Problem Statement

Write a function that orders two lists or arrays filled with numbers. The function should accept two lists as arguments and return true if the first list should be ordered before the second, and false otherwise. The order is determined by lexicographic order: Comparing the first element of each list. If the first elements are equal, then the second elements should be compared, and so on, until one of the list has no more elements. If the first list runs out of elements the result is true. If the second list or both run out of elements the result is false. Note: further clarification of lexicographical ordering is expounded on the talk page here and here.

Let's start with the solution:

#lang racket

(define (lex<? a b)
  (cond ((null? b) #f)
        ((null? a) #t)
        ((= (car a) (car b)) (lex<? (cdr a) (cdr b)))
        (else (< (car a) (car b)))))

(lex<? '(1 2 3 4 5) '(1 2 3 4 4)) ; -> #f