4

Typed λ-Terms and Formulas

The previous chapters have dealt with logic programming in the context of first-order logic. We are now interested in moving the discussion to the setting of a higher-order logic. The particular logic that we will use for this purpose is one based on the simply typed λ-calculus, generalized to allow for a form of polymorphic typing. This underlying calculus has several nontrivial computational characteristics that themselves merit discussion. We undertake this task in this chapter, delaying the presentation of the higher-order logic and the logic programming language based on it until Chapter 5.

The first two sections of this chapter describe the syntax of the simply typed *λ-calculus* and an equality relation called ...

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