; Various ways to implement the factorial function

; If using GNU Guile uncomment the following:

; (use-modules (srfi srfi-1))
; (define foldl fold)

; The standard recursive factorial

(define fact1
  (lambda (n)
    (if (= n 0)
        1
        (* n (fact1 (- n 1))))))

(fact1 5)
(fact1 100)

; We can modify this to be tail recursive

(define tfact
  (lambda (n m)
    (if (= n 0)
        m
        (tfact (- n 1) (*  n m)))))

(define (fact2 n) (tfact n 1))

(fact2 5)
(fact2 100)

; Alternatively, a "named" let is commmon when writing tail recursive
; functions. For example, here is another tail recursive factorial.

(define fact3 
  (lambda (n)
    (let tfact ((n n) (m 1))
      (if (= n 0)
          m
          (tfact (- n 1) (* m n))))))

(fact3 5)
(fact3 100)

;; enumerate a list from n downto 1
(define enum-to-1 (lambda (n)
                    (if (= 0 n)
                        '()
                        (cons n (enum-to-1 (- n 1)))
                        )))

;; factorial using a foldl over a list from n..1
(define fact4 
  (lambda (n)
    (let ((lst (enum-to-1 n)))
     (foldl * 1 lst))))

(fact4 5)
(fact4 100)