https://github.com/dirkgroot/extended-set

Extended sets in Kotlin
https://github.com/dirkgroot/extended-set

extended-set-theory kotlin tdd xst

Last synced: 28 days ago
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Extended sets in Kotlin

• Host: GitHub
• URL: https://github.com/dirkgroot/extended-set
• Owner: dirkgroot
• Created: 2021-12-23T18:52:18.000Z (about 3 years ago)
• Default Branch: main
• Last Pushed: 2021-12-24T21:40:42.000Z (about 3 years ago)
• Last Synced: 2024-11-17T15:57:49.128Z (3 months ago)
• Topics: extended-set-theory, kotlin, tdd, xst
• Language: Kotlin
• Homepage:
• Size: 66.4 KB
• Stars: 0
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

        
# Extended sets in Kotlin

## Goal

Practice, learning, having fun.

## Introduction

Since about 1-2 years ago, I'm a somewhat regular reader of Ron Jeffries' blog

(). Recently he started a new series of blogs about extended set theory,

or XST for short. In this series Ron shares the adventures het has in implementing a set-theoretic

data structure, based on XST, in Codea Lua.

I didn't know about XST before Ron started writing about it, but now I know of it's existence, it

has me thoroughly intrigued. So much, that I felt the urge to see how extended sets (or XSets for

short) could be implemented in a somewhat useful way in Kotlin.

## What is XST?

Extended set theory is a replacement for set theory, invented by Dave Childs, which extends set

theory with the concept of scopes. Every element in a set is an element of that set under a certain

scope.

In "classical" set theory, we write **x ∈ S** to denote that **x** is an element of **S**. In

extended set theory, we write **x ∈s S** to denote that **x** is an element of **S**

under scope **s**. A "classical" set looks like this: **{ Mike, London, 42 }**. An extended version

of this set could look like this: **{ Mikename, Londoncity, 42age

}**.

From this simple example, I think it's clear that thanks to the added scope, we could represent any

data structure as a set (of sets (of sets (of... well, you get it))).

## More information

Information about XST is not easy to find online (it doesn't even have it's own Wikipedia page).

However,  contains a couple of articles and papers about XST. I found

[this paper](http://xsp.xegesis.org/Xsp-uxr.pdf) quite easy to read and informative.