Equational Logic and Set-Theoretic Models for Multi-Languages
conference contributionposted on 08.07.2021, 09:59 by Samuele Buro, Roy Crole, Isabella Mastroeni
Interoperability is the capability of two languages to interact
render webpages. Some object oriented languages have interoperability via
a virtual machine host (.NET CLI compliant languages in the Common
Language Runtime). A high-level language can be interoperable with a
low-level one (Apple’s Swift and Objective-C). While there has been some
research in the foundations of interoperability there is little supporting
This paper is based upon our existing work on combining languages to
produce so-called multi-languages. Here, we define an equational logic for
deducing valid equations, from axioms that postulate properties of the
multi-language. We define set-theoretic multi-language algebras as models,
and provide algebraic constructions such as congruences and quotient
algebras. Such models, and the constructions, provide the ingredients for
the main deliverable, soundness and completeness for the equational logic.
We illustrate the basic ideas with a running example.