Mathematics and Computation http://math.andrej.com Mathematics for computers Tue, 06 May 2008 22:32:33 +0000 http://wordpress.org/?v=2.3.3 en An object-oriented language Boa http://math.andrej.com/2008/05/07/an-object-oriented-language-boa/ http://math.andrej.com/2008/05/07/an-object-oriented-language-boa/#comments Tue, 06 May 2008 22:32:33 +0000 Andrej Bauer http://math.andrej.com/2008/05/07/an-object-oriented-language-boa/ I have added another language, called Boa, to the Programming Languages Zoo. It is an object-oriented language with the following features:

  • integers and booleans as base types,
  • first-class functions,
  • dynamically typed,
  • objects are extensible records with mutable fields,
  • there are no classes, instead we can define “prototype” objects and extend them
    to create instances.

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]]> http://math.andrej.com/2008/05/07/an-object-oriented-language-boa/feed/ The Programming Languages Zoo http://math.andrej.com/2008/05/06/the-programming-languages-zoo/ http://math.andrej.com/2008/05/06/the-programming-languages-zoo/#comments Tue, 06 May 2008 10:43:42 +0000 Andrej Bauer http://math.andrej.com/2008/05/06/the-programming-languages-zoo/ I teach Theory of Programing Languages (page in Slovene). For the course I implemented languages which demonstrate basic concepts such as parsing, type checking, type inference, dynamic types, evaluation strategies, and compilation. My teaching assistant Iztok Kavkler contributed to the source code as well. I decided to publish the source code as a Programming Language Zoo for anyone who wants to know more about design and implementation of programming languages.
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]]> http://math.andrej.com/2008/05/06/the-programming-languages-zoo/feed/ Representations of uncomputable and uncountable sets http://math.andrej.com/2008/02/06/representations-of-uncomputable-and-uncountable-sets/ http://math.andrej.com/2008/02/06/representations-of-uncomputable-and-uncountable-sets/#comments Wed, 06 Feb 2008 10:27:10 +0000 Andrej Bauer http://math.andrej.com/2008/02/06/representations-of-uncomputable-and-uncountable-sets/ 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 whose main point is:

It is meaningless to discuss representations of a set by a datatype without also considering operations that we want to perform on the set.

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]]> http://math.andrej.com/2008/02/06/representations-of-uncomputable-and-uncountable-sets/feed/ The hydra game http://math.andrej.com/2008/02/02/the-hydra-game/ http://math.andrej.com/2008/02/02/the-hydra-game/#comments Sat, 02 Feb 2008 01:13:21 +0000 Andrej Bauer http://math.andrej.com/2008/02/02/the-hydra-game/ Today I lectured about the Hydra game by Laurence Kirby and Jeff Paris (Accessible Independence Results for Peano Arithmetic, Kirby and Paris, Bull. London Math. Soc. 1982; 14: 285-293). For the occasion I implemented the game in Java. I am publishing the code for anyone who wants to play, or use it for teaching. (more…)

]]> http://math.andrej.com/2008/02/02/the-hydra-game/feed/ Lambda calculus for real analysis by Paul Taylor http://math.andrej.com/2008/02/02/lambda-calculus-for-real-analysis-by-paul-taylor/ http://math.andrej.com/2008/02/02/lambda-calculus-for-real-analysis-by-paul-taylor/#comments Fri, 01 Feb 2008 23:28:14 +0000 Andrej Bauer http://math.andrej.com/2008/02/02/lambda-calculus-for-real-analysis-by-paul-taylor/ Paul Taylor has published a revised version of his `lambda`-calculus for real analysis. I recommend it to anyone who is interested in real analysis, be it a computer scientist, numerical analyst, or just a “true” analyst.

The first, second, and third time I talked to Paul I could not understand a word of what he was saying, and that’s not just because he is a native speaker of English English. I only began to “get it” when he visited me in Ljubljana. So I think it’s perhaps worth explaining a bit what this “`lambda`-calculus for real analysis” is about.

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