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https://github.com/dmxlarchey/quasi-morphisms

Quasi morphisms for Almost Full relations
https://github.com/dmxlarchey/quasi-morphisms

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Quasi morphisms for Almost Full relations

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README 

        
```

(**************************************************************)

(*   Copyright Dominique Larchey-Wendling [*]                 *)

(*                                                            *)

(*                             [*] Affiliation LORIA -- CNRS  *)

(**************************************************************)

(*      This file is distributed under the terms of the       *)

(*        Mozilla Public License Version 2.0, MPL-2.0         *)

(**************************************************************)

```



# Quasi Morphisms for Almost Full relations (artifact)



This repository contains the artifact for the submission

[_Quasi Morphisms for Almost Full relations_](https://members.loria.fr/DLarchey/files/papers/types2024.pdf)

to the [TYPES 2024](https://types2024.itu.dk/Index.html) conference.



The standalone Coq file [`af_morphism.v`](af_morphism.v)

contains the developement and is largely commented. It has minimal dependencies, only on the standard 

library (distributed with Coq), and only on the `List` and `Utf8` modules within the standard library. 

It is intented to be read and executed within an IDE for Coq such as eg [CoqIDE](https://coq.inria.fr/download) or 

[vscoq](https://github.com/coq-community/vscoq). 



Any version of Coq starting from `8.13.0` and 

upto at least `8.19.1` should be ok to compile and/or review the file [`af_morphism.v`](af_morphism.v).

Since this is a single file, there is no need to pre-compile before reviewing. 



For further information about Almost Full relations in Coq,

the following libraries may be of interest:

- [`Kruskal-AlmostFull`](https://github.com/DmxLarchey/Kruskal-AlmostFull):

  general tools and definitions for AF relations and inductive bar predicates,

  including _surjective relational morphisms_ and Coquand's constructivized

  Ramsey's theorem;

- [`Kruskal-Higman`](https://github.com/DmxLarchey/Kruskal-Higman):

  _quasi-morphisms_ then applied to the proof of Higman's lemma;

- [`Kruskal-Veldman`](https://github.com/DmxLarchey/Kruskal-Veldman):

  the proof of Wim Veldman's variant of Kruskal's tree theorem 

  adapted to type theory makes a central use of quasi-morphisms

  but in a more complicated setting compare to [`Kruskal-Higman`](https://github.com/DmxLarchey/Kruskal-Higman)

  above;

- [`Kruskal-Theorems`](https://github.com/DmxLarchey/Kruskal-Theorems):

  "easy" consequences of [`Kruskal-Veldman`](https://github.com/DmxLarchey/Kruskal-Veldman)

  derived using surjective relational morphisms.



The artifact file [`af_morphism.v`](af_morphism.v) was designed by

extracting the necessary code from these libraries (so they are __not

needed__ for the review) and then cleaning up and commenting more specifically.



# Remarks



Concerning the use of `Utf8` symbols in the code, we did not experience any display issues 

with CoqIDE in any of the [`opam` installed](https://coq.inria.fr/opam-using.html) versions from `8.13.0` and `8.19.1`. Similarly,

viewing the code in the Chrome browser directly on GitHub looks fine on our systems. 

Depending on the operating system, distribution or the IDE/browser, such issues might 

possibly arise if OS installed `Utf8` symbols are incomplete/inconsistent with the IDE/browser. 



Anyway, to possibly avoid such issues, we suggest the usage of an `opam` installed version 

of CoqIDE rather than the default OS version of the tool. This also allows to easily switch

between different versions of Coq when developping general purpose code.