Meta Reasoning in ACL2

Hunt, Warren A.; Kaufmann, Matt; Krug, Robert Bellarmine; Moore, J. Strother; Smith, Eric

doi:10.1007/11541868_11

Cited by 20 publications

(22 citation statements)

References 2 publications

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“…It recursively calls itself to get 1 To be precise, the real left-hand side is abs(term + poly) > C. The ACL2 theorem prover is trying to rewrite it to nil.…”

Section: Algorithmmentioning

confidence: 99%

Proving a specific type of inequality theorems in ACL2

Liu

2009

Proceedings of the Eighth International Workshop on the ACL2 Theorem Prover and Its Applications

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We describe how we guide ACL2 to follow a divide-andconquer strategy for proving inequalities of the type |P ( e)| ≤ C. P ( e) is a polynomial in variables e and C is a constant.Our approach involves (1) writing an ACL2 program to estimate the upper-bound of such polynomials and (2) using the bind-free mechanism to integrate the upper-bound estimation program to guide rewriting. We think it is interesting to showcase how we extract the relevant information from the hypothesis and how such information is used to influence rewriting.Techniques like ours can be useful to ACL2 users who want to better control rewriting when their problems share specific characteristics with our |P ( e)| ≤ C type problem.

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“…It recursively calls itself to get 1 To be precise, the real left-hand side is abs(term + poly) > C. The ACL2 theorem prover is trying to rewrite it to nil.…”

Section: Algorithmmentioning

confidence: 99%

Proving a specific type of inequality theorems in ACL2

Liu

2009

Proceedings of the Eighth International Workshop on the ACL2 Theorem Prover and Its Applications

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“…To emulate them with a theorem prover, the simplification engine and lemma libraries must be powerful enough to encode such transformations. ACL2 provides a meta reasoning facility [42], allowing the user to augment its native simplification heuristics. We are investigating its use to encode the analysis performed by a practical VCG.…”

Section: Discussionmentioning

confidence: 99%

Verification Condition Generation Via Theorem Proving

Matthews

Moore

Ray

et al. 2006

Lecture Notes in Computer Science

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Abstract. We present a method to convert (i) an operational semantics for a given machine language, and (ii) an off-the-shelf theorem prover, into a high assurance verification condition generator (VCG). Given a program annotated with assertions at cutpoints, we show how to use the theorem prover directly on the operational semantics to generate verification conditions analogous to those produced by a custom-built VCG. Thus no separate VCG is necessary, and the theorem prover can be employed both to generate and to discharge the verification conditions. The method handles both partial and total correctness. It is also compositional in that the correctness of a subroutine needs to be proved once, rather than at each call site. The method has been used to verify several machine-level programs using the ACL2 theorem prover.

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“…Using and verifying guards is optional in ACL2, and all procedures need to be completely defined in case that guard checking mode is turned off. ACL2 has a first-order programming language, so second-order procedures such as map or foldl cannot be defined in a way that would allow procedure calls like map(f, l) for concrete functions f [5,7].…”

Section: Related Workmentioning

confidence: 99%

Second-Order Programs with Preconditions

Aderhold

2010

Verification, Induction, Termination Analysis

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Abstract. In the implementation of procedures, developers often assume that the input satisfies certain properties; for example, binary search assumes the array to be sorted. Such requirements on the input can be formally expressed as preconditions of procedures. If a secondorder procedure p (e.g., map or foldl ) is called with a first-order procedure f that has a precondition, the question arises whether p will call f only with arguments that satisfy the precondition of f . In this paper, we propose a method to statically analyze if all procedure calls in a given second-order program satisfy the respective preconditions. In particular, we consider indirect calls of procedures that are passed as an argument to a second-order procedure.

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Meta Reasoning in ACL2

Cited by 20 publications

References 2 publications

Proving a specific type of inequality theorems in ACL2

Proving a specific type of inequality theorems in ACL2

Verification Condition Generation Via Theorem Proving

Second-Order Programs with Preconditions

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