A Formal Algebraic Framework for DSL Composition

Abstract: We discuss a formal framework for using algebraic structures to model a meta-language that can write, compose, and provide interoperability between abstractions of DSLs. The purpose of this formal framework is to provide a verification of compositional properties of the meta-language. Throughout our paper we discuss the construction of this formal framework, as well its relation to our team's work on the DARPA V-SPELLS program via the pipeline we have developed for completing our verification tasking on V-SPELLS. We aim to give a broad overview of this verification pipeline in our paper. The pipeline can be split into four main components: the first is providing a formal model of the meta-language in Coq; the second is to give a specification in Coq of our chosen algebraic structures; third, we need to implement specific instances of our algebraic structures in Coq, as well as give a proof in Coq that this implementation is an algebraic structure according to our specification in the second step; and lastly, we need to give a proof in Coq that the formal model for the meta-language in the first step is an instance of the implementation in the third step.