### Abstract

Indeed, there have been numerous misunderstandings on what exactly a given algorithm is supposed to realize in what kinds of environments. Moreover, the abundance of subtly different computational models complicates comparisons between different algorithms. Charron-Bost and Schiper introduced the Heard-Of model for representing algorithms and failure assumptions in a uniform framework, simplifying comparisons between algorithms.

In this contribution, we represent the Heard-Of model in Isabelle/HOL. We define two semantics of runs of algorithms with different unit of atomicity and relate these through a reduction theorem that allows us to verify algorithms in the coarse-grained semantics (where proofs are easier) and infer their correctness for the fine-grained one (which corresponds to actual executions). We instantiate the framework by verifying six Consensus algorithms that differ in the underlying algorithmic mechanisms and the kinds of faults they tolerate.