如何使用Yices和Z3-SMT-LIB计算归纳数据类型
使用Yices使用归纳数据类型进行计算的一个简单示例是:如何使用Yices和Z3-SMT-LIB计算归纳数据类型,z3,Z3,使用Yices使用归纳数据类型进行计算的一个简单示例是: (define-type T (datatype c1 c2 (c3 val::bool))) (define x1::T) (define x2::T) (assert (/= x1 x2)) (check) 相应的输出为: sat (= x1 c1) (= (c3 false) x2) 使用以下代码使用Z3-SMT-LIB解决此示例 (decl
(define-type T (datatype c1
c2
(c3 val::bool)))
(define x1::T)
(define x2::T)
(assert (/= x1 x2))
(check)
相应的输出为:
sat
(= x1 c1)
(= (c3 false) x2)
使用以下代码使用Z3-SMT-LIB解决此示例
(declare-datatypes () ((T c1 ( c3 (T Bool)))))
(declare-fun x1 () T)
(declare-fun x2 () T)
(assert (not (= x2 x1)))
(check-sat)
(get-model)
相应的输出是
sat
(model
(define-fun x2 () T (c3 false))
(define-fun x1 () T c1)
)
在线运行此示例
正如观察到的,Yices和Z3产生相同的结果
其他例子:
Yices:
(define-type T (datatype c1
c2
(c3 val::bool)))
(define x1::T)
(define x2::T)
(define x3::T)
(define x4::T)
(assert (/= x1 x2))
(assert (/= x1 x3))
(assert (/= x1 x4))
(assert (/= x2 x3))
(assert (/= x2 x4))
(assert (/= x3 x4))
(check)
sat
(= x1 c1)
(= x3 c2)
(= (c3 false) x4)
(= (c3 true) x2)
Z3:
在线运行此示例
正如在本例中所观察到的,Yices和Z3产生不同的结果
其他示例:自然数作为归纳类型:
易斯
Z3
在线运行此示例
正如在本例中所观察到的,Yices和Z3产生不同的结果
问题是,
您的示例有无限多个模型。 Z3和Yices产生不同的模型,但它们产生的解决方案都是正确的 Z3和Yices对归纳数据类型使用稍微不同的决策过程。这就是为什么他们生产不同的型号。没有办法强迫他们总是为具有多个模型的断言输入集生成相同的解决方案 关于枚举所有可能的模型,我们可以使用Z3API。见此帖:
(declare-datatypes () ((T c1 c2 ( c3 (T Bool)))))
(declare-fun x1 () T)
(declare-fun x2 () T)
(declare-fun x3 () T)
(declare-fun x4 () T)
(assert (not (= x4 x3)))
(assert (not (= x4 x2)))
(assert (not (= x4 x1)))
(assert (not (= x3 x2)))
(assert (not (= x3 x1)))
(assert (not (= x2 x1)))
(check-sat)
(get-model)
sat
(model
(define-fun x3 () T c2)
(define-fun x2 () T (c3 false))
(define-fun x1 () T c1)
(define-fun x4 () T (c3 true))
)
(define-type Nat (datatype zero
(succ val::Nat)))
(define x1::Nat)
(define x2::Nat)
(define x3::Nat)
(assert (/= x1 x2))
(assert (/= x1 x3))
(assert (/= x2 x3))
(check)
sat
(= zero x1)
(= (succ x2) x3)
(= (succ x1) x2)
(declare-datatypes () ((Nat zero (succ (Nat Nat)))))
(declare-fun x1 () Nat)
(declare-fun x2 () Nat)
(declare-fun x3 () Nat)
(assert (not (= x1 x2)))
(assert (not (= x1 x3)))
(assert (not (= x2 x3)))
(check-sat)
(get-model)
sat
(model
(define-fun x3 () Nat (succ (succ (succ zero))))
(define-fun x2 () Nat (succ zero))
(define-fun x1 () Nat zero)
)