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Formally verifying hybrid protocols with the Nuprl logical programming environment
, 2001
"... We describe a generic switching protocol for the construction of hybrid protocols and prove it correct with the Nuprl proof development system. We introduce the concept of metaproperties to characterize communication properties that can be preserved by switching and identify switching invariants th ..."
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We describe a generic switching protocol for the construction of hybrid protocols and prove it correct with the Nuprl proof development system. We introduce the concept of metaproperties to characterize communication properties that can be preserved by switching and identify switching invariants that an implementation of the switching protocol must satisfy in order to work correctly. Our work shows how a theorem prover with a rich specification language can contribute to the design and implementation of verifiably correct adaptive protocols and that it can have a large impact when being engaged at the
An interpretation of isabelle/hol in hol light
 In Furbach and Shankar [20
"... Abstract. We define an interpretation of the Isabelle/HOL logic in HOL Light and its metalanguage, OCaml. Some aspects of the Isabelle logic are not representable directly in the HOL Light object logic. The interpretation thus takes the form of a set of elaboration rules, where features of the Isabe ..."
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Cited by 3 (1 self)
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Abstract. We define an interpretation of the Isabelle/HOL logic in HOL Light and its metalanguage, OCaml. Some aspects of the Isabelle logic are not representable directly in the HOL Light object logic. The interpretation thus takes the form of a set of elaboration rules, where features of the Isabelle logic that cannot be represented directly are elaborated to functors in OCaml. We demonstrate the effectiveness of the interpretation via an implementation, translating a significant part of the Isabelle standard library into HOL Light. 1
An executable formalization of the HOL/Nuprl connection in the metalogical framework Twelf
 In Geoff Sutcliffe and Andrei Voronkov, editors, Proceedings of Logic for Programming, Artificial Intelligence, and Reasoning (LPAR), Montego
, 2005
"... Abstract. Howe’s HOL/Nuprl connection is an interesting example of a translation between two fundamentally different logics, namely a typed higherorder logic and a polymorphic extensional type theory. In earlier work we have established a prooftheoretic correctness result of the translation in a w ..."
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Abstract. Howe’s HOL/Nuprl connection is an interesting example of a translation between two fundamentally different logics, namely a typed higherorder logic and a polymorphic extensional type theory. In earlier work we have established a prooftheoretic correctness result of the translation in a way that complements Howe’s semanticsbased justification and furthermore goes beyond the original HOL/Nuprl connection by providing the foundation for a proof translator. Using the Twelf logical framework, the present paper goes one step further. It presents the first rigorous formalization of this treatment in a logical framework, and hence provides a safe alternative to the translation of proofs. 1
Formalizing Automata II: Decidable Properties
"... Is it possible to create formal proofs of interesting mathematical theorems which are mechanically checked in every detail and yet are readable and even faithful to the best expositions of those results in the literature? This paper answers that question positively for theorems about decidable prope ..."
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Is it possible to create formal proofs of interesting mathematical theorems which are mechanically checked in every detail and yet are readable and even faithful to the best expositions of those results in the literature? This paper answers that question positively for theorems about decidable properties of nite automata. The exposition is from Hopcroft and Ullman's classic 1969 textbook Formal Languages and Their Relation to Automata. This paper describes a successful formalization which is faithful to that book. The requirement of being faithful to the book has unexpected consequences, namely that the underlying formal theory must include primitive notions of computability. This requirement makes a constructive formalization especially suitable. It also opens the possibility ofusingthe formal proofs to decide properties of automata. The paper shows how to do this. 1
Encoding the HOL Light logic in Coq
"... Abstract. We show how to encode the HOL Light logic in Coq. This makes an automatic translation of HOL proofs to Coq possible. The translated HOL proofs refer to translated HOL data types but those data types can be related to the standard Coq data types, making the HOL results useful for Coq. The t ..."
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Abstract. We show how to encode the HOL Light logic in Coq. This makes an automatic translation of HOL proofs to Coq possible. The translated HOL proofs refer to translated HOL data types but those data types can be related to the standard Coq data types, making the HOL results useful for Coq. The translated proofs have a size linear in the time HOL takes to process the original proofs. However the constant of linearity is large. The approach described in this paper is similar to the method of Pavel Naumov, MarkOliver Stehr and José Mesequer for translating HOL98 proofs to Nuprl [10].
