Full Abstraction for Free

Structured recursion schemes such as folds and unfolds have been widely used for structuring both functional programs and program semantics. In this context, it has been customary to implement denotational semantics as folds over an inductive data type to ensure termination and compositionality. Separately, operational models can be given by unfolds, and naturally not all operational models coincide with a given denotational semantics in a meaningful way. To ensure these semantics are coherent it is important to consider the property of full abstraction which relates the denotational and the operational model. In this paper, we show how to engineer a compositional semantics such that full abstraction comes for free. We do this by using distributive laws from which we generate both the operational and the denotational model. The distributive laws ensure the semantics are fully abstract at the type level, thus relieving the programmer from the burden of the proofs.