A linear logical framework in hybrid (invited talk).

We present a linear logical framework implemented within the Hybrid system [Felty and Momigliano 2012]. Hybrid is designed to support the use of higher-order abstract syntax for representing and reasoning about formal systems, implemented in the Coq Proof Assistant. In this work, we extend the system with a linear specification logic, which provides infrastructure for reasoning directly about object languages with linear features. We developed this framework in order to address the challenges of reasoning about the type system of a quantum lambda calculus. In particular, we started by considering the Proto-Quipper language [Ross 2015], which contains the core of Quipper [Green et al. 2013; Selinger and Val- iron 2006]. Quipper is a new quantum programming language under active development with a linear type system. We have completed a formal proof of type soundness for Proto-Quipper [Mahmoud and Felty 2018b]. Our current work includes extending this work to other properties of Proto-Quipper as well as reasoning about other quantum programming languages [Mahmoud and Felty 2018a]. It also includes reasoning about other object languages with linear features in areas such as meta-theory of low-level abstract machine code, proof theory of focused linear sequent calculi, and modeling biological processes as transition systems and proving properties about them [Despeyroux et al. 2018].