## Section:
Application Domains2>
### The impact of Coq3>

Coq is one of the 8 most used proof assistants in the world. In Europe, its main challengers are Isabelle (developed in Munich, Germany), HOL (developed in Cambridge, UK) and Mizar (developed in Białystok, Poland).

Coq is used in various research contexts and in a few industrial contexts. It is used in the context of formal mathematics at the University of Nijmegen (constructive algebra and analysis), Inria Sophia-Antipolis (number theory and algebra), Inria-MSR joint lab (group theory), the University of Nice (algebra). It is used in France in the context of computer science at Inria-Rocquencourt (certified compilation), Inria-Saclay (certification of imperative programs), LORIA, Strasbourg (certification of geometry algorithms). Outside France, it is used in the context of computer science e.g. at U. Penn, Harvard (programming languages, semantics), Yale, Ottawa and Berkeley Universities (building of a certified platform for proof-carrying code), University of Princeton (certified compilation), AIST at Tokyo (certification of cryptographic protocols), Microsoft Research Cambridge (proof of imperative programs), ... In the industry, it is used by Gemalto and Trusted Logic (JavaCard formal model and commercial applets certification).

All in all, it is difficult to evaluate how much Coq is used. Two indicators are the readership of the textbook on Coq by Yves Bertot and Pierre Castéran [35] and the number of subscribers to the Coq-club mailing list. More than 1200 copies of the book have been sold. There has been a second printing , and a Chinese translation of the book has been published. There are around 600 subscribers to the mailing list. Coq is taught or used for teaching in many universities: Paris, Bordeaux, Lyon, Nice, Strasbourg, CNAM, Nottingham, Ottawa, U. Penn, Harvard, MIT, Princeton, Yale, Berkeley, Warsaw, Krakow, Rosario in Argentina, ...

Users of the assistant are also disseminating the use of the tool: A collaborative effort led by B. Pierce's team at U. Penn gave rise to a set of courses named Software Foundations (http://www.seas.upenn.edu/~cis500/current/sf/index.html ) [66] on basic logic and computer science in Coq, that is used by many universities and individuals throughout the world. A. Chlipala wrote an advanced textbook on “Certified Programming with Dependent Types” in Coq, freely available on the web and soon to be published by MIT Press [37] .