Talk:Don't fear the Monad

Broken symmetry causes confusion (with Monad) (start at 2400)

The following definition shows a structure asymmetry...

M a >>= a -> M a

The LHS and RHS across the >>= operator has two different types. In order to restore the symmetry, we need to put a $\lambda$ expression (\a -> M a) in front of the overall structure, to get back the world of compositions. We just have to put one little $\lambda$ from the outside, the entire expression is back to our compositional universe. It is almost exactly the same as a Monoid.

\a -> ( M a >>= a -> M a )

{{#ev:youtube|ZhuHCtR3xq8|||| |start=2430&end=2442}}

The Definition of Monad: (start at 2442)

The functions \a -> M a live in a Monoid and this data: M a, live in a Monad, that's the definition. ... (because) we want compositionality, for the same reasons we mentioned before, we want our functions to live in a Monoid, but we need this extra data, so that we can do concurrency, side effects, I/O, whatever else ... (to make programs useful). {{#ev:youtube|ZhuHCtR3xq8|||| |start=252&end=2577}}