是否可以将一位的位向量转换为SMTLib2中的布尔变量? [英] Is it possible to cast a bitvector of one bit into a boolean variable in SMTLib2?

问题描述

我想要一个布尔变量，用于测试例如位向量的第三位是否为0.位向量理论允许提取1位作为位向量，但不能提取布尔类型.我想知道我是否可以做这个演员.谢谢.

I want to have a boolean variable that test if, e.g., the third bit of a bit vector is 0. The theory of bitvector allows to extract 1 bit as a bitvector, but not a boolean type. I wonder if I can do this cast. Thank you.

===更新===

很抱歉，我的问题不清楚.但是尼古拉·比约纳(Nikolaj Bjorner)的答案是如何测试位向量的某个位.虽然我想将位向量的第一位的值分配给一个变量.我尝试将示例修改如下:

I'm sorry if my question is not clear. But the answer of Nikolaj Bjorner is how to test a certain bit of a bit vector. While I want to assign the value of the first bit of a bit vector to a variable. I try to modify the example as follows:

(declare-fun x () (_ BitVec 5))
(declare-fun bit0 () Bool)
(assert (= (= #b1 ((_ extract 0 0) x)) bit0 ))
(check-sat)

z3抱怨:

(error "line 2 column 25: invalid declaration, builtin symbol bit0")
(error "line 3 column 44: invalid function application, sort mismatch on argument at position 2")

我需要该变量bit0供以后使用.你能给我一个提示吗?谢谢.

I need that variable bit0 for later use. Could you please give me a hint? Thanks.

推荐答案

在第三位的提取与值为1(和一位)的位向量之间创建相等.

Create an equality between the extraction of the third bit and a bit-vector with value 1 (and one bit).

例如，

(declare-const x (_ BitVec 5))
(assert (= #b1 ((_ extract 2 2) x)))
(check-sat)
(get-model)

产生

sat
(model
  (define-fun x () (_ BitVec 5)
    #b00100)
)

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