; Streams Example
(define s (cons-stream 1
            (cons-stream 2 (/ 1 0))
          )
)


; Recursive implementation of factorial
(define (fact-r n)
    (if (= n 0)
        1
        (* n (fact-r (- n 1)))
    )
)


; Tail recursive implementation of k * n!
(define (fact-alt n k)
    (if (= n 0)
        k
        (fact-alt (- n 1) (* k n))
    )
)


; Tail recursive implementation of factorial
(define (fact-i n)
    (define (helper total n)
        (if (= n 0)
            total
            (helper (* total n) (- n 1))
        )
    )
    (helper 1 n)
)


; Non tail recursive implementation of length
(define (length lst)
    (+ 1 (if (null? lst)
             -1
             (length (cdr lst))
         )
    )
)


; Tail recursive implementation of contains
(define (contains s v)
    (if (null? s)
        #f
        (if (= v (car s))
            #t
            (contains (cdr s) v)
        )
    )
)

; Non tail recursive implementation of length
(define (length lst)
    (if (null? lst)
        0
        (+ 1 (length (cdr lst)))
    )
)


; Tail recursive implementation of length
(define (length lst)
    (define (helper lst total)
        (if (null? lst)
            total
            (helper (cdr lst) (+ 1 total))
        )
    )
    (helper lst 0)
)


; Tail recursive implementation of reverse
(define (reverse lst)
    (define (helper lst r)
        (if (null? lst)
            r
            (helper (cdr lst) (cons (car lst) r))
        )
    )
    (helper lst '())
)


; Tail recursive implementation of map
(define (map fn lst)
    (define (helper lst res)
        (if (null? lst)
            res
            (helper (cdr lst) (cons (fn (car lst)) res))
        )
    )
    (reverse (helper lst '()))
)