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Comparing mathematical provers
 In Mathematical Knowledge Management, 2nd Int’l Conf., Proceedings
, 2003
"... Abstract. We compare fifteen systems for the formalizations of mathematics with the computer. We present several tables that list various properties of these programs. The three main dimensions on which we compare these systems are: the size of their library, the strength of their logic and their le ..."
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Abstract. We compare fifteen systems for the formalizations of mathematics with the computer. We present several tables that list various properties of these programs. The three main dimensions on which we compare these systems are: the size of their library, the strength of their logic and their level of automation. 1
CCoRN, the Constructive Coq Repository at Nijmegan
"... We present CCoRN, the Constructive Coq Repository at Nijmegen. It consists of a library of constructive algebra and analysis, formalized in the theorem prover Coq. In this paper we explain the structure, the contents and the use of the library. Moreover we discuss the motivation and the (possible) ..."
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We present CCoRN, the Constructive Coq Repository at Nijmegen. It consists of a library of constructive algebra and analysis, formalized in the theorem prover Coq. In this paper we explain the structure, the contents and the use of the library. Moreover we discuss the motivation and the (possible) applications of such a library.
Formalizing Arrow’s theorem
"... Abstract. We present a small project in which we encoded a proof of Arrow’s theorem – probably the most famous results in the economics field of social choice theory – in the computer using the Mizar system. We both discuss the details of this specific project, as well as describe the process of for ..."
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Abstract. We present a small project in which we encoded a proof of Arrow’s theorem – probably the most famous results in the economics field of social choice theory – in the computer using the Mizar system. We both discuss the details of this specific project, as well as describe the process of formalization (encoding proofs in the computer) in general. Keywords: formalization of mathematics, Mizar, social choice theory, Arrow’s theorem, GibbardSatterthwaite theorem, proof errors.
Towards MKM in the Large: Modular Representation and Scalable Software Architecture
 Intelligent Computer Mathematics, volume 6167 of Lecture Notes in Computer Science
, 2010
"... Abstract. MKM has been defined as the quest for technologies to manage mathematical knowledge. MKM “in the small ” is wellstudied, so the real problem is to scale up to large, highly interconnected corpora: “MKM in the large”. We contend that advances in two areas are needed to reach this goal. We ..."
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Abstract. MKM has been defined as the quest for technologies to manage mathematical knowledge. MKM “in the small ” is wellstudied, so the real problem is to scale up to large, highly interconnected corpora: “MKM in the large”. We contend that advances in two areas are needed to reach this goal. We need representation languages that support incremental processing of all primitive MKM operations, and we need software architectures and implementations that implement these operations scalably on large knowledge bases. We present instances of both in this paper: the MMT framework for modular theorygraphs that integrates metalogical foundations, which forms the base of the next OMDOC version; and TNTBase, a versioned storage system for XMLbased document formats. TNTBase becomes an MMT database by instantiating it with special MKM operations for MMT. 1
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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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
Towards knowledge management for HOL Light
 Proc. of the 7th Conference on Intelligent Computer Mathematics (CICM’14), volume 8543 of LNCS
, 2014
"... Abstract. The libraries of deduction systems are growing constantly, so much that knowledge management concerns are becoming increasingly urgent to address. However, due to time constraints and legacy design choices, there is barely any deduction system that can keep up with the MKM state of the art ..."
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Abstract. The libraries of deduction systems are growing constantly, so much that knowledge management concerns are becoming increasingly urgent to address. However, due to time constraints and legacy design choices, there is barely any deduction system that can keep up with the MKM state of the art. HOL Light in particular was designed as a lightweight deduction system that systematically relegates most MKM aspects to external solutions — not even the list of theorems is stored by the HOL Light kernel. We make the first and hardest step towards knowledge management for HOL Light: We provide a representation of the HOL Light library in a standard MKM format that preserves the logical semantics and notations but is independent of the system itself. This provides an interface layer at which independent MKM applications can be developed. Moreover, we develop two such applications as examples. We employ the MMT system and its interactive web browser to view and navigate the library. And we
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
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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Cited by 1 (0 self)
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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
A Framework for Interactive Sharing and Searching Distributed Heterogeneous Collections of Formalized Mathematics
"... 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
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