λλ: A Programming Language for Silicon Photonics | Proceedings of the ACM SIGCOMM 2026 Conference

Abstract

Abstract

We present _λλ_1, a programming language for silicon photonics. λλ uses a linear type system to encode the physical constraints of optics, rejecting unrealizable programs at compile time. The compiler lowers well-typed programs to a graph-based intermediate representation, then solves a constrained embedding problem to map these graphs onto arbitrary silicon photonic switch targets while minimizing signal loss. We validate λλ on a commercial photonic switch, demonstrating correct operation for circuit switching, time-varying rotor switching and analog in-network computation. Across various hardware targets and programs, the λλ compiler scales to silicon photonic switches with over 100,000 programmable elements and handles switch programs with 128 input-output pairs. Finally, we develop a synthesizer to automatically generate λλ programs from high-level specifications, allowing users to program photonic hardware without reasoning about optical primitives.

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References

[1]

Carolyn Jane Anderson, Nate Foster, Arjun Guha, Jean-Baptiste Jeannin, Dexter Kozen, Cole Schlesinger, and David Walker. 2014. NetKAT: semantic foundations for networks. SIGPLAN Not. 49, 1 (jan 2014), 113–126.

[2]

Mina Tahmasbi Arashloo, Yaron Koral, Michael Greenberg, Jennifer Rexford, and David Walker. 2016. SNAP: Stateful Network-Wide Abstractions for Packet Processing. In SIGCOMM.

[3]

Hitesh Ballani, Paolo Costa, Raphael Behrendt, Daniel Cletheroe, István Haller, Krzysztof Jozwik, Fotini Karinou, Sophie Lange, Kai Shi, Benn Thomsen, and Hugh Williams. 2020. Sirius: A Flat Datacenter Network with Nanosecond Optical Switching. In SIGCOMM '20: Proceedings of the 2020 Annual conference of the ACM Special Interest Group on Data Communication on the applications, technologies, architectures, and protocols for computer communication, Virtual Event, USA, August 10–14, 2020, Henning Schulzrinne and Vishal Misra (Eds.). ACM, 782–797.

[4]

Shrutarshi Basu, Nate Foster, Hossein Hojjat, Paparao Palacharla, Christian Skalka, and Xi Wang. 2017. Life on the Edge: Unraveling Policies into Configurations. In 2017 ACM/IEEE Symposium on Architectures for Networking and Communications Systems (ANCS). 178–190.

[5]

Ryan Beckett, Michael Greenberg, and David Walker. 2016. Temporal NetKAT. In PLDI. 386–401.

[6]

Benjamin Bichsel, Maximilian Baader, Timon Gehr, and Martin Vechev. 2020. Silq: a high-level quantum language with safe uncomputation and intuitive semantics. In Proceedings of the 41st ACM SIGPLAN Conference on Programming Language Design and Implementation (PLDI 2020). Association for Computing Machinery, New York, NY, USA, 286–300.

[7]

Pat Bosshart, Dan Daly, Glen Gibb, Martin Izzard, Nick McKeown, Jennifer Rexford, Cole Schlesinger, Dan Talayco, Amin Vahdat, George Varghese, and David Walker. 2014. P4: Programming Protocol-Independent Packet Processors. ACM SIGCOMM Computer Communication Review 44, 3 (July 2014), 87–95.

[8]

José Capmany and Daniel Pérez. 2020. Programmable integrated photonics. Oxford University Press.

[9]

Lukas Chrostowski and Michael Hochberg. 2015. Silicon Photonics Design: From Devices to Systems. Cambridge University Press.

[10]

William R. Clements, Peter C. Humphreys, Benjamin J. Metcalf, W. Steven Kolthammer, and Ian A. Walmsley. 2016. Optimal design for universal multiport interferometers. Optica 3, 12 (Dec 2016), 1460–1465.

[11]

Charles Clos. 1953. A study of non-blocking switching networks. The Bell System Technical Journal 32, 2 (1953), 406–424.

[12]

NVIDIA Corporation. [n. d.]. Co-Packaged Silicon Photonics Networking Switches. https://www.nvidia.com/en-us/networking/products/silicon-photonics/. ([n. d.]). Accessed: 2025-04-08.

[13]

Arjun Devraj, Bill Owens, Daniel Pérez-López, and Rachee Singh. 2026. In-Network Analog AllReduce for ML with Programmable Integrated Photonics. In 2026 Optical Fiber Communications Conference and Exhibition (OFC). 1–3.

