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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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Cited by 3 (3 self)
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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.
First Order Logic With Domain Conditions
 in `Theorem Proving in Higher Order Logics, TPHOLs 2003', Vol. 2758 of LNCS
, 2001
"... The correctness of proofs is increasingly being veried with computer programs called `proof checkers'. Examples of such proof checkers are Mizar, ACL2, PVS, Nuprl, HOL, Isabelle and Coq. This paper addresses what is one of the most important problems for that kind of system, which is how to deal wit ..."
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Cited by 2 (0 self)
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The correctness of proofs is increasingly being veried with computer programs called `proof checkers'. Examples of such proof checkers are Mizar, ACL2, PVS, Nuprl, HOL, Isabelle and Coq. This paper addresses what is one of the most important problems for that kind of system, which is how to deal with partial functions and the related issue of how to treat undened terms. In many systems the problem is avoided by articially making all functions total. However that does not correspond to the practice of every day mathematics. In type theory partial functions are modeled by giving functions extra arguments which are proof objects. Because of that it is not possible to apply a function outside its domain. However having proofs as rst class objects makes the logic nonstandard. This has the disadvantages that it is unfamiliar to most mathematicians and that many proof tools won't be usable for it. For instance a theorem prover like Otter cannot be easily used for this kind of logic. Also expressions in type theoretical systems get clumsy because they contain proof objects. The PVS system solves the problem of partial functions dierently. PVS generates typecorrectness conditions or TCCs for statements in its language. These are proof obligations that have to be satised `on the side' to show that the statements are wellformed. In this paper we relate the type theoretical approach to one resembling the PVS approach. We add domain conditions to ordinary rst order logic (which in this paper will be classical and onesorted) and we show that the combination corresponds precisely to a rst order system that treats partial functions in the style of type theory. 1
Statistics on digital libraries of mathematics
"... Abstract. We present statistics on the standard libraries of four major ..."