; Preconditions: special conditions that need to be true for your procedure 
; to work
;
; we will give specific error messages when the user does not follow the
; preconditions
;
; example of a procedure that needs preconditions:

;(define add-pairs
;  (lambda (ls)
;    (if (null? ls)
;        '()
;        (cons (+ (car ls) (cadr ls)) (add-pairs (cddr ls))))))

; What are the preconditions on ls?
; ls needs to be of even length, we can test this with (even? (length ls))
; also, all elements of ls need to be numbers

(define all-numbers?
  (lambda (ls)
    (if (null? ls)
        #t
        (if (number? (car ls))
            (all-numbers? (cdr ls))
            #f))))

(define all-numbers2?
  (lambda (ls)
    (or (null? ls)
        (and (number? (car ls)) (all-numbers2? (cdr ls))))))
             
;(define add-pairs
;  (lambda (ls)
;    (if (not (all-numbers? ls))
;        (error "add-pairs: needs the input to be a list of all numbers")
;        (if (odd? (length ls)) 
;            (error "add-pairs: need a an even-length list")
;            (if (null? ls)
;                '()
;                (cons (+ (car ls) (cadr ls)) (add-pairs (cddr ls))))))))

 (define add-pairs
  (lambda (ls)
    (if (not (all-numbers? ls))
        (error "add-pairs: needs the input to be a list of all numbers")
        (if (odd? (length ls)) 
            (error "add-pairs: need a an even-length list")
            (add-pairs-kernel ls)))))
            
 (define add-pairs-kernel
   (lambda (ls)
     (if (null? ls)
         '()
         (cons (+ (car ls) (cadr ls)) (add-pairs-kernel (cddr ls))))))