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20
Semantic Foundations for Embedding HOL in Nuprl
 ALGEBRAIC METHODOLOGY AND SOFTWARE TECHNOLOGY
, 1996
"... We give a new semantics for Nuprl's constructive type theory that justifies a useful embedding of the logic of the HOL theorem prover inside Nuprl. The embedding gives Nuprl effective access to most of the large body of formalized mathematics that the HOL community has amassed over the last dec ..."
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Cited by 29 (2 self)
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We give a new semantics for Nuprl's constructive type theory that justifies a useful embedding of the logic of the HOL theorem prover inside Nuprl. The embedding gives Nuprl effective access to most of the large body of formalized mathematics that the HOL community has amassed over the last decade. The new semantics is dramatically simpler than the old, and gives a novel and general way of adding settheoretic equivalence classes to untyped functional programming languages.
Importing mathematics from hol into Nuprl
 Theorem Proving in Higher Order Logics (TPHOLs 1996), volume 1125 of LNCS
, 1996
"... Abstract. Nuprl and HOL are both tacticbased interactive theorem provers for higherorder logic, and both have been used in many substantial applications over the last decade. However, the HOL community has accumulated a much larger collection of formalized mathematics of the kind useful for hardwa ..."
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Cited by 27 (2 self)
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Abstract. Nuprl and HOL are both tacticbased interactive theorem provers for higherorder logic, and both have been used in many substantial applications over the last decade. However, the HOL community has accumulated a much larger collection of formalized mathematics of the kind useful for hardware and software veri cation. This collection would be of great bene t in applying Nuprl to veri cation problems of real practical interest. This paper describes a connection we have implemented between HOL and Nuprl that gives Nuprl e ective access to mathematics formalized in HOL. In designing this connection, we had to overcome a number of problems related to di erences in the logics, logical infrastructures and stylistic conventions of Nuprl and HOL. 1
Exploring Properties of Residue Classes
, 2000
"... We report on an experiment in exploring properties of residue classes over the integers with the combined effort of a multistrategy proof planner and two computer algebra systems. An exploration module classifies a given set and a given operation in terms of the algebraic structure they form. It th ..."
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Cited by 18 (11 self)
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We report on an experiment in exploring properties of residue classes over the integers with the combined effort of a multistrategy proof planner and two computer algebra systems. An exploration module classifies a given set and a given operation in terms of the algebraic structure they form. It then calls the proof planner to prove or refute simple properties of the operation. Moreover, we use different proof planning strategies to implement various proving techniques: from naive testing of all possible cases to elaborate techniques of equational reasoning and reduction to known cases.
Building Reliable, HighPerformance Networks with the Nuprl Proof Development System
 UNDER CONSIDERATION FOR PUBLICATION IN J. FUNCTIONAL PROGRAMMING
"... Proof systems for expressive type theories provide a foundation for the verification and synthesis of programs. But despite their successful application to numerous programming problems there remains an issue with scalability. Are proof environments capable of reasoning about large software systems? ..."
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Cited by 17 (4 self)
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Proof systems for expressive type theories provide a foundation for the verification and synthesis of programs. But despite their successful application to numerous programming problems there remains an issue with scalability. Are proof environments capable of reasoning about large software systems? Can the support they offer be useful in practice? In this article we answer this question by showing how the Nuprl proof development system and its rich type theory have contributed to the design of reliable, highperformance networks by synthesizing optimized code for application configurations of the Ensemble group communication toolkit. We present a typetheoretical semantics of OCaml, the implementation language of Ensemble, and tools for automatically importing system code into the Nuprl system. We describe reasoning strategies for generating verifiably correct fastpath optimizations of application configurations that substantially reduce endtoend latency in Ensemble. We also discuss briefly how to use Nuprl for checking configurations against specifications and for the design of reliable adaptive network protocols.
A TwoLevel Approach towards Lean ProofChecking
, 1996
"... We present a simple and effective methodology for equational reasoning in proof checkers. The method is based on a twolevel approach distinguishing between syntax and semantics of mathematical theories. The method is very general and can be carried out in any type system with inductive and oracle t ..."
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Cited by 16 (4 self)
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We present a simple and effective methodology for equational reasoning in proof checkers. The method is based on a twolevel approach distinguishing between syntax and semantics of mathematical theories. The method is very general and can be carried out in any type system with inductive and oracle types. The potential of our twolevel approach is illustrated by some examples developed in Lego.
