The Coq system is a proof assistant. It is designed to build and verify mathematical proofs. The Coq system contains the functional programming language Gallina and is capable of proving properties about programs written in this language.

Coq is a dependently typed language. This means that the types of the language may depend on the values of variables. In this respect, it is similar to other related languages such as Agda, Idris, F*, Lean, and others. Via the Curry-Howard correspondence, programs, properties and proofs are formalized in the same language.

Coq is developed in OCaml and shares some syntactic and conceptual similarity with it. Coq is a language containing many fascinating but difficult topics. This tutorial will focus on the programming aspects of Coq, rather than the proving. It may be helpful, but not necessary to learn some OCaml first, especially if you are unfamiliar with functional programming. This tutorial is based upon its OCaml equivalent

The standard usage model of Coq is to write it with interactive tool assistance, which operates like a high powered REPL. Two common such editors are the CoqIDE and Proof General Emacs mode.

Inside Proof General Ctrl+C Ctrl+<Enter> will evaluate up to your cursor.