#lang racket

(require racket/trace)

; plain recursive
(define fact
  (lambda (n)
    (if (= n 1)
        1
        (* n (fact (- n 1))))))

; tail recursive
(define fact-acc
  (lambda (n acc)
    (if (= n 1)
        acc
        (fact-acc (- n 1) (* n acc)))))

(trace fact fact-acc)

(define id
  (lambda (x)
    x))

(define square-sum
  (lambda (n)
    (if (= n 1)
        1
        (+ (square-sum (- n 1)) (* n n)))))

(define square-all
  (lambda (lon)
    (if (null? lon)
        '()
        (cons (* (car lon) (car lon)) (square-all (cdr lon))))))

(define make-list
  (lambda (n obj)
    (if (zero? n)
        '()
        (cons obj (make-list (- n 1) obj)))))