Description

Since the beginning of the 21st century, formal proof methods have become standard in industrial hardware verification, particularly in CPU verification (Intel, AMD). During the past decade, the proof assistant technology has matured enough to also enable formal certification of substantial software systems. Two major success stories are the seL4 operating system microkernel and the CompCert optimising C compiler. Recently, deductive program verification has attracted increasing attention in the software industry (Microsoft, Amazon, Facebook, Galois). To quote Nikhil Swamy from Microsoft Research:

"Today, what seemed impossible just a few years ago is becoming a reality. We can, in certain domains, produce fully verified software at a nontrivial scale and with runtime performance that meets or exceeds the best unverified software."

This lecture is about writing functional programs in a dependently typed language and proving them correct.

Coq - the 2013 ACM Software System Award winner - is an interactive proof assistant for the development of formally certified software and mathematical theories. Its underlying theory is the Calculus of Inductive Constructions - a variant of dependent type theory with inductive types. The lecture covers programming and proving in Coq, dependent type theory, and applications to program verification. There is overlap with LMSE 1 & 2, but no familiarity with type theory is necessary. ATLSE focuses on the following aspects:

• dependently typed functional programming
• verification of functional programs
• proof automation
• theory of inductive types

Prerequisites

Some experience with functional programming and formal logic. You should understand mathematical induction. If you liked the logic and/or the functional programming bachelor courses then this lecture is for you. If you're interested in formal methods and security then this may also be for you. The lecture is self-contained: knowledge of type theory or previous participation in LMSE are not necessary.

Supplementary Materials

• Certified Programming with Dependent Types and Formal Reasoning About Programs by Adam Chlipala
• Software Foundations by Benjamin C. Pierce et. al.
• Interactive Theorem Proving and Program Development by Yves Bertot and Pierre Casteran
• Inductive definitions in the system Coq: rules and properties by Christine Paulin-Mohring
• History of Interactive Theorem Proving by John Harrison, Josef Urban and Freek Wiedijk