Mathematical Components is the name of a library of formalized mathematics for the Coq system. It covers a variety of topics, from the theory of basic data structures (e.g., numbers, lists, finite sets) to advanced results in various flavors of algebra. This library constitutes the infrastructure for the machine checked proofs of the Four Color Theorem and of the Odd Order Theorem.
The reason of existence of this book is to break down the barriers to entry. While there are several books around covering the usage of the Coq system and the theory it is based on, the Mathematical Components library is built in an unconventional way. As a consequence this book provides a non standard presentation of Coq, putting upfront the formalization choices and the proof style that are the pillars of the library.
This books targets two classes of public. On one hand newcomers, even the more mathematical inclined ones, find a soft introduction to the programming language of Coq, Gallina, and the Ssreflect proof language. On the other hand accustomed Coq users find a substantial account of the formalization style that made the Mathematical Components library possible.
The book in PDF format. (last update Sat Aug 11 18:12:20 CEST 2018)
The book printed on demand (TBD)
Feedback on the book is very welcome. Issues can be reported on the github page of the book.
The current version of the book "Mathematical Components" was written by Assia Mahboubi and Enrico Tassi with contributions by Yves Bertot and Georges Gonthier.
The Coq painting(s) are by Hanna.
Financial support was provided by the Inria -- Microsoft Research Joint Centre.