Structures for Symbolic Mathematical Reasoning and Computation
 DESIGN AND IMPLEMENTATION OF SYMBOLIC COMPUTATION SYSTEMS, DISCO'96, NUMBER1128 IN LNCS
, 1996
"... Recent research towards integrating symbolic mathematical reasoning and computation has led to prototypes of interfaces and environments. This paper introduces computation theories and structures to represent mathematical objects and applications of algorithms occuring in algorithmic services. The ..."
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Cited by 15 (5 self)
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Recent research towards integrating symbolic mathematical reasoning and computation has led to prototypes of interfaces and environments. This paper introduces computation theories and structures to represent mathematical objects and applications of algorithms occuring in algorithmic services. The composition of reasoning and computation theories and structures provide a formal framework for the specification of symbolic mathematical problem solving by cooperation of algorithms and theorems.
NuprlLight: An implementation framework for higherorder logics
 IN 14TH INTERNATIONAL CONFERENCE ON AUTOMATED DEDUCTION
, 1997
"... Recent developments in higherorder logics and theorem prover design have led to an ..."
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Cited by 12 (7 self)
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Recent developments in higherorder logics and theorem prover design have led to an
Classification of Communication and Cooperation Mechanisms for Logical and Symbolic Computation Systems
, 1996
"... . The combination of logical and symbolic computation systems has recently emerged from prototype extensions of standalone systems to the study of environments allowing interaction among several systems. Communication and cooperation mechanisms of systems performing any kind of mathematical service ..."
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Cited by 10 (4 self)
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. The combination of logical and symbolic computation systems has recently emerged from prototype extensions of standalone systems to the study of environments allowing interaction among several systems. Communication and cooperation mechanisms of systems performing any kind of mathematical service enable to study and solve new classes of problems and to perform efficient computation by distributed specialized packages. The classification of communication and cooperation methods for logical and symbolic computation systems given in this paper provides and surveys different methodologies for combining mathematical services and their characteristics, capabilities, requirements, and differences. The methods are illustrated by recent wellknown examples. We separate the classification into communication and cooperation methods. The former includes all aspects of the physical connection, the flow of mathematical information, the communication language(s) and its encoding, encryption, and ...
Automated Theorem Proving in Support of Computer Algebra: Symbolic Definite Integration as a Case Study
"... We assess the current state of research in the application of computer aided formal reasoning to computer algebra, and argue that embedded verification support allows users to enjoy its benefits without wrestling with technicalities. We illustrate this claim by considering symbolic definite integrat ..."
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Cited by 10 (5 self)
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We assess the current state of research in the application of computer aided formal reasoning to computer algebra, and argue that embedded verification support allows users to enjoy its benefits without wrestling with technicalities. We illustrate this claim by considering symbolic definite integration, and present a verifiable symbolic definite integral table look up: a system which matches a query comprising a definite integral with parameters and side conditions, against an entry in a verifiable table and uses a call to a library of lemmas about the reals in the theorem prover PVS to aid in the transformation of the table entry into an answer. We present the full model of such a system as well as a description of our prototype implementation showing the efficacy of such a system: for example, the prototype is able to obtain correct answers in cases where computer algebra systems [CAS] do not. We extend upon Fateman's webbased table by including parametric limits of integration and queries w...
Classifying Isomorphic Residue Classes
 In Proceedings of the 8th International Workshop on Computer Aided Systems Theory (EuroCAST 2001), volume 2178 of LNCS
, 2001
"... We report on a case study on combining proof planning with computer algebra systems. We construct proofs for basic algebraic properties of residue classes as well as for isomorphisms between residue classes using different proving techniques, which are implemented as strategies in a multistrategy p ..."
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Cited by 9 (6 self)
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We report on a case study on combining proof planning with computer algebra systems. We construct proofs for basic algebraic properties of residue classes as well as for isomorphisms between residue classes using different proving techniques, which are implemented as strategies in a multistrategy proof planner. We show how these techniques help to successfully derive proofs in our domain and explain how the search space of the proof planner can be drastically reduced by employing computations of two computer algebra systems during the planning process. Moreover, we discuss the results of experiments we conducted which give evidence that with the help of the computer algebra systems the planner is able to solve problems for which it would fail to create a proof otherwise.