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

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9

Implementing Proof Systems

We showed in Chapter 7 that λ-terms provide a natural means for representing logical formulas and, in particular, for capturing the binding aspects of quantification. We illustrated the benefits of such representations by considering structural manipulations on formulas, such as the implementation of substitution and conversion to normal forms. A common computation concerning logical formulas is that of attempting to show that they are theorems in a given proof system. In this chapter we show how a higher-order logic programming language can be used to specify and implement proof systems. In the first two sections we consider proof systems for intuitionistic logic, and in the third section we discuss a proof system ...

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