behavior emerges from the types, as it did for the previously
considered monads. But we can't do that if we leave the list type as
a primitive OCaml type. However, we know several ways of implementing
-lists using just functions. In what follows, we're going to use type
+lists using just functions. In what follows, we're going to use version
3 lists, the right fold implementation (though it's important and
intriguing to wonder how things would change if we used some other
strategy for implementing lists). These were the lists that made
So an `('a, 'b) list'` is a list containing elements of type `'a`,
where `'b` is the type of some part of the plumbing. This is more
general than an ordinary OCaml list, but we'll see how to map them
-into OCaml lists soon. We don't need to fully grasp the role of the `'b`'s
+into OCaml lists soon. We don't need to fully grasp the role of the `'b`s
in order to proceed to build a monad:
l'_unit (a : 'a) : ('a, 'b) list = fun a -> fun k z -> k a z
-No problem. Arriving at bind is a little more complicated, but
-exactly the same principles apply, you just have to be careful and
-systematic about it.
+Take an `'a` and return its v3-style singleton. No problem. Arriving at bind
+is a little more complicated, but exactly the same principles apply, you just
+have to be careful and systematic about it.
l'_bind (u : ('a,'b) list') (f : 'a -> ('c, 'd) list') : ('c, 'd) list' = ...
deeply embedded branches: complex structure created by repeated
application of simple rules.
-[This would be a good time to try to build your own term for the types
-just given. Doing so (or attempting to do so) will make the next
+[This would be a good time to try to reason your way to your own term having the type just specified. Doing so (or attempting to do so) will make the next
paragraph much easier to follow.]
As usual, we need to unpack the `u` box. Examine the type of `u`.