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}


#lang racket/base
(require rackunit
         ;; usually, included in "racket", but we're using racket/base so we
         ;; show where this comes from
         (only-in racket/list cartesian-product))
;; these tests will pass silently
(check-equal? (cartesian-product '(1 2) '(3 4))
             '((1 3) (1 4) (2 3) (2 4)))
(check-equal? (cartesian-product '(3 4) '(1 2))
             '((3 1) (3 2) (4 1) (4 2)))
(check-equal? (cartesian-product '(1 2) '()) '())
(check-equal? (cartesian-product '() '(1 2)) '())
 
;; these will print
(cartesian-product '(1776 1789) '(7 12) '(4 14 23) '(0 1))
(cartesian-product '(1 2 3) '(30) '(500 100))
(cartesian-product '(1 2 3) '() '(500 100))