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Metatheory and Reflection in Theorem Proving: A Survey and Critique
, 1995
"... One way to ensure correctness of the inference performed by computer theorem provers is to force all proofs to be done step by step in a simple, more or less traditional, deductive system. Using techniques pioneered in Edinburgh LCF, this can be made palatable. However, some believe such an appro ..."
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Cited by 53 (2 self)
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One way to ensure correctness of the inference performed by computer theorem provers is to force all proofs to be done step by step in a simple, more or less traditional, deductive system. Using techniques pioneered in Edinburgh LCF, this can be made palatable. However, some believe such an approach will never be efficient enough for large, complex proofs. One alternative, commonly called reflection, is to analyze proofs using a second layer of logic, a metalogic, and so justify abbreviating or simplifying proofs, making the kinds of shortcuts humans often do or appealing to specialized decision algorithms. In this paper we contrast the fullyexpansive LCF approach with the use of reflection. We put forward arguments to suggest that the inadequacy of the LCF approach has not been adequately demonstrated, and neither has the practical utility of reflection (notwithstanding its undoubted intellectual interest). The LCF system with which we are most concerned is the HOL proof ...
Extending the HOL theorem prover with a Computer Algebra System to Reason about the Reals
 Higher Order Logic Theorem Proving and its Applications (HUG `93
, 1993
"... In this paper we describe an environment for reasoning about the reals which combines the rigour of a theorem prover with the power of a computer algebra system. 1 Introduction Computer theorem provers are a topic of research interest in their own right. However much of their popularity stems from ..."
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Cited by 33 (4 self)
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In this paper we describe an environment for reasoning about the reals which combines the rigour of a theorem prover with the power of a computer algebra system. 1 Introduction Computer theorem provers are a topic of research interest in their own right. However much of their popularity stems from their application in computeraided verification, i.e. proving that designs of electronic or computer systems, programs, protocols and cryptosystems satisfy certain properties. Such proofs, as compared with the proofs one finds in mathematics books, usually involve less sophisticated central ideas, but contain far more technical Supported by the Science and Engineering Research Council, UK. y Supported by SERC grant GR/G 33837 and a grant from DSTO Australia. details and therefore tend to be much more difficult for humans to write or check without making mistakes. Hence it is appealing to let computers help. Some fundamental mathematical theories, such as arithmetic, are usually requi...
First Steps Towards Automating Hardware Proofs in HOL (Extended Abstract)
, 1991
"... ) Ramayya Kumar, Thomas Kropf, Klaus Schneider University of Karlsruhe, Institute of Computer Design and Fault Tolerance (Prof. Dr. ##. Schmid) P.O. Box 6980, W7500 Karlsruhe, Germany 1. INTRODUCTION The use of higherorder logic and an associated interactive theorem proving environment for hardwar ..."
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Cited by 2 (2 self)
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) Ramayya Kumar, Thomas Kropf, Klaus Schneider University of Karlsruhe, Institute of Computer Design and Fault Tolerance (Prof. Dr. ##. Schmid) P.O. Box 6980, W7500 Karlsruhe, Germany 1. INTRODUCTION The use of higherorder logic and an associated interactive theorem proving environment for hardware verification has established itself as an important technique for formal hardware validation [CaGM 86, FFFH 89]. In spite of the fact that such techniques are powerful and can be used for validation of complex systems, they continue to remain purely within the purview of theorem proving specialists. The only way to bring such a system closer to circuit designers is to augment the degree of automation and provide a camouflaged environment which mirrors the designer's view of hardware. The first step in this direction is to automate the proofs of all firstorder and simple higherorder statements, within such systems, which has been achieved by the tool FAUST [KuKS 91, ScKK 91a]. Further aut...