Introduction to the Coq Proof-Assistant for Practical Software Verification

This paper is a tutorial on using the Coq proof-assistant for reasoning on software correctness. It illustrates features of Coq like inductive definitions and proof automation on a few examples including arithmetic, algorithms on functional and imperative lists and cryptographic protocols. Coq is not a tool dedicated to software verification but a general purpose environment for developing mathematical proofs. However, it is based on a powerful language including basic functional programming and high-level specifications. As such it offers modern ways to literally program proofs in a structured way with advanced data-types, proofs by computation, and general purpose libraries of definitions and lemmas. Coq is well suited for software verification of programs involving advanced specifications like language semantics and real numbers. The Coq architecture is also based on a small trusted kernel, making possible to use third-party libraries while being sure that proofs are not compromised.