Most known results on avoiding the occur-check are based on the notion of "not subject to occur-check" (NSTO). It means that unification is performed only on such pairs of atoms for which the occur-check never succeeds in any run of a nondeterministic unification algorithm. Here we show that this requirement is too strong. We show how to weaken it, and present some related sufficient conditions under which the occur-check may be safely omitted. We show examples for which the proposed approach provides more general results than the approaches based on well-moded and nicely moded programs (this includes cases to which the latter approaches are inapplicable).

中文翻译：

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Occur-Check 的注意事项

避免发生检查的大多数已知结果都基于“不受发生检查”(NSTO) 的概念。这意味着统一仅在非确定性统一算法的任何运行中发生检查永远不会成功的原子对上执行。在这里我们表明这个要求太强了。我们展示了如何削弱它，并提出一些相关的充分条件，在这些条件下可以安全地省略发生检查。我们展示了一些示例，其中所提出的方法比基于模型良好和模型良好的程序的方法提供了更一般的结果（这包括后一种方法不适用的情况）。