https://github.com/algebraic-graphs/agda

The theory of algebraic graphs formalised in Agda
https://github.com/algebraic-graphs/agda

agda algebra graph

Last synced: about 1 year ago
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The theory of algebraic graphs formalised in Agda

• Host: GitHub
• URL: https://github.com/algebraic-graphs/agda
• Owner: algebraic-graphs
• License: mit
• Created: 2017-03-16T00:08:12.000Z (about 9 years ago)
• Default Branch: master
• Last Pushed: 2018-07-15T23:24:38.000Z (almost 8 years ago)
• Last Synced: 2024-08-03T15:05:21.958Z (almost 2 years ago)
• Topics: agda, algebra, graph
• Language: Agda
• Homepage:
• Size: 42 KB
• Stars: 86
• Watchers: 5
• Forks: 6
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

          
# The theory of algebraic graphs

[![Build Status](https://travis-ci.org/algebraic-graphs/agda.svg?branch=master)](https://travis-ci.org/algebraic-graphs/agda)

We use Agda to formalise the theory of [algebraic graphs](https://github.com/snowleopard/alga-paper)

and prove a few key theorems.

## Code overview

This repository is fully self-contained and does not depend on any Agda libraries. We use

[this Travis build script](https://github.com/scott-fleischman/agda-travis) for continuous

verification of the proofs. To verify whether your implementation is correct, 

you can invoke the `verify.sh` script.

Below we describe the purpose of all source files contained in the `src` directory.

* Inside the `Algebra` folder, we define the following structures:

  * `Dioid`, a semiring (or rng) where the `+` operation is idempotent.

  * `Bool`, an implementation of a dioid.

  * `ShortestDistance`, another instance.

  * `Graph`, an [algebraic graphs](https://github.com/snowleopard/alga-paper).

  * `LabelledGraph`, an extension of a `Graph`.

  for each of these there are three files:

  * `Structure.agda`, the main implementation.

  * `Structure/Reasoning.agda`, syntactic sugar for writing equational proofs.

  * `Structure/Theorems.agda`, some theorems of the structure.

* `Prelude` defines products, lists and other functionality for describing Haskell APIs.

* `API` defines key functions from the API of the algebraic-graphs library.

* `API/Theorems` proves theorems of the API.