## How to read this book

This is a Reference Manual, not a User Manual, then it is not made for a continuous reading. However, it has some structure that is explained below.

- The first part describes the specification language, Gallina. The chapters 1 and 2 describe the concrete syntax as well as the meaning of programs, theorems and proofs in the Calculus of Inductive Construction. The chapter 3 describes the standard library of Coq. The chapter 4 is a mathematical description of the formalism.
- The second part describes the proof engine. It is divided in three chapters. Chapter 5 presents all commands (we call them vernacular commands) that are not directly related to interactive proving: requests to the environment, complete or partial evaluation, loading and compiling files. How to start and stop proofs, do multiple proofs in parallel is explained in the chapter 6. In chapter 7, all commands that realize one or more steps of the proof are presented: we call them tactics.
- The third part describes how to extend the system in two ways: adding parsing and pretty-printing rules (chapter 9) and writing new tactics (chapter 10)
- In the fourth part more practical tools are documented. First in the chapter 11 the usage of `coqc` (batch mode) and `coqtop` (interactive mode) with their options is described. Then (in chapter 12) various utilities that come with the Coq distribution are presented.

At the end of the document, after the global index, the user can find a tactic index and a vernacular command index.