A Course on Correctness by Construction

Motivation and Goals

Software is becoming increasingly complex and responsible for critical tasks. Any technology aimed at ensuring the reliability and quality of software will be increasingly relevant, if not utterly necessary.

Only rigorous (e.g., mathematically sound) approaches can certify software with the highest possible assurance. These approaches include, among others, the use of specification languages, high-level programming languages (including equational, functional, and logic languages), the use of model checking and deductive verification, language-based approaches often interacting with theorem provers.

In this course we will give a hands-on introduction to rigorous software development methods that follow a “correctness-by-construction” approach.

While the course is not heavy in theory, everyone is expected to have a good understanding of first-order logic and programming experience. We will explore several methodologies that have approaches and underlying technical bases, but which share a common overarching goal: develop programs while making sure that non-trivial properties, expressing high-level design requirements regarding correctness, fairness and sometimes efficiency, are continuously respected.

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To follow this course, you should have programming experience (three years or more), familiarity with formal (first-order) logic, formal proofs, logic programming, and concurrent programming. If you think you do not meet these requirements, please get in touch ASAP with one instructor to recommend you reading material.

Course Log and Pointers to Class Material

Click on the dates to expand the lecture’s content.

System Modelling using Refinement and Interactive Theorem Proving

05/02/2025: Introduction to rigorous software construction & first steps in Event B.

General introduction and the initial part of the Introduction to Event-B.

12/02/2025: Invariants, sequent calculus, proofs, inference rules

We continue with the Introduction to Event-B with the Event-B version of an algorithm for division which we will prove correct. In the meantime, we will see sequent calculus, inference rules, and some proof obligations.

19/02/2025: Sequent calculus, proofs, first steps with Rodin

We finished our terse review of logic and sequent calculus and how they are used to proof properties of models. We also started working with Rodin and writing some simple models for the integer division and search in an array.

26/02/2025: Sequential search, starting binary search.

We finished the example of sequential search in an array and proved correctness and termination using invariants that partially keep track of the story of the computation. We started to craft a model for binary search. Please find here the slides and the Rodin model so far.

5/3/2025: Sequential search, starting a reactive systems

We finished our sequential search example and model, including all the proofs and interaction with the theorem provers. We started an example of a reactive system: a controller for cars crossing a narrow bridge, including a minimal Rodin model.

Project Presentation Sessions

We plan one or two presentation sessions. We may have to use additional sessions depending on the number of project teams.

Location, Schedule, Administrivia

Place and time

During the academic year 2024-2025 we will meet physically at classroom 6205 from 3pm to 6pm on Wednesdays. We will post any exception on the course mailing list (see below) and the course log.

Teaching

Manuel Carro (coordinator)

Office 035 at the IMDEA Software Institute (under appointment)- mcarro |at| fi DOT upm DOT es.

Communication

For security reasons, you cannot subscribe to the mailing list by yourself. You should have been subscribed by some instructor, and you should have received a welcome message with the initial subscription. Note that you can only post to the list from the mail address that has been subscribed. If you want to change it, please let an instructor know. In normal situations, all important classroom announcements will go through the course mailing list, so please be sure to read the subscribed address regularly.

Course Policy

To keep this landing page short, the course policy appears in a separate page. This does not mean it is less important. Please make sure to read it.

Academic Resources

Please have a look as well at the Assorted Resources. It contains not-strictly-academic (but interesting) material!

Logic

  • Lawrence Paulson’s Logic and Proof are the course notes of the author for a Logic course in Cambridge. Highly recommended, as they are both rigorous and very concise. They provide very good background material for both parts of the course.
  • A very good book on the use of logic in computer science is Logic in Computer Science, by Huth and Ryan. It seems to be out of print, but the Computer Science School should have several copies. You may also consider locating an electronic copy on the Internet, if possible of the second edition.
  • Mathematical Logic for Computer Science. Mordechai Ben-Ari. There should be copies in the School’s library.
  • Sweet Reason: a Field Guide to Modern Logic.  James M. Henle, Jay L. Garfield, Thomas Tymoczko. This book explains several topics on logic and logic reasoning with many entertaining non-technical examples from many sources. It does not focus on logic and computation, however.
  • Class notes on Gentzen systems and single-conclusioned Gentzen systems and refinement logic (the sequent calculus we use in the lectures) from the Spring 2009 CS 4860 (Applied Logic) course in Cornell. Syntax node: these classnotes sometimes use “⊃” to denote implication, when we (and many others) use “⇒”.

Formal Development

  • Faultless Systems: Yes, we Can! is a short article by Jean-Raymond Abrial, the creator of Event-B (among other systems and proposals for rigorous software development) that explains the ideas behind the Event-B methodology.
  • Twenty-Five Years of the B-Method: a short overview of the history of B and its descendant Event B and some of the projects in which it has been used.

Event B Reference

  • The definitive reference for Event B is Modeling in Event-B: System and Software Engineering, by Jean-Raymond Abrial.
  • The richest information point for Event B is the Event B wiki. A summary of the inference and equality rules, axioms, proof obligations, and syntax of Event B can be found in these slides.
  • This reference card has a (very useful) summary of the Event B notation.
  • The mathematical toolkit of Event B is explained in a report.
  • An introduction to the Event-B method with a description of its phases.

Tools

Rodin

The essential tool to perform development with Event B is Rodin, an Eclipse-based tool. It includes an editor for the components of an Event B project that keeps track of the pending proof obligations and tries to discharge them on the fly. It has many plugins (installable directly from Rodin) that provide advanced theorem proving capabilities (to discharge proof obligations on demand and, hopefully, with only a button press), model checkers, animation, printout generation, and much more. You need to install it, as it will be use extensively during the course.

Please read this quick guide to installing Rodin. It includes some tips and instructions to perform several common tasks. This will save you time! At point, you will need to interact with the theorem provers. A page with tips for proving will be handy!

  • Homepage of the Rodin versions. Please make sure to download the latest version.
  • Installation instructions for RODIN.
  • The handbook for Rodin. It does not correspond the latest tool version: some details differ, but the basic ideas remain.
  • The Atelier B Provers plugin is necessary for any non-trivial development. Install it by going to Help ⇒ Install new software ⇒ select Atelier B Provers ⇒ Select in box ⇒ Click Next ⇒ Follow instructions. If you do not install these provers, many course examples will not work.
  • Relevant sections of the manuals:
    • How to set up a Rodin project (we will see it during the lectures).
    • Hints on discharging proofs using RODIN. Read it: it contains many hints and information on how to use the built-in and external theorem provers.
    • An explanation of the proving perspective from the user interface point of view.
    • A catalog of the proof obligations generated by RODIN and their meaning.
  • A list of the inference rules and rewriting rules in the default Event B prover (extracted from the Event B website).