2018-03-01

Altnerative Applicative and Monad formulations

There’s a little known alternative class definitions of Applicative and Monad that I haven’t seen presented in an article before, so I thought I’d share:

class Functor f => Applicative f where
  pure :: f ()
  (**) :: f a -> f b -> f (a, b)

-- Left identity : pure ** v     ≅ v
-- Right identity: v    ** pure  ≅ v
-- Associativity : u ** (v ** w) ≅ (u ** v) ** w
-- (≅ means isomorphism)

class Applicative m => Monad m where
  join :: m (m a) -> m a

-- join . fmap join = join . join
-- join . fmap pure = join . pure = id

See: