formform is a modular Clojure/ClojureScript library all about the 4-valued logic of cognition first introduced 2017 by Ralf Peyn in uFORM iFORM. In its core, the purpose of the library is to enable the representation, evaluation and algebraic simplification of all (undetermined, imaginary, unclear, …) FORMs that have been introduced in the book.
Please note that this library is still in an alpha state and breaking api changes might happen (although I try to keep them to a minimum), so do not rely on it for your projects yet. Otherwise, make sure to follow the Change Log where I document all breaking changes between releases.
The library is divided into 3 core modules:
calc: calculate with the 4 value constants or create and transform value structures such as value tables/maps and what I call formDNAexpr: construct, simplify and evaluate various FORM expressions or define and use powerful abstractions I call symbolic expressionsemul: (unreleased) emulate FORMal systems as cellular automata that can be composed à la carte from declarative building-blocks
In addition, the io module can read and print strings in FORMula notation, which is easier for end users to read and write
To visualize expressions, value structures and cellular automata, I created the formform-vis library (wip).
As a helpful tool for researchers and enthusiasts and as a demonstration of the library's capabilities I have also created the FORM tricorder (it still uses an old, but stable version of formform). It can calculate, represent and visualize FORMs using an older version of FORMula syntax, which is explained in the app (click on Show explanations). A complete redesign of the app is coming very soon.
Further applications (like a cellular automaton) are listed on the formform website.
The main goals of formform are:
- to be correct and complete with regards to the calculus
- to be flexible and extendable enough for any imaginable application
- to provide a clear, simple and efficient API
- to provide reliable output that can be easily transformed and shared
Although I constantly try to improve performance, it is not a main goal and I am not qualified enough for sophisticated optimizations. You are very welcome to contribute in this area and correct my mistakes.
I do also want to stress that I am neither an academic mathematician/logician nor a professional software engineer. It is my ambition to reach the goals stated above as closely as possible, but you should make sure to double-check any results if you want to work with this library in a serious manner. I have written a lot of tests for each module in the test/ directory, so you may use these as a reference point.
Another thing to keep in mind is that I made lots of unconventional creative choices in the design of formform. In many cases this is due to my own curiosity that I wanted to satisfy using the library as a tool for exploration. In other cases it is because I am building specialized apps on top of formform. Still, I always try to make it as useful as possible for most typical use-cases. Please let me know if you are missing something that would be useful to you and I see if I can implement it.
If you want to learn more about the calculus, ideas and theories formform is based upon, here are some helpful resources:
- About uFORM iFORM (mostly German as is the language of the book by Ralf Peyn, but you can try DeepL to translate the gist of it)
- Here is a list of links on the theoretical background behind uFORM iFORM (mostly German resources, but you can just translate the keywords and google them)
- 3-dimensional FORM animations and FORM-builder (a project I made back in 2017 that greatly influenced my approach to formform)
- Blog s y s t e m z e i t by Gitta Peyn – German and English articles about systemic research based on uFORM iFORM
- About FORMWELT – a coding language for language and meaning founded on the logic of cognition introduced in uFORM iFORM (by the way, we appreciate any support for the development of FORMWELT Online!)
This library has become my personal project since I first began studying uFORM iFORM, published by Ralf Peyn in 2017. Ralf's “SelFis” (visual interpretation of a partial System of the self-referential System of the FORM) inspired me to develop my own cellular automaton in the programming environment Processing to dig deeper and gain a deeper unterstanding of these systems.
Working with lookup-tables for FORM calculations was okay for a while, but also very tedious and impractical for my research, so I began working on some functions that would do the calculations for me. In 2018 I was finally able to implement an algorithm to calculate all self-equivalent re-entry FORMs as described in uFORM iFORM. I immediately did countless calculations by hand and let Ralf also check that the algorithm is solid and its results are correct.
As soon as I was able to automate calculation with undetermined FORMs, I saw that there was much more potential in this and that it could be very helpful for other people who want to work with FORM logic as well. So I began working on a JavaScript library to elaborate my ideas, which gradually became formform. Since its early development, formform has always evolved in a fruitful interplay with the applications built on top of it.
A first application that I have developed in parallel from the beginning was the FORM tricorder – a swiss army knife for FORM calculation, representation and visualization. In September 2019 I was finally able to develop a new cellular automaton for FORM logic SelFis with formform that is much more user-friendly and much more versatile than what I have done two years earlier.
My experiments with rule extraction by bitmasking in CAs led me to a code format I call formDNA that is an abstraction of the value table (I later found out that there is a very similar code format for CA rules called Wolfram Code that is expressed as a decimal number). It not only made my CA faster and more flexible, it also inspired me to create the vmap: a recursive variable/value map to visualize formDNA, that has great potential for pattern recognition in FORMs.
Many of these experiments have found their way into formform and made their re-entry back into my apps and research. I would love to see this feedback loop expanding to projects from other people as well. :)
If you want to support my work, consider buying me a coffee. ☕
(c) 2018–2025 by Peter Hofmann
License: MIT