README.md

chapter18 - Monads

1. Monads are applicative functors.

class Applicative m => Monad m where
    (>>=) :: m a -> (a -> m b) -> m b --Binding Operation
    (>>) :: m a -> m b -> m b  --Sequencing Operation
    return :: a -> m a

fmap using Monadic Operations

fmap f xs = xs >>= return . f

Dependency Chain

Functor -> Applicative -> Monad

• Eventhough there are three monadic operations, we only (>>=) to be a minimally complete monad instance.

join :: Monad m => m (m a) => m a

bind :: Monad m => (a -> m b) -> m a -> m b
bind f xs =
     join $ fmap f xs

• Monad is not impure.
• Monad is not an embedded language for doing impure programming.
• Monad is not a value. It's a typeclass just like functor, applicative.
• Monad is not about strictness.

Identity Laws

m >>= return = m
return x >> = f = f x

Associativity Law

(m >>= f) >>= g = m >>= (\x -> f x >>= g)

Monadic Composition - Kleisli Composition

(>=>) :: Monad m => (a -> m b) -> (b -> m c) -> a -> m c