Bertrand Meyer's technology+ blog https://bertrandmeyer.com/ Software engineering, programming methodology, languages, verification, general technology, publication culture, and more Wed, 18 Mar 2026 16:23:43 +0000 en-US hourly 1 https://wordpress.org/?v=6.8.5 Celebrating Tony Hoare’s mark on computer science https://bertrandmeyer.com/2026/03/16/celebrating-tony-hoares-mark-on-computer-science/ https://bertrandmeyer.com/2026/03/16/celebrating-tony-hoares-mark-on-computer-science/#comments Mon, 16 Mar 2026 18:07:39 +0000 https://bertrandmeyer.com/?p=6935 Tony Hoare at the LASER summer school, September 2007 (All photographs in this article are by the author) Had they included just one of Tony Hoare’s major achievements, many scientific careers would be considered prestigious enough. His had a long list, which I am going to try to summarize, not pretending to get anywhere close ... Read more

The post Celebrating Tony Hoare’s mark on computer science appeared first on Bertrand Meyer's technology+ blog.

]]> https://bertrandmeyer.com/2026/03/16/celebrating-tony-hoares-mark-on-computer-science/feed/ 2 Yes, AI is intelligent. Prove me wrong. https://bertrandmeyer.com/2026/02/26/yes-ai-is-intelligent-prove-me-wrong/ https://bertrandmeyer.com/2026/02/26/yes-ai-is-intelligent-prove-me-wrong/#comments Thu, 26 Feb 2026 20:41:46 +0000 https://bertrandmeyer.com/?p=6915 It must be a sign of how terrified people are of Modern-AI, and running out of arguments to decry it, that we now read and hear, ever more often, pronouncements that “it is not intelligent”. They come from the many self-appointed great minds who pontificate about AI these days, as well as some truly great ... Read more

The post Yes, AI is intelligent. Prove me wrong. appeared first on Bertrand Meyer's technology+ blog.

]]> https://bertrandmeyer.com/2026/02/26/yes-ai-is-intelligent-prove-me-wrong/feed/ 3 Assemblée annuelle de la SDIS https://bertrandmeyer.com/2026/01/20/assemblee-annuelle-de-la-sdis/ https://bertrandmeyer.com/2026/01/20/assemblee-annuelle-de-la-sdis/#respond Tue, 20 Jan 2026 09:41:35 +0000 https://bertrandmeyer.com/?p=6855 Société pour la Défense de l’Imparfait du Subjonctif (SDIS) Compte-rendu de l’assemblée annuelle 2025, 1er décembre 2025. Présents : Président, Secrétaire, Premier et Second vice-présidents, Trésorier, représentant des adhérents. Le Secrétaire (Bertrand Meyer) ouvre la séance à 17 heures et souhaite la bienvenue à tous les participants. La séance se poursuit avec le rapport du ... Read more

The post Assemblée annuelle de la SDIS appeared first on Bertrand Meyer's technology+ blog.

]]> https://bertrandmeyer.com/2026/01/20/assemblee-annuelle-de-la-sdis/feed/ 0 CloudFlare outage: the lesson that will not be drawn https://bertrandmeyer.com/2026/01/06/cloudflare-outage-the-lesson-that-will-not-be-drawn/ https://bertrandmeyer.com/2026/01/06/cloudflare-outage-the-lesson-that-will-not-be-drawn/#respond Mon, 05 Jan 2026 23:05:55 +0000 https://bertrandmeyer.com/?p=6822 [This note was first published in my newsletter (23 November 2025. One can subscribe to the newsletter here.] I might sound like a broken record, but the CloudFlare outage is one more example of the consequences of the software industry making the wrong technical choices. Where were the contracts? Rust, by all accounts the language ... Read more

The post CloudFlare outage: the lesson that will not be drawn appeared first on Bertrand Meyer's technology+ blog.

]]> https://bertrandmeyer.com/2026/01/06/cloudflare-outage-the-lesson-that-will-not-be-drawn/feed/ 0 Criteria and recipes for good technical definitions https://bertrandmeyer.com/2025/12/29/criteria-and-recipes-for-good-technical-definitions/ https://bertrandmeyer.com/2025/12/29/criteria-and-recipes-for-good-technical-definitions/#respond Mon, 29 Dec 2025 11:59:33 +0000 https://bertrandmeyer.com/?p=6820 (A version of this note was published as three separate articles in the Communications of the ACM blog.) Work in engineering, science or technology can only be effective if it relies on precisely defined concepts. For the fundamental notions taught at school, particularly in mathematics, physics, and chemistry, the definitions, honed over centuries, have become ... Read more

The post Criteria and recipes for good technical definitions appeared first on Bertrand Meyer's technology+ blog.

