Modern computing systems have grown in complexity, and even though system components are generally carefully designed and even verified by different groups of people, the composition of 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.