{"id":13686481,"url":"https://github.com/algebraic-graphs/agda","last_synced_at":"2025-05-01T09:31:49.824Z","repository":{"id":72911243,"uuid":"85133513","full_name":"algebraic-graphs/agda","owner":"algebraic-graphs","description":"The theory of algebraic graphs formalised in Agda","archived":false,"fork":false,"pushed_at":"2018-07-15T23:24:38.000Z","size":43,"stargazers_count":86,"open_issues_count":0,"forks_count":6,"subscribers_count":5,"default_branch":"master","last_synced_at":"2024-08-03T15:05:21.958Z","etag":null,"topics":["agda","algebra","graph"],"latest_commit_sha":null,"homepage":"","language":"Agda","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":"mit","status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/algebraic-graphs.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":"LICENSE","code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null,"governance":null,"roadmap":null,"authors":null}},"created_at":"2017-03-16T00:08:12.000Z","updated_at":"2024-07-08T06:01:54.000Z","dependencies_parsed_at":"2023-05-26T01:15:15.717Z","dependency_job_id":null,"html_url":"https://github.com/algebraic-graphs/agda","commit_stats":null,"previous_names":[],"tags_count":0,"template":false,"template_full_name":null,"repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/algebraic-graphs%2Fagda","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/algebraic-graphs%2Fagda/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/algebraic-graphs%2Fagda/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/algebraic-graphs%2Fagda/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/algebraic-graphs","download_url":"https://codeload.github.com/algebraic-graphs/agda/tar.gz/refs/heads/master","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":224250217,"owners_count":17280522,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2022-07-04T15:15:14.044Z","host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":["agda","algebra","graph"],"created_at":"2024-08-02T15:00:33.082Z","updated_at":"2024-11-12T09:30:55.105Z","avatar_url":"https://github.com/algebraic-graphs.png","language":"Agda","funding_links":[],"categories":["Agda"],"sub_categories":[],"readme":"# The theory of algebraic graphs\n\n[![Build Status](https://travis-ci.org/algebraic-graphs/agda.svg?branch=master)](https://travis-ci.org/algebraic-graphs/agda)\n\nWe use Agda to formalise the theory of [algebraic graphs](https://github.com/snowleopard/alga-paper)\nand prove a few key theorems.\n\n## Code overview\n\nThis repository is fully self-contained and does not depend on any Agda libraries. We use\n[this Travis build script](https://github.com/scott-fleischman/agda-travis) for continuous\nverification of the proofs. To verify whether your implementation is correct, \nyou can invoke the `verify.sh` script.\n\nBelow we describe the purpose of all source files contained in the `src` directory.\n\n* Inside the `Algebra` folder, we define the following structures:\n\n  * `Dioid`, a semiring (or rng) where the `+` operation is idempotent.\n  * `Bool`, an implementation of a dioid.\n  * `ShortestDistance`, another instance.\n  * `Graph`, an [algebraic graphs](https://github.com/snowleopard/alga-paper).\n  * `LabelledGraph`, an extension of a `Graph`.\n\n  for each of these there are three files:\n\n  * `Structure.agda`, the main implementation.\n  * `Structure/Reasoning.agda`, syntactic sugar for writing equational proofs.\n  * `Structure/Theorems.agda`, some theorems of the structure.\n\n\n* `Prelude` defines products, lists and other functionality for describing Haskell APIs.\n* `API` defines key functions from the API of the algebraic-graphs library.\n* `API/Theorems` proves theorems of the API.\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Falgebraic-graphs%2Fagda","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Falgebraic-graphs%2Fagda","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Falgebraic-graphs%2Fagda/lists"}