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27
Merging HOL with Set Theory  preliminary experiments
, 1994
"... Set theory is the standard foundation for mathematics, but the majority of general purpose mechanised proof assistants support versions of type theory (higher order logic). Examples include Alf, Automath, Coq, EHDM, HOL, IMPS, LAMBDA, LEGO, Nuprl, PVS and Veritas. For many applications type theory w ..."
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Cited by 11 (1 self)
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Set theory is the standard foundation for mathematics, but the majority of general purpose mechanised proof assistants support versions of type theory (higher order logic). Examples include Alf, Automath, Coq, EHDM, HOL, IMPS, LAMBDA, LEGO, Nuprl, PVS and Veritas. For many applications type theory works well and provides, for specification, the benefits of typechecking that are wellknown in programming. However, there are areas where types get in the way or seem unmotivated. Furthermore, most people with a scientific or engineering background already know set theory, whereas type theory may appear inaccessable and so be an obstacle to the uptake of proof assistants based on it. This paper describes some experiments (using HOL) in combining set theory and type theory; the aim is to get the best of both worlds in a single system. Three approaches have been tried, all based on an axiomatically specified type V of ZFlike sets: (i) HOL is used without any additions besides V; (ii) an emb...
A Mechanized Theory of the picalculus in HOL
, 1992
"... : The ßcalculus is a process algebra for modelling concurrent systems in which the pattern of communication between processes may change over time. This paper describes the results of preliminary work on a definitional formal theory of the ßcalculus in higher order logic using the HOL theorem prov ..."
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Cited by 8 (0 self)
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: The ßcalculus is a process algebra for modelling concurrent systems in which the pattern of communication between processes may change over time. This paper describes the results of preliminary work on a definitional formal theory of the ßcalculus in higher order logic using the HOL theorem prover. The ultimate goal of this work is to provide practical mechanized support for reasoning with the ßcalculus about applications. Introduction The ßcalculus [17, 18] is a process algebra proposed by Milner, Parrow and Walker for modelling concurrent systems in which the pattern of interconnection between processes may change over time. This paper describes work on a mechanized formal theory of the ßcalculus in higher order logic using the HOL theorem prover [8]. The main aim of this work is to construct a practical and sound theoremproving tool to support reasoning about applications using the ßcalculus, as well as metatheoretic reasoning about the ßcalculus itself. Four general prin...
Set Theory, Higher Order Logic or Both?
"... The majority of general purpose mechanised proof assistants support versions of typed higher order logic, even though set theory is the standard foundation for mathematics. For many applications higher order logic works well and provides, for specification, the benefits of typechecking that are ..."
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Cited by 7 (0 self)
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The majority of general purpose mechanised proof assistants support versions of typed higher order logic, even though set theory is the standard foundation for mathematics. For many applications higher order logic works well and provides, for specification, the benefits of typechecking that are wellknown in programming. However, there are areas where types get in the way or seem unmotivated. Furthermore, most people with a scientific or engineering background already know set theory, but not higher order logic. This paper discusses some approaches to getting the best of both worlds: the expressiveness and standardness of set theory with the efficient treatment of functions provided by typed higher order logic.
Using HOL to study Sugar 2.0 semantics
 Track B Proceedings of the 15th International Conference on Theorem Proving in Higher Order Logics, TPHOLs2002, volume CP2002211736 of NASA Conference Proceedings
, 2002
"... Abstract. The Accellera standardspromoting organisation has selected Sugar 2.0, IBM’s formal specification language, as a standard that it says will drive assertionbased verification. Sugar 2.0 combines aspects of Interval Temporal Logic (ITL), Linear Temporal Logic (LTL) and Computation Tree Logi ..."
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Cited by 5 (2 self)
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Abstract. The Accellera standardspromoting organisation has selected Sugar 2.0, IBM’s formal specification language, as a standard that it says will drive assertionbased verification. Sugar 2.0 combines aspects of Interval Temporal Logic (ITL), Linear Temporal Logic (LTL) and Computation Tree Logic (CTL) into a property language suitable for both formal verification and use with simulation test benchs. As industrial strength languages go it is remarkably elegant, consisting of a small kernel conservatively extended by numerous definitions. We are constructing a semantic embedding of Sugar 2.0 in the version of higher order logic supported by the HOL system. To ‘sanity check ’ the semantics we tried to prove some simple properties and as a result a few bugs were discovered. Further analysis may well reveal more. We are contemplating a variety of applications of the mechanised semantics, including the exploitation of existing work to build a Sugar model checker inside HOL. In the longer term we want to investigate the use
STRUCTURAL EMBEDDINGS: MECHANIZATION WITH METHOD
, 1999
"... The most powerful tools for analysis of formal specifications are generalpurpose theorem provers and model checkers, but these tools provide scant methodological support. Conversely, those approaches that do provide a welldeveloped method generally have less powerful automation. It is natural, the ..."
