dc.contributor.advisor Moore, J Strother, 1947- en dc.creator Davis, Jared Curran en dc.date.accessioned 2010-08-24T17:49:22Z en dc.date.accessioned 2010-08-24T17:49:30Z en dc.date.available 2010-08-24T17:49:22Z en dc.date.available 2010-08-24T17:49:30Z en dc.date.issued 2009-12 en dc.date.submitted December 2009 en dc.identifier.uri http://hdl.handle.net/2152/ETD-UT-2009-12-435 en dc.description text en dc.description.abstract Programs 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? en 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. dc.format.mimetype application/pdf en dc.language.iso eng en dc.subject Milawa en dc.subject mathematical logic en dc.subject formal verification en dc.subject Lisp en dc.subject proof checking en dc.subject theorem proving en dc.subject automated reasoning en dc.subject reflection en dc.subject soundness en dc.subject fidelity en dc.subject faithfulness en dc.subject rewriting en dc.subject proof building en dc.subject tactics en dc.subject first-order logic en dc.subject verified verifier en dc.title A self-verifying theorem prover en dc.date.updated 2010-08-24T17:49:30Z en dc.contributor.committeeMember Emerson, E. Allen en dc.contributor.committeeMember Harrison, John en dc.contributor.committeeMember Hunt, Jr., Warren A. en dc.contributor.committeeMember Kaufmann, Matt en dc.contributor.committeeMember Lifschitz, Vladimir en dc.description.department Computer Sciences dc.type.genre thesis en thesis.degree.department Computer Sciences en thesis.degree.discipline Computer Sciences en thesis.degree.grantor The University of Texas at Austin en thesis.degree.level Doctoral en thesis.degree.name Doctor of Philosophy en
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