Text - Marvin BornerArticles about my projects.
https://text.marvinborner.de
Crafting Formulas: Lambdas All the Way DownToday we build complex mathematical formulas bottom-up using pure lambda calculus. This includes instructions of how to translate Taylor series and other approximations to lambda terms.
https://text.marvinborner.de/2024-04-16-10.html
2024-04-16-10Tue, 06 Aug 2024 01:57:06 +0000Lambda Screen: Fractals in Pure Lambda CalculusLambda Screen allows you to draw images using terms of pure lambda calculus. By using fixed-point combinators, you can even create infinitely detailed fractals.
https://text.marvinborner.de/2024-03-25-02.html
2024-03-25-02Mon, 08 Apr 2024 01:23:14 +0000Metaprogramming and self-interpretationWith inspiration from John Tromp's 232 bit lambda calculus self interpreter I created a universal machine for a homoiconic meta encoding based on the Mogensen-Scott encoding and Church-encoded De Bruijn indices.
https://text.marvinborner.de/2023-09-03-21.html
2023-09-03-21Sat, 11 Nov 2023 19:35:42 +0000Unary combinatory logicTwo symbols for programming are clearly too many -- that's why I created a unary basis for the esoteric programming language Jot called Jottary. It's a unary combinatory logic miracle!
https://text.marvinborner.de/2023-10-05-15.html
2023-10-05-15Fri, 06 Oct 2023 18:57:11 +0000(nω) vs. (ωn)Short post about two similar and yet quite different sequences in lambda calculus involving the omega combinator and Church encoded numerals.
https://text.marvinborner.de/2023-07-27-23.html
2023-07-27-23Fri, 28 Jul 2023 02:41:16 +0000Variadic fixed-point combinatorsThis article describes an extension to the default fixed-point combinator – namely the Y-combinator. We do this by translating the Scheme code from a paper to bruijn (lambda calculus).
https://text.marvinborner.de/2023-06-18-15.html
2023-06-18-15Sat, 08 Jul 2023 18:44:42 +0000The bruijn programming languageThe bruijn programming language is pure lambda calculus with some syntactic improvements. It doesn’t have any primitive functions – how is that possible?
https://text.marvinborner.de/2023-04-06-01.html
2023-04-06-01Thu, 06 Apr 2023 01:32:16 +0000Data structures in pure lambda calculusThis article explains different strategies of encoding data as pure lambda calculus expressions – from simple states and boxes to more complex data structures like lists and trees.
https://text.marvinborner.de/2023-04-07-01.html
2023-04-07-01Fri, 07 Apr 2023 01:17:32 +0000Space-efficient binary lambda calculus encoding for binary dataSpace-efficient binary lambda calculus encoding for binary data
https://text.marvinborner.de/2023-04-24-13.html
2023-04-24-13Mon, 24 Apr 2023 13:46:15 +0000Hash-based approach to building shared λ-graphsAn algorithm for deriving shared λ-graphs from expressions in pure lambda calculus by using hashes in a postorder tree traversal.
https://text.marvinborner.de/2023-05-30-16.html
2023-05-30-16Tue, 30 May 2023 16:15:25 +0000