Exercise 3.9. In section 1.2.1 we used the substitution model to analyze two procedures for computing factorials, a recursive version
(define (factorial n)
(if (= n 1)
1
(* n (factorial (- n 1)))))
and an iterative version
(define (factorial n)
(fact-iter 1 1 n))
(define (fact-iter product counter max-count)
(if (> counter max-count)
product
(fact-iter (* counter product)
(+ counter 1)
max-count)))
Show the environment structures created by evaluating (factorial 6) using each version of the factorial procedure.
递归版本的 environment
+-------------------------------------------------------------------------------+
| |
| factorial:----+ |
| | |
+----------------+--------------------------------------------------------------+
| ^ ^ ^ ^ ^ ^
| E1 | E2 | E3 | E4 | E5 | E6 |
| +-+-+ +-+-+ +-+-+ +-+-+ +-+-+ +-+-+
| |n:6| |n:5| |n:4| |n:3| |n:2| |n:1|
v +---+ +---+ +---+ +---+ +---+ +---+
parameter: n
body: (if (= n 1)
1
(* n (factorial (- n 1))))迭代版本的 environment
首先是定义后的全局环境
results of defining factorial and fact-iter in global environment
+---------------------------------------+
| fact-iter: -----------+ |
| factorial: ---+ | |
| | | |
+----------------+-------+--------------+
| |
| |
| v
| Parameter: product counter max-count
| body: (if (> counter max-count)..)
|
|
v
Parameter: n
body: (fact-iter 1 1n)在这个环境中，调用 (factorial 6)
+-----------------------------------------------------------------------------------------------------------------------+
| factorial: ... |
| fact-iter: ... |
+-----------------------------------------------------------------------------------------------------------------------+
^ ^ ^ ^ ^ ^ ^ ^
| | | | | | | |
E1 | | | | | | | |
+-+-+ +-----+------+ +-----+------+ +-----+------+ +-----+------+ +-----+------+ +-----+------+ +-----+------+
|n:6| |product:1 | |product:1 | |product:2 | |product:6 | |product:24 | |product:120 | |product:720 |
+---+ |counter:1 | |counter:2 | |counter:3 | |counter:4 | |counter:5 | |counter:6 | |counter:1 |
|max-count: 6| |max-count: 6| |max-count: 6| |max-count: 6| |max-count: 6| |max-count: 6| |max-count: 6|
+------------+ +------------+ +------------+ +------------+ +------------+ +------------+ +------------+