4.53 Exercise 4.53

We are asked to determine the result of evaluating the following:

(let ((pairs '()))

(if-fail (let ((p (prime-sum-pair '(1 3 5 8) '(20 35 110))))

(permanent-set! pairs (cons p pairs))

(amb))

pairs))

It’s important to keep two different levels of failure continuations straight. The failure continuation constructed by the if-fail expression that leads to pairs being returned is only evaluated if the entire value expression fails. However, the (amb) call inside the let body is not going to immediately cause the entire expression evaluation to fail – it’s merely going to backtrack far enough for prime-sum-pair to select another pair, which, after being selected, will be permanently added to pairs. The expression as a whole will only fail when all of the pairs have been evaluated, meaning that this is one way to collect all of the prime sum pairs that will be found.

The three prime sum pairs for these lists are (3, 20), (3, 113), and (8, 35). Given that the first list controls the outermost iteration, and that both lists are iterated in order, the pairs will be discovered in this order, and therefore prepended in this order. This leads to a final result of

’((8 35) (3 113) (3 20))