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Programming with Higher-Order Logic by Gopalan Nadathur, Dale Miller

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5

Using Quantification at Higher-Order Types

First-order logic programming uses first-order terms to represent objects and predicate constants to represent relations between such objects. In Chapter 4 we presented an enrichment to formulas that replaces first-order terms with λ-terms and that permits quantification over predicate names. These additions can have significant practical benefits: For example, since predicates correspond to procedures, the ability to treat predicates as variables can be used as the basis for higher-order programming. Before we can harness this potential, however, it is necessary to explain how the enhanced logic can be used to define a logic programming language. We do this in the first two sections of this chapter. ...

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