]]> https://bertrandmeyer.com/2025/12/29/criteria-and-recipes-for-good-technical-definitions/feed/ 0 A revolutionary approach to university teaching https://bertrandmeyer.com/2025/11/11/a-revolutionary-approach-to-university-teaching/ https://bertrandmeyer.com/2025/11/11/a-revolutionary-approach-to-university-teaching/#comments Tue, 11 Nov 2025 18:02:45 +0000 https://bertrandmeyer.com/?p=6700 We are all familiar with the classical mode of teaching. The instructor and other attendees, each sitting alone in a geographical location as far away as possible from all the others,  look at shared PowerPoint slide and a grid of black rectangles with names. The names refer to students, although they are usually not their ... Read more

The post A revolutionary approach to university teaching appeared first on Bertrand Meyer's technology+ blog.

]]> https://bertrandmeyer.com/2025/11/11/a-revolutionary-approach-to-university-teaching/feed/ 1 Thanks for your help but I write my own texts https://bertrandmeyer.com/2025/11/02/thanks-for-your-help-but-i-write-my-own-texts/ https://bertrandmeyer.com/2025/11/02/thanks-for-your-help-but-i-write-my-own-texts/#comments Sun, 02 Nov 2025 21:07:57 +0000 https://bertrandmeyer.com/?p=6696 Here is an extract from of an exchange between ChatGPT and me. Previous elements: I am writing a text on a topic that I know well but not to the point of considering myself an expert. Along the way, I am asking ChatGPT for information, or confirmation of information that I think I know. Indeed, ... Read more

The post Thanks for your help but I write my own texts appeared first on Bertrand Meyer's technology+ blog.

]]> https://bertrandmeyer.com/2025/11/02/thanks-for-your-help-but-i-write-my-own-texts/feed/ 1 Exponentially bad phrasing https://bertrandmeyer.com/2025/09/12/exponentially-bad-phrasing/ https://bertrandmeyer.com/2025/09/12/exponentially-bad-phrasing/#respond Fri, 12 Sep 2025 12:08:13 +0000 https://bertrandmeyer.com/?p=6660 The news is so bad right now everywhere that it is natural to take refuge in discussing matters of (bad) style. I have things to say about the real issues too but not this time. I am following in the tradition of Niklaus Wirth who told me that he regularly sent letters of complaint to ... Read more

The post Exponentially bad phrasing appeared first on Bertrand Meyer's technology+ blog.

]]> https://bertrandmeyer.com/2025/09/12/exponentially-bad-phrasing/feed/ 0 More sizzle than steak? Using an LLM to produce verified bug fixes (new preprint) https://bertrandmeyer.com/2025/07/24/more-sizzle-than-steak-using-an-llm-to-produce-verified-bug-fixes-new-paper/ https://bertrandmeyer.com/2025/07/24/more-sizzle-than-steak-using-an-llm-to-produce-verified-bug-fixes-new-paper/#respond Thu, 24 Jul 2025 16:44:00 +0000 https://bertrandmeyer.com/?p=6642 New article: “Do AI models help produce verified bug fixes?” (Huang Li, Ilgiz Mustafin, Marco Piccioni, Alessandro Schena, Reto Weber and Bertrand Meyer), submitted for publication, preprint available on arXiv.  Automatic Program Repair (APR) involves four steps: Locating the bug. Producing candidate corrections. Validating them (to make sure that they do correct the problem). Selecting the ... Read more

The post More sizzle than steak? Using an LLM to produce verified bug fixes (new preprint) appeared first on Bertrand Meyer's technology+ blog.