An Executable Formalization of the HOL/Nuprl Connection
 in the Metalogical Framework Twelf. LPAR 2004
"... Abstract. Howe’s HOL/Nuprl connection is an interesting example of a translation between two fundamentally different logics, namely a typed higherorder logic and a polymorphic extensional type theory. In earlier work we have established a prooftheoretic correctness result of the translation in a w ..."
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Abstract. Howe’s HOL/Nuprl connection is an interesting example of a translation between two fundamentally different logics, namely a typed higherorder logic and a polymorphic extensional type theory. In earlier work we have established a prooftheoretic correctness result of the translation in a way that complements Howe’s semanticsbased justification and furthermore goes beyond the original HOL/Nuprl connection by providing the foundation for a proof translator. Using the Twelf logical framework, the present paper goes one step further. It presents the first rigorous formalization of this treatment in a logical framework, and hence provides a safe alternative to the translation of proofs. 1
Exercising Nuprl's OpenEndedness
"... Abstract. Nuprl is an interactive theorem prover that implements an extensional constructive type theory, where types are interpreted as partial equivalence relations on closed terms. Nuprl is both computationally and typetheoretically openended in the sense that both its computation system and i ..."
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Abstract. Nuprl is an interactive theorem prover that implements an extensional constructive type theory, where types are interpreted as partial equivalence relations on closed terms. Nuprl is both computationally and typetheoretically openended in the sense that both its computation system and its type theory can be extended as needed by checking a handful of conditions. For example, Doug Howe characterized the computations that can be added to Nuprl in order to preserve the congruence of its computational equivalence relation. We have implemented Nuprl's computation and type systems in Coq, and we have showed among other things that it is consistent. Using our Coq framework we can now easily and rigorously add new computations and types to Nuprl by mechanically verifying that all the necessary conditions still hold. We have recently exercised Nuprl's openendedness by adding nominal features to Nuprl in order to prove a version of Brouwer's continuity principle, as well as choice sequences in order to prove truncated versions of the axiom of choice and of Brouwer's bar induction principle. This paper illustrates the process of extending Nuprl with versions of the axiom of choice.
Abstract Innovations in Computational Type Theory using
"... For twenty years the Nuprl (“new pearl”) system has been used to develop software systems and formal theories of computational mathematics. It has also been used to explore and implement computational type theory (CTT) – a formal theory of computation closely related to MartinLöf’s intuitionistic ..."
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For twenty years the Nuprl (“new pearl”) system has been used to develop software systems and formal theories of computational mathematics. It has also been used to explore and implement computational type theory (CTT) – a formal theory of computation closely related to MartinLöf’s intuitionistic type theory (ITT) and to the calculus of inductive constructions (CIC) implemented in the Coq prover. This article focuses on the theory and practice underpinning our use of Nuprl for much of the last decade. We discuss innovative elements of type theory, including new type constructors such as unions and dependent intersections, our theory of classes, and our theory of event structures. We also discuss the innovative architecture of Nuprl as a distributed system and as a transactional database of formal mathematics using the notion of abstract object identifiers. The database has led to an independent project called the Formal Digital Library, FDL, now used as a repository for Nuprl results as well as selected results from HOL, MetaPRL, and PVS. We discuss Howe’s set theoretic semantics that is used to relate such disparate theories and systems as those represented by these provers. 1
A Framework for Interactive Sharing and Deductive Searching in Distributed Heterogeneous Collections of Formalized
"... Abstract. Peertopeer technology implemented in systems like Napster allowed sharing of digitized music across the web in an incredibly easy to use system. This paper describes a prototype peertopeer system for networking distributed and heterogeneous databases of formalized mathematics. We also ..."
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Abstract. Peertopeer technology implemented in systems like Napster allowed sharing of digitized music across the web in an incredibly easy to use system. This paper describes a prototype peertopeer system for networking distributed and heterogeneous databases of formalized mathematics. We also propose a general framework for deductive search in heterogeneous libraries of formal content. As participants in this conference well know, a significant body of mathematics has been formalized in theorem provers. We believe that a truly distributed mechanism for sharing formal content will multiply efforts of individual users of theorem proving systems, will invigorate ongoing formalization efforts, and will spur new research in deductive search and contentbased addressing. Interactive sharing has the potential to be a significant new methodology for theorem proving. A basic tenet of our approach is that users of the system must be able to account for results and methods for accountability are incorporated into the proposed methods. 1