SICP 习题参考答案 3.3

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Exercise 3.35.  Ben Bitdiddle tells Louis that one way to avoid the trouble in exercise 3.34 is to define a squarer as a new primitive constraint. Fill in the missing portions in Ben's outline for a procedure to implement such a constraint:

(define (squarer a b)
  (define (process-new-value)
    (if (has-value? b)
        (if (< (get-value b) 0)
            (error "square less than 0 -- SQUARER" (get-value b))
            <alternative1>)
        <alternative2>))
  (define (process-forget-value) <body1>)
  (define (me request) <body2>)
  <rest of definition>
  me)

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1. 
   
2. (define (squarer a b)
   
3.   (define (process-new-value)
   
4.     (if (has-value? b)
   
5.         (if (< (get-value b) 0)
   
6.             (error "square less than 0 -- SQUARER" (get-value b))
   
7.             (set-value! a (sqrt (get-value b)) me))
   
8.         (if (has-value? a)
   
9.             (set-value! b (* (get-value a) (get-value a)) me))))
   
10.     (define (process-forget-value)
    
11.       (forget-value! a me)
    
12.       (forget-value! b me)
    
13.       (process-new-value))
    
14.     (define (me request)
    
15.       (cond ((eq? request 'I-have-a-value)
    
16.              (process-new-value))
    
17.             ((eq? request 'I-lost-my-value)
    
18.              (process-forget-value))
    
19.             (else
    
20.              (error "Unknown request -- SQUARER" request))))
    
21.     (connect a me)
    
22.     (connect b me)
    
23.     me)
    

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演示使用的代码

1. 
   
2. (load "3.35.scm")
   
3. 
   
4. (define a (make-connector))
   
5. (define b (make-connector))
   
6. 
   
7. 
   
8. (squarer a b)
   
9. (probe 'a a)
   
10. (probe 'b b)
    

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交互环境中的演示：

1. 
   
2. > (load "test.scm")
   
3. > (set-value! a 100 'zxl)
   
4. 
   
5. Probe: a = 100
   
6. Probe: b = 10000done
   
7. > (forget-value! a 'zxl)
   
8. 
   
9. Probe: a = ?
   
10. Probe: b = ?done
    
11. > (set-value! b 100 'zxl)
    
12. 
    
13. Probe: b = 100
    
14. Probe: a = 10.0done
    
15. > (forget-value! b 'zxl)
    
16. 
    
17. Probe: b = ?
    
18. Probe: a = ?done
    
19. > (set-value! a -10 'zxl)
    
20. 
    
21. Probe: a = -10
    
22. Probe: b = 100done
    

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Exercise 3.36.  Suppose we evaluate the following sequence of expressions in the global environment:

(define a (make-connector))
(define b (make-connector))
(set-value! a 10 'user)

At some time during evaluation of the set-value!, the following expression from the connector's local procedure is evaluated:

(for-each-except setter inform-about-value constraints)

Draw an environment diagram showing the environment in which the above expression is evaluated.

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<wait for pic>

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Exercise 3.37.  The celsius-fahrenheit-converter procedure is cumbersome when compared with a more expression-oriented style of definition, such as

(define (celsius-fahrenheit-converter x)
  (c+ (c* (c/ (cv 9) (cv 5))
          x)
      (cv 32)))
(define C (make-connector))
(define F (celsius-fahrenheit-converter C))

Here c+, c*, etc. are the ``constraint'' versions of the arithmetic operations. For example, c+ takes two connectors as arguments and returns a connector that is related to these by an adder constraint:

(define (c+ x y)
  (let ((z (make-connector)))
    (adder x y z)
    z))

Define analogous procedures c-, c*, c/, and cv (constant value) that enable us to define compound constraints as in the converter example above.

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1. 
   
2. (define (c+ x y)
   
3.   (let ((z (make-connector)))
   
4.     (adder x y z)
   
5.     z))
   
6. 
   
7. (define (c* x y)
   
8.   (let ((z (make-connector)))
   
9.     (multiplier x y z)
   
10.     z))
    
11. 
    
12. (define (c/ x y)
    
13.   (let ((z (make-connector)))
    
14.     (multiplier z y x)
    
15.     z))
    
16. 
    
17. (define (cv c)
    
18.   (let ((x (make-connector)))
    
19.     (constant c x)
    
20.     x))
    
21. 
    
22. (define (celsius-fahrenheit-converter x)
    
23.   (c+ (c* (c/ (cv 9) (cv 5))
    
24.           x)
    
25.       (cv 32)))
    
26. 
    
27. (define C (make-connector))
    
28. (define F (celsius-fahrenheit-converter C))
    
29. (probe 'C C)
    
30. (probe 'F F)
    

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本节完。