[14]

Eric Ding and Rachee Singh. 2025. PipSwitch: A Circuit Switch Using Programmable Integrated Photonics, In Optical Fiber Communication Conference (OFC) 2025. Optical Fiber Communication Conference (OFC) 2025, W2A.41.

[15]

Manuel Fahndrich and Robert DeLine. 2002. Adoption and focus: practical linear types for imperative programming. In Proceedings of the ACM SIGPLAN 2002 Conference on Programming Language Design and Implementation (PLDI '02). Association for Computing Machinery, New York, NY, USA, 13–24.

[16]

Nathan Farrington, George Porter, Sivasankar Radhakrishnan, Hamid Hajabdolali Bazzaz, Vikram Subramanya, Yeshaiahu Fainman, George Papen, and Amin Vahdat. 2010. Helios: A Hybrid Electrical/Optical Switch Architecture for Modular Data Centers. SIGCOMM Comput. Commun. Rev. 40, 4 (aug 2010), 339–350.

[17]

Nate Foster, Rob Harrison, Michael J. Freedman, Christopher Monsanto, Jennifer Rexford, Alec Story, and David Walker. 2011. Frenetic: A Network Programming Language. In ICFP. 279–291.

[18]

Peng Fu, Kohei Kishida, Neil J. Ross, and Peter Selinger. 2022. Proto-Quipper with dynamic lifting. (2022). arXiv:cs.PL/2204.13041 https://arxiv.org/abs/2204.13041

[19]

Peng Fu, Kohei Kishida, and Peter Selinger. 2022. Linear Dependent Type Theory for Quantum Programming Languages. Logical Methods in Computer Science Volume 18, Issue 3 (Sept. 2022).

[20]

Monia Ghobadi, Ratul Mahajan, Amar Phanishayee, Nikhil Devanur, Janardhan Kulkarni, Gireeja Ranade, Pierre-Alexandre Blanche, Houman Rastegarfar, Madeleine Glick, and Daniel Kilper. 2016. ProjecToR: Agile Reconfigurable Data Center Interconnect. In Proceedings of the 2016 ACM SIGCOMM Conference (SIGCOMM '16). Association for Computing Machinery, New York, NY, USA, 216–229.

[21]

Jean-Yves Girard. 1987. Linear logic. Theoretical computer science 50, 1 (1987), 1–101.

[22]

Albert Greenberg, James R. Hamilton, Navendu Jain, Srikanth Kandula, Changhoon Kim, Parantap Lahiri, David A. Maltz, Parveen Patel, and Sudipta Sengupta. 2009. VL2: A Scalable and Flexible Data Center Network. In Proceedings of the ACM SIGCOMM 2009 Conference on Data Communication (SIGCOMM '09). Association for Computing Machinery, New York, NY, USA, 51–62.

[23]

Navid Hamedazimi, Zafar Qazi, Himanshu Gupta, Vyas Sekar, Samir R. Das, Jon P. Longtin, Himanshu Shah, and Ashish Tanwer. 2014. FireFly: A Reconfigurable Wireless Data Center Fabric Using Free-Space Optics. In Proceedings of the 2014 ACM Conference on SIGCOMM (SIGCOMM '14). Association for Computing Machinery, New York, NY, USA, 319–330.

[24]

Nicholas C. Harris et al. 2018. Linear programmable nanophotonic processors. Optica 5, 12 (2018), 1623–1631.

[25]

Nicholas C Harris, Darius Bunandar, Ajay Joshi, Ayon Basumallik, and Robert Turner. 2022. Passage: A wafer-scale programmable photonic communication substrate. In 2022 IEEE Hot Chips 34 Symposium (HCS). IEEE Computer Society, 1–26.

[26]

Roger A. Horn and Charles R. Johnson. 1985. Matrix Analysis. Cambridge University Press.

[27]

Kazuhiro Ikeda, Keijiro Suzuki, Ryotaro Konoike, Shu Namiki, and Hitoshi Kawashima. 2020. Large-scale silicon photonics switch based on 45-nm CMOS technology. Optics Communications 466 (2020), 125677.

[28]

iPronics. 2026. iPronics ONE Silicon Photonics Optical Switch. https://ipronics.com/product/. (2026).

[29]

Warren Jin, Avi Feshali, Mario Paniccia, and John E. Bowers. 2021. Seamless multi-reticle photonics. Opt. Lett. 46, 12 (Jun 2021), 2984–2987.

