors, applicative functors, and monads each deal with a different potential use case. Look at the specific type signatures: plain functor - fmap: (a -> b) -> (F a -> F b) applicative functor - ap: A (a ->…
The order of operations here is "right associative". So A -> B -> C -> D is equivalent to any of the following A -> (B -> C -> D) A -> (B -> (C -> D)) A -> B -> (C -> D) They're equivalent through currying. But you can…
Whoever told you it has to do with IO and functional purity vastly oversimplified things. That is just one use case. Monads take care of a very common computation pattern: wrapping and unwrapping data from a container…
That operation is called fmap, and it's characteristic of a functor. In Haskell, it's called liftM for monads, but they're really the same thing (and I think recent proposals are going to iron out this redundancy). fmap…
No, plain functors, applicative functors, and monads each deal with a different potential use case. Look at the specific type signatures: plain functor - fmap: (a -> b) -> (F a -> F b) applicative functor - ap: A (a ->…
The order of operations here is "right associative". So A -> B -> C -> D is equivalent to any of the following A -> (B -> C -> D) A -> (B -> (C -> D)) A -> B -> (C -> D) They're equivalent through currying. But you can…
Whoever told you it has to do with IO and functional purity vastly oversimplified things. That is just one use case. Monads take care of a very common computation pattern: wrapping and unwrapping data from a container…