# Proving uniformity and independence by self-composition and coupling

## TL;DR

This paper introduces a novel approach using the program logic pRHL and couplings to formally verify uniformity and independence properties in probabilistic programs, extending the application of coupling techniques.

## Contribution

It demonstrates that probabilistic couplings can be effectively used for verifying non-relational properties like uniformity and independence in probabilistic programs.

## Key findings

- Formal verification of uniformity using pRHL
- Formal verification of independence using pRHL
- Successful implementation in EasyCrypt proof assistant

## Abstract

Proof by coupling is a classical proof technique for establishing probabilistic properties of two probabilistic processes, like stochastic dominance and rapid mixing of Markov chains. More recently, couplings have been investigated as a useful abstraction for formal reasoning about relational properties of probabilistic programs, in particular for modeling reduction-based cryptographic proofs and for verifying differential privacy. In this paper, we demonstrate that probabilistic couplings can be used for verifying non-relational probabilistic properties. Specifically, we show that the program logic pRHL---whose proofs are formal versions of proofs by coupling---can be used for formalizing uniformity and probabilistic independence. We formally verify our main examples using the EasyCrypt proof assistant.