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 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

Formalization of various geometry models and applications in verification of automated theorem provers

У овој тези представљена је интерактивна формализација модела разних геометрија и алгебарских метода аутоматског доказивања геометријских те- орема...In this thesis is presented interactive formalization of various models of geometry and algebraic methods for automated proving geometry theorems...