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Proving existential theorems when importing results from MDG to HOL
 TPHOLS 2001 SUPPLEMENTAL PROCEEDINGS, INFORMATIC RESEARCH REPORT EDIINFRR0046
, 2001
"... An existential theorem, for the specification or implementation of hardware, states that for any inputs there must exist at least one output which is consistent with it. It is proved to prevent an inconsistent model being produced and it is required to formally import the verification result from on ..."
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An existential theorem, for the specification or implementation of hardware, states that for any inputs there must exist at least one output which is consistent with it. It is proved to prevent an inconsistent model being produced and it is required to formally import the verification result from one verification system to another system. In this paper, we investigate the verification of the existential theorems of hardware specifications and implementations. Whilst much of the approach is generally applicable, we specifically consider a hybrid system linking the MDG hardware verification system with the HOL interactive proof system. We investigate existential theorems based on the syntax and semantics of the MDG input language (MDGHDL) in HOL. We define an output representation for each component in the MDGHDL component library. We summarize a general method which is used to prove the existential theorem for any MDGHDL program. The method can also be used to solve other existentially quantified goals.
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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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.
Formally Linking MDG and HOL Based on a Verified MDG System
"... We describe an approach for formally linking a symbolic state enumeration system and a theorem proving system based on a verified version of the former. It has been realized using a simplified version of the MDG system and the HOL system. Firstly, we have verified aspects of correctness of a simp ..."
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We describe an approach for formally linking a symbolic state enumeration system and a theorem proving system based on a verified version of the former. It has been realized using a simplified version of the MDG system and the HOL system. Firstly, we have verified aspects of correctness of a simplified version of the MDG system. We have made certain that the semantics of a program is preserved in those of its translated form. Secondly, we have provided a formal linkage between the MDG system and the HOL system based on importing theorems. The MDG verification results can be formally imported into HOL to form a HOL theorem. Thirdly, we have combined the translator correctness theorems and importing theorems. This allows the MDG verification results to be imported in terms of a high level language (MDGHDL) rather than a low level language. We also summarize a general method to prove existential theorems for the design. The feasibility of this approach is demonstrated in a case study that integrates two applications: hardware verification (in MDG) and usability verification (in HOL). A single HOL theorem is proved that integrates the two results.
, Soene Tahar
"... Abstract. An existential theorem, for the specication or implementation of hardware, states that for any inputs there must exist at least one output which is consistent with it. It is proved to prevent an inconsistent model being produced and it is required to formally import the verication result ..."
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Abstract. An existential theorem, for the specication or implementation of hardware, states that for any inputs there must exist at least one output which is consistent with it. It is proved to prevent an inconsistent model being produced and it is required to formally import the verication result from one verication system to another system. In this paper, we investigate the verication of the existential theorems of hardware specications and implementations. Whilst much of the approach is generally applicable, we specically consider a hybrid system linking the MDG hardware verication system with the HOL interactive proof system. We investigate existential theorems based on the syntax and semantics of the MDG input language (MDGHDL) in HOL. We de ne an output representation for each component in the MDGHDL component library. We summarize a general method which is used to prove the existential theorem for any MDGHDL program. The method can also be used to solve other existentially quantied goals. 1