Fault attacks present unique safety and security challenges that require dedicated countermeasures, even for bug-free programs. Models of these complex attacks are made workable by approximating their effects to a suitable level of abstraction. The common practice of targeting the Instruction Set Architecture (ISA) level isn't ideal because it discards important micro-architectural information, leading to weaker security guarantees. Conversely, including micro-architectural details makes countermeasures harder to model and reason about, creating a new challenge in validating and trusting protections.

We argue that monadic interpreters built as layers of handlers stacked atop the free monad, as advocated notably by the ITree library, also constitute a promising way to implement and verify abstract interpreters in dependently-typed theories such as the one underlying the Coq proof assistant. The approach enables both code reuse across projects and modular proofs of soundness of the resulting interpreters. We provide generic abstract control flow combinators proven correct once and for all against their concrete counterpart. We demonstrate how to relate concrete handlers implementing effects to abstract variants of these handlers, essentially capturing the traditional soundness of transfer functions in the context of monadic interpreters. Finally, we provide generic results to lift soundness statements via the interpretation of stateful and failure effects. We formalize all the aforementioned combinators and theories into a Coq library, and demonstrate their benefits by implementing and proving correct two illustrative abstract interpreters respectively for a structured imperative language and a toy assembly.