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
