[SOLVED] CS (define (range a b)

(define (range a b)
(if (> a b) ()
(cons a (range (+ a 1) b))))

;(range 1 5)
;(cons 1 (range (+ 1 1) 5))
;(cons 1 (range 2 5))
;(cons 1 (cons 2 (range 3 5)))
;(cons 1 (cons 2 (cons 3 (range 4 5))))
;(cons 1 (cons 2 (cons 3 (cons 4 (range 5 5)))))
;(cons 1 (cons 2 (cons 3 (cons 4 (cons 5 (range 6 5))))))
;(cons 1 (cons 2 (cons 3 (cons 4 (cons 5 ())))))
;(cons 1 (cons 2 (cons 3 (cons 4 (list 5)))))
;(1 2 3 4 5)

(define (range-it a b)
(define (helper i L)
(if (< i a) L(helper (- i 1)(cons i L))))(helper b ‘()));(range-it 1 4);(helper 4 ‘());(helper (- 4 1)(cons 4 ‘()));(helper 3 (list 4));(helper (- 3 1)(cons 3 (list 4)));(helper 2 (list 3 4));(helper 1 (list 2 3 4));(helper 0 (list 1 2 3 4));(1 2 3 4)(define (get-element L i)(if (= i 0) (car L) (get-element (cdr L) (- i 1))));(get-element (list 1 2 3 4) 2);(get-element (cdr (list 1 2 3 4)) (- 2 1));(get-element (list2 3 4) 1);(get-element (list 3 4) 0);(car (list 3 4));3(define (length L)(if (null? L) 0(+ 1 (length (cdr L)))));(length (list 1 2 3));(+ 1 (length (cdr (list 1 2 3))));(+ 1 (length (list 2 3)));(+ 1 (+ 1 (length (cdr (list 2 3)))));(+ 1 (+ 1 (length (list 3))));(+ 1 (+ 1 (+ 1 (length ‘()))));(+ 1 (+ 1 (+ 1 0)));…;3(define L1 (list 1 2 3))(define L2 (list 4 5 6))(define L3 (cons L1 L2))(define (append L1 L2)(if (null? L1) L2(cons (car L1)(append (cdr L1) L2))));(append (list 1 2)(list 3 4));(cons (car (list 1 2)) (append (cdr (list 1 2)) (list 3 4)));(cons 1 (append (list 2)(list 3 4)));(cons 1 (cons 2 (append ‘() (list 3 4))));(cons 1 (cons 2 (list 3 4)));…;(list 1 2 3 4)(define (scale-list L x)(if (null? L) ‘()(cons (* x (car L))(scale-list (cdr L) x))));(scale-list (list 1 2 3) 10);(cons (* 10 (car (list 1 2 3))) (scale-list (cdr (list 1 2 3)) 10));(cons (* 10 1) (scale-list (list 2 3) 10));(cons 10 (scale-list (list 2 3) 10));(cons 10 (cons 20 (scale-list (list 3) 10)));(cons 10 (cons 20 (cons 30 (scale-list ‘() 10))));(cons 10 (cons 20 (cons 30 ‘())));…;(list 10 20 30)(define (map f L)(if (null? L) ‘()(cons (f (car L))(map f (cdr L)))))(define (filter predicate L)(cond ((null? L) ‘())((predicate (car L)) (cons (car L) (filter predicate (cdr L))))(else (filter predicate (cdr L)))));(filter odd? (list 1 2 3 4 5));(odd? (car (list 1 2 3 4 5)));(cons (car (list 1 2 3 4 5)) (filter odd? (cdr (list 1 2 3 4 5))));(cons 1 (filter odd? (list 2 3 4 5)));(cons 1 (filter odd? (list 3 4 5)));(cons 1 (cons 3 (filter odd? (list 4 5))));(cons 1 (cons 3 (filter odd? (list 5))));(cons 1 (cons 3 (cons 5 (filter odd? ‘()))));(cons 1 (cons 3 (cons 5 ‘())));..;(list 1 3 5)(define (reduce operator initial lis)(if (null? lis) initial(operator (car lis)(reduce operator initial (cdr lis)))));(reduce + 0 (list 1 2 3));(+ 1 (reduce + 0 (list 2 3)));(+ 1 (+ 2 (reduce + 0 (list 3))));(+ 1 (+ 2 (+ 3 (reduce + 0 ‘()))));(+ 1 (+ 2 (+ 3 0)));..;60(define (reduce-it op total lis)(if (null? lis) total(reduce-it op (op total (car lis)) (cdr lis))));(reduce-it + 0 (list 1 2 3));(reduce-it + (+ 0 1) (cdr (list 1 2 3)));(reduce-it + 1 (list 2 3));(reduce-it + 3 (list 3));(reduce-it + 6 ‘());6(reduce / 1 (list 10 2 2)) ;=> (10 / (2 / (2/1))) => 10 ;rFold
(reduce-it / 1 (list 10 2 2));=> ((1 / 10)/2)/2=> 1/40;lFold