TinySets

This is, or will be, an implementation of tiny sets (defined as parts aka subsets of a given set of eight points) together with tiny maps (functions between tiny sets) and tiny relations (parts of binary products of tiny sets) between them -- typed, so that each map and relation has a specific tiny set as domain and a specific tiny set as codomain.

The module is developed as a learning experience. Initial topics to learn, apart from the Julia language, include some of the lesser topics in ETCS (the set theory) and basic combinatorics. Eventual further topics might include something on finite topological spaces.

However, while the /author/ has already learned a lot and expects to learn more still, there is /absolutely no warranty/ that any beneficial effects occur for anybody else. That would be nice but nothing more.

The author has no intention to expand to bigger sets. That would be a different project. Note that there are millions of functions and billions of relations at hand even for the relatively small number of 256 tiny sets.

Contents

• Boolean lattice operations, inclusion (for sets, for relations, for monomaps with the same codomain)

• Composition of maps, composition of relations (if compatible)

• Inverse of a map (if invertible), opposite relation

• Identity map of a set, graph of a map as a relation

• Image of a map, preimage of a set along a map (as sets)

• Product of sets (as a relation)

• Random set, map, monomap, part, epimap, partition

• Random relation, random equivalence relation

• Each set, map, and so on (generated on demand)

• Todo: left and right inverses (if any) of a map

• Todo: partial order relations

• Todo: something about partitions

News

• Initial draft has been basically re-drafted and much expanded (early relations were not really typed, and there were no functions at all)

"Property"

Copyright 2016 Jussi Piitulainen

The code can be freely shared (copied, studied, modified, distributed) under the terms of the GNU General Public License, either version 3 or a later version, as published by the Free Software Foundation.