如何在Z3中添加toUpperCase函数？

我在Z3中尝试了以下代码。但Z3表示目前还没有这一型号

(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)

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)

---

如果您能提供任何指导，我将不胜感激。谢谢。

这将超出字符串过程处理约束饱和的范围。 你基本上是在描述一个传感器。除了举例说明传感器的公理外，目前还不支持关于传感器的推理。 有一些工具可以本地处理传感器，并在其周围解决约束。例如，Bek/Bex工具（，）和自动机工具包（，）

(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)