Re:Swift Functors, Applicatives, and Monads in Pictures
by dllthomas on Wednesday July 15, 2015 @12:17PM
(#9892154)
Cleaning up the parent's formatting as I think it's too late for them to edit. Content is unchanged:
That is, a monad is a type parametrized by some other type, with the following two functions:
1) return :: a -> m a
2) (>>=) :: m a -> (a -> m b) -> m b
a) return x >>= f == f x
b) m >>= return == m
c) (m >>= f) >>= g == m >>= (\x -> f x >>= g)
What you'll usually see people insist is to describe monads by their operations, rather than through metaphor. That is, a monad is a type parametrized by some other type, with the following two functions:
1) return :: a -> m a 2) (>>=) :: m a -> (a -> m b) -> m b
such that three laws hold:
a) return x >>= f == f x b) m >>= return == m c) (m >>= f) >>= g == m >>= (\x -> f x >>= g)
For monads in Haskell, this is the technically correct definition.
That said, most people will tell you the best way to understand monads is to look at a few basic monad instance implementations (Maybe, Either a) and program with them, slowly learning new instances.