{"id":27162961,"url":"https://github.com/logsem/synthetic_domains","last_synced_at":"2025-04-09T01:34:42.985Z","repository":{"id":286843037,"uuid":"777689546","full_name":"logsem/synthetic_domains","owner":"logsem","description":null,"archived":false,"fork":false,"pushed_at":"2025-04-08T16:25:00.000Z","size":601,"stargazers_count":1,"open_issues_count":0,"forks_count":0,"subscribers_count":2,"default_branch":"main","last_synced_at":"2025-04-08T16:47:47.227Z","etag":null,"topics":[],"latest_commit_sha":null,"homepage":null,"language":"Coq","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":null,"status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/logsem.png","metadata":{"files":{"readme":"Readme.md","changelog":null,"contributing":null,"funding":null,"license":null,"code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null,"governance":null,"roadmap":null,"authors":null,"dei":null,"publiccode":null,"codemeta":null}},"created_at":"2024-03-26T10:31:49.000Z","updated_at":"2025-04-08T16:25:04.000Z","dependencies_parsed_at":"2025-04-08T16:57:55.942Z","dependency_job_id":null,"html_url":"https://github.com/logsem/synthetic_domains","commit_stats":null,"previous_names":["logsem/synthetic_domains"],"tags_count":0,"template":false,"template_full_name":null,"repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/logsem%2Fsynthetic_domains","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/logsem%2Fsynthetic_domains/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/logsem%2Fsynthetic_domains/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/logsem%2Fsynthetic_domains/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/logsem","download_url":"https://codeload.github.com/logsem/synthetic_domains/tar.gz/refs/heads/main","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":247957879,"owners_count":21024774,"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":"2025-04-09T01:34:42.333Z","updated_at":"2025-04-09T01:34:42.975Z","avatar_url":"https://github.com/logsem.png","language":"Coq","funding_links":[],"categories":[],"sub_categories":[],"readme":"To compile use `make`. This project has been tested using the following dependencies (packages) installed via `opam`:\n\n# Dependencies\n\n|Name                  |Installed                   | Synopsis|\n|----------------------|----------------------------|---------|\n|`coq`                 |`8.20.1`                    |The Coq Proof Assistant\n|`coq-stdpp`           |`dev.2025-01-17.0.9e1cd491` |An extended \"Standard Library\" for Coq|\n|`ocaml`               |`5.3.0`                     |The OCaml compiler (virtual package)|\n\n# Project layout\n```\n.\n+-- Readme.md\n+-- Makefile\n+-- _CoqProject\n+-- theories/prelude.v (global parameters)\n+-- theories/quotient.v (quotients in Rocq)\n+-- theories/stepindex.v (ordinals interface)\n+-- theories/ordinals (ordinals framework)\n+-- theories/existential_prop\n|   +-- classical.v (Choice+FunExt+PI-\u003eEM)\n|   +-- sigma.v (equality of sigma-types)\n|   +-- existential_prop.v (existential property)\n+-- theories/categories/\n|   +-- category.v (general constructions)\n|   +-- contractive.v (subclass of locally contractive functors, example)\n|   +-- coprod.v (coproducts)\n|   +-- domain.v (uniqueness of solution, later is locally contractive, symmetrization, )\n|   +-- enriched.v (partial isomorphisms and pointwise-enriched limits)\n|   +-- logic.v (logical connectives for step-indexed logic)\n|   +-- ord_cat.v (presheaves over ordinals, later, next, earlier, fixpoint)\n|   +-- solution.v (solver for recursive domain equations)\n```\n\n# Paper-formalization glossary\n| Paper entry | Rocq qualified identifier |\n| ----------- | -------------- |\n| later | ```SynthDom.categories.ord_cat.later``` |\n| earlier | ```SynthDom.categories.ord_cat.earlier``` |\n| next | ```SynthDom.categories.ord_cat.next``` |\n| def. 3 | ```SynthDom.categories.ord_cat.Contractive``` |\n| lemma 4 | ```SynthDom.categories.ord_cat.