Theorem proving for untyped constructive λ-calculus : implementation and application

This paper presents a theorem prover for a highly intensional logic, namely a constructive version of property theory [25] (this language essentially provides a combination of constructive first-order logic and the λ-calculus). The paper presents the basic theorem prover, which is a higher-order extension of Manthey and Bry’s model generation theorem prover for first-order logic [14]; considers issues relating to the compile-time optimisations that are often used with first-order theorem provers; and shows how the resulting system can be used in a natural language understanding system.

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