A verified Common Lisp implementation of Buchberger's algorithm in ACL2
In this article, we present the formal verification of a Common Lisp implementation of Buchberger's algorithm for computing Gröbner bases of polynomial ideals. This work is carried out in ACL2, a system which provides an integrated environment where programming (in a pure functional subset of C...
| Autores: | , , |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2010 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/86196 |
| Acceso en línea: | https://hdl.handle.net/11441/86196 https://doi.org/10.1016/j.jsc.2009.07.002 |
| Access Level: | acceso abierto |
| Palabra clave: | Formal verification ACL2 Computer Algebra Buchberger's algorithm |
| Sumario: | In this article, we present the formal verification of a Common Lisp implementation of Buchberger's algorithm for computing Gröbner bases of polynomial ideals. This work is carried out in ACL2, a system which provides an integrated environment where programming (in a pure functional subset of Common Lisp) and formal verification of programs, with the assistance of a theorem prover, are possible. Our implementation is written in a real programming language and it is directly executable within the ACL2 system or any compliant Common Lisp system. We provide here snippets of real verified code, discuss the formalization details in depth, and present quantitative data about the proof effort. |
|---|