]]> https://bertrandmeyer.com/2025/07/24/more-sizzle-than-steak-using-an-llm-to-produce-verified-bug-fixes-new-paper/feed/ 0 A paean to programming https://bertrandmeyer.com/2025/04/23/a-paean-to-programming/ https://bertrandmeyer.com/2025/04/23/a-paean-to-programming/#respond Wed, 23 Apr 2025 13:08:00 +0000 https://bertrandmeyer.com/?p=6557 A Google search for something entirely unrelated led me to a very old issue of the Daily Nexus, the student newspaper of the University of California, Santa Barbara, where I was teaching back then.  Apparently (I had forgotten all about it of course) I was piqued by a student’s letter to the editor, where he ... Read more

The post A paean to programming appeared first on Bertrand Meyer's technology+ blog.

]]> https://bertrandmeyer.com/2025/04/23/a-paean-to-programming/feed/ 0 New article: obituary of Niklaus Wirth https://bertrandmeyer.com/2025/03/04/new-article-obituary-of-niklaus-wirth/ https://bertrandmeyer.com/2025/03/04/new-article-obituary-of-niklaus-wirth/#respond Tue, 04 Mar 2025 20:52:22 +0000 https://bertrandmeyer.com/?p=6508 Bertrand Meyer: Obituary for Niklaus Wirth, in Formal Aspects of Computing, volume 37, issue 2, pages 1-11, published 3 March 2025, available here (publisher’s site). Shortly after Niklaus Wirth — Turing Award winner for his many seminal contributions including Pascal, Algol W, Modula, virtual machines, Lilith/Ceres, railway diagrams, PL/360, seminal textbooks…  — passed away last ... Read more

The post New article: obituary of Niklaus Wirth appeared first on Bertrand Meyer's technology+ blog.

]]> https://bertrandmeyer.com/2025/03/04/new-article-obituary-of-niklaus-wirth/feed/ 0 New preprint: Lessons from Formally Deployed Software Systems https://bertrandmeyer.com/2025/03/04/new-preprint-lessons-from-formally-deployed-software-systems/ https://bertrandmeyer.com/2025/03/04/new-preprint-lessons-from-formally-deployed-software-systems/#respond Tue, 04 Mar 2025 15:44:22 +0000 https://bertrandmeyer.com/?p=6502 Li Huang, Sophie Ebersold, Alexander Kogtenkov, Bertrand Meyer and Yinling Liu, Lessons from Formally Verified Deployed Software Systems, submitted for publication (since March 2023), preprint available here for the full version (with detailed review of all 32 projects) and here for a shorter one (with same core content but only 11 detailed reviews, the others ... Read more

The post New preprint: Lessons from Formally Deployed Software Systems appeared first on Bertrand Meyer's technology+ blog.

]]> https://bertrandmeyer.com/2025/03/04/new-preprint-lessons-from-formally-deployed-software-systems/feed/ 0 New preprint: Seamless and Traceable Requirements https://bertrandmeyer.com/2025/03/03/new-preprint-seamless-and-traceable-requirements/ https://bertrandmeyer.com/2025/03/03/new-preprint-seamless-and-traceable-requirements/#respond Mon, 03 Mar 2025 10:09:49 +0000 https://bertrandmeyer.com/?p=6496 Maria Naumcheva, Sophie Ebersold, Jean-Michel Bruel and Bertrand Meyer, UOOR: Seamless and Traceable Requirements, submitted for publication, February 2025, preprint available on arXiv. This article grew out of Maria Naumcheva’s PhD thesis defended on December 18 at the University of Toulouse (I will write separately about the thesis as a whole). It is part of ... Read more

The post New preprint: Seamless and Traceable Requirements appeared first on Bertrand Meyer's technology+ blog.

]]> https://bertrandmeyer.com/2025/03/03/new-preprint-seamless-and-traceable-requirements/feed/ 0 New preprint: Loop unrolling — formal definition and application to testing https://bertrandmeyer.com/2025/02/28/new-preprint-loop-unrolling-formal-definition-and-application-to-testing/ https://bertrandmeyer.com/2025/02/28/new-preprint-loop-unrolling-formal-definition-and-application-to-testing/#respond Fri, 28 Feb 2025 12:36:52 +0000 https://bertrandmeyer.com/?p=6486 Li Huang, Bertrand Meyer and Reto Weber, New preprint: Loop unrolling:  formal definition and application to testing, February 2025, submitted to publication. Available here on arXiv and also here. Abstract Testing coverage criteria usually make a gross simplification: they assume that loops will have their bodies executed 0 or 1 time. How much (specificall,y how ... Read more

The post New preprint: Loop unrolling — formal definition and application to testing appeared first on Bertrand Meyer's technology+ blog.

