Host-Core Calculi for Non-classical Computations: A First Insight

In many situations, programming languages with varying levels of expressiveness need to interact to achieve a final result. This paper is about HC, a framework derived from a categorical model that formalizes how two typed paradigmatic programming languages H and C can interact in a hierarchical manner: the host language H can operate on the core terms of C, but not the other way around. We recall the essential structure of the categorical model, and present a specific example of HC where H is capable of composing circuits that can be modeled using C. Finally, we discuss potential straightforward and natural generalizations of this instance of HC.