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The BoyerMoore Prover and Nuprl: An Experimental Comparison
 LOGICAL FRAMEWORKS
, 1991
"... We use an example to compare the BoyerMoore Theorem Prover and the Nuprl Proof Development System. The respective machine verifications of a version of Ramsey's theorem illustrate similarities and differences between the two systems. The proofs are compared using both quantitative and nonquantitat ..."
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Cited by 24 (8 self)
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We use an example to compare the BoyerMoore Theorem Prover and the Nuprl Proof Development System. The respective machine verifications of a version of Ramsey's theorem illustrate similarities and differences between the two systems. The proofs are compared using both quantitative and nonquantitative measures, and we examine difficulties in making such comparisons.
Connectionbased Theorem Proving in Classical and Nonclassical Logics
 Journal of Universal Computer Science
, 1999
"... Abstract: We present a uniform procedure for proof search in classical logic, intuitionistic logic, various modal logics, and fragments of linear logic. It is based on matrix characterizations of validity in these logics and extends Bibel’s connection method, originally developed for classical logic ..."
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Cited by 22 (14 self)
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Abstract: We present a uniform procedure for proof search in classical logic, intuitionistic logic, various modal logics, and fragments of linear logic. It is based on matrix characterizations of validity in these logics and extends Bibel’s connection method, originally developed for classical logic, accordingly. Besides combining a variety of different logics it can also be used to guide the development of proofs in interactive proof assistants and shows how to integrate automated and interactive theorem proving. 1
Higher Order Logic
 In Handbook of Logic in Artificial Intelligence and Logic Programming
, 1994
"... Contents 1 Introduction : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2 2 The expressive power of second order Logic : : : : : : : : : : : 3 2.1 The language of second order logic : : : : : : : : : : : : : 3 2.2 Expressing size : : : : : : : : : : : : : : : : : : : : : : : : 4 2.3 Definin ..."
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Cited by 19 (0 self)
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Contents 1 Introduction : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2 2 The expressive power of second order Logic : : : : : : : : : : : 3 2.1 The language of second order logic : : : : : : : : : : : : : 3 2.2 Expressing size : : : : : : : : : : : : : : : : : : : : : : : : 4 2.3 Defining data types : : : : : : : : : : : : : : : : : : : : : 6 2.4 Describing processes : : : : : : : : : : : : : : : : : : : : : 8 2.5 Expressing convergence using second order validity : : : : : : : : : : : : : : : : : : : : : : : : : 9 2.6 Truth definitions: the analytical hierarchy : : : : : : : : 10 2.7 Inductive definitions : : : : : : : : : : : : : : : : : : : : : 13 3 Canonical semantics of higher order logic : : : : : : : : : : : : 15 3.1 Tarskian semantics of second order logic : : : : : : : : : 15 3.2 Function and re
Correct and UserFriendly Implementations of Transformation Systems
, 1996
"... . We present an approach to integrate several existing tools and methods to a technical framework for correctly developing and executing program transformations. The resulting systems enable program derivations in a userfriendly way. We illustrate the approach by proving and implementing the transf ..."
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Cited by 18 (9 self)
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. We present an approach to integrate several existing tools and methods to a technical framework for correctly developing and executing program transformations. The resulting systems enable program derivations in a userfriendly way. We illustrate the approach by proving and implementing the transformation Global Search on the basis of the tactical theorem prover Isabelle. A graphical userinterface based on the XWindow toolkit Tk provides user friendly access to the underlying machinery. 1 Introduction Development by transformation is a prominent approach in formal program development (CIP [Bau + 85], PROSPECTRA [HK 93], KIDS [Smi 90]). Many case studies have proven its feasibility and demonstrated how much more abstract and useroriented developments could be achieved than using usual postverification approaches (fundamental for systems like PVS [OSR 93]). One recent case study is [KW 95]; and a prominent one is [SPW 95] where a strategic transportation scheduling algorithm is de...
Moving proofsasprograms into practice
 In: Proceedings of the 12 th IEEE International Conference on Automated Software Engineering, IEEE Computer Society
, 1997
"... Proofs in the Nuprl system, an implementation of a constructive type theory, yield “correctbyconstruction ” programs. In this paper a new methodology is presented for extracting efficient and readable programs from inductive proofs. The resulting extracted programs are in a form suitable for use i ..."
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Cited by 18 (5 self)
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Proofs in the Nuprl system, an implementation of a constructive type theory, yield “correctbyconstruction ” programs. In this paper a new methodology is presented for extracting efficient and readable programs from inductive proofs. The resulting extracted programs are in a form suitable for use in hierarchical verifications in that they are amenable to clean partial evaluation via extensions to the Nuprl rewrite system. The method is based on two elements: specifications written with careful use of the Nuprl settype to restrict the extracts to strictly computational content; and on proofs that use induction tactics that generate extracts using familiar fixedpoint combinators of the untyped lambda calculus. In this paper the methodology is described and its application is illustrated by example. 1.
