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Faster Proof Checking in the Edinburgh Logical Framework
 In 18th International Conference on Automated Deduction
, 2002
"... This paper describes optimizations for checking proofs represented in the Edinburgh Logical Framework (LF). The optimizations allow large proofs to be checked eciently which cannot feasibly be checked using the standard algorithm for LF. The crucial optimization is a form of result caching. To f ..."
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Cited by 17 (3 self)
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This paper describes optimizations for checking proofs represented in the Edinburgh Logical Framework (LF). The optimizations allow large proofs to be checked eciently which cannot feasibly be checked using the standard algorithm for LF. The crucial optimization is a form of result caching. To formalize this optimization, a path calculus for LF is developed and shown equivalent to a standard calculus.
Generating Proofs from a Decision Procedure
 Proceedings of the FLoC Workshop on RunTime Result Verification
, 1999
"... Fully automatic decision procedures are used to improve performance in many different applications of formal verification. In most cases, the decision procedures are treated as trusted components of the verification system. Because the decision procedures may be experimental and highly complex to ..."
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Cited by 17 (0 self)
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Fully automatic decision procedures are used to improve performance in many different applications of formal verification. In most cases, the decision procedures are treated as trusted components of the verification system. Because the decision procedures may be experimental and highly complex tools, it is desirable to have a way of independently confirming their results.
Deriving Safety Cases for the Formal Safety Certification of Automatically Generated Code
"... We present an approach to systematically derive safety cases for automatically generated code from information collected during a formal, Hoarestyle safety certification of the code. This safety case makes explicit the formal and informal reasoning principles, and reveals the toplevel assumptions ..."
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Cited by 6 (1 self)
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We present an approach to systematically derive safety cases for automatically generated code from information collected during a formal, Hoarestyle safety certification of the code. This safety case makes explicit the formal and informal reasoning principles, and reveals the toplevel assumptions and external dependencies that must be taken into account; however, the evidence still comes from the formal safety proofs. It uses a generic goalbased argument that is instantiated with respect to the certified safety property (i.e., safety claims) and the program. This will be combined with a complementary safety case that argues the safety of the framework itself, in particular the correctness of the Hoare rules with respect to the safety property and the trustworthiness of the certification system and its individual components.
Practical Proof Checking for Program Certification
 Proceedings of the CADE20 Workshop on Empirically Successful Classical Automated Reasoning (ESCAR’05
, 2005
"... Program certification aims to provide explicit evidence that a program meets a specified level of safety. This evidence must be independently reproducible and verifiable. We have developed a system, based on theorem proving, that generates proofs that autogenerated aerospace code adheres to a numbe ..."
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Cited by 5 (4 self)
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Program certification aims to provide explicit evidence that a program meets a specified level of safety. This evidence must be independently reproducible and verifiable. We have developed a system, based on theorem proving, that generates proofs that autogenerated aerospace code adheres to a number of safety policies. For certification purposes, these proofs need to be verified by a proof checker. Here, we describe and evaluate a semantic derivation verification approach to proof checking. The evaluation is based on 109 safety obligations that are attempted by EP and SPASS. Our system is able to verify 129 out of the 131 proofs found by the two provers. The majority of the proofs are checked completely in less than 15 seconds wall clock time. This shows that the proof checking task arising from a substantial prover application is practically tractable. 1
Producing Proofs from an Arithmetic Decision Procedure in Elliptical LF
 In 3rd International Workshop on Logical Frameworks and MetaLanguages
"... Software that can produce independently checkable evidence for the correctness of its output has received recent attention for use in certifying compilers and proofcarrying code. CVC (“a Cooperating Validity Checker) is a proofproducing validity checker for a decidable fragment of firstorder logic ..."
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Cited by 3 (1 self)
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Software that can produce independently checkable evidence for the correctness of its output has received recent attention for use in certifying compilers and proofcarrying code. CVC (“a Cooperating Validity Checker) is a proofproducing validity checker for a decidable fragment of firstorder logic enriched with background theories. This paper describes how proofs of valid formulas are produced from the decision procedure for linear real arithmetic implemented in CVC. It is shown how extensions to LF which support proof rules schematic in an arity (“elliptical ” rules) are very convenient for this purpose. 1
Embedding and Verification of an MDGHDL Translator in HOL
, 2000
"... We investigate the verification of a translation phase of the Multiway Decision Graphs (MDG) verification system using the Higher Order Logic (HOL) theorem prover. In this paper, we deeply embed the semantics of a subset of the MDGHDL language and its Table subset into HOL. We define a set of funct ..."
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Cited by 2 (1 self)
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We investigate the verification of a translation phase of the Multiway Decision Graphs (MDG) verification system using the Higher Order Logic (HOL) theorem prover. In this paper, we deeply embed the semantics of a subset of the MDGHDL language and its Table subset into HOL. We define a set of functions which translate this subset MDGHDL language to its Table subset. A correctness theorem for this translator, which quantifies over its syntactic structure, has been proved. This theorem states that the semantics of the MDGHDL program is equivalent to the semantics of its Table subset.
Proof Production in Decision Procedures
, 2002
"... Software that can produce independently checkable evidence for the correctness of its output has received recent attention for use in certifying compilers and proofcarrying code. This paper describes how proofs of valid formulas are produced by the new version of the Stanford Validity Checker (SVC) ..."
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Cited by 1 (1 self)
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Software that can produce independently checkable evidence for the correctness of its output has received recent attention for use in certifying compilers and proofcarrying code. This paper describes how proofs of valid formulas are produced by the new version of the Stanford Validity Checker (SVC), a highperformance decision procedure for a decidable fragment of firstorder logic enriched with background theories.
Providing a Formal Linkage between MDG and
, 2002
"... The contribution of this thesis is that we have produced a methodology which can provide a formal linkage between a symbolic state enumeration system and a theorem proving system based on a verified symbolic state enumeration system. The methodology has been partly realized in two simplified version ..."
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The contribution of this thesis is that we have produced a methodology which can provide a formal linkage between a symbolic state enumeration system and a theorem proving system based on a verified symbolic state enumeration system. The methodology has been partly realized in two simplified versions of the MDG system
(Datum der Disputation)
, 2002
"... The observation that the development of mathematical theories and the development of information systems essentially involves the same activities, namely modeling, specification, and validation, with special attention to important aspects such as modularity, reusability and information hiding and un ..."
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The observation that the development of mathematical theories and the development of information systems essentially involves the same activities, namely modeling, specification, and validation, with special attention to important aspects such as modularity, reusability and information hiding and under consideration of related notions of calculation, computation, and proof, has on many occasions challenged my mind with the question if the apparently artificial gap, which is for instance especially evident between the disciplines of mathematics and software engineering, could eventually be reduced, possibly even on the basis of a unified language. Although this thesis does by no means answer this difficult question, I have learned much in the recent years, especially during the occupation with my thesis, about several formalisms which seem to contribute to this goal in their own limited way. Two of these formalisms, type theory and rewriting logic, constitute the basis of this thesis, which is concerned with new applications and a possible integration of these approaches. It is needless to say that this thesis would not have been possible without the great