Task

Show one or more idiomatic ways of generating the Cartesian product of two arbitrary lists in your language.

Demonstrate that your function/method correctly returns:

{1, 2} × {3, 4} = {(1, 3), (1, 4), (2, 3), (2, 4)}
and, in contrast:

{3, 4} × {1, 2} = {(3, 1), (3, 2), (4, 1), (4, 2)}
Also demonstrate, using your function/method, that the product of an empty list with any other list is empty.

 {1, 2} × {} = {}
 {} × {1, 2} = {}
For extra credit, show or write a function returning the n-ary product of an arbitrary number of lists, each of arbitrary length. Your function might, for example, accept a single argument which is itself a list of lists, and return the n-ary product of those lists.

Use your n-ary Cartesian product function to show the following products:

 {1776, 1789} × {7, 12} × {4, 14, 23} × {0, 1}
 {1, 2, 3} × {30} × {500, 100}
 {1, 2, 3} × {} × {500, 100}


 
(define cartesian-product (lambda (xs ys)
 (if (or (zero? (length xs)) (zero? (length ys)))
     '()
     (fold append (map (lambda (x) (map (lambda (y) (list x y)) ys)) xs)))))
 
(define nary-cartesian-product (lambda (ls)
 (if (fold (lambda (a b) (or a b)) (map (compose zero? length) ls))
     '()
     (map flatten (fold cartesian-product ls)))))
 
> (cartesian-product '(1 2) '(3 4))
((1 3) (1 4) (2 3) (2 4))
> (cartesian-product '(3 4) '(1 2))
((3 1) (3 2) (4 1) (4 2))
> (cartesian-product '(1 2) '())
()
> (cartesian-product '() '(1 2))
()
> (nary-cartesian-product '((1 2)(a b)(x y)))
((1 a x) (1 a y) (1 b x) (1 b y) (2 a x) (2 a y) (2 b x) (2 b y))
 