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14
Theory Interpretation in Simple Type Theory
 HIGHERORDER ALGEBRA, LOGIC, AND TERM REWRITING, VOLUME 816 OF LECTURE NOTES IN COMPUTER SCIENCE
, 1993
"... Theory interpretation is a logical technique for relating one axiomatic theory to another with important applications in mathematics and computer science as well as in logic itself. This paper presents a method for theory interpretation in a version of simple type theory, called lutins, which admit ..."
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Cited by 36 (17 self)
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Theory interpretation is a logical technique for relating one axiomatic theory to another with important applications in mathematics and computer science as well as in logic itself. This paper presents a method for theory interpretation in a version of simple type theory, called lutins, which admits partial functions and subtypes. The method is patterned on the standard approach to theory interpretation in rstorder logic. Although the method is based on a nonclassical version of simple type theory, it is intended as a guide for theory interpretation in classical simple type theories as well as in predicate logics with partial functions.
Locales: A sectioning concept for Isabelle
 IN BERTOT ET AL
, 1999
"... Locales are a means to define local scopes for the interactive proving process of the theorem prover Isabelle. They delimit a range in which fixed assumption are made, and theorems are proved that depend on these assumptions. A locale may also contain constants defined locally and associated with pr ..."
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Cited by 35 (10 self)
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Locales are a means to define local scopes for the interactive proving process of the theorem prover Isabelle. They delimit a range in which fixed assumption are made, and theorems are proved that depend on these assumptions. A locale may also contain constants defined locally and associated with pretty printing syntax. Locales can be seen as a simple form of modules. They are similar to reasoning and similar applications of theorem provers. This paper motivates the concept of locales by examples from abstract algebraic reasoning. It also discusses some implementation issues.
Specification of the IEEE854 FloatingPoint Standard in HOL and PVS
, 1995
"... The IEEE854 Standard for radixindependent floatingpoint arithmetic has been partially defined within two mechanical verification systems. We present the specification of key parts of the standard in both HOL and PVS. This effort to formalize IEEE854 has given the opportunity to compare the st ..."
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Cited by 24 (1 self)
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The IEEE854 Standard for radixindependent floatingpoint arithmetic has been partially defined within two mechanical verification systems. We present the specification of key parts of the standard in both HOL and PVS. This effort to formalize IEEE854 has given the opportunity to compare the styles imposed by the two verification systems on the specification.
A Theory of Generic Interpreters
, 1993
"... We present an abstract theory of interpreters. Interpreters are models of computation that are specifically designed for use as templates in computer system specification and verification. The generic interpreter theory contains an abstract representation which serves as an interface to the theory a ..."
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Cited by 13 (3 self)
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We present an abstract theory of interpreters. Interpreters are models of computation that are specifically designed for use as templates in computer system specification and verification. The generic interpreter theory contains an abstract representation which serves as an interface to the theory and as a guide to specification. A set of theory obligations ensure that the theory is being used correctly and provide a guide to system verification. The generic interpreter theory provides a methodology for deriving important definitions and lemmas that were previously obtained in a largely ad hoc fashion. Many of the complex data and temporal abstractions are done in the abstract theory and need not be redone when the theory is used.
Modular Reasoning in Isabelle
, 1999
"... The concept of locales for Isabelle enables local definition and assumption for interactive mechanical proofs. Furthermore, dependent types are constructed in Isabelle/HOL for first class representation of structure. These two concepts are introduced briefly. Although each of them has proved use ..."
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Cited by 13 (2 self)
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The concept of locales for Isabelle enables local definition and assumption for interactive mechanical proofs. Furthermore, dependent types are constructed in Isabelle/HOL for first class representation of structure. These two concepts are introduced briefly. Although each of them has proved useful in itself, their real power lies in combination. This paper illustrates by examples from abstract algebra how this combination works and argues that it enables modular reasoning.
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...
Mechanised Formal Reasoning About Modular Programs
, 2000
"... of the Thesis . ..................... 1 1.2 Motivation . . . ......................... 2 1.3 Outline of the Thesis . . ..................... 4 2 The Refinement Calculus theory 7 2.1 Introduction . . . ......................... 7 2.2 The Refinement Calculus . . . ................. 8 2.3 Underlyi ..."
