## Question:

Im a Haskell beginner and I'm still learning about Category Theory and its practical use in computer science.

I've spent last day watching couple lectures from Berkley's university about category theory, most of its content was showing a mathematical view of Rings, Semigroups, Groups, Magmas, Monoids, etc.

Hence, questions raised in my mind about monadic composition and kleisli category. Therefore, I would like to questions Haskell/Category Theory experts.

Is do notation a sort of monad composition?

Regards,

Do notation is just syntactic sugar for `>>=`. Code such as

``````do x <- a
b  -- b is an expression possibly involving x
``````

is desugared to

``````a >>= \x -> b
``````

If you are studying monads in CT, you will probably find that they are being defined as functors with two natural transformations

``````unit :: a -> m a        -- also known as η
join :: m (m a) -> m a  -- also known as μ
``````

``````return :: a -> m a
(>>=)  :: m a -> (a -> m b) -> m b
``````

Both presentations are equivalent. Indeed, `unit` and `return` are exactly the same thing. Instead, `join` can be expressed in terms of `(>>=)` as follows

``````join x = x >>= id
``````

and, vice versa, `(>>=)` can be expressed in terms of `join`.

``````x >>= f = join (fmap f x)
``````

above note that `fmap` takes `a -> m b` and `m a` to return `m (m b)`, which is then flattened to `m b` by `join`.

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