Abstract Modern computing systems have grown in complexity, and even though system components are generally carefully designed and even verified by different groups of people, thecompositionof these components is often regarded with less attention. Inconsistencies between components’ assumptions on the rest of the system can have significant repercussions on this system, and may ultimately lead to safety or security issues. In this article, we introduce FreeSpec, a formalismbuilt upon the key idea that components can bemodeled as programs with algebraic effects to be realized by other components. FreeSpec allows for the modular modeling of a complex system, by defining idealized components connected together, and the modular verification of the properties of their composition. In addition, we have implemented a framework for the Coq proof assistant based on FreeSpec.

FreeSpec is a framework for the Coq theorem prover which allows for specifying and verifying complex systems as hierarchies of components verified both in isolation and in composition. While FreeSpec was originally introduced for reasoning about hardware architectures, in this article we propose a novel iteration of FreeSpec formalism specifically designed to write certified programs and libraries. Then, we present in depth how we use this formalism to verify a static files webserver. We use this opportunity to present FreeSpec proof automation tactics, and to demonstrate how they successfully erase FreeSpec internal definitions to let users focus on the core of their proofs. Finally, we introduce FreeSpec.Exec, a plugin for Coq to seamlessly execute certified programs written with FreeSpec.