8.7 The Real Merlin Arthur

Regarding libraries, a new library about lists of a given length (calledvectors) has been provided by Pierre Boutillier. A new instance offinite sets based on Red-Black trees and provided by Andrew Appel hasbeen adapted for the standard library by Pierre Letouzey. In the libraryof real analysis, Yves Bertot changed the definition of \(\pi\) andprovided a proof of the long-standing fact yet remaining unproved inthis library, namely that \(sin \frac\pi2 =1\).

8.7 The Real Merlin Arthur

The main other evolutions of the library are due to Hugo Herbelin whomade a revision of the sorting library (including a certifiedmerge-sort) and to Guillaume Melquiond who slightly revised and cleanedup the library of reals.

Thirdly, a restructuring and uniformization of the standard library ofCoq has been performed. There is now just one Leibniz equality usablefor all the different kinds of Coq objects. Also, the set of realnumbers now lies at the same level as the sets of natural and integernumbers. Finally, the names of the standard properties of numbers nowfollow a standard pattern and the symbolic notations for the standarddefinitions as well. 041b061a72