►zthomae’s SICP solutions
▼3 Chapter 3
3.1 Exercise 3.1
3.2 Exercise 3.2
3.3 Exercise 3.3
3.4 Exercise 3.4
3.5 Exercise 3.5
3.6 Exercise 3.6
3.7 Exercise 3.7
3.8 Exercise 3.8
3.9 Exercise 3.9
3.10 Exercise 3.10
3.11 Exercise 3.11
3.12 Exercise 3.12
3.13 Exercise 3.13
3.14 Exercise 3.14
3.15 Exercise 3.15
3.16 Exercise 3.16
3.17 Exercise 3.17
3.18 Exercise 3.18
3.19 Exercise 3.19
3.20 Exercise 3.20
3.21 Exercise 3.21
3.22 Exercise 3.22
3.23 Exercise 3.23
3.24 Exercise 3.24
3.25 Exercise 3.25
3.26 Exercise 3.26
3.27 Exercise 3.27
3.28 Exercise 3.28
3.29 Exercise 3.29
3.30 Exercise 3.30
3.31 Exercise 3.31
3.32 Exercise 3.32
3.33 Exercise 3.33
3.34 Exercise 3.34
3.35 Exercise 3.35
3.36 Exercise 3.36
3.37 Exercise 3.37
3.38 Exercise 3.38
3.39 Exercise 3.39
3.40 Exercise 3.40
3.41 Exercise 3.41
3.42 Exercise 3.42
3.43 Exercise 3.43
3.44 Exercise 3.44
3.45 Exercise 3.45
3.46 Exercise 3.46
3.47 Exercise 3.47
3.48 Exercise 3.48
3.49 Exercise 3.49
3.50 Exercise 3.50
3.51 Exercise 3.51
3.52 Exercise 3.52
3.53 Exercise 3.53
3.54 Exercise 3.54
3.55 Exercise 3.55
3.56 Exercise 3.56
3.57 Exercise 3.57
3.58 Exercise 3.58
3.59 Exercise 3.59
3.60 Exercise 3.60
3.61 Exercise 3.61
3.62 Exercise 3.62
3.63 Exercise 3.63
3.64 Exercise 3.64
3.65 Exercise 3.65
3.66 Exercise 3.66
3.67 Exercise 3.67
3.68 Exercise 3.68
3.69 Exercise 3.69
3.70 Exercise 3.70
3.71 Exercise 3.71
3.72 Exercise 3.72
3.73 Exercise 3.73
3.74 Exercise 3.74
3.75 Exercise 3.75
3.76 Exercise 3.76
3.77 Exercise 3.77
3.78 Exercise 3.78
3.79 Exercise 3.79
3.80 Exercise 3.80
3.81 Exercise 3.81
3.82 Exercise 3.82
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3.74 Exercise 3.74

To detect zero crossings, we can use the generalized form of stream-map to map the sign-change-detector procedure over each stream element as well as the previous stream element. It is unclear whether a stream starting out with a negative value starts out with a zero crossing (since 0 is considered positive), but I make the assumption that this is the case. (If one were to disagree, then the first stream element could be duplicated, to force the first value in the new stream to be 0).

First, a definition of sign-change-detector, just for fun:

(define (sign-change-detector previous-value current-value)
  (cond ((and (< previous-value 0) (>= current-value 0)) 1)
        ((and (>= previous-value 0) (< current-value 0)) -1)
        (else 0)))

Now, the definition of zero-crossings:
(define zero-crossings
  (stream-map sign-change-detector
              sense-data
              (cons-stream 0 sense-data)))

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