[30]

Norman P. Jouppi, George Kurian, Sheng Li, Peter Ma, Rahul Nagarajan, Lifeng Nai, Nishant Patil, Suvinay Subramanian, Andy Swing, Brian Towles, Cliff Young, Xiang Zhou, Zongwei Zhou, and David Patterson. 2023. TPU v4: An Optically Reconfigurable Supercomputer for Machine Learning with Hardware Support for Embeddings. (2023). arXiv:cs.AR/2304.01433 https://arxiv.org/abs/2304.01433

[31]

Vaibhav Mehta. 2026. LambdaLambda Compiler. (June 2026). https://github.com/vaibhavmehta1/LambdaLambda/

[32]

William M. Mellette, Rob McGuinness, Arjun Roy, Alex Forencich, George Papen, Alex C. Snoeren, and George Porter. 2017. RotorNet: A Scalable, Low-Complexity, Optical Datacenter Network. In Proceedings of the Conference of the ACM Special Interest Group on Data Communication (SIGCOMM '17). Association for Computing Machinery, New York, NY, USA, 267–280.

[33]

Christopher Monsanto, Joshua Reich, Nate Foster, Jennifer Rexford, and David Walker. 2013. Composing Software Defined Networks. In NSDI.

[34]

Jeremie Eliahou Ontiveros, Dylan Patel, and Wei Zhou. 2025. xAI's Colossus 2 - First Gigawatt Datacenter In The World, Unique RL Methodology, Capital Raise. SemiAnalysis. (Sept. 2025). https://newsletter.semianalysis.com/p/xais-colossus-2-first-gigawatt-datacenter Accessed: 2026-01-23.

[35]

Daniel Pérez, Ivana Gasulla, José Capmany, and Richard A. Soref. 2016. Reconfigurable lattice mesh designs for programmable photonic processors. Opt. Express 24, 11 (May 2016), 12093–12106.

[36]

Benjamin C. Pierce. 2004. Advanced Topics in Types and Programming Languages. The MIT Press.

[37]

George Porter, Richard Strong, Nathan Farrington, Alex Forencich, Pang Chen-Sun, Tajana Rosing, Yeshaiahu Fainman, George Papen, and Amin Vahdat. 2013. Integrating Microsecond Circuit Switching into the Data Center. SIGCOMM Comput. Commun. Rev. 43, 4 (aug 2013), 447–458.

[38]

Michael Reck, Anton Zeilinger, Herbert J. Bernstein, and Philip Bertani. 1994. Experimental realization of any discrete unitary operator. Phys. Rev. Lett. 73 (Jul 1994), 58–61. Issue 1.

[39]

Graham T. Reed and Andrew P. Knights. 2004. Silicon Photonics: An Introduction. John Wiley & Sons.

[40]

JJ Schäffer. 1955. On unitary dilations of contractions. In Proc. Amer. Math. Soc, Vol. 6. 322.

[41]

PETER SELINGER and BENOIT VALIRON. 2006. A lambda calculus for quantum computation with classical control. Mathematical Structures in Computer Science 16, 3 (2006), 527–552.

[42]

Yichen Shen et al. 2017. Deep learning with coherent nanophotonic circuits. Nature Photonics 11 (2017), 441–446.

[43]

Mohammad Shoeybi, Mostofa Patwary, Raul Puri, Patrick LeGresley, Jared Casper, and Bryan Catanzaro. 2019. Megatron-LM: Training Multi-Billion Parameter Language Models Using Model Parallelism. CoRR abs/1909.08053 (2019). arXiv:1909.08053 http://arxiv.org/abs/1909.08053

[44]

Vishal Shrivastav, Asaf Valadarsky, Hitesh Ballani, Paolo Costa, Ki Suh Lee, Han Wang, Rachit Agarwal, and Hakim Weatherspoon. 2019. Shoal: A Network Architecture for Disaggregated Racks. In 16th USENIX Symposium on Networked Systems Design and Implementation (NSDI 19). USENIX Association, Boston, MA, 255–270. https://www.usenix.org/conference/nsdi19/presentation/shrivastav

[45]

Arjun Singh, Joon Ong, Amit Agarwal, Glen Anderson, Ashby Armistead, Roy Bannon, Seb Boving, Gaurav Desai, Bob Felderman, Paulie Germano, Anand Kanagala, Jeff Provost, Jason Simmons, Eiichi Tanda, Jim Wanderer, Urs Hölzle, Stephen Stuart, and Amin Vahdat. 2015. Jupiter Rising: A Decade of Clos Topologies and Centralized Control in Google's Datacenter Network. In Sigcomm '15.