]]> https://bertrandmeyer.com/2025/02/28/new-preprint-loop-unrolling-formal-definition-and-application-to-testing/feed/ 0 New preprint: a standard framework for research on bugs and automatic program repair https://bertrandmeyer.com/2025/02/27/new-preprint-a-standard-framework-for-research-on-bugs-and-automatic-program-repair/ https://bertrandmeyer.com/2025/02/27/new-preprint-a-standard-framework-for-research-on-bugs-and-automatic-program-repair/#respond Thu, 27 Feb 2025 15:11:34 +0000 https://bertrandmeyer.com/?p=6472 Preprint of new article: Victoria Kananchuk, Ilgiz Mustafin and Bertrand Meyer, Bugfix: a standard language, database schema and repository for research on bugs and automatic program repair, submitted for publication, February 2025. Available on arXiv here. Also available here. What this is in a nutshell (there is a longer abstract below): a proposal for, and ... Read more

The post New preprint: a standard framework for research on bugs and automatic program repair appeared first on Bertrand Meyer's technology+ blog.

]]> https://bertrandmeyer.com/2025/02/27/new-preprint-a-standard-framework-for-research-on-bugs-and-automatic-program-repair/feed/ 0 New paper: seeding contradiction https://bertrandmeyer.com/2025/02/26/new-paper-seeding-contradiction/ https://bertrandmeyer.com/2025/02/26/new-paper-seeding-contradiction/#respond Wed, 26 Feb 2025 21:25:03 +0000 https://bertrandmeyer.com/?p=6475 Just published: Li Huang, Bertrand Meyer and Manuel Oriol, Seeding Contradiction: a fast method for generating full-coverage test suites, in Springer Nature Computer Science, vol. 6, no. 4, 2025. The text is available here on the publisher’s site. Also available is a preprint version. This just published SNCS article and revised and extended from a ... Read more

The post New paper: seeding contradiction appeared first on Bertrand Meyer's technology+ blog.

]]> https://bertrandmeyer.com/2025/02/26/new-paper-seeding-contradiction/feed/ 0 New preprint: Programming Really Is Simple Mathematics https://bertrandmeyer.com/2025/02/25/new-preprint-programming-really-is-simple-mathematics/ https://bertrandmeyer.com/2025/02/25/new-preprint-programming-really-is-simple-mathematics/#respond Tue, 25 Feb 2025 18:05:34 +0000 https://bertrandmeyer.com/?p=6465 Bertrand Meyer and Reto Weber: Meaning as Programs — Programming Really Is Simple Mathematics, February 2025 preprint available here and also on arXiv. Theories of programming can be quite complicated; the presentation here is a return to essentials, defining programming and associated concepts (programming languages, programming methodology) entirely from elementary set-theoretical concepts. Unlike much of ... Read more

The post New preprint: Programming Really Is Simple Mathematics appeared first on Bertrand Meyer's technology+ blog.

]]> https://bertrandmeyer.com/2025/02/25/new-preprint-programming-really-is-simple-mathematics/feed/ 0 This is much worse than Munich https://bertrandmeyer.com/2025/02/21/this-is-much-worse-than-munich/ https://bertrandmeyer.com/2025/02/21/this-is-much-worse-than-munich/#respond Fri, 21 Feb 2025 17:46:00 +0000 https://bertrandmeyer.com/?p=6459 In Munich in 1938, Chamberlain and Daladier made the wrong decision, but they were driven by honorable motives. Chamberlain was weak but wanted to preserve short-term peace at all costs; Daladier was entirely lucid, but he had taken a look at the state of preparation of the French forces and wanted to buy time to ... Read more

The post This is much worse than Munich appeared first on Bertrand Meyer's technology+ blog.

]]> https://bertrandmeyer.com/2025/02/21/this-is-much-worse-than-munich/feed/ 0 New preprint: Software engineering as a domain to formalize https://bertrandmeyer.com/2025/02/13/software-engineering-as-a-domain-to-formalize/ https://bertrandmeyer.com/2025/02/13/software-engineering-as-a-domain-to-formalize/#respond Thu, 13 Feb 2025 21:27:12 +0000 https://bertrandmeyer.com/?p=6457 Bertrand Meyer, Software engineering as a domain to formalize, available here. This article is meant as a blog but was written as a standard text and I haven’t had the time to HTML-ize yet. So I am just providing an abstract below, and linking to the PDF which gives the details. The purpose is simple: ... Read more

The post New preprint: Software engineering as a domain to formalize appeared first on Bertrand Meyer's technology+ blog.

