Data structures 表达式的模式匹配

我希望你能帮我一点忙。作为家庭作业，我应该编写一个函数，用模式匹配检查表达式是否对应于某个结构定义

; Expression -> S-Expression
; converts an expression into the corresponding S-Expression
(check-expect (expr->sexpr EXPRESSION-1) '42)
(check-expect (expr->sexpr EXPRESSION-2) '(+ 4 (* 5 8)))
(check-expect (expr->sexpr EXPRESSION 3) '(/ (- 11 7) 2))
(check-expect (expr->sexpr (make-addition (make-literal 1) (make-literal 2)) 
'(+ 1 2))
(define (expr->sexpr e)
(match e
[(literal value) 'value]
[(addition lhs rhs) '(+ (addition lhs) (addition rhs))]
[(subtraction lhs rhs) '(- (subtraction lhs) (subtraction rhs))]
[...]
[...]
))

以下是定义：

(define-struct literal (value))
(define-struct addition (lhs rhs))
(define-struct subtraction (lhs rhs))
(define-struct multiplication (lhs rhs))
(define-struct division (lhs rhs))

我的代码如下所示：

; An Expression is one of:
; - (make-literal Number)
; - (make-addition Expression Expression)
; - (make-subtraction Expression Expression)
; - (make-multiplication Expression Expression)
; - (make-division Expression Expression)
; interp. abstract syntax tree of arithmetic expressions

(define EXPRESSION-1 (make-literal 42))

(define EXPRESSION-2
  (make-addition (make-literal 4) (make-multiplication (make-literal 5) (make-literal 8))))

(define EXPRESSION-3
  (make-division (make-subtraction (make-literal 11) (make-literal 7)) (make-literal 2)))


; Any -> Boolean
; checks whether e is an Expression
(check-expect (expression? EXPRESSION-1) #true)
(check-expect (expression? EXPRESSION-2) #true)
(check-expect (expression? (make-literal "42")) #false)
(define (expression? e)
  (match e
    [(and (literal?) (number? literal-value)) #true]
    [(and (addition?) (number? addition-lhs) (addition-rhs)) #true]
    [substraction? #true]
    [multiplication? #true]
    [division? #true]
    [... #false]   
))

(define (expression? e)
  (match e
    [(literal v) (number? v)]
    [(or (addition l r) (subtraction l r)
         (multiplication l r) (division l r))
     (and (expression? l) (expression? r))]
    [_ #false]))

我这样做的原因是因为我必须检查表达式是否是scstructure，我还必须确保该结构的元素只不过是数字，因为第二次测试会失败。 但不知何故，我的方法不起作用，因为表达式-1和表达式-2的测试已经失败了，我无法得到我的头Straighth，为什么

我把下面的四行保留在开头，因为我想把重点放在加法行上，因为我希望这是对“加法”行的简单重复。 你将如何着手使之正确？ 此外，您是否建议将数字检查作为结构元素外包到单独的功能中

干杯

编辑： 现在，正如我想我已经明白了，我正在努力完成下一个任务，我相信它的工作方式必须与下面阿萨瓦·舒克拉建议的几乎相同。任务是将表达式转换为s表达式，例如，从make addition make literal 1 make literal 2到“+1 2”，也使用模式匹配

; Expression -> S-Expression
; converts an expression into the corresponding S-Expression
(check-expect (expr->sexpr EXPRESSION-1) '42)
(check-expect (expr->sexpr EXPRESSION-2) '(+ 4 (* 5 8)))
(check-expect (expr->sexpr EXPRESSION 3) '(/ (- 11 7) 2))
(check-expect (expr->sexpr (make-addition (make-literal 1) (make-literal 2)) 
'(+ 1 2))
(define (expr->sexpr e)
(match e
[(literal value) 'value]
[(addition lhs rhs) '(+ (addition lhs) (addition rhs))]
[(subtraction lhs rhs) '(- (subtraction lhs) (subtraction rhs))]
[...]
[...]
))

---

模式中指定的字段名将绑定到各自的子句中。所以不需要谓词

(define (expression? e)
  (match e
    [(literal v) (number? v)]
    [(addition l r) (and (expression? l) (expression? r))]
    [(subtraction l r) (and (expression? l) (expression? r))]
    [(multiplication l r) (and (expression? l) (expression? r))]
    [(division l r) (and (expression? l) (expression? r))]
    [_ #false]))

最后一个子句是通配符，即对RHS的任何值进行求值

第2-5条的相同RHS可抽象如下：

; An Expression is one of:
; - (make-literal Number)
; - (make-addition Expression Expression)
; - (make-subtraction Expression Expression)
; - (make-multiplication Expression Expression)
; - (make-division Expression Expression)
; interp. abstract syntax tree of arithmetic expressions

(define EXPRESSION-1 (make-literal 42))

(define EXPRESSION-2
  (make-addition (make-literal 4) (make-multiplication (make-literal 5) (make-literal 8))))

(define EXPRESSION-3
  (make-division (make-subtraction (make-literal 11) (make-literal 7)) (make-literal 2)))


; Any -> Boolean
; checks whether e is an Expression
(check-expect (expression? EXPRESSION-1) #true)
(check-expect (expression? EXPRESSION-2) #true)
(check-expect (expression? (make-literal "42")) #false)
(define (expression? e)
  (match e
    [(and (literal?) (number? literal-value)) #true]
    [(and (addition?) (number? addition-lhs) (addition-rhs)) #true]
    [substraction? #true]
    [multiplication? #true]
    [division? #true]
    [... #false]   
))

(define (expression? e)
  (match e
    [(literal v) (number? v)]
    [(or (addition l r) (subtraction l r)
         (multiplication l r) (division l r))
     (and (expression? l) (expression? r))]
    [_ #false]))

但是，我更喜欢第一个版本，因为它反映了表达式定义

编辑12/1/20：

这与前面的示例类似，但我们在进行时构造列表

(check-expect (compile-expression EXPRESSION-1) 42)
(check-expect (compile-expression EXPRESSION-2) `(+ 4 (* 5 8)))
(check-expect (compile-expression EXPRESSION-3) `(/ (- 11 7) 2))

(define (compile-expression e)
  (match e
    [(literal v) v]
    [(addition l r) (list '+ (compile-expression l) (compile-expression r))]
    [(subtraction l r) (list '- (compile-expression l) (compile-expression r))]
    [(multiplication l r) (list '* (compile-expression l) (compile-expression r))]
    [(division l r) (list '/ (compile-expression l) (compile-expression r))]
    [_ (error "Not an Expression")]))

我更喜欢此版本，因为它允许您轻松创建更复杂的结构：

(define (compile-expression e)
  (match e
    [(literal v) v]
    [(addition l r) `(+ ,(compile-expression l) ,(compile-expression r))]
    [(subtraction l r) `(- ,(compile-expression l) ,(compile-expression r))]
    [(multiplication l r) `(* ,(compile-expression l) ,(compile-expression r))]
    [(division l r) `(/ ,(compile-expression l) ,(compile-expression r))]
    [_ (error "Not an Expression")]))

---

您可以了解有关Quote、QUISQUOTE和Unquote的更多信息。

一些入门文档：非常感谢您的回复，它帮助我更好地理解模式匹配，并且我还能够创建一个计算实际算术表达式的函数。但现在，正如我所想，我正在努力完成下一个任务，我相信它必须以几乎相同的方式工作。任务是将表达式转换为s表达式，例如，从make addition make literal 1 make literal 2到“+1 2”，也使用模式匹配。我将在另一条评论中发布代码，也许你还有一点提示？