这次回顾Assignment 3 Graphing with higher-order procedures。

学习资料：

作业地址：

https://mitpress.mit.edu/sites/default/files/sicp/psets/index.html

1. Procedure Types and Procedure Constructors

Exercise 1.A

(define (thrice f)
	(compose (compose f f) f))

((thrice thrice) f)
((compose (compose thrice thrice) thrice)) f)
((compose (lambda (x) (thrice (thrice x))) thrice)) f)
((lambda (x) ((lambda (x) (thrice (thrice x))) (thrice x))) f)

(repeated f 27)

代码对应的效果：

(((thrice thrice) 1+) 6)

6 + 27 = 33

(((thrice thrice) identity) compose)

identity是恒等映射，所以最后的结果为compose。

(((thrice thrice) square) a)

$a^{2^{27}}$

所以

(((thrice thrice) square) 1)

为$1$；

(((thrice thrice) square) 2)

为$2^{2^{27}}$

Exercise 1.B

代码验证：

(load "utils.scm")

(((thrice thrice) 1+) 6)

(((thrice thrice) identity) compose)

(((thrice thrice) square) 1)

; 数字太大导致溢出
; (((thrice thrice) square) 2)

实验结果：

1 ]=> (((thrice thrice) 1+) 6)
;Value: 33

1 ]=> (((thrice thrice) identity) compose)
;Value 13: #[compound-procedure 13 compose]

1 ]=> (((thrice thrice) square) 1)
;Value: 1

1 ]=> ; 数字太大导致溢出
; (((thrice thrice) square) 2)

2. Curves as Procedures and Data

Exercise 2

1

$\text{unit-line-at}: \text{Sch-Num} \to \text{Curve} \\ (\text{Sch-Num}\to \text{Point})$

2

代码：

(load "curves.scm")

(define (vertical-line point length)
    (lambda (t)
        (make-point 
            (x-of point)
            (+ (y-of point) (* t length)))))

3

$\text{vertical-line}: (\text{Point}, \text{Sch-Nonneg-Int}) \to \text{Curve}$

Exercise 3

映射关系：

$(x,y)\to (-x, y)$

代码：

(load "curves.scm")

(define (reflect-through-y-axis curve)
  (lambda (t)
    (let ((ct (curve t)))
      (make-point
       (- (x-of ct))
       (y-of ct)))))

Exercise 4

参考资料：

https://github.com/AyberkSorgun/Project2-Graphing-with-Higher-Order-Procedures/blob/master/project2.scm

先平移至重合，然后合并：

要使得

$(x_1, y_1), (x_0, y_0)$

重合，做如下变换即可；

$\begin{aligned} x_0 &=x _0 + (x_1 -x_0)\\ y_0 &=y _0 + (y_1 -y_0)\\ \end{aligned}$

代码：

(load "curves.scm")

(define (connect-ends curve1 curve2)
    (connect-rigidly 
        curve1 
        ((translate (- (x-of (curve1 1)) (x-of (curve1 0))) 
                    (- (y-of (curve1 1)) (y-of (curve1 0)))) curve2)))

3. Drawing Curves

由于没有图片，这部分从略。