Certified Programming with Dependent Types: A Pragmatic Introduction to the Coq Proof Assistant

by Adam Chlipala

The technology of mechanized program verification can play a supporting role in many kinds of research projects in computer science, and related tools for formal proof-checking are seeing increasing adoption in mathematics and engineering. This book provides an introduction to the Coq software for writing and checking mathematical proofs. It takes a practical engineering focus throughout, emphasizing techniques that will help users to build, understand, and maintain large Coq developments and minimize the cost of code change over time. Two topics, rarely discussed elsewhere, are covered in detail: effective dependently typed programming (making productive use of a feature at the heart of the Coq system) and construction of domain-specific proof tactics. Almost every subject covered is also relevant to interactive computer theorem proving in general, not just program verification, demonstrated through examples of verified programs applied in many different sorts of formalizations. The book develops a unique automated proof style and applies it throughout; even experienced Coq users may benefit from reading about basic Coq concepts from this novel perspective. The book also offers a library of tactics, or programs that find proofs, designed for use with examples in the book. Readers will acquire the necessary skills to reimplement these tactics in other settings by the end of the book. All of the code appearing in the book is freely available online.

Genres: Computer Science, Programming, Mathematics, Nonfiction, Textbooks

424 pages, Hardcover

First published February 3, 2010

Reviews

[Nick Black]

Heard good things about this from numerous people within Google and beyond. I haven't looked at theorem proving software or proof assistants in over a decade, probably, and only really played with HOL4 back then (despite one of the world's authorities on the subject, Mary Jean Harrold, being at Georgia Tech...alas).

[Jakub · Rating 5 out of 5]

Excellent book, though a bit difficult to follow in places. You should also be prepared to look in the Coq manual a lot, or work with another book in parallel, as some things aren't explained in great detail, only showed in practices. This isn't such a big obstacle though, since the Coq manual works well in those cases.

[Marvin · Rating 4 out of 5]

Very clear and informative book about Coq and dependent types. Requires some background in those areas, though.