A linear logical framework in Hybrid (invited talk)

Amy P Felty

doi:10.1145/3293880.3294088

Abstract

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].

Highlights

We are interested in applying this framework to applications outside the domain of metatheory of programming languages and have focused on two areas – formal reasoning about the proof theory of focused linear sequent calculi and modeling biological processes as transition systems and proving properties about them
We found that a slight extension of the initial linear specification logic allowed us to provide succinct encodings and facilitate reasoning in these new domains
This work illustrates the use of Hybrid as a meta-logical framework for fast prototyping of logical frameworks, which is achieved by defining inference rules of a specification logic inductively in Coq and building a library of definitions and lemmas used to reason about a class of object logics

Summary

Introduction

We are interested in applying this framework to applications outside the domain of metatheory of programming languages and have focused on two areas – formal reasoning about the proof theory of focused linear sequent calculi and modeling biological processes as transition systems and proving properties about them. We found that a slight extension of the initial linear specification logic allowed us to provide succinct encodings and facilitate reasoning in these new domains.

Results

Conclusion