Certified binary search tree on W-types

TL;DR

This paper introduces a new approach to certified programming by defining new types using well-founded types and applying these ideas to binary search trees, enhancing guarantees of program correctness.

Contribution

It develops a novel elimination rule for well-founded types and demonstrates its application to binary search trees for certified programming.

Findings

New elimination rule for well-founded types

Application to certified binary search trees

Potential for improved program correctness guarantees

Abstract

Software bugs have caused enormous economic and human loss in recent years. Certified programming seeks to solve this problem by developing languages where we can make demonstrations that guarantee that our programs work properly. However, the rapid evolution of modern algorithms constantly forces us to develop new tools for this task. In this article we explore the possibility of defining new types using well-founded types. In particular, we developed a new elimination rule on the terms of the type. We apply these ideas to binary search trees to illustrate the power of the method.