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Formal Verification EPFL Course (CS-550), Fall 2019

Moodle

Autumn 2019 Semester. 2h Lectures, 2h Exercises, 2h Labs. Continuous Control

Instructors: Viktor Kuncak, Jad Hamza, with the help of Romain Edelmann, Georg Schmid, Romain Ruetschi

One of the verification tools used: Stainless

Introduction

In this course we introduce formal verification as a principled approach for developing systems that do what they should do.

Formal verification finds proofs that computer systems work under all scenarios of interest. Formal verification tools help developers construct such proofs, automatically searching for proofs using theorem proving and constraint solving (using, e.g. SMT solvers), and static analysis to discover program invariants. When it succeeds, formal verification is guaranteed to identify all software errors, including, for example, security vulnerabilities or cases when the computation produces a wrong numerical or symbolic result. The best approach to obtain formally verified software is to perform formal verification while software is developed, as opposed to after the fact.

Companies, research labs and research groups have developed proofs of correctness of operating system kernels, brake system for a metro line in Paris, compilers, databases, data structures, smartcard wallets, communication protocols, and distributed systems.

In this course we will learn how to use formal verification tools and explain the theory and the practice behind them.

Warmup videos by others:

Outline

First class: Thursday 19 September at 15:15 in the classroom INF213.

Part I: Introduction and Finite State Systems

Week 01, September 16

Thursday 15:15 Lecture 01: Introduction. State machines
Thursday 17:15 Labs 01: Scala, Stainless, and State Machines
Friday 13:15 Exercises 01: Proofs about state machines

Week 02, September 23

Thursday 15:15 Lecture 02: Explicit-State Exploration
Thursday 17:15 Labs 02: Explicit-State Reachability Checker
Friday 13:15 Exercises 02

Week 03, September 30

BDDs

Week 04

Hardware verification tools. Guest Lecture.

Part II: Deductive Program Verification

Part III: Verified Functional Programming

Topics

  • Importance of Reliable Systems. Methodology of Formal Verification. Soundness and Completeness in Modeling and Tools. Successful Tools and Flagship Case Studies
  • Review of Sets, Relations, Computability, Propositional and First-Order Logic Syntax, Semantics, Sequent Calculus.
  • Completeness and Semi-Decidability for First-Order Logic. Inductive Definitions and Proof Trees. Higher-Order Logic and LCF Approach.
  • State Machines. Transition Formulas. Traces. Strongest Postconditions and Weakest Preconditions.
  • Hoare Logic. Inductive Invariants. Well-Founded Relations and Termination Measures
  • Modeling Hardware: Verilog to Sequential Circuits
  • Linear Temporal Logic. System Verilog Assertions. Monitors
  • SAT Solvers and Bounded Model Checking
  • Model Checking using Binary Decision Diagrams
  • Loop Invariants. Hoare Logic. Statically Checked Function Contracts. Relational Semantics and Fixed-Point Semantics
  • Symbolic Execution. Satisfiability Modulo Theories
  • Abstract Interpretation and Predicate Abstraction
  • Information Flow and Taint Analysis
  • Verification of Security Protocols
  • Dependent and Refinement Types

Relevant Textbooks

  • Michael Huth and Mark Rayan: Logic in Computer Science - Modelling and Reasoning about Systems. Cambridge University Press 2004.
  • Handbook of Model Checking, https://www.springer.com/de/book/9783319105741 Springer 2018. Including Chapter Model Checking Security Protocols by David Basin.
  • Tobias Nipkow, Gerwin Klein: Concrete semantics with Isabelle/HOL. http://concrete-semantics.org/concrete-semantics.pdf
  • Aaron Bradley and Zohar Manna: The Calculus of Computation - Decision Procedures with Applications to Verification, Springer 2007.
  • Nielson, Flemming, Nielson, Hanne R., Hankin, Chris: Principles of Program Analysis. ISBN 978-3-662-03811-6. Springer 1999.
  • Peter B. Andrews: An Introduction to Mathematical Logic and Type Theory (To Truth Through Proof), Springer 2002.
  • http://logitext.mit.edu/tutorial

Background