I'm a little confused about how to do this in a way such that the two constructions are strictly inverses of each other (as per 5c). In particular, when I go from the carrier type of the list, X, to the set for the monoid, I had to modify it to be 1 + X instead of X. Because how else am I going to guarantee that my monoid set has a unit in it?

(I assume that the function associated with the list algebra uses identity on the carrier type when the second parameter is the empty list.)

(I assume that the function associated with the list algebra uses identity on the carrier type when the second parameter is the empty list.)