racket - 使用带有自定义结构的内置数学运算符

Question

我希望能够做这样的事情:

(struct point (x y))

(define p1 (point 1 2))
(define p2 (point 10 20))

(+ p1 p2)  ; -> (point 11 22)

是否可以教授像 point 这样的结构？使用内置数学运算符，如 + ?

文档似乎设法实现自定义 (equal? ...)在 this page 上的第 5.5 节中处理.我正在尝试做的非常相似......

或者我应该定义像 (point-add p1 p2) 这样的函数?

Answer 1

你可以

一起去 point-add

使用您自己的 +与您想要采用的所有可能的值类型相匹配。如果您事先知道所有可能的值类型，这就足够了，但是扩展它以在客户端代码中包含新创建的结构定义并不容易。例如:

;; We will "shadow" Racket's + with our own +, but we still
;; need the functionality of Racket's +, so let's require
;; Racket's + but use the name racket:+ instead
(require (only-in racket/base [+ racket:+]))

(struct point (x y) #:transparent)

(define (+ x y)
  (match* (x y)
    [((point a b) (point c d)) (point (+ a c) (+ b d))]
    [((point _ _) _) (error '+ "Can't add a point with non point")]
    [(_ (point _ _)) (error '+ "Can't add a point with non point")]
    [(_ _) (racket:+ x y)]))

;; in client's code

(+ (point 1 2) (point 3 4)) ;=> (point 4 6)
(+ 1 2)                     ;=> 3

定义一个新的 generics这样我们就可以做类似 gen:equal+hash 的事情为 equal? .例如:

(require racket/generic
         (only-in racket/base [+ racket:+]))

(define-generics addable
  (add addable _)
  #:fast-defaults ([number?
                    (define (add x y) (racket:+ x y))]))

(define + add)

;; in client's code

(struct point (x y)
  #:transparent
  #:methods gen:addable
  [(define (add x y)
     (match* (x y)
       [((point a b) (point c d)) (point (+ a c) (+ b d))]
       [(_ _) (error 'add "Can't add a point with non point")]))])

(struct point-3d (x y z)
  #:transparent
  #:methods gen:addable
  [(define (add x y)
     (match* (x y)
       [((point-3d a b c) (point-3d d e f))
        (point-3d (+ a d) (+ b e) (+ c f))]
       [(_ _) (error '+ "Can't add a point-3d with non point-3d")]))])

(+ (point 1 2) (point 3 4)) ;=> (point 4 6)
(+ (point-3d 1 2 3) (point-3d 4 5 6)) ;=> (point-3d 5 7 9)
(+ 1 2) ;=> 3

要接受多个参数，将(3)修改如下

(define +
  (case-lambda
    [() 0]
    [(x . xs) (foldl add x xs)]))

;; client's code

(+ (point 1 2) (point 3 4) (point 5 6)) ;=> (point 9 12)
(+ 1 2 3) ;=> 6
(+) ;=> 0
(+ 1) ;=> 1
(+ (point-3d 1 2 3)) ;=> (point-3d 1 2 3)