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arXiv · 1812.03624

Formalization of Metatheory of the Quipper Quantum Programming Language in a Linear Logic

Mohamed Yousri Mahmoud·Amy P. Felty
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Abstract

We develop a linear logical framework within the Hybrid system and use it to reason about the type system of a quantum lambda calculus. In particular, we consider a practical version of the calculus called Proto-Quipper, which contains the core of Quipper. Quipper is a new quantum programming language under active development and recently has gained much popularity among the quantum computing communities. Hybrid is a system that is designed to support the use of higher-order abstract syntax (HOAS) 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 (SL) in order to reason about the linear type system of Quipper. To this end, we formalize the semantics of Proto-Quipper by encoding the typing and evaluation rules in the SL, and prove type soundness.

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Mohamed Yousri Mahmoud, Amy P. Felty. 2018-12-10. Formalization of Metatheory of the Quipper Quantum Programming Language in a Linear Logic. https://arxiv.org/abs/1812.03624

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