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 the use of this meta-logic to formalize logics and proofs. Axioms for first-order logic are shown to be 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.
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Paulson, L.C. The foundation of a generic theorem prover. J Autom Reasoning 5, 363–397 (1989). https://doi.org/10.1007/BF00248324
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DOI: https://doi.org/10.1007/BF00248324