Question

我在Z3中尝试了以下代码。但是Z3说模型不可用。

(declare-const s String)
(declare-fun toUppercase (String) (String))

(assert (= (str.len s) (str.len (toUppercase s))))
(assert (forall ((i Int) (x String))
  (let ((a!1 (and (not (= (str.at x i) "a"))
                  (not (= (str.at x i) "b"))
                  (not (= (str.at x i) "c"))
                  (not (= (str.at x i) "d"))
                  (not (= (str.at x i) "e"))
                  (not (= (str.at x i) "f"))
                  (not (= (str.at x i) "g"))
                  (not (= (str.at x i) "h"))
                  (not (= (str.at x i) "i"))
                  (not (= (str.at x i) "j"))
                  (not (= (str.at x i) "k"))
                  (not (= (str.at x i) "l"))
                  (not (= (str.at x i) "m"))
                  (not (= (str.at x i) "n"))
                  (not (= (str.at x i) "o"))
                  (not (= (str.at x i) "p"))
                  (not (= (str.at x i) "q"))
                  (not (= (str.at x i) "r"))
                  (not (= (str.at x i) "s"))
                  (not (= (str.at x i) "t"))
                  (not (= (str.at x i) "u"))
                  (not (= (str.at x i) "v"))
                  (not (= (str.at x i) "w"))
                  (not (= (str.at x i) "x"))
                  (not (= (str.at x i) "y"))
                  (not (= (str.at x i) "z"))
                  (= (str.at x i) (str.at (toUppercase x) i)))))
  (let ((a!2 (or (and (= (str.at x i) "a") (= (str.at (toUppercase x) i) "A"))
                 (and (= (str.at x i) "b") (= (str.at (toUppercase x) i) "B"))
                 (and (= (str.at x i) "c") (= (str.at (toUppercase x) i) "C"))
                 (and (= (str.at x i) "d") (= (str.at (toUppercase x) i) "D"))
                 (and (= (str.at x i) "e") (= (str.at (toUppercase x) i) "E"))
                 (and (= (str.at x i) "f") (= (str.at (toUppercase x) i) "F"))
                 (and (= (str.at x i) "g") (= (str.at (toUppercase x) i) "G"))
                 (and (= (str.at x i) "h") (= (str.at (toUppercase x) i) "H"))
                 (and (= (str.at x i) "i") (= (str.at (toUppercase x) i) "I"))
                 (and (= (str.at x i) "j") (= (str.at (toUppercase x) i) "J"))
                 (and (= (str.at x i) "k") (= (str.at (toUppercase x) i) "K"))
                 (and (= (str.at x i) "l") (= (str.at (toUppercase x) i) "L"))
                 (and (= (str.at x i) "m") (= (str.at (toUppercase x) i) "M"))
                 (and (= (str.at x i) "n") (= (str.at (toUppercase x) i) "N"))
                 (and (= (str.at x i) "o") (= (str.at (toUppercase x) i) "O"))
                 (and (= (str.at x i) "p") (= (str.at (toUppercase x) i) "P"))
                 (and (= (str.at x i) "q") (= (str.at (toUppercase x) i) "Q"))
                 (and (= (str.at x i) "r") (= (str.at (toUppercase x) i) "R"))
                 (and (= (str.at x i) "s") (= (str.at (toUppercase x) i) "S"))
                 (and (= (str.at x i) "t") (= (str.at (toUppercase x) i) "T"))
                 (and (= (str.at x i) "u") (= (str.at (toUppercase x) i) "U"))
                 (and (= (str.at x i) "v") (= (str.at (toUppercase x) i) "V"))
                 (and (= (str.at x i) "w") (= (str.at (toUppercase x) i) "W"))
                 (and (= (str.at x i) "x") (= (str.at (toUppercase x) i) "X"))
                 (and (= (str.at x i) "y") (= (str.at (toUppercase x) i) "Y"))
                 (and (= (str.at x i) "z") (= (str.at (toUppercase x) i) "Z"))
                 a!1)))
    (=> (and (>= i 0) (< i (str.len x))) a!2)))))
(assert (str.prefixof "hE" s))

(check-sat)
(get-model)

我想也许我可以实现一个replaceAll函数来用大写字符替换所有小写字符。但是我无法使replaceAll函数正常工作。

这是我第一次尝试使用define-fun-rec：

(set-option :smt.mbqi true)
(define-fun-rec replaceAll ((x!1 String) (x!2 String) (x!3 String)) (String)
  (let ((I (str.indexof x!1 x!2) )) 
    (if (= I -1) x!1
      (replaceAll (str.replace x!1 x!2 x!3) x!2 x!3)
    )
  )
)
(declare-const a String)
(simplify (replaceAll "aba" "a" "A"))
(assert (= (replaceAll a "a" "A") "Ab"))

(check-sat)
(get-model)
(exit)

这是我第二次尝试使用条件宏：

(declare-fun replaceAll (String String String String) Bool)

(assert (forall ((x!1 String) (x!2 String) (x!3 String) (x!4 String)) 
                (=> (= -1 (str.indexof x!1 x!2)) (replaceAll x!1 x!2 x!3 x!4))))
(assert (forall ((S String) (r String) (T String) (R String)) 
                (=>
                  (>= (str.indexof S r) 0)
                  (exists ((U String) (M String) (S1 String) (R1 String))
                    (and (= S (str.++ U M S1))
                         (= R (str.++ U T R1))
                         (= M r)
                         (= (str.len U) (str.indexof S r))
                         (replaceAll S1 r T R1))
                    )
                  ))) 

(declare-const a String)
(assert (= a "ab"))
(assert (replaceAll a "a" "A" "Ab") )

(check-sat)
(get-model)

我很感激您提供的任何指导。谢谢。

Answer 1

这将超出String过程如何处理约束饱和的范围。您基本上是在描述换能器。除了实例化关于它们的公理之外，目前还没有关于换能器的推理的支持。有一些工具可以原生地处理传感器并围绕它们进行约束求解。例如，Bek / Bex工具（http://rise4fun.com/bex，http://rise4fun.com/bek）和自动机工具包（http://research.microsoft.com/~margus，https://github.com/AutomataDotNet/Automata）。

如何在Z3中添加toUpperCase函数？

1 个答案: