Formalization of Metatheory of the Quipper Quantum Programming Language in a Linear Logic
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 quantum programming language u...
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| Veröffentlicht in: | Journal of automated reasoning 2019-12, Vol.63 (4), p.967-1002 |
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| container_title | Journal of automated reasoning |
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| creator | Mahmoud, Mohamed Yousri Felty, Amy P. |
| description | 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 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 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. |
| doi_str_mv | 10.1007/s10817-019-09527-x |
| format | Article |
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| ispartof | Journal of automated reasoning, 2019-12, Vol.63 (4), p.967-1002 |
| issn | 0168-7433 1573-0670 |
| language | eng |
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| source | SpringerLink Journals - AutoHoldings |
| subjects | Artificial Intelligence Computer Science Hybrid systems Mathematical Logic and Formal Languages Mathematical Logic and Foundations Programming languages Quantum computing Semantics Symbolic and Algebraic Manipulation |
| title | Formalization of Metatheory of the Quipper Quantum Programming Language in a Linear Logic |
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