]]> https://bertrandmeyer.com/2025/02/13/software-engineering-as-a-domain-to-formalize/feed/ 0 “I don’t have time for administration” https://bertrandmeyer.com/2025/02/03/dont-time-administration/ https://bertrandmeyer.com/2025/02/03/dont-time-administration/#respond Mon, 03 Feb 2025 22:10:30 +0000 https://bertrandmeyer.com/?p=6441 Academic life includes self-governance and require people to sit in committees, take on various duties, serve as director of studies, graduate program director, chair of PhD chair of external relations, department vice chair or chair, dean… Not everyone wants to play. It is not rare to encounter faculty members who tell you bluntly that as ... Read more

The post “I don’t have time for administration” appeared first on Bertrand Meyer's technology+ blog.

]]> https://bertrandmeyer.com/2025/02/03/dont-time-administration/feed/ 0 The path wrongly taken https://bertrandmeyer.com/2024/11/07/path-wrongly-taken/ https://bertrandmeyer.com/2024/11/07/path-wrongly-taken/#comments Thu, 07 Nov 2024 00:10:07 +0000 https://bertrandmeyer.com/?p=6421 The dominant discourse right now is “Calm down, this is just the normal game of democracy”. Actually, “this” is not the normal course of democracy. Everyone has experienced the disappointment of a favored candidate losing. The result of Tuesday is something else, not seen before in our lifetime: the triumph of indecency and the rout ... Read more

The post The path wrongly taken appeared first on Bertrand Meyer's technology+ blog.

]]> https://bertrandmeyer.com/2024/11/07/path-wrongly-taken/feed/ 5 Europe asleep (a key-not) https://bertrandmeyer.com/2024/10/29/europe-asleep-key-not/ https://bertrandmeyer.com/2024/10/29/europe-asleep-key-not/#respond Tue, 29 Oct 2024 00:58:32 +0000 https://bertrandmeyer.com/?p=6387 This week, Informatics Europe, the association of European computer science departments and industry research centers, is holding its annual ECSS event, bizarrely billed as “20 years of Informatics Europe”. (Informatics Europe was created at the end of 2006 and incorporated officially in 2011. The first ever mention of the name appeared in an email from ... Read more

The post Europe asleep (a key-not) appeared first on Bertrand Meyer's technology+ blog.

]]> https://bertrandmeyer.com/2024/10/29/europe-asleep-key-not/feed/ 0 The power and terror of imagination https://bertrandmeyer.com/2024/09/03/power-terror-imagination/ https://bertrandmeyer.com/2024/09/03/power-terror-imagination/#respond Tue, 03 Sep 2024 19:44:23 +0000 https://bertrandmeyer.com/?p=6355 Reading notes. From: Quelques éléments d’histoire des nombres négatifs (Elements of a history of negative numbers) by Anne Boyé, Proyecto Pénélope, 2002, revision available here; On Solving Equations, Negative Numbers, and Other Absurdities: Part II by Ralph Raimi, available  here; Note sur l’histoire des nombres entiers négatifs (Note on the History of Negative Numbers) by ... Read more

The post The power and terror of imagination appeared first on Bertrand Meyer's technology+ blog.

]]> https://bertrandmeyer.com/2024/09/03/power-terror-imagination/feed/ 0 Freely accessible books https://bertrandmeyer.com/2024/08/15/freely-accessible-books/ https://bertrandmeyer.com/2024/08/15/freely-accessible-books/#comments Thu, 15 Aug 2024 18:36:19 +0000 https://bertrandmeyer.com/?p=6334 Recently I prepared some of my books for free access on the Web (after gaining agreement from the publishers). Here are the corresponding links. They actually point to pages that present the respective books and have further links to the actual PDF versions. Although the texts are essentially those of the books as published, I ... Read more

The post Freely accessible books appeared first on Bertrand Meyer's technology+ blog.

