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LCF Examples in HOL
 The Computer Journal
, 1994
"... The LCF system provides a logic of fixed point theory and is useful to reason about nontermination, recursive definitions and infinitevalued types such as lazy lists. Because of continual presence of bottom elements, it is clumsy for reasoning about finitevalued types and strict functions. The ..."
Abstract

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The LCF system provides a logic of fixed point theory and is useful to reason about nontermination, recursive definitions and infinitevalued types such as lazy lists. Because of continual presence of bottom elements, it is clumsy for reasoning about finitevalued types and strict functions. The HOL system provides set theory and supports reasoning about finitevalued 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 wellfounded induction.