{Contractive_comp_l,Contractive_comp_r}``` |\n| def. 5 | ```SynthDom.categories.ord_cat.{fixpoint, fixpoint_unfold, fixpoint_unique}``` |\n| theorem 7 | ```SynthDom.categories.ord_cat.{contr_fix, contr_fix_unfold, contr_fix_unique}``` |\n| def. 9 | ```SynthDom.categories.category.Enriched``` |\n| def. 10 | ```SynthDom.categories.category.EnrichedFunctor``` |\n| def. 11 | ```SynthDom.categories.enriched.LocallyContractiveFunctor``` |\n| lemma 12 | ```SynthDom.categories.enriched.{LocallyContractiveFunctor_comp_l, LocallyContractiveFunctor_comp_r}``` |\n| def. 13 | ```SynthDom.categories.enriched.is_iso_at``` |\n| lemma 15 | ```SynthDom.categories.enriched.is_iso_upto_total``` |\n| lemma 16 | ```SynthDom.categories.enriched.is_iso_at_func``` |\n| lemma 17 | ```SynthDom.categories.enriched.iso_upto_contr_func``` |\n| def. 18 | ```SynthDom.categories.enriched.enr_cone``` |\n| def. 19 | ```SynthDom.categories.enriched.enr_cone_hom``` |\n| def. 20 | ```SynthDom.categories.enriched.enr_cone_is_limit``` |\n| lemma 21 | ```SynthDom.categories.enriched.{strongly_connected_iso_at_diagram_enr_cone, limit_side_iso_at', limit_side_iso_at}``` |\n| corollary 22 | ```SynthDom.categories.enriched.limit_side_iso_at_cofinal``` |\n| theorem 23 | ```SynthDom.categories.domain.alg_of_solution_is_initial``` |\n| def. 24 | ```SynthDom.categories.solution.partial_solution``` |\n| def. 25 | ```SynthDom.categories.solution.par_sol_extension``` |\n| lemma 26 | ```SynthDom.categories.solution.the_extension``` |\n| def. 27 | ```SynthDom.categories.solution.is_canonical_par_sol``` |\n| lemma 28 | ```SynthDom.categories.solution.canonical_eq``` |\n| lemma 29 | ```SynthDom.categories.solution.tower``` |\n| theorem 30 | ```SynthDom.categories.solution.solver``` |\n| example 32 | ```SynthDom.categories.solution.simplified_gitree_dom``` |\n| lemma 33 | ```SynthDom.categories.domain.symmetrization_sol``` |\n| theorem 34 | ```SynthDom.existential_prop.existential_prop.forall_exists_swap``` |\n| def. 36 | ```SynthDom.existential_prop.existential_prop.regular``` |\n| theorem 37 | ```SynthDom.categories.domain.{later_enriched, later_lc}``` |\n| remark 40 | ```SynthDom.categories.enriched.{isomorphism_at_id, compose_along_isomorphism_at_left, compose_along_isomorphism_at_right, compose_along_is_iso_at_left, compose_along_is_iso_at_right, compose_along_is_iso_at_left', compose_along_is_iso_at_right', is_iso_at_compose, is_iso_at_uncompose_l, is_iso_at_uncompose_r}``` |\n| theorem 42 | ```SynthDom.categories.ord_cat.later_adj``` |\n| theorem 43 | ```SynthDom.categories.category.{func_limit, func_cat_limits_pointwise}``` |\n| theorem 44 | ```SynthDom.categories.category.alg_complete``` |\n\n# Notation glossary\n## Category theory\n| Construction | Rocq notation |\n| -- | ----------------- |\n| Isomorphism | ```≃``` |\n| Terminal object | ```1ₒ``` |\n| Products | ```a ×ₒ b``` |\n| Unique product morphism | ```\u003c\u003c f, g \u003e\u003e``` |\n| Product of morphisms | ```f ×ₕ g``` |\n| Coproduct | ```a +ₒ b``` |\n| Unique coproduct morphism | ```\u003c\u003c f ∣ g \u003e\u003e``` |\n| Coproduct of morphisms | ```f +ₕ g``` |\n| Exponential | ```b ↑ₒ a``` |\n| Functor object action | ```F ₒ a``` |\n| Functor morphism action | ```F ₕ f``` |\n| Natural transformation component | ```H ₙ a``` |\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Flogsem%2Fsynthetic_domains","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Flogsem%2Fsynthetic_domains","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Flogsem%2Fsynthetic_domains/lists"}