LCF Examples in HOL

The LCF system provides a logic of xed point theory and is useful to reason about nontermination, recursive deenitions and innnite-valued types such as lazy lists. Because of continual presence of bottom elements, it is clumsy for reasoning about nite-valued types and strict functions. The HOL system provides set theory and supports reasoning about nite-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 beneets of both systems. The examples illustrate reasoning about innnite 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 uniication algorithm using well-founded induction.