{"id":19730570,"url":"https://github.com/begriffs/mother-structures","last_synced_at":"2025-07-09T07:09:19.187Z","repository":{"id":1712208,"uuid":"2441811","full_name":"begriffs/mother-structures","owner":"begriffs","description":"Programming via abstract math","archived":false,"fork":false,"pushed_at":"2013-02-23T06:35:07.000Z","size":211,"stargazers_count":8,"open_issues_count":0,"forks_count":3,"subscribers_count":3,"default_branch":"master","last_synced_at":"2025-07-09T07:06:59.564Z","etag":null,"topics":[],"latest_commit_sha":null,"homepage":"","language":"CoffeeScript","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/begriffs.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}},"created_at":"2011-09-23T03:44:12.000Z","updated_at":"2017-12-20T05:43:22.000Z","dependencies_parsed_at":"2022-08-22T22:31:21.433Z","dependency_job_id":null,"html_url":"https://github.com/begriffs/mother-structures","commit_stats":null,"previous_names":[],"tags_count":0,"template":false,"template_full_name":null,"purl":"pkg:github/begriffs/mother-structures","repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/begriffs%2Fmother-structures","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/begriffs%2Fmother-structures/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/begriffs%2Fmother-structures/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/begriffs%2Fmother-structures/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/begriffs","download_url":"https://codeload.github.com/begriffs/mother-structures/tar.gz/refs/heads/master","sbom_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/begriffs%2Fmother-structures/sbom","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":264411163,"owners_count":23603804,"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":"2024-11-12T00:16:49.889Z","updated_at":"2025-07-09T07:09:19.168Z","avatar_url":"https://github.com/begriffs.png","language":"CoffeeScript","funding_links":[],"categories":[],"sub_categories":[],"readme":"In 1950 the Bourbaki group of mathematicians (particularly Jean\nDieudonné) published an article called \"The Architecture of Mathematics\"\nwhich introduces the motivations behind Bourbaki's multi-volume\nwork \"The Elements of Mathematics.\" I'd like to conceive a similar\narchitecture of computing, with a primordial software library of \"mother\nstructures\" that can combine to efficiently distill any program.\n\n\u003cblockquote\u003eAt the center of our universe are found the great types\nof structures, ... they might be called the mother structures ...\nBeyond this first nucleus, appear the structures which might be\ncalled multiple structures. They involve two or more of the great\nmother-structures not in simple juxtaposition (which would not produce\nanything new) but combined organically by one or more axioms which\nset up a connection between them... Farther along we come finally to\nthe theories properly called particular. In these the elements of\nthe sets under consideration, which in the general structures have\nremained entirely indeterminate, obtain a more definitely characterized\nindividuality.\u003c/blockquote\u003e — [The Architecture of Mathematics](http://mduchin.math.tufts.edu/UCD/111/readings/architecture.pdf)\n\nProgramming is a young field and deeply affected by its mercantile\nallure. Developers create most code without concern for the fundamental\npatterns and problems involved. The myopic redundancy of this code is a\nvicious cycle. The new code accommodates faults of the old.\n\n\u003cblockquote\u003eNothing is more necessary to the culture of the higher\nsciences, or of the more elevated departments of science, than\nmeditation; and nothing is less suited to meditation than the structure\nof democratic society. ... Everyone is actively in motion: some in\nquest of power, others of gain. In the midst of this universal tumult -\nthis incessant conflict of jarring interests - this continual stride of\nmen after fortune - where is that calm to be found which is necessary\nfor the deeper combinations of the intellect?\u003c/blockquote\u003e — Alexis de\nTocqueville, Democracy in America\n\nIn particular the requirements to cobble shoddy software are quite\nmeager. Most devs are ignorant, especially of math which they know as an\nirrelevant highschool potpourri of numerical techniques. What we have in\nmath is actually a centuries-old dialog of the most widely applicable\nstructural rules imaginable, rules that cover our software applications\nas a trivial side effect.\n\n\u003cblockquote\u003eThe truths of arithmetic govern all that is numerable. This\nis the widest domain of all; for to it belongs not only the actual,\nnot only the intuitable, but everything thinkable. Should not the\nlaws of number, then, be connected very intimately with the laws of\nthought?\u003c/blockquote\u003e — Gottlob Frege, Foundations of Arithmetic\n\nI am curious how to write programs using the concepts from abstract\nmath. Can our programs manipulate topologies, groups, and orders\ndirectly? How useful are algorithms expressed entirely in these terms?\nCan we operate on quotient structures?\n\nI don't want this investigation to devolve into crippling type theory\nbanalities or academic drivel. The concepts involved are sharp and\nlively and the resulting programs should be too. I hereby promise to\nnever present any esoteric implementation of the factorial function.\n\nStriving after this noble goal doesn't come cheap. Every day spent in\nthis investigation is a day I make myself less familiar with the latest\ntrends, a less attractive employee. However my thoughts of doing this\nproject and the urge have recurred for years.\n\n\u003cblockquote\u003eI had only to will to go -- but to will powerfully and\nwholly, not to turn and twist a will half-wounded this way and that,\nwith the part that would rise struggling against the part that would\nkeep to the earth.\u003c/blockquote\u003e — St. Augustine, Confessions\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fbegriffs%2Fmother-structures","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fbegriffs%2Fmother-structures","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fbegriffs%2Fmother-structures/lists"}