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Cited by 6 (0 self)
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of the Thesis . ..................... 1 1.2 Motivation . . . ......................... 2 1.3 Outline of the Thesis . . ..................... 4 2 The Refinement Calculus theory 7 2.1 Introduction . . . ......................... 7 2.2 The Refinement Calculus . . . ................. 8 2.3 Underlying Logic ......................... 10 2.4 State Predicates and Predicate Transformers ......... 11 2.5 Language of Program Statements . . . ............. 13 2.6 Data Refinement ......................... 17 2.7 History . ............................. 18 3 Mechanisation of the Refinement Calculus 19 3.1 Introduction . . . ......................... 19 3.2 The HOL Proof Assistant . . . ................. 20 3.3 The HOL Theory of the Refinement Calculus ......... 23 3.4 Using Window Inference ..................... 27 3.5 The Refinement Calculator Tool . . . ............. 30 3.6 Extensions of the Refinement Calculator . . . ......... 33 3.7 Conclusions . . . ......................... 34 ...
Embedding Hardware Description Languages in Proof Systems
 In Proceedings of the XIII Conference of the Brazilian Computer Society, Florianopolis
, 1992
"... The aim of this thesis is to investigate the integration of hardware description languages (hdls) and automated proof systems. Simulation of circuit designs written in an hdl is an important method of testing their correctness. However, due to the combinatorial explosion of possible inputs it is not ..."
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Cited by 6 (1 self)
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The aim of this thesis is to investigate the integration of hardware description languages (hdls) and automated proof systems. Simulation of circuit designs written in an hdl is an important method of testing their correctness. However, due to the combinatorial explosion of possible inputs it is not feasible to verify designs using simulation alone. Formal hardware verification, using a proof system, has tried to address this issue. Whilst some mediumsized designs have been (partially) verified, industrial takeup of formal methods has been slow. This is partly due to the use of specialised, nonstandard notations employed in various formalisms. By embedding a hardware description language in a proof system we hope to clarify the semantics of the particular hdl, and present a more standard interface to formal methodologies. We have given a new static structural operational semantics for a subset of the ella hardware description language. The formal dynamic semantics of this subset is based on an existing informal model.
Alexandria: Libraries of abstract, verified hardware modules
 In 2nd Workshop on Libraries, Component Modeling, and Quality Assurance
, 1997
"... Abstract Individual pieces to support hierarchical verification have existed for several years but have not been integrated into one tool. The tool for creating abstract libraries described in this paper ties the various techniques into one package designed to support hierarchical verification among ..."
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Cited by 5 (5 self)
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Abstract Individual pieces to support hierarchical verification have existed for several years but have not been integrated into one tool. The tool for creating abstract libraries described in this paper ties the various techniques into one package designed to support hierarchical verification among collaborating researchers. In these libraries, predicate types organize specification information, abstract theories model modular components and public key encryption increases the trustworthiness of externally proven theorems. A prototype tool for creating libraries called Alexandria has been implemented in the HOL90 proof assistant for use with the BOLT HDL using PGP encryption to sign verified theorems. 1 Introduction Useful hardware modules are complex and often designed by teams using existing components. Hardware verification on the other hand is typically performed by one person making no use of preverified moduleseven if other modules exist. Hierarchical verification of largescale designs is impeded by several obstacles:
Specifying InstructionSet Architectures in HOL: A Primer
, 1994
"... . This paper presents techniques for specifying microprocessor instruction set syntax and semantics in the HOL theorem proving system. The paper describes the use of abstract representations for operators and data, gives techniques for specifying instruction set syntax, outlines the use of recor ..."
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Cited by 5 (0 self)
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. This paper presents techniques for specifying microprocessor instruction set syntax and semantics in the HOL theorem proving system. The paper describes the use of abstract representations for operators and data, gives techniques for specifying instruction set syntax, outlines the use of records in specifying semantic domains, presents the creation of parameterized semantic frameworks, and shows how all of these can be used to create a semantics for a microprocessor instruction set. The verified microprocessor Uinta provides examples for each of these. 1 Introduction Much has been written over the years regarding the formal specification and verification of microprocessors [CCLO88, Bow87, Hun87, Coh88b, Coh88a, Gor83, Joy88, Hun89, Joy89, SB90, Her92, SWL93, TK93]. These efforts use many different proof systems and styles. We have verified a number of microprocessors in the HOL theorem proving system [Win90a, Win90b, Win94, WC94] and have developed techniques which clarify t...