A Gradual Probabilistic Lambda Calculus

Explore a groundbreaking presentation on the Gradual Probabilistic Lambda Calculus (GPLC) from the OOPSLA 2023 conference. Delve into the innovative fusion of gradual typing and probabilistic programming languages, addressing the challenges of static type checking in domains like machine learning and differential privacy. Discover how GPLC allows for a smooth transition between static and dynamic checking, introducing a binary probabilistic choice operator and flexible type-and-probability annotations. Examine the formalization of GPLC's static semantics using probabilistic couplings and its dynamic semantics through elaboration to the target language TPLC. Gain insights into the language's metatheory, including type safety and adherence to refined criteria for gradual languages. Understand the significance of this work in expanding the benefits of gradual typing to probabilistic languages, potentially revolutionizing type systems in probabilistic programming.