We can implement it with a single `amb` function, too (I took some shortcuts that might have hidden some of the nature of the implementation)!

    -- Lifts a list into Amb.
    amb :: [a] -> Amb a

If we assume Amb is just List, then:

    amb = id

If we write the example in the original article in desugared style, we get:

    amb [1, 2, 3] >>= \x ->
    amb [4, 5, 6] >>= \y ->
    if x * y /= 8 then amb [] else pure () >>
    pure (x, y)

(we are forced to use an awkward condition with `pure ()` on the else branch when calling `amb` because Haskell requires us to return values on all branches. We can rewrite it equivalently in terms of `when` to hide that detail:

    amb [1, 2, 3] >>= \x ->
    amb [4, 5, 6] >>= \y ->
    when (x * y /= 8) (amb []) >>
    pure (x, y)

It now looks more similar to the original example.)

It ends up looking like continuation-passing style: conceptually, if we encounter `amb []` in the nested function, the nested computation ends and we start examining the next value in the list values being assigned to `x`: the implementation given in the original post does end up using callcc, so with some imagination you might be able to derive some kind of equivalence here :)