LCF在HOL中的例子

Sten Agerholm
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引用次数: 24

摘要

LCF系统提供了不动点理论的逻辑,对非终止性、递归定义和无限值类型(如惰性列表)的推理很有用。由于底部元素的持续存在,对于有限值类型和严格函数的推理是笨拙的。HOL系统提供了集合理论,并很好地支持有限值类型和全函数的推理。在本文中,用一些例子证明了HOL的扩展与领域理论结合了这两个系统的优点。这些例子说明了关于无限值和非终止函数的推理,并展示了如何将定义域和集合论推理结合起来。一个例子给出了用成立良好的归纳法证明递归统一算法的正确性。
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LCF Examples in HOL
The LCF system provides a logic of fixed point theory and is useful to reason about nontermination, recursive definitions and infinite-valued types such as lazy lists. Because of continual presence of bottom elements, it is clumsy for reasoning about finite-valued types and strict functions. The HOL system provides set theory and supports reasoning about finite-valued types and total functions well. In this paper a number of examples are used to demonstrate that an extension of HOL with domain theory combines the benefits of both systems. The examples illustrate reasoning about infinite values and nonterminating functions and show how domain and set theoretic reasoning can be mixed to advantage. An example presents a proof of correctness of a recursive unification algorithm using well-founded induction.
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