> For the complete documentation index, see [llms.txt](https://mandober.gitbook.io/math-debrief/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://mandober.gitbook.io/math-debrief/260-function-theory/fn.links.md).

# Function Theory: LINKS

<http://www.math.hawaii.edu/\\~heiner/relations.pdf> <https://arxiv.org/ftp/arxiv/papers/1501/1501.01914.pdf> <https://schoolnova.org/classes/ay2020/math9b/math9b-2020-12-13-file1.pdf> <https://www.cerritos.edu/dford/SitePages/Math\\_140/Math140Lecture3.pdf> <https://homepages.hass.rpi.edu/heuveb/Teaching/Logic/CompLogic/Web/Handouts/SetsRelationsFunctions.pdf>

<https://proofwiki.org/wiki/Definition:One-to-Many\\_Relation>

<http://www.ltcconline.net/greenl/courses/152a/functgraph/relfun.htm>

<https://www.bookofproofs.org/branches/total-and-unique-binary-relations/>

<https://math.stackexchange.com/questions/945874/is-every-left-unique-relation-right-uniqe>

<https://osera.cs.grinnell.edu/csc208/readings/relations-equivalences-and-functions.html>

<https://mathoverflow.net/questions/17854/do-you-need-to-say-what-left-unique-and-right-unique-means>

<https://www.lesswrong.com/posts/vTS8K4NBSi9iyCrPo/a-reckless-introduction-to-hindley-milner-type-inference>

<https://courses.lumenlearning.com/ivytech-collegealgebra/chapter/determine-whether-a-relation-represents-a-function/>

* Simple Laws about Nonprominent Properties of Binary Relations Jochen Burghardt 2020 <https://hal.archives-ouvertes.fr/hal-02948115/document> Abstract We checked each binary relation on a 5-element set for a given set of properties, including usual ones like asymmetry and less known ones like Euclideanness. Using a poor man's Quine-McCluskey algorithm, we computed prime implicants of non-occurring property combinations, like "not irreflexive, but asymmetric". We considered the laws obtained this way, and manually proved them true for binary relations on arbitrary sets, thus contributing to the encyclopedic knowledge about less known properties. Keywords: Binary relation; Quine-McCluskey algorithm; Hypotheses generation

A Library Based Approach to the Verification of Languages with Linear Types Computer-verified proof of type soundness for the Linear Language with Locations