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- Jan Herman Geuvers, Herman Geuvers, Bernard Koeman
- 1993

- Herman Geuvers, Mark-Jan Nederhof
- J. Funct. Program.
- 1991

- Herman Geuvers, Freek Wiedijk, Jan Zwanenburg
- TYPES
- 2000

In the FTA project in Nijmegen we have formalized a constructive proof of the Fundamental Theorem of Algebra. In the formal-ization, we have first defined the (constructive) algebraic hierarchy of groups, rings, fields, etcetera. For the reals we have then defined the notion of real number structure, which is basically a Cauchy complete Archimedean ordered… (More)

- Luís Cruz-Filipe, Herman Geuvers, Freek Wiedijk
- MKM
- 2004

We present C-CoRN, 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.

- Herman Geuvers, Randy Pollack, Freek Wiedijk, Jan Zwanenburg
- J. Symb. Comput.
- 2002

We describe a framework of algebraic structures in the proof assistant Coq. We have developed this framework as part of the FTA project in Nijmegen, in which a constructive proof of the Fundamental Theorem of Algebra has been formalized in Coq. The algebraic hierarchy that is described here is both abstract and structured. Structures like groups and rings… (More)

- Hendrik Pieter Barendregt, Herman Geuvers
- Handbook of Automated Reasoning
- 2001

- Herman Geuvers, Milad Niqui
- TYPES
- 2000

We describe a construction of the real numbers carried out in the Coq proof assistant. The basis is a set of axioms for the constructive real numbers as used in the FTA (Fundamental Theorem of Algebra) project, carried out at Nijmegen University. The aim of this work is to show that these axioms can be satisfied, by constructing a model for them. Apart from… (More)

- Franco BARBANERA, Maribel FERN ANDEZ, Herman GEUVERS, Franco Barbanera, Maribel Fern, Herman Geuvers
- 1996

In this paper we present the algebraic-cube, an extension of Barendregt's-cube with rst-and higher-order algebraic rewriting. We show that strong normalization is a modular property of all systems in the algebraic-cube, provided that the rst-order rewrite rules are non-duplicating and the higher-order rules satisfy the general schema of Jouannaud and Okada.… (More)

- Josef Urban, Jesse Alama, Piotr Rudnicki, Herman Geuvers
- AISC/MKM/Calculemus
- 2010

Formal mathematics has so far not taken full advantage of ideas from collaborative tools such as wikis and distributed version control systems (DVCS). We argue that the field could profit from such tools, serving both newcomers and experts alike. We describe a preliminary system for such collaborative development based on the Git DVCS. We focus, initially,… (More)

- Herman Geuvers
- TLCA
- 2001