Applications of Metric Coinduction

TL;DR

This paper explores metric coinduction as a versatile proof technique for establishing properties of limit objects in various mathematical structures, simplifying complex analytic arguments.

Contribution

It demonstrates the broad applicability of metric coinduction across multiple domains, highlighting its utility as a general proof method.

Findings

Simplifies proofs involving limits and convergence.

Applies to infinite streams, Markov chains, and non-well-founded sets.

Shows coinduction as a powerful alternative to analytic arguments.

Abstract

Metric coinduction is a form of coinduction that can be used to establish properties of objects constructed as a limit of finite approximations. One can prove a coinduction step showing that some property is preserved by one step of the approximation process, then automatically infer by the coinduction principle that the property holds of the limit object. This can often be used to avoid complicated analytic arguments involving limits and convergence, replacing them with simpler algebraic arguments. This paper examines the application of this principle in a variety of areas, including infinite streams, Markov chains, Markov decision processes, and non-well-founded sets. These results point to the usefulness of coinduction as a general proof technique.