{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/programming-really-is-simple-mathematics","title":"Programming Really Is Simple Mathematics","arxiv_id":"2502.17149","date":"2025-02-24","proceeding":null,"authors":["Bertrand Meyer","Reto Weber"],"abstract":"A re-construction of the fundamentals of programming as a small mathematical theory (PRISM) based on elementary set theory. Highlights: $\\bullet$ Zero axioms. No properties are assumed, all are proved (from standard set theory). $\\bullet$ A single concept covers specifications and programs. $\\bullet$ Its definition only involves one relation and one set. $\\bullet$ Everything proceeds from three operations: choice, composition and restriction. $\\bullet$ These techniques suffice to derive the axioms of classic papers on the \"laws of programming\" as consequences and prove them mechanically. $\\bullet$ The ordinary subset operator suffices to define both the notion of program correctness and the concepts of specialization and refinement. $\\bullet$ From this basis, the theory deduces dozens of theorems characterizing important properties of programs and programming. $\\bullet$ All these theorems have been mechanically verified (using Isabelle/HOL); the proofs are available in a public repository. This paper is a considerable extension and rewrite of an earlier contribution [arXiv:1507.00723]","url_abs":"https://arxiv.org/abs/2502.17149v3","url_pdf":"https://arxiv.org/pdf/2502.17149v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"programming-really-is-simple-mathematics","repo_url":"https://github.com/ci-cse/prism","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}