Verification of Parameterised FPGA Circuit Descriptions with Layout ...

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CHAPTER 2. BACKGROUND AND RELATED WORK 26 with a few primitive inference rules and axioms. HOL has only a few kinds of primitive terms: variables, constants, function applications and λ-abstractions with all other notations are derived from them (it is worth remembering that higher-order logic is based on typed λ-calculus). This simple core logic means that eventually all reasoning should be reduced to these primitive inference steps and this approach is quite low level relative to other theorem provers. HOL uses tactics to guide the system in the application of primitive steps toward solving theorem proving goals. A tactic can be regarded as a high level proof step where the primitive steps necessary to achieve the same functionality are carried out automatically. Tacticals are functions are used to combine a series of tactics into a larger step of inference. HOL has been used extensively in hardware verification, including the verification of full microprocessors [18, 33]. PVS, the Prototype Verification System [59], is a general-purpose interactive verification environment developed at SRI International. The specification language of PVS is based on higher-order logic but also incorporates predicate types and subtypes that allow the definition of partial functions. These constrained types lead to a type checking process that is undecidable and type correctness may incur additional proof obligations for the user to manage. Inference steps in PVS proceed at a high level, with primitive rules for operations such as boolean simplification and decision procedures for linear arithmetic. Unlike HOL it is therefore not necessary to rely on tactics to the same extent in order to build usable proof steps for the interactive environment. Strategies, which are analogous to HOL tactics, can be constructed to automate a sequence of PVS inference steps. PVS is less customisable than other theorem provers, however the high degree of automation makes it a very practical tool. One example of the large-scale use of PVS is the verification of the AAMP5 microprocessor [79], a commercial processor with around half a million transistors. ACL2 [34] is an automated reasoning system based on Boyer-Moore logic [9], a first-order, quantifier-free logic. ACL’s logic is a very small subset of Common Lisp, a standard list
CHAPTER 2. BACKGROUND AND RELATED WORK 27 processing language. Models of all kinds of systems can be built in ACL2 and, once written, can be executed as Lisp programs. Since ACL2 is based on a first-order logic it is considerably less expressive than theorem provers such as HOL which use higher-order logic, however the simply logic allows a very high degree of automation with little user intervention required. The user directs the proof search procedure by proving supporting lemmas. ACL2 has been used to verify some industrial processors, for example a Motorola digital signal processing chip [10]. Isabelle [61] is a descendant of the LCF system [21]. Unlike most theorem provers which focus on providing a single underlying formalism, Isabelle is intended to be used as a general platform for the implementation of theorem provers in a large variety of logics. The motiva- tion behind the creation of Isabelle is that, while theorem proving is an extremely difficult problem, most of the difficulties have to do with logic in general rather than any particular logic. A generic theorem prover will probably never provide the full range of support that a dedicated prover for each logic could, however by reducing the “barriers to entry” it makes it more likely that some proof support will be available for less common or application specific logics. Furthermore, since it is currently easier to learn a logic than to learn how to use a theorem prover it is also easier for users to learn a single prover and then use the most appropriate logic for their needs. 2.4.6 Embeddings In order to using theorem proving for verification of hardware written in a description language it is necessary to develop an implementation of the language in a logic within a theorem prover. This process is referred to as embedding and broadly speaking these can be further sub-divided [8] into deep embeddings and shallow embeddings. A shallow embedding, or semantic embedding, involves the definition of the meaning of the language directly in terms of the connectives in the logic. A deep embedding is characterised by the definition of the syntax of a language in a formal logic, typically as some sort of abstract data type and the definition of a semantic meaning function.
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Page 3 and 4: Acknowledgements Firstly, I’d lik
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CHAPTER 4. VERIFYING CIRCUIT LAYOUT
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CHAPTER 6. LAYOUT CASE STUDIES 131
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CHAPTER 7. CONCLUSION AND FUTURE WO
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Bibliography [1] A. Aggoun and N. B
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BIBLIOGRAPHY 177 [19] H. Gelernter.
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BIBLIOGRAPHY 179 [41] Y. Li and M.
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BIBLIOGRAPHY 181 [60] L. C. Paulson
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BIBLIOGRAPHY 183 [83] J. Voeten. On
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APPENDIX A. QUARTZ LANGUAGE GRAMMAR
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Appendix B Theoretical Basis for La
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APPENDIX B. THEORETICAL BASIS FOR L
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Appendix C Placed Combinator Librar
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