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Cited by 5 (1 self)
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The most powerful tools for analysis of formal specifications are generalpurpose theorem provers and model checkers, but these tools provide scant methodological support. Conversely, those approaches that do provide a welldeveloped method generally have less powerful automation. It is natural, therefore, to try to combine the betterdeveloped methods with the more powerful generalpurpose tools. An obstacle is that the methods and the tools often employ very different logics. We argue that methods are separable from their logics and are largely concerned with the structure and organization of specifications. We propose a technique called structural embedding that allows the structural elements of a method to be supported by a generalpurpose tool, while substituting the logic of the tool for that of the method. We have found this technique quite e ective and we provide some examples of its application. We also suggest how generalpurpose systems could be restructured to support this activity better.
A Functional Approach for Formalizing Regular Hardware Structures
"... An approach for formalizing hardware behaviour is presented which is based on a small functional programming language called primitive ML (PML). Since the basic constructs of PML are simply typed terms, PML lends itself both to simulation and verification. The semantics of PML is formally embe ..."
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Cited by 4 (3 self)
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An approach for formalizing hardware behaviour is presented which is based on a small functional programming language called primitive ML (PML). Since the basic constructs of PML are simply typed terms, PML lends itself both to simulation and verification. The semantics of PML is formally embedded in higherorder logic. The formalization
From specifications to code in Casl
 Proc. 9th Intl. Conf. on Algebraic Methodology and Software Technology, AMAST'02. Springer LNCS 2422, 114 (2002). [ABK + 02
, 2002
"... The status of the Common Framework Initiative (CoFI) and the Common Algebraic Specification Language (Casl) are briefly presented. ..."
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Cited by 4 (1 self)
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The status of the Common Framework Initiative (CoFI) and the Common Algebraic Specification Language (Casl) are briefly presented.
Application Specific Higher Order Logic Theorem Proving
 in Proc. of the Verification Workshop  VERIFY’02, S. Autexier and
, 2002
"... Theorem proving allows the formal verification of the correctness of very large systems. In order to increase the acceptance of theorem proving systems during the design process, we implemented higher order logic proof systems for ANSIC and Verilog within a framework for application specific proo ..."
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Theorem proving allows the formal verification of the correctness of very large systems. In order to increase the acceptance of theorem proving systems during the design process, we implemented higher order logic proof systems for ANSIC and Verilog within a framework for application specific proof systems. Furthermore, we implement the language of the PVS theorem prover as wellestablished higher order specification language. The tool allows the verification of the design languages using a PVS specification and the verification of hardware designs using a C program as specification. We implement powerful decision procedures using Model Checkers and satisfiability checkers. We provide experimental results that compare the performance of our tool with PVS on large industrial scale hardware examples.
Automatic Verification of Arithmetic Circuits in RTL using Term Rewriting Systems
 In Accepted in IEEE Transactions on Computers
, 2003
"... for being my quest... for showing me the way... Acknowledgments I’d like to thank my advisor, Dr. Jacob Abraham for his invaluable support and guidance through the course of this work. His novel ideas, infectious enthusiasm and intellectually stimulating discussions kept me motivated and encouraged ..."
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Cited by 4 (1 self)
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for being my quest... for showing me the way... Acknowledgments I’d like to thank my advisor, Dr. Jacob Abraham for his invaluable support and guidance through the course of this work. His novel ideas, infectious enthusiasm and intellectually stimulating discussions kept me motivated and encouraged through the entire course of my Graduate Studies. Thank you Sir, for your firm belief in me. It kept me going in the most trying times. I’d also like to thank my colleague and fellow PhD student, Vinod Viswanath, for his support and assistance through my Masters. His experience, insight, resourcefulness, skills and alacrity have been a priceless source of inspiration and and help in obtaining this degree. Without his contribution, I don’t imagine I could have got this far. I’d like to thank Linda, Andrew, Shirley and Ruth for their promptness and efficiency in matters that required their attention. I’d also like to thank my labmates for their cooperation. I’d like to thank my friends Siddarth and Kunal, for bringing a lot of joy in my life in the U.S. Lastly, I’d like to thank my parents and sister for making me who I am. v