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Hask is not a category 06 August 2016 Andrej Bauer Computation, Programming 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 someone does some serious work. Let us look at the matter a bit closer. The Haskell wiki page on Hask says: The objects of Hask

Brazilian type checking 06 May 2014 Andrej Bauer Type theory, Talks 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, the “paths” and the “strict” ones. It is based on a homotopy type system proposed by Vladimir Voevodsky. The slides contain talk n

How to implement dependent type theory I 08 November 2012 Andrej Bauer Type theory, Programming, Software, Tutorial I am spending a semester at the Institute for Advanced Study where we have a special year on Univalent foundations. We are doing all sorts of things, among others experimenting with type theories. We have got some real experts here who know type theory and Coq inside out, and much mo

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Representations of uncomputable and uncountable sets 06 February 2008 Andrej Bauer Computation, Tutorial Occasionally I hear claims that uncountable and uncomputable sets cannot be represented on computers. More generally, there are all sorts of misguided opinions about representations of data on computers, especially infinite data of mathematical nature. Here is a quick tutorial on the matter who

Seemingly impossible functional programs 28 September 2007 Martin Escardo Computation, Guest post, Tutorial Andrej has invited me to write about certain surprising functional programs. The first program, due to Ulrich Berger (1990), performs exhaustive search over the “Cantor space” of infinite sequences of binary digits. I have included references at the end. A weak form of exhaustive search amou