;;; Model for Assignment 1

;;; Ben Gum
;;; Department of Mathematics and Computer Science
;;; Grinnell College
;;; gum@cs.grinnell.edu

;;; created January 28, 2002
;;; last revised January 28, 2002


;;; Procedure: LENGTH computes the number of items in a list
;;;
;;; Given: LS a list
;;;
;;; Result: LEN an integer
;;;
;;; Preconditions: none
;;;
;;; Postconditions: LEN is the number of items in LS
;;;

(define length
  (lambda (ls)
    (if (null? ls)
        0
        (+ 1 (length (cdr ls))))))


;;; Procedure: APPEND sticks together two lists
;;;
;;; Given: LS1, LS2 lists
;;;
;;; Result: LS3 a list
;;;
;;; Preconditions: none
;;;
;;; Postconditions: LS3 contains the LS1 appended to LS2
;;;

(define append
  (lambda (ls1 ls2) 
    (if (null? ls1)
        ls2
        (cons (car ls1) (append (cdr ls1) ls2)))))


;;; Procedure: REVERSE reverses the input list
;;;
;;; Given: LS, a list
;;;
;;; Result: REV, a list
;;;
;;; Preconditions: none
;;;
;;; Postconditions: REV contains the items in LS, in reverse order
;;;

(define reverse
  (lambda (ls)
    (if (null? ls)
        '()
        (append (reverse (cdr ls)) (list (car ls))))))


;;; Procedure: LIST-REF picks a particular element out of a list
;;;
;;; Given: LS a list, N an integer
;;;
;;; Result: ITEM an item
;;;
;;; Preconditions: N >= 0 and N < the length of LS
;;;
;;; Postconditions: ITEM is the N+1st item in LS 
;;;

(define list-ref
  (lambda (ls n)
    (if (zero? n)
        (car ls)
        (list-ref (cdr ls) (- n 1)))))