Section 4.3.3

当初上数分课，傅里叶级数把我们搞的欲仙欲死，过后到了常微分方程，课上老韩笑着说到了轻松的部分了，就像他爬泰山时候那个“快活三里”。这小节这几个小题是为了巩固amb-eval基础的，4.3整节的最后出现，实在有点“快活三里”的感觉。

4.50
主要不同之处就是amb中的序列是从左到右依次抽取，用的是car cdr，而这里用的是random-choose。
(define (analyze-ramb exp)
  (let ((cprocs (map analyze (amb-choices exp))))
    (lambda (env succeed fail)
      (define (try-next choices)
        (if (null? choices)
            (fail)
            (let ((random-pick (random-choose choices)))
              (let ((the-right-one (car random-pick))
                    (rest-ones (cdr random-pick)))
                (the-right-one env
                               succeed
                               (lambda() (try-next rest-ones)))))))
        (try-next cprocs))))

random-choose参数为一个list，结果是一个序对，car为抽取的元素，cdr为其余的。       
(define (random-choose seq)
  (define (random-integer-between low high)
    (+ low (random (+ (- high low) 1))))
  (let ((ref (random-integer-between 1 (length seq))))
    (define (foo k items)
      (if (= k 1)
          items
          (let ((foo-next (foo (- k 1) (cdr items))))
            (cons (car foo-next)
                  (cons (car items) (cdr foo-next))))))
    (foo ref seq)))
   
应用ramb去实现ex 4.49中的语句生成：
把里面所有的amb全部改为ramb就可以了，这样执行(parse '())就可以生成句子，不过有时动不动就出现几万、几十万字的句子……

为了控制一下句子的长度，便增加了两个全局变量verb-layer和noun-layer，利用它们控制动词短语和名词短语的层数。
(define verb-layer 0)
(define noun-layer 0)
然后在parse-verb-phrase和parse-noun-phrase中控制：
(define (parse-verb-phrase)
  (define (maybe-extend verb-phrase)
    (require (< verb-layer 3))
    (ramb verb-phrase
          (begin (set! verb-layer (+ 1 verb-layer))
                 (maybe-extend (list 'verb-phrase
                                     verb-phrase
                                     (parse-prepositional-phrase))))))
  (maybe-extend (parse-word verbs)))
(define (parse-noun-phrase)
  (define (maybe-extend noun-phrase)
    (require (< noun-layer 3))
    (ramb noun-phrase
          (begin (set! noun-layer (+ 1 noun-layer))
                 (maybe-extend (list 'noun-phrase
                                     noun-phrase
                                     (parse-prepositional-phrase))))))
  (maybe-extend (parse-simple-noun-phrase)))

每次分析开始都要清0，以便重新构造。
(define (parse-sentence)
  (set! verb-layer 0)
  (set! noun-layer 0)
  (list 'sentence (parse-noun-phrase) (parse-verb-phrase)))

这样，运行(parse '())就可以生成不太长的句子了，而且不断的try-again可以遍历它们！可惜速度有些慢。


ps. 做这题的时候出了点小毛病：开始做的时候random-integer-between中的random部分我没+1，结果代价就是(random-integer-between 1 2)只会出现1.。这一小错不要紧，导致后面的an-element-of只是顺序取值。我当时还是没发现病因，就胡乱猜测ramb不能用an-element-of这种递归形式，而只能用(ramb 1 2 3 4 5)这种（当时竟然没发现这个式子从来第一次没出现过5）。然后又用宏实现了一个amb-eval中类似scheme中的apply过程，这样就可以把多个参数作为一个列表传过来……前后折腾了两个多小时，才走上正道。

4.51
比原来的set!要简单，就是去掉消除副作用的部分就行了。
(define (analyze-permanent-assignment exp)
  (let ((var (assignment-variable exp))
        (vproc (analyze (assignment-value exp))))
    (lambda (env succeed fail)
      (vproc env
             (lambda (val fail2)
               (set-variable-value! var val env)
               (succeed 'ok
                        fail2))
             fail))))
             
4.52
只要看出aproc应该在cproc的fail部分被调用就明白了。
(define (analyze-if-fail exp)
  (let ((cproc (analyze (if-fail-consequent exp)))
        (aproc (analyze (if-fail-alternative exp))))
    (lambda (env succeed fail)
      (cproc env
             succeed
             (lambda ()
               (aproc env succeed fail))))))
(define (if-fail-consequent exp) (cadr exp))
(define (if-fail-alternative exp) (caddr exp))

4.53             
生成和为素数的序对，就和当初的map-filter一样。
((8 35) (3 110) (3 20))

4.54
(define (analyze-require exp)
  (let ((pproc (analyze (require-predicate exp))))
    (lambda (env succeed fail)
      (pproc env
             (lambda (pred-val fail2)
               (if (false? pred-val)
                   (fail2)
                   (succeed 'ok fail2)))
             fail))))