[46]

Arjun Singh, Joon Ong, Amit Agarwal, Glen Anderson, Ashby Armistead, Roy Bannon, Seb Boving, Gaurav Desai, Bob Felderman, Paulie Germano, Anand Kanagala, Jeff Provost, Jason Simmons, Eiichi Tanda, Jim Wanderer, Urs Hölzle, Stephen Stuart, and Amin Vahdat. 2015. Jupiter Rising: A Decade of Clos Topologies and Centralized Control in Google's Datacenter Network. In Sigcomm '15.

[47]

Anirudh Sivaraman, Alvin Cheung, Mihai Budiu, Changhoon Kim, Mohammad Alizadeh, Hari Balakrishnan, George Varghese, Nick McKeown, and Steve Licking. 2016. Packet Transactions: High-Level Programming for Line-Rate Switches. In SIGCOMM. 15–28.

[48]

John Sonchack, Devon Loehr, Jennifer Rexford, and David Walker. 2021. Lucid: A Language for Control in the Data Plane. In SIGCOMM.

[49]

Sam Staton. 2015. Algebraic Effects, Linearity, and Quantum Programming Languages. SIGPLAN Not. 50, 1 (Jan. 2015), 395–406.

[50]

Abhishek Vijaya Kumar, Arjun Devraj, Darius Bunandar, and Rachee Singh. 2024. A case for server-scale photonic connectivity. In Proceedings of the 23rd ACM Workshop on Hot Topics in Networks (HotNets '24). Association for Computing Machinery, New York, NY, USA, 290–299.

[51]

Abhishek Vijaya Kumar, Eric Ding, Arjun Devraj, Darius Bunandar, and Rachee Singh. 2026. Reconfigurable Torus Fabrics for Multi-tenant ML. In Proceedings of the 31st ACM International Conference on Architectural Support for Programming Languages and Operating Systems, Volume 2 (ASPLOS '26). Association for Computing Machinery, New York, NY, USA, 1547–1565.

[52]

Jens Vygen. 1995. NP-completeness of some edge-disjoint paths problems. Discrete Applied Mathematics 61, 1 (1995), 83–90.

[53]

Philip Wadler. 1990. Linear types can change the world!. In Programming concepts and methods, Vol. 3. North-Holland, Amsterdam, 5.

[54]

David Walker and Kevin Watkins. 2001. On regions and linear types. ACM Sigplan Notices 36, 10 (2001), 181–192.

[55]

Guohui Wang, David G. Andersen, Michael Kaminsky, Konstantina Papagiannaki, T.S. Eugene Ng, Michael Kozuch, and Michael Ryan. 2010. C-Through: Part-Time Optics in Data Centers. SIGCOMM Comput. Commun. Rev. 40, 4 (aug 2010), 327–338.

[56]

Yuepeng Wu, Cen Wang, Hongxiang Guo, Yuta Wakayama, Qiuyan Li, Noboru Yoshikane, Takehiro Tsuritani, and Jian Wu. 2025. Optical AllReduce: Ready to Eliminate Intra-DC In-cast Vulnerability for Deep Learning Training. In Optical Fiber Communication Conference. Optica Publishing Group, W4D-5.

[57]

Charles Yuan and Michael Carbin. 2022. Tower: data structures in Quantum superposition. Proceedings of the ACM on Programming Languages 6, OOPSLA2 (2022), 259–288.

[58]

Shizhen Zhao, Rui Wang, Junlan Zhou, Joon Ong, Jeffrey C. Mogul, and Amin Vahdat. 2019. Minimal Rewiring: Efficient Live Expansion for Clos Data Center Networks. In 16th USENIX Symposium on Networked Systems Design and Implementation, NSDI 2019, Boston, MA, February 26–28, 2019, Jay R. Lorch and Minlan Yu (Eds.). USENIX Association, 221–234. https://www.usenix.org/conference/nsdi19/presentation/zhao

[59]

Yazhou Zu, Alireza Ghaffarkhah, Hoang-Vu Dang, Brian Towles, Steven Hand, Safeen Huda, Adekunle Bello, Alexander Kolbasov, Arash Rezaei, Dayou Du, Steve Lacy, Hang Wang, Aaron Wisner, Chris Lewis, and Henri Bahini. 2024. Resiliency at Scale: Managing Google's TPUv4 Machine Learning Supercomputer. In 21st USENIX Symposium on Networked Systems Design and Implementation (NSDI 24). USENIX Association, Santa Clara, CA, 761–774. https://www.usenix.org/conference/nsdi24/presentation/zu