Is there any intuition to understand join two functions in Monad?

Question

join is defined along with bind to flatten the combined data structure into single structure.

From type system view, (+) 7 :: Num a =>

Answer 1

how to get some intuition about it instead of just relying on type system?

I'd rather say that relying on the type system is a great way to build a specific sort of intuition. The type of join is:

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

Specialised to (->) r, it becomes:

(r -> (r -> a)) -> (r -> a)

Now let's try to define join for functions:

-- join :: (r -> (r -> a)) -> (r -> a)
join f = -- etc.

We know the result must be a r -> a function:

join f = \x -> -- etc.

However, we do not know anything at all about what the r and a types are, and therefore we know nothing in particular about f :: r -> (r -> a) and x :: r. Our ignorance means there is literally just one thing we can do with them: passing x as an argument, both to f and to f x:

join f = \x -> f x x

Therefore, join for functions passes the same argument twice because that is the only possible implementation. Of course, that implementation is only a proper monadic join because it follows the monad laws:

join . fmap join = join . join
join . fmap return = id
join . return = id

Verifying that might be another nice exercise.