{"id":13749140,"url":"https://github.com/advancedresearch/avatar_hypergraph_rewriting","last_synced_at":"2025-05-09T12:30:29.516Z","repository":{"id":46108484,"uuid":"427773145","full_name":"advancedresearch/avatar_hypergraph_rewriting","owner":"advancedresearch","description":"Hypergraph rewriting system with avatars for symbolic distinction","archived":false,"fork":false,"pushed_at":"2021-11-14T07:43:30.000Z","size":14,"stargazers_count":3,"open_issues_count":1,"forks_count":1,"subscribers_count":3,"default_branch":"main","last_synced_at":"2024-05-22T21:33:16.420Z","etag":null,"topics":[],"latest_commit_sha":null,"homepage":null,"language":"Rust","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":"apache-2.0","status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/advancedresearch.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":"LICENSE-APACHE","code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null}},"created_at":"2021-11-13T21:09:44.000Z","updated_at":"2024-04-29T23:17:30.000Z","dependencies_parsed_at":"2022-09-26T18:31:56.752Z","dependency_job_id":null,"html_url":"https://github.com/advancedresearch/avatar_hypergraph_rewriting","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/advancedresearch%2Favatar_hypergraph_rewriting","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/advancedresearch%2Favatar_hypergraph_rewriting/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/advancedresearch%2Favatar_hypergraph_rewriting/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/advancedresearch%2Favatar_hypergraph_rewriting/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/advancedresearch","download_url":"https://codeload.github.com/advancedresearch/avatar_hypergraph_rewriting/tar.gz/refs/heads/main","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":224859694,"owners_count":17381676,"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":[],"created_at":"2024-08-03T07:00:55.928Z","updated_at":"2024-11-15T23:32:07.173Z","avatar_url":"https://github.com/advancedresearch.png","language":"Rust","funding_links":[],"categories":["Projects"],"sub_categories":["Libraries"],"readme":"# Avatar Hypergraph Rewriting\nHypergraph rewriting system with avatars for symbolic distinction\n\nBased on paper [Avatar Hypergraph Rewriting](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip2/avatar-hypergraph-rewriting.pdf).\n\nAvatars can be used on the left side of rewriting rules to control\nsymbolic distinction of nodes in the hypergraph evolution.\nThey can be used on any hyperedge.\n\n### Example: Wolfram vs Avatar\n\n```rust\nuse avatar_hypergraph_rewriting::*;\n\nuse Expr::*;\n\nfn main() {\n    // `{0,0}`\n   let a = vec![Nat(0), Nat(0)];\n\n    // `{1,2} -\u003e {}`\n    let wolfram_rule = Rule(vec![Nat(1), Nat(2)], vec![]);\n    // prints `{}` because `{0,0}` is reduced.\n    println!(\"{}\", format(\u0026wolfram_rule.parallel(\u0026a)));\n\n    // `{a'(1),b'(2)} -\u003e {}`\n    let avatar_rule = Rule(vec![ava(\"a\", 1), ava(\"b\", 2)], vec![]);\n    // prints `{0,0}` because avatars \"a\" and \"b\" must be different nodes.\n    println!(\"{}\", format(\u0026avatar_rule.parallel(\u0026a)));\n}\n```\n\n### Motivation\n\nAvatar Hypergraph Rewriting (AHR) is an attempt to find an\n[Avatar Extension](https://advancedresearch.github.io/avatar-extensions/summary.html)\nof Wolfram models that satisfies the assumptions in the paper\n[Consciousness in Wolfram Models](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip2/consciousness-in-wolfram-models.pdf).\n\nWolfram models are used in the [Wolfram Physics Project](https://wolframphysics.org/),\nwhich seeks to explain fundamental physics\nusing a hypergraph rewriting system.\n\nWolfram models correspond to theorem proving with\n[Intuitionistic Propositional Logic](https://en.wikipedia.org/wiki/Intuitionistic_logic) (IPL),\nwhich can be generalised to Homotopy Type Theory.\nFor more information, see [this paper](https://arxiv.org/abs/2111.03460) by\nXerxes D. Arsiwalla and Jonathan Gorard.\n\nIPL is the foundation for Type Theory and modern mathematical foundations.\nIPL is weaker than\n[Propositional Logic](https://en.wikipedia.org/wiki/Propositional_calculus) (PL).\n\n- PL is called \"classical\" logic and satisfies a Boolean algebra\n- IPL is called \"constructive\" logic and satisfies a Heyting algebra\n\nHowever, in [Path Semantics](https://github.com/advancedresearch/path_semantics)\nthere is an even weaker logic called Path Semantical Intuitionistic Propositional Logic (PSI).\n\nPSI is much less understood than IPL and PL,\nbut is relevant for the philosophy of mathematical language design.\nOne thing that makes PSI different from IPL is that a quality operator `~~`\nlifts biconditions with symbolic distinction (quality is a partial equivalence).\n\nA closely related research topic to PSI is\n[Avatar Extensions](https://advancedresearch.github.io/avatar-extensions/summary.html).\n\nThis hypergraph rewriting system combines the property of symbolic distinction with avatars.\nThe avatars is a design choice to express symbolic distinction efficiently.\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fadvancedresearch%2Favatar_hypergraph_rewriting","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fadvancedresearch%2Favatar_hypergraph_rewriting","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fadvancedresearch%2Favatar_hypergraph_rewriting/lists"}