Some misunderstanding between me and Scheme

Question

I'm just started learning scheme and can't quite understand why this function does not work:

;(define (sort l)
  (define (sorted? l)
    (if (= (length l) 2)            
        ; if simple list:
        (if (< (head l) (tail l)) 
            #t  
            #f) 
        ; if complex list:
        (if (and (< (head l) (head (tail l))) 
                 (sorted? (tail l)))
            #t  
            #f)))

Output:

(sorted? (1 0)) . . procedure application: expected procedure, given: 1; arguments were: 0 (sorted? '(1 0)) . . <: expects type as 2nd argument, given: (0); other arguments were: 1

Racket, R5RS

Answer 1

This is because you compare an integer and a list, cadr or if (< (head l) (head (tail l))) instead of if (< (head l) (tail l)) after a line ; if simple list would have more chances to work for you.

The following definition works for me:

(define (sorted? xs)
  (cond
    ((<= (length xs) 1)
     #t)
    ((< (car xs) (cadr xs))
     (sorted? (cdr xs)))
    (else #f)))

Answer 2

What scheme do you use? In R5RS (scheme standard), use car and cdr to get head and tail.

And cdr will give you PAIR, not atom. That's working.

(define (sorted? l) (if (= (length l) 2)
; if simple list: (if (< (car l) (cadr l)) #t
#f) ; if complex list: (if (and (< (head l) (head (tail l))) (sorted? (tail l))) #t
#f)))