I am interested in the denotational semantics of programming languages, especially those for probabilistic programming and quantum computation.
- Probabilistic programming is the idea to express complicated statistical models succinctly using a programming language, with special constructs for both sampling and Bayesian inference.
- Probabilistic languages range from specialized ones to completely general-purpose languages, commonly trading flexibility for