Question

我使用Alloy * hola-0.2.jar来表示和研究高阶问题。以下代码check isAR for 1 but exactly 1 Node, exactly 1 Edge只会因一个反例而失败。

是的，Alloy *快速找到了反例。但是，当我点击＆＃34;下一步＆＃34;为了找到另一个反例，求解器从不完成它。（我在macbook pro中运行了至少3个小时。）

事实上，从理论上讲，不存在更多的反例。所以Alloy *应该说没有发现反例。断言可能有效。但是，它永远不会弹出。

我意识到解决高阶问题需要更多的计算工作。然而，我的这个问题非常小。所以我怀疑我的代码。问题是什么？

// a Heyting Algebra of subgraphs of a given graph

sig Node {}
sig Edge {
    source: Node,
    target: Node}
fun Edge.proj : set Node { this.source + this.target}
pred isGraph[ns: set Node, es: set Edge] {es.proj in ns}

// Cmpl[sns,ses,cns,ces] means: a pseudo-complement of a subgraph s is a subgraph c.
pred Cmpl[sns: set Node, ses: set Edge, cns: set Node, ces: set Edge] { 
    !((cns!=none or ces!=none) and Node in sns and Edge in ses)
    Node in sns + cns
    Edge in ses + ces
    all ns: set Node | all es: set Edge when isGraph[ns,es] and (Node in sns + ns) and (Edge in ses + es)|
        (cns in ns and ces in es)
}

/* An element x of a Heyting algebra H is called regular 
 * if x = ¬y for some y in H. 
 */

pred isRegular [xns: set Node, xes: set Edge] {
    some yns: set Node | some yes: set Edge when isGraph[yns,yes]|
        one cyns: set Node | one cyes: set Edge |
            isGraph[cyns,cyes] and Cmpl[yns,yes,cyns,cyes] and (cyns=xns and cyes=xes)
}

assert isAR { // is always regular?
    all subns: set Node, subes: set Edge when isGraph[subns,subes] |
        isRegular[subns,subes]
} 

check isAR for 1 but exactly 1 Node, exactly 1 Edge 
// this should fail with 1 couterexample (by theory)

Alloy *不会在非常小的高阶空间中停止求解

0 个答案: