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1995•The Computer JournalOpen access

Representing higher-order logic proofs in HOL

J. von Wright

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Abstract

We describe an embedding of higher order logic in the HOL theorem proving system. Types, terms, sequents and inferences are represented as new types in the logic of the HOL system, and notions of proof and provability are defined. Using this formalisation, it is possible to reason about the correctness of derived rules of inference and about the relations between different notions of proofs. The formalisation is also intended to make it possible to reason about programs that handle proofs as their data (e.g., proof checkers).

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What this paper is about

We describe an embedding of higher order logic in the HOL theorem proving system. Types, terms, sequents and inferences are represented as new types in the logic of the HOL system, and notions of proof and provability are defined. Using this formalisation, it is possible to reason about the correctness of derived rules of inference and about the relations between different notions of proofs. The formalisation is also intended to make it possible to reason about programs that handle proofs as their data (e.g., proof checkers).

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Available abstract

We describe an embedding of higher order logic in the HOL theorem proving system. Types, terms, sequents and inferences are represented as new types in the logic of the HOL system, and notions of proof and provability are defined. Using this formalisation, it is possible to reason about the correctness of derived rules of inference and about the relations between different notions of proofs. The formalisation is also intended to make it possible to reason about programs that handle proofs as their data (e.g., proof checkers).

Key concepts: HOL, Mathematical proof, Correctness, Computer science, Higher-order logic, Proof assistant, Rule of inference, Automated theorem proving

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