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This document describes a set of extensions to the proof scripting language of the Coq proof assistant. While these extensions were developed to support a particular proof methodology small-scaleâ€¦ (More)

- FranÃ§ois Garillot, Georges Gonthier, Assia Mahboubi, Laurence Rideau
- TPHOLs
- 2009

This paper proposes generic design patterns to define and combine algebraic structures, using dependent records, coercions and type inference, inside the Coq system. This alternative to telescopes inâ€¦ (More)

- Georges Gonthier, Assia Mahboubi
- J. Formalized Reasoning
- 2010

Small-scale reflection is a formal proof methodology based on the pervasive use of computation with symbolic representations. Symbolic representations are usually hidden in traditional computationalâ€¦ (More)

- Benjamin GrÃ©goire, Assia Mahboubi
- TPHOLs
- 2005

We present a new implementation of a reflexive tactic which solves equalities in a ring structure inside the Coq system. The efficiency is improved to a point that we can now prove equalities thatâ€¦ (More)

- Georges Gonthier, Andrea Asperti, +12 authors Laurent ThÃ©ry
- ITP
- 2013

This paper reports on a six-year collaborative effort that culminated in a complete formalization of a proof of the Feit-Thompson Odd Order Theorem in the Coq proof assistant. The formalized proof isâ€¦ (More)

- Assia Mahboubi
- Mathematical Structures in Computer Science
- 2007

The Coq system is a Curryâ€“Howard based proof assistant. Therefore, it contains a full functional, strongly typed programming language, which can be used to enhance the system with powerful automationâ€¦ (More)

- FranÃ§ois Bobot, Sylvain Conchon, +4 authors Guillaume Melquiond
- IJCAR
- 2012

This paper describes a novel decision procedure for quantifierfree linear integer arithmetic. Standard techniques usually relax the initial problem to the rational domain and then proceed either byâ€¦ (More)

- Georges Gonthier, Assia Mahboubi, Laurence Rideau, Enrico Tassi, Laurent ThÃ©ry
- TPHOLs
- 2007

In this paper, we present a formalisation of elementary group theory done in Coq. This work is the first milestone of a long-term effort to formalise Feit-Thompson theorem. As our furtherâ€¦ (More)

- Cyril Cohen, Assia Mahboubi
- Logical Methods in Computer Science
- 2011

This paper describes a formalization of discrete real closed fields in the Coq proof assistant. This abstract structure captures for instance the theory of real algebraic numbers, a decidable subsetâ€¦ (More)

- Yves Bertot, FrÃ©dÃ©rique Guilhot, Assia Mahboubi
- Mathematical Structures in Computer Science
- 2011

Bernstein coe cients provide a discrete approximation of the behavior of a polynomial inside an interval. This can be used for example to isolate real roots of polynomials. We prove a criterion forâ€¦ (More)