W. Wong. Validation of HOL Proofs by Proof Checking. Formal Methods in System Design, 14(2):193-212, 1999.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....is a form of result caching. To formalize this optimization, a path calculus for LF is developed and shown equivalent to a standard calculus. 1 Introduction The ability for automated reasoning systems to produce easily veri able proofs has been widely recognized as valuable (e.g. [23, 4]) Recently, applications like proof carrying code and proof carrying authentication have created a new need for proofs that can be eciently veri ed by a simple proof checker [15, 2] The Edinburgh Logical Framework (LF) 10] is a widely used meta language for representing proof systems for these ....

W. Wong. Validation of HOL Proofs by Proof Checking. Formal Methods in System Design, 14(2):193-212, 1999.

....checker. Also, although it is not entirely clear from the available tech reports, it appears that the code to produce proofs from NEVER is intertwined with the original code for the theorem prover. Our implementation separates the proof producing code from the code for the decision procedure. In [23], Wong describes work on logging and checking proofs in the HOL system. Wong s work resembles the work on NEVER, in that the proof system is directly axiomatized and the code for producing proofs is intertwined with the original code for the theorem prover. Hence our work differs from his in the ....

....in a logical framework may thus be attractive even for systems with as concise a core logic as HOL s. A final note is that while the problems Wong is targetting are similar to the problems we are designing SVC to solve, the performance Wong reports is far below our goals. The sample formulas of [23] are taken from an application of hardware verification, and the resulting proofs are relatively large (from 2M to 43M uncompressed) But for the test case he describes, it actually takes longer to check the proof than to generate it. We anticipate proof checking in a high performance LF proof ....

W. Wong. Validation of HOL Proofs by Proof Checking. Formal Methods in System Design, 14(2):193--212, 1999. 15

....handle signi cantly larger formulas than Necula s. More ecient algorithms are thus required. Furthermore, the use of proofs for con ict clauses and the notion of abstract proofs presented below are novel. Other related work is proof logging and proof checking in EVES[11, 10] and in the HOL system [23]. One interesting note on the latter is that Wong lists nding ways of rapidly developing proof checkers for di erent logics as possible future research. The approach to proof checking proposed by Necula and adopted in SVC solves this problem (see Section 4.1 below) 3 Introduction to SVC SVC ....

W. Wong. Validation of HOL Proofs by Proof Checking. Formal Methods in System Design, 14(2):193-212, 1999.

....other systems [24,14] In some proof assistants (e.g. ALF, Coq, LEGO) the proof terms of all deduction steps are explicitly stored. In other systems, proof term memorising was not given the rst priority but some attempts have been done to get this feature, for example, in Isabelle [6] or in HOL [35]. Term rewriting has been shown to be fundamental for both programming and proving. In proof assistants, term rewriting is very useful since it eases equational reasoning and considerably simplify proofs by abstracting the computational arguments [16] However, in a system like Coq [20] term ....

....is not always a simple task since they need to bridge the gap between di erent logical foundations on which these systems are based. Our work is more restrictive since we only consider equational proofs. Therefore, we can avoid the semantics issues and concentrate on the syntax of proof terms. In [35], Wong traces HOL proofs in order to check them by an independent proof checker which has been developed itself by the author. On the contrary, as what is done in [7] we use Coq kernel as proof checker. This fact requires us to respect Coq syntax when building proof terms. However, we think that ....

W. Wong. Validation of HOL proofs by proof checking. Formal Methods in System Design: An International Journal, 14(2):193-212, 1999. 21

....on these ideas which accepts a wide variety of HOL proofs. We believe that the approach we have taken has potential for more general application. In order to communicate proofs, there must be a proof representation, some form of proof object [Bar96,BD93] The starting point for this work is [Won99] which describes an extension of HOL with the ability to record proofs in a particular internal format (as a sequence of inference steps) A different approach is taken by the logical framework, LF [HHP87] which uses the dependently typed lambda calculus to represent proofs. An improved ....

....inference rules and axioms. Using these primitive rules and axioms, about 40 so called basic rules are derived: introduction and elimination rules for the logical operators, congruence rules for equality, and so on. It is applications of these rules that are recorded in Wong s HOL proof format [Won99] and treated as though primitive. Proofs using HOL tactics compile down into basic rules. This Hilbert style approach is not really in the spirit of the Coq typetheoretic style of proof development. Although Coq is implemented in terms of about seven primitive tactics (Intro, Clear, Change, ....

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Wai Wong. Validation of HOL proofs by proof checking. Formal Methods in System Design: An International Journal, 14(2):193--212, March 1999.

....about the translation, which quanti es over its syntactic structure, is described. Finally, our conclusions and ideas for further work are presented in Section 5. 2 Related Work There have been several previous projects concerned with the validation of results from veri cation systems. Wong [15] developed a proof checker to examine the correctness of proof les lists of inferences generated by the HOL system. The proof checker rst took a proof le as an argument and then checked whether the proofs were correct or not. A log le was then produced that contained the hypotheses, lemmas ....

W. Wong. Validation of HOL proofs by proof checking. Formal Methods in System Design, 14(2):193-212, March 1999.

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