]]> https://bertrandmeyer.com/2024/08/15/freely-accessible-books/feed/ 2 And what if everything went well? https://bertrandmeyer.com/2024/07/25/everything-went-well/ https://bertrandmeyer.com/2024/07/25/everything-went-well/#respond Thu, 25 Jul 2024 20:44:58 +0000 https://bertrandmeyer.com/?p=6330 After all, for the first time in decades, France has had a competent government since 2017, and it shows.

The post And what if everything went well? appeared first on Bertrand Meyer's technology+ blog.

]]> https://bertrandmeyer.com/2024/07/25/everything-went-well/feed/ 0 The French School of Programming https://bertrandmeyer.com/2024/07/14/french-school-programming/ https://bertrandmeyer.com/2024/07/14/french-school-programming/#comments Sun, 14 Jul 2024 21:43:33 +0000 https://bertrandmeyer.com/?p=6320 July 14 (still here for 15 minutes) is not a bad opportunity to announced the publication of a new book: The French School of Programming. The book is a collection of chapters, thirteen of them, by rock stars of programming and software engineering research (plus me), preceded by a Foreword by Jim Woodcock and a ... Read more

The post The French School of Programming appeared first on Bertrand Meyer's technology+ blog.

]]> https://bertrandmeyer.com/2024/07/14/french-school-programming/feed/ 2 Descente aux enfers https://bertrandmeyer.com/2024/06/25/descente-aux-enfers/ https://bertrandmeyer.com/2024/06/25/descente-aux-enfers/#comments Tue, 25 Jun 2024 17:12:42 +0000 https://bertrandmeyer.com/?p=6311 [English version forthcoming.] Que peut-on faire ? Un pays vieux d’un millénaire et demi est en train de se suicider. Pour tentant que soit le désespoir, il est encore temps d’agir. Le pire scénario, c’est la menace de la gauche. Ce qu’il restait de sociaux-démocrates s’est prosterné devant une bande d’extrémistes décidés à détruire toute ... Read more

The post Descente aux enfers appeared first on Bertrand Meyer's technology+ blog.

]]> https://bertrandmeyer.com/2024/06/25/descente-aux-enfers/feed/ 1 Upside down https://bertrandmeyer.com/2024/06/04/upside-down/ https://bertrandmeyer.com/2024/06/04/upside-down/#comments Tue, 04 Jun 2024 20:59:18 +0000 https://bertrandmeyer.com/?p=6254 What is going on? In the US, the leading presidential candidate is a vulgar crook, a serial business failure and convicted business fraudster; more ominously, he acts like a vassal to Putin. His first term was an endless string of catastrophes, including the deaths of hundreds of thousands of his compatriots through gross mismanagement. And ... Read more

The post Upside down appeared first on Bertrand Meyer's technology+ blog.

]]> https://bertrandmeyer.com/2024/06/04/upside-down/feed/ 1 Horribly transparent https://bertrandmeyer.com/2024/06/02/horribly-transparent/ https://bertrandmeyer.com/2024/06/02/horribly-transparent/#respond Sun, 02 Jun 2024 19:51:27 +0000 https://bertrandmeyer.com/?p=6227 A few years ago I was driving on a freeway in France and turned on the radio, chancing on France-Culture. (In passing it is fair to note the abundance of quality programs on that station. It has its share of empty Parisian intellectual chit-chat but much of the time I learn something interesting.) I was ... Read more

The post Horribly transparent appeared first on Bertrand Meyer's technology+ blog.

]]> https://bertrandmeyer.com/2024/06/02/horribly-transparent/feed/ 0 Mathematics is not a game of hit and miss https://bertrandmeyer.com/2024/05/28/mathematics-not-game-hit-miss/ https://bertrandmeyer.com/2024/05/28/mathematics-not-game-hit-miss/#respond Tue, 28 May 2024 16:39:12 +0000 https://bertrandmeyer.com/?p=6225 I was recently looking at the math exercises of a 14-year-old, having to do with quadratic (second-degree) equations. The first thing that caught my eye is not a surprise: the difference between school and life. The quadratic polynomials appearing in the exercises, such as x2 – x – 6, all happen to have integer roots ... Read more

The post Mathematics is not a game of hit and miss appeared first on Bertrand Meyer's technology+ blog.

]]> https://bertrandmeyer.com/2024/05/28/mathematics-not-game-hit-miss/feed/ 0