Hilbert-Post completeness for the state and the exception effects

TL;DR

This paper develops a new framework for analyzing the syntactic completeness of computational effects, specifically applying it to exceptions and states, with formal proofs verified in Coq.

Contribution

It introduces a relative notion of Hilbert-Post completeness for effects and proves the exception effect's completeness within this framework, generalizing prior work.

Findings

Exception effect is relatively Hilbert-Post complete

Framework applies to state and exception effects

Proofs are formalized in Coq

Abstract

In this paper, we present a novel framework for studying the syntactic completeness of computational effects and we apply it to the exception effect. When applied to the states effect, our framework can be seen as a generalization of Pretnar's work on this subject. We first introduce a relative notion of Hilbert-Post completeness, well-suited to the composition of effects. Then we prove that the exception effect is relatively Hilbert-Post complete, as well as the "core" language which may be used for implementing it; these proofs have been formalized and checked with the proof assistant Coq.