Several authors have proposed formal models of FaaS. Jangda et al.  and Obetz et al.  both introduce formal models of FaaS and event-driven computation. Gabrielli et al.  propose the Serverless Kernel Calculus, which is similar and includes a stateful extension. Burckhardt et al.  analyze durable functions in the context of a formal model, providing one demonstration of the value of these techniques.
- Abhinav Jangda, Donald Pinckney, Yuriy Brun, and Arjun Guha. 2019. Formal Foundations of Serverless Computing. Proceedings of the ACM on Programming Languages 3, OOPSLA (2019), 1–26.
- Matthew Obetz, Anirban Das, Timothy Castiglia, Stacy Patterson, and Ana Milanova. 2020. Formalizing Event-Driven Behavior of Serverless Applications. In European Conference on Service-Oriented and Cloud Computing, Springer, 19–29.
- Maurizio Gabbrielli, Saverio Giallorenzo, Ivan Lanese, Fabrizio Montesi, Marco Peressotti, and Stefano Pio Zingaro. 2019. No More, No Less - A Formal Model for Serverless Computing. In International Conference on Coordination Languages and Models, Springer, 148–157.
- Sebastian Burckhardt, Chris Gillum, David Justo, Konstantinos Kallas, Connor McMahon, and Christopher S. Meiklejohn. 2021. Durable Functions: Semantics for Stateful Serverless. Proceedings of the ACM on Programming Languages 5, OOPSLA (2021), 1–27.