[lambdas]

> Is that so? Sounds very wrong to me. If we want to go the monad joke way, monads have to have an operation (a -> m b) that composes, but those are just normal functions, and there’s nothing curried about it. It’s a statement that one could bend enough so it’s kind of right, but what it really does is raise eyebrows.

I can see where they’re coming from, but they certainly haven’t set the stage for it to be a something you could deduce without already knowing what they’re referencing.

So to me, it seems they’re referencing the Free Monad, recursion schemes and a little of HomFunctor/Yoneda Lemma.

The free monad gives a coproduct of functions, where the value is either a recursive call or a value (branch vs node). To get from a set to a free monad, you need to define a Functor over the set, and given most things are representable, this is trivial.

Given this free monad, an algebra can be formed over it by providing a catamorphism, where the binary function would indeed be composition.