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Coq'Art

Coq'Art is the familiar name for the first book on the Coq proof assistant and its underlying theory, the Calculus of Inductive Constructions. This project contains the Coq sources of all examples and the solution to 170 out of over 200 exercises from the book.

Meta

• Author(s):
  • Yves Bertot (initial)
  • Pierre Castéran (initial)
• Coq-community maintainer(s):
  • Yves Bertot (@ybertot)
  • Pierre Castéran (@Casteran)
• License: MIT License
• Compatible Coq versions: 8.16 or later (use the corresponding release for other Coq versions)
• Additional dependencies: none
• Coq namespace: coqart
• Related publication(s):
  • Interactive Theorem Proving and Program Development doi:10.1007/978-3-662-07964-5

Building instructions

git clone https://github.com/coq-community/coq-art
cd coq-art
make   # or make -j <number-of-cores-on-your-machine>

Documentation

For more information, see the book website and the publisher's website. The repository is also used as the source for this website.

Book chapters

The repository is structured as follows.

1. A Brief Presentation of Coq
2. Gallina: Coq as a Programming Language
3. Propositions and Proofs
4. Dependent Product
5. Everyday Logic
6. Inductive Data Structures
7. Tactics and automation
8. Inductive Predicates
9. Functions and their specification
10. Extraction and imperative programming
11. A Case Study: binary search trees
12. The Module System
13. Infinite Objects and Proofs
14. Foundations of Inductive Types
15. General Recursion
16. Proof by reflection

Additional material

• Tutorial on type classes
• Tutorial on inductive and coinductive types
• More exercises