I have been studying some category theory only to understand the "why" behind the various categorical constructs we use ("borrow") in the world of functional programming.
One of the oft cited maxims is this:
A monad is just a monoid in the category of endofunctors
Can we structure all programs to be a composition of pure and monadic functions and nothing else? If so, would the resultant "compositional structure" be monoidal?
Is it fair to infer such a "monoidal property" to exist for all programs (i.e., computable functions) ?
It seems that this should be intuitively true, but I'm not sure where (if at all) is a flaw in this inference? What may I be missing?