A self-verifying theorem prover

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dc.contributor.advisorMoore, J Strother, 1947-en
dc.contributor.committeeMemberEmerson, E. Allenen
dc.contributor.committeeMemberHarrison, Johnen
dc.contributor.committeeMemberHunt, Jr., Warren A.en
dc.contributor.committeeMemberKaufmann, Matten
dc.contributor.committeeMemberLifschitz, Vladimiren
dc.creatorDavis, Jared Curranen
dc.date.accessioned2010-08-24T17:49:22Zen
dc.date.accessioned2010-08-24T17:49:30Zen
dc.date.accessioned2017-05-11T22:20:07Z
dc.date.available2010-08-24T17:49:22Zen
dc.date.available2010-08-24T17:49:30Zen
dc.date.available2017-05-11T22:20:07Z
dc.date.issued2009-12en
dc.date.submittedDecember 2009en
dc.date.updated2010-08-24T17:49:30Zen
dc.descriptiontexten
dc.description.abstractPrograms have precise semantics, so we can use mathematical proof to establish their properties. These proofs are often too large to validate with the usual "social process" of mathematics, so instead we create and check them with theorem-proving software. This software must be advanced enough to make the proof process tractable, but this very sophistication casts doubt upon the whole enterprise: who verifies the verifier? We begin with a simple proof checker, Level 1, that only accepts proofs composed of the most primitive steps, like Instantiation and Cut. This program is so straightforward the ordinary, social process can establish its soundness and the consistency of the logical theory it implements (so we know theorems are "always true"). Next, we develop a series of increasingly capable proof checkers, Level 2, Level 3, etc. Each new proof checker accepts new kinds of proof steps which were not accepted in the previous levels. By taking advantage of these new proof steps, higher-level proofs can be written more concisely than lower-level proofs, and can take less time to construct and check. Our highest-level proof checker, Level 11, can be thought of as a simplified version of the ACL2 or NQTHM theorem provers. One contribution of this work is to show how such systems can be verified. To establish that the Level 11 proof checker can be trusted, we first use it, without trusting it, to prove the fidelity of every Level n to Level 1: whenever Level n accepts a proof of some phi, there exists a Level 1 proof of phi. We then mechanically translate the Level 11 proof for each Level n into a Level n - 1 proof---that is, we create a Level 1 proof of Level 2's fidelity, a Level 2 proof of Level 3's fidelity, and so on. This layering shows that each level can be trusted, and allows us to manage the sizes of these proofs. In this way, our system proves its own fidelity, and trusting Level 11 only requires us to trust Level 1.en
dc.format.mimetypeapplication/pdfen
dc.identifier.urihttp://hdl.handle.net/2152/ETD-UT-2009-12-435en
dc.language.isoengen
dc.subjectMilawaen
dc.subjectmathematical logicen
dc.subjectformal verificationen
dc.subjectLispen
dc.subjectproof checkingen
dc.subjecttheorem provingen
dc.subjectautomated reasoningen
dc.subjectreflectionen
dc.subjectsoundnessen
dc.subjectfidelityen
dc.subjectfaithfulnessen
dc.subjectrewritingen
dc.subjectproof buildingen
dc.subjecttacticsen
dc.subjectfirst-order logicen
dc.subjectverified verifieren
dc.titleA self-verifying theorem proveren
dc.type.genrethesisen

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