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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.
The QED Manifesto Revisited
 Studies in Logic, Grammar and Rhetoric
, 2007
"... We present an overview of the current state of formalization of mathematics, and argue what will be needed to make the vision from the QED manifesto come true. ..."
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We present an overview of the current state of formalization of mathematics, and argue what will be needed to make the vision from the QED manifesto come true.
Hierarchical Reflection
"... Abstract. The technique of reflection is a way to automate proof construction in type theoretical proof assistants. Reflection is based on the definition of a type of syntactic expressions that gets interpreted in the domain of discourse. By allowing the interpretation function to be partial or even ..."
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Abstract. The technique of reflection is a way to automate proof construction in type theoretical proof assistants. Reflection is based on the definition of a type of syntactic expressions that gets interpreted in the domain of discourse. By allowing the interpretation function to be partial or even a relation one gets a more general method known as ``partial reflection''. In this paper we show how one can take advantage of the partiality of the interpretation to uniformly define a family of tactics for equational reasoning that will work in different algebraic structures. The tactics then follow the hierarchy of those algebraic structures in a natural way.
Statistics on digital libraries of mathematics
"... Abstract. We present statistics on the standard libraries of four major ..."
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Abstract. We present statistics on the standard libraries of four major
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].