使用替换模型的评估函数中的DrRacket类型不匹配错误

Question

我已经实现了语言"ROL"，现在我正在尝试扩展该语言以支持乐趣并调用我正在尝试在替换模型中实现它。

这是我的 eval 函数代码(请注意，这段代码在没有乐趣和调用的情况下工作得很好。 所以问题一定出在这两个实现上

(: eval : RegE -> RES)
;; evaluates RegE expressions by reducing them to bit-lists
(define (eval expr)
  (cases expr
    [(Reg right) (RegV right)]
    [(Bool b) (RES_Bool b)]
    [(Id name) (error 'eval "free identifier: ~s" name)]
    [(And left right) (reg-arith-op bit-and  (eval left ) (eval right) )]
    [(Or left right) (reg-arith-op bit-or (eval left )  (eval right) )]
    [(Shl E1) (RegV (shift-left (RegV->bit-list (eval E1))))]
    [(Maj E1) (RES_Bool (majority? (RegV->bit-list (eval E1))))]
    [(Geq E1 E2) (RES_Bool (geq-bitlists? (RegV->bit-list (eval E1)) (RegV->bit-list (eval E2))))]
    [(With bound-id named-expr bound-body)
       (eval (subst bound-body
                    bound-id
                    (Reg (RegV->bit-list(eval named-expr)))))]
    [(Fun bound-id bound-body) expr]
    [(Call fun-expr arg-expr)
       (let ([fval (eval fun-expr)])
         (cases fval
           [(Fun bound-id bound-body)
            (eval (subst bound-body
                   bound-id
                   (eval arg-expr)))]
           [else (error 'eval "`call' expects a function, got: ~s"
                              fval)]))]
    [(If E1 E2 E3) (if (RegV->boolean (eval E1)) (eval E2) (eval E3))]

))

这是我的 sunst 函数：

(define (subst expr from to)
  (cases expr
    [(Reg g) expr]
    [(Bool g) expr]
    [(And left right)(And (subst left from to)(subst right from to))]
    [(Or left right)(Or (subst left from to)(subst right from to))]
    [(If bool ifBody elseBody) (If (subst bool from to) (subst ifBody from to) (subst elseBody from to))]
    [(Maj left)(Maj (subst left from to))]
    [(Geq left right)(Geq (subst left from to)(subst right from to))]
    [(Shl left)(Shl (subst left from to))]
    [(Id name) (if (eq? name from) to expr)]
    [(With bound-id named-expr bound-body)
           (if (eq? bound-id from)
               expr
               (With bound-id
                     named-expr
               (subst bound-body from to)))]
    [(Call left right) (Call (subst left from to) (subst right from to))]
    [(Fun bound-id bound-body)
         (if (eq? bound-id from)
           expr
           (Fun bound-id (subst bound-body from to)))]))

我收到错误：

Type Checker: type mismatch
  expected: RegE
  given: RES in: fval
. Type Checker: type mismatch
  expected: RegE
  given: RES in: (eval arg-expr)
. Type Checker: type mismatch
  expected: RES
  given: Fun in: (cases expr ((Reg right) (RegV right)) ((Bool b) (RES_Bool b)) ((Id name) (error (quote eval) "free identifier: ~s" name)) ((And left right) (reg-arith-op bit-and (eval left) (eval right))) ((Or left right) (reg-arith-op bit-or (eval left) (eval right))) ((Shl E1) (RegV (shift-left (RegV->bit-list (eval E1))))) ((Maj E1) (RES_Bool (majority? (RegV->bit-list (eval E1))))) ((Geq E1 E2) (RES_Bool (geq-bitlists? (RegV->bit-list (eval E1)) (RegV->bit-list (eval E2))))) ((With bound-id named-expr bound-body) (eval (subst bound-body bound-id (Reg (RegV->bit-list (eval named-expr)))))) ((Fun bound-id bound-body) expr) ((Call fun-expr arg-expr) (let ((fval (eval fun-expr))) (cases fval ((Fun bound-id bound-body) (eval (subst bound-body bound-id (eval arg-expr)))) (else (error (quote eval) "`call' expects a function, got: ~s" fval))))) ((If E1 E2 E3) (if (RegV->boolean (eval E1)) (eval E2) (eval E3))))
. Type Checker: Summary: 3 errors encountered in:
  fval
  (eval arg-expr)
  (cases expr ((Reg right) (RegV right)) ((Bool b) (RES_Bool b)) ((Id name) (error (quote eval) "free identifier: ~s" name)) ((And left right) (reg-arith-op bit-and (eval left) (eval right))) ((Or left right) (reg-arith-op bit-or (eval left) (eval right))) ((Shl E1) (RegV (shift-left (RegV->bit-list (eval E1))))) ((Maj E1) (RES_Bool (majority? (RegV->bit-list (eval E1))))) ((Geq E1 E2) (RES_Bool (geq-bitlists? (RegV->bit-list (eval E1)) (RegV->bit-list (eval E2))))) ((With bound-id named-expr bound-body) (eval (subst bound-body bound-id (Reg (RegV->bit-list (eval named-expr)))))) ((Fun bound-id bound-body) expr) ((Call fun-expr arg-expr) (let ((fval (eval fun-expr))) (cases fval ((Fun bound-id bound-body) (eval (subst bound-body bound-id (eval arg-expr)))) (else (error (quote eval) "`call' expects a function, got: ~s" fval))))) ((If E1 E2 E3) (if (RegV->boolean (eval E1)) (eval E2) (eval E3))))
>

我的数据类型是：

(define-type RegE
[Reg Bit-List]
[Xor RegE RegE]
[And RegE RegE]
[Or RegE RegE]
[Shl RegE]
[Id Symbol]
[With Symbol RegE RegE]
[Bool Boolean]
[Geq RegE RegE]
[Maj RegE]
[If RegE RegE RegE]
[Fun Symbol RegE]
[Call RegE RegE])

和：

(define-type RES
[RES_Bool Boolean]
[RegV Bit-List])

我可以看到，对于(let ([fval (eval fun-expr)做(eval fun-expr)会返回 RES，我猜这可能是问题所在，还有其他方法可以解决这个问题吗？ 任何帮助将不胜感激。

Answer 1

关键问题是您希望如何在运行时表示函数。eval的定义是：

(: eval : RegE -> RES)
;; evaluates RegE expressions by reducing them to bit-lists
(define (eval expr)
  (cases expr
  ...
  [(Fun bound-id bound-body) expr]
  ...

评估(Fun bound-id bound-body)的结果需要是RES。也许将 RES 扩展为：

(define-type RES
    [RES_Bool Boolean]
    [RegV Bit-List]
    [FunV Symbol RegE])

然后让eval返回一个(FunV bound-id bound-body).

在 Call 的评估中，您需要切换到

     (cases fval
       [(FunV bound-id bound-body)

因为fval是RES。