A Simple Model for Quotient Types
 Proceedings of TLCA'95, volume 902 of Lecture Notes in Computer Science
, 1995
"... . We give an interpretation of quotient types within in a dependent type theory with an impredicative universe of propositions (Calculus of Constructions). In the model, type dependency arises only at the propositional level, therefore universes and large eliminations cannot be interpreted. In excha ..."
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Cited by 17 (0 self)
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. We give an interpretation of quotient types within in a dependent type theory with an impredicative universe of propositions (Calculus of Constructions). In the model, type dependency arises only at the propositional level, therefore universes and large eliminations cannot be interpreted. In exchange, the model is much simpler and more intuitive than the one proposed by the author in [10]. Moreover, we interpret a choice operator for quotient types that, under certain restrictions, allows one to recover a representative from an equivalence class. Since the model is constructed syntactically, the interpretation function from the syntax with quotient types to the model gives rise to a procedure which eliminates quotient types by replacing propositional equality by equality relations defined by induction on the type structure ("book equalities"). 1 Introduction Intensional type theories like the Calculus of Constructions have been proposed as a framework in which to formalise mathemati...
Generating Proofs from a Decision Procedure
 Proceedings of the FLoC Workshop on RunTime Result Verification
, 1999
"... Fully automatic decision procedures are used to improve performance in many different applications of formal verification. In most cases, the decision procedures are treated as trusted components of the verification system. Because the decision procedures may be experimental and highly complex to ..."
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Cited by 16 (0 self)
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Fully automatic decision procedures are used to improve performance in many different applications of formal verification. In most cases, the decision procedures are treated as trusted components of the verification system. Because the decision procedures may be experimental and highly complex tools, it is desirable to have a way of independently confirming their results.
TPS: A TheoremProving System for Classical Type Theory
, 1996
"... . This is description of TPS, a theoremproving system for classical type theory (Church's typed #calculus). TPS has been designed to be a general research tool for manipulating wffs of first and higherorder logic, and searching for proofs of such wffs interactively or automatically, or in a comb ..."
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Cited by 16 (0 self)
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. This is description of TPS, a theoremproving system for classical type theory (Church's typed #calculus). TPS has been designed to be a general research tool for manipulating wffs of first and higherorder logic, and searching for proofs of such wffs interactively or automatically, or in a combination of these modes. An important feature of TPS is the ability to translate between expansion proofs and natural deduction proofs. Examples of theorems that TPS can prove completely automatically are given to illustrate certain aspects of TPS's behavior and problems of theorem proving in higherorder logic. AMS Subject Classification: 0304, 68T15, 03B35, 03B15, 03B10. Key words: higherorder logic, type theory, mating, connection, expansion proof, natural deduction. 1. Introduction TPS is a theoremproving system for classical type theory ## (Church's typed #calculus [20]) which has been under development at Carnegie Mellon University for a number years. This paper gives a general...
Un Calcul De Constructions Infinies Et Son Application A La Verification De Systemes Communicants
, 1996
"... m networks and the recent works of Thierry Coquand in type theory have been the most important sources of motivation for the ideas presented here. I wish to specially thank Roberto Amadio, who read the manuscript in a very short delay, providing many helpful comments and remarks. Many thanks also to ..."
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Cited by 16 (0 self)
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m networks and the recent works of Thierry Coquand in type theory have been the most important sources of motivation for the ideas presented here. I wish to specially thank Roberto Amadio, who read the manuscript in a very short delay, providing many helpful comments and remarks. Many thanks also to Luc Boug'e, who accepted to be my oficial supervisor, and to the chair of the jury, Michel Cosnard, who opened to me the doors of the LIP. During these last three years in Lyon I met many wonderful people, who then become wonderful friends. Miguel, Nuria, Veronique, Patricia, Philippe, Pia, Rodrigo, Salvador, Sophie : : : with you I have shared the happiness and sadness of everyday life, those little things which make us to remember someone forever. I also would like to thank the people from "Tango de Soie", for all those funny nights at the Caf'e Moulin Joly. Thanks too to the Uruguayan research community in Computer Science (specially to Cristina Cornes and Alberto Pardo) w
A Tutorial on Using PVS for Hardware Verification
 Proc. 2nd International Conference on Theorem Provers in Circuit Design (TPCD94), volume 901 of Lecture Notes in Computer Science
, 1995
"... PVS stands for "Prototype Verification System." It consists of a specification language integrated with support tools and a theorem prover. PVS tries to provide the mechanization needed to apply formal methods both rigorously and productively. This tutorial serves to introduce PVS and its use in the ..."
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Cited by 15 (0 self)
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PVS stands for "Prototype Verification System." It consists of a specification language integrated with support tools and a theorem prover. PVS tries to provide the mechanization needed to apply formal methods both rigorously and productively. This tutorial serves to introduce PVS and its use in the context of hardware verification. In the first section, we briefly sketch the purposes for which PVS is intended and the rationale behind its design, mention some of the uses that we and others are making of it. We give an overview of the PVS specification language and proof checker. The PVS language, system, and theorem prover each have their own reference manuals, which you will need to study in order to make productive use of the system. A pocket reference card, summarizing all the features of the PVS language, system, and prover is also available. The purpose of this tutorial is not to describe in detail the features of PVS and how to use the system. Rather, its purpose is to...