A calculus for set-based program development part I: mathematical foundations
- We propose an algebraic core calculus for naive or intuitive set theory. We reconstruct a fragment of set theory via atomic distributive lattices. Semantically, atomic distributive lattices extend boolean reasoning about sets by element-wise reasoning; the ontological commitment to a universal set is avoided. Operationally, reasoning with atomic distributive lattices yields abtract, concise, elegant proofs for sets from a few elementary principles. We also present an algebraic treatment of extensionality in terms of a lattice congruence. Our results are particularly suited for automated proof search in set theory. Main application is the proof support for set-based program development methods like B or Z.
| Author: | Georg StruthGND |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-1740 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/223 |
| Series (Serial Number): | Reports / Technische Berichte der Fakultät für Angewandte Informatik der Universität Augsburg (2003-15) |
| Publisher: | Institut für Informatik, Universität Augsburg |
| Place of publication: | Augsburg |
| Type: | Report |
| Language: | English |
| Year of first Publication: | 2003 |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2006/06/12 |
| Tag: | naive set theory; set-based program development; lattice theory; sectional complements; extensionality; atomicity |
| Institutes: | Fakultät für Angewandte Informatik |
| Fakultät für Angewandte Informatik / Institut für Informatik | |
| Fakultät für Angewandte Informatik / Institut für Informatik / Professur für Programmiermethodik und Multimediale Informationssysteme | |
| Dewey Decimal Classification: | 0 Informatik, Informationswissenschaft, allgemeine Werke / 00 Informatik, Wissen, Systeme / 004 Datenverarbeitung; Informatik |
