Example: List (law verification)

Example: List is a functor (join is ⊙)

• \(M ⊙ (M ⊙ M) = (M ⊙ M) ⊙ M\)
• \(η ⊙ M = M = M ⊙ η\)

join [ join [[x,y,...,z]] ] = join [[x,y,...,z]]
                            = join (join [[[x,y,...,z]]])
join (η [x]) = [x] = join [η x]

Therefore ([],join,η) is a monad.