A An Abstract Model of Certificate Translation

A certificate is a mathematical object that establishes the validity of a logical formula and that is self-contained, self-explanatory, and can be checked independently and automatically. Certificates arise naturally in many areas of mathematics, and in many different forms. In particular, certificates are common in the context of program verification, where they are used for automatic checking of program correctness; in this context, certificates provide evidence that a program meets its specification, where specifications may take the form of type annotations or assertions, and certificates may take the form of type derivations, derivations in Hoare like logics, or proof terms for verification conditions. While certificate checking for program correctness is reasonably understood, certificate generation remains a challenging problem. Although it is possible to generate certificates automatically for specific properties that are enforceable by automated program analyses, and in particular type systems, certificate generation remains interactive in the general case. It is therefore of interest to develop methods that assist and simplify the construction of certificates. The purpose of this paper is to investigate methods for transforming certificates of program correctness. We focus on two instances of this general goal: certifying analysis and certificate translation. The aim of certifying analysis is to transform a proof of program correctness from one verification formalism to another; typically, a certi-