The Foundation of a Generic Theorem Prover
Logic in Computer Science
2009-09-25 v1
Abstract
Isabelle 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.
Keywords
Cite
@article{arxiv.cs/9301105,
title = {The Foundation of a Generic Theorem Prover},
author = {Lawrence C. Paulson},
journal= {arXiv preprint arXiv:cs/9301105},
year = {2009}
}