http://math.andrej.com Mathematics for computers Tue, 06 May 2008 22:32:33 +0000 http://backend.userland.com/rss092 en 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 ... http://math.andrej.com/2008/05/07/an-object-oriented-language-boa/ 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 ... http://math.andrej.com/2008/05/06/the-programming-languages-zoo/ 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 ... http://math.andrej.com/2008/02/06/representations-of-uncomputable-and-uncountable-sets/ 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, ... http://math.andrej.com/2008/02/02/the-hydra-game/ 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 ... http://math.andrej.com/2008/02/02/lambda-calculus-for-real-analysis-by-paul-taylor/