# Coinductive Uniform Proofs

## TL;DR

This paper introduces a unified proof-theoretic framework for coinductive reasoning in Horn clause logic, addressing proofs of circular properties and infinite data construction with formal soundness guarantees.

## Contribution

It presents a novel coinductive extension of the uniform proof framework, systematically analyzing two types of coinductive proofs and establishing their soundness.

## Key findings

- Unified framework for coinductive proofs in Horn clause logic
- Proof of soundness relative to coinductive models
- Formal analysis of circular and infinite data proofs

## Abstract

Coinduction occurs in two guises in Horn clause logic: in proofs of circular properties and relations, and in proofs involving construction of infinite data. Both instances of coinductive reasoning appeared in the literature before, but a systematic analysis of these two kinds of proofs and of their relation was lacking. We propose a general proof-theoretic framework for handling both kinds of coinduction arising in Horn clause logic. To this aim, we propose a coinductive extension of Miller et al framework of uniform proofs and prove its soundness relative to coinductive models of Horn clause logic.