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Costa’s minimal surface with PovRay
A student of mine worked on a project to produce beautiful pictures of Costa’s minimal surface with the PovRay ray tracer. For this purpose she needed to triangulate the and compute normals to it at...
View ArticleUnivalent foundations subsume classical mathematics
A discussion on the homotopytypetheory mailing list prompted me to write this short note. Apparently a mistaken belief has gone viral among certain mathematicians that Univalent foundations is somehow...
View ArticleIntuitionistic Mathematics and Realizability in the Physical World
This is a draft version of my contribution to “A Computable Universe: Understanding and Exploring Nature as Computation”, edited by Hector Zenil. Consider it a teaser for the rest of the book, which...
View ArticleBrazilian type checking
I just gave a talk at “Semantics of proofs and certified mathematics”. I spoke about a new proof checker Chris Stone and I are working on. The interesting feature is that it has both kinds of equality,...
View ArticleReductions in computability theory from a constructive point of view
Here are the slides from my Logic Coloquium 2014 talk in Vienna. This is joint work with Kazuto Yoshimura from Japan Advanced Institute for Science and Technology. Abstract: In constructive mathematics...
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TEDx “Zeroes”
I spoke at TEDx University of Ljubljana. The topic was how programming influences various aspects of life. I showed the audence how a bit of simple programming can reveal the beauty of mathematics....
View ArticleA HoTT PhD position in Ljubljana
I am looking for a PhD student in mathematics. Full tuition & stipend will be provided for a period of three years, which is also the official length of the programme. The topic of research is...
View ArticleAnother PhD position in Ljubljana
It is my pleasure to announce a second PhD position in Ljubljana! A position is available for a PhD student at the University of Ljubljana in the general research area of modelling and reasoning about...
View ArticleThe troublesome reflection rule (TYPES 2015 slides)
Here are the slides of my TYPES 2015 talk “The troublesome reflection rule” with fairly detailed presenter notes. The meeting is taking place in Tallinn, Estonia – a very cool country in many senses...
View ArticleIntermediate truth values
I have not written a blog post in a while, so I decided to write up a short observation about truth values in intuitionistic logic which sometimes seems a bit puzzling. Let $\Omega$ be the set of truth...
View ArticleProvably considered harmful
This is officially a rant and should be read as such. Here is my pet peeve: theoretical computer scientists misuse the word “provably”. Stop it. Stop it! Theoretical computer science is closer to...
View ArticleAgda Writer
My student Marko Koležnik is about to finish his Master’s degree in Mathematics at the University of Ljubljana. He implemented Agda Writer, a graphical user interface for the Agda proof assistant on...
View ArticlePostdoc position in Ljubljana
A postdoc position in the Effmath research project is available at the University of Ljubljana, Faculty of Mathematics and Physics. The precise topic is flexible, but should generally be aligned with...
View ArticleA Brown-Palsberg self-interpreter for Gödel’s System T
In a paper accepted at POPL 2016 Matt Brown and Jens Palsberg constructed a self-interpreter for System $F_\omega$, a strongly normalizing typed $\lambda$-calculus. This came as a bit of a surprise as...
View ArticleThe Andromeda proof assistant (Leeds workshop slides)
I am about to give an invited talk at the Workshop on Categorical Logic and Univalent Foundations 2016 in Leeds, UK. It’s a charming workshop that I am enjoing a great deal. Here are the slides of my...
View ArticleHask is not a category
This post is going to draw an angry Haskell mob, but I just have to say it out loud: I have never seen a definition of the so-called category Hask and I do not actually believe there is one until...
View ArticleWhat is a formal proof?
Mike Shulman just wrote a very nice blog post on what is a formal proof. I much agree with what he says, but I would like to offer my own perspective. I started writing it as a comment to Mike’s post...
View ArticleFormal proofs are not just deduction steps
I have participated in a couple of lengthy discussions about formal proofs. I realized that an old misconception is creeping in. Let me expose it. In traditional mathematical logic (by which I mean...
View ArticleThe new and improved Programming languages zoo
It is my pleasure to announce the new and improved Programming languages Zoo, a potpourri of miniature but fully functioning programming language implementations. The new zoo has a decent web site, it...
View ArticleFive stages of accepting constructive mathematics
In 2013 I gave a talk about constructive mathematics “Five stages of accepting constructive mathematics” (video) at the Institute for Advanced Study. I turned the talk into a paper, polished it up a...
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