Scheme Factorial (fact* l) Question

Question

I'm a newbie at Scheme, so forgive the question: I have a function that calculates the factorials of a list of numbers, but it gives me a period before the last number in the results. Where am I going wrong?

code:

#lang scheme

 (define fact
    (lambda (n)
      (cond
        ((= n 0) 1)
        ((= n 1) 1)
        (else (* n (fact (- n 1)))))))

 (define fact*
   (lambda (l)
     (cond
       ((null? (cdr l)) (fact (car l)))
       (else
        (cons (fact (car l)) (fact* (cdr l)))))))

output:

> (fact* '(3 6 7 2 4 5))
(6 720 5040 2 24 . 120)

Answer 1

What you have done is create an improper list. Try this:

(define fact*
   (lambda (l)
     (cond
       ((null? (cdr l)) (list (fact (car l))))
       (else
        (cons (fact (car l)) (fact* (cdr l)))))))

The addition of the list in the fourth line should make this work as you expect. Better might be the following:

(define fact*
   (lambda (l)
     (cond
       (null? l) '())
       (else
        (cons (fact (car l)) (fact* (cdr l)))))))

This allows your fact* function to work on the empty list, as well as reducing the number of places where you make a call to fact.

Answer 2

Use append instead of cons. cons is used to construct pairs, which is why you have the "." that is used to separate the elements of a pair. Here's an example:

(define (factorial n)
  (if (<= n 1)
      1
      (* n (factorial (- n 1)))))

(define (factorial-list l)
  (if (null? l)
      '()
      (append (list (factorial (car l))) 
              (factorial-list (cdr l)))))

Answer 3

The other answers have pointed out the reason why you get an improper list as a result of your fact* function. I would only like to point out that you could use the higher-order function map:

(define fact*
  (lambda (l)
    (map fact l))

(fact* '(3 6 7 2 4 5))

map takes a function and a list as arguments and applies the function to every element in the list, producing a new list.