The Foundation of a Generic Theorem Prover

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The Foundation of a Generic Theorem Prover (1989)

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by Lawrence C. Paulson

Venue:	Journal of Automated Reasoning
Citations:	467 - 48 self

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@ARTICLE{Paulson89thefoundation,
    author = {Lawrence C. Paulson},
    title = {The Foundation of a Generic Theorem Prover},
    journal = {Journal of Automated Reasoning},
    year = {1989},
    volume = {5}
}

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Abstract

Isabelle [28, 30] is an interactive theorem prover that supports a variety of logics. It represents rules as propositions (not as functions) and builds proofs by combining rules. These operations constitute a meta-logic (or `logical framework') in which the object-logics are formalized. Isabelle is now based on higher-order logic --- a precise and well-understood foundation. Examples illustrate use of this meta-logic to formalize logics and proofs. Axioms for first-order logic are shown sound and complete. Backwards proof is formalized by meta-reasoning about object-level entailment. Higher-order logic has several practical advantages over other meta-logics. Many proof techniques are known, such as Huet's higher-order unification procedure. Key words: higher-order logic, higher-order unification, Isabelle, LCF, logical frameworks, meta-reasoning, natural deduction Contents 1 History and overview 2 2 The meta-logic M 4 2.1 Syntax of the meta-logic ......................... 4 2.2 ...

Keyphrases

higher-order logic generic theorem prover logical framework well-understood foundation higher-order unification procedure higher-order unification natural deduction content several practical advantage object-level entailment many proof technique interactive theorem prover key word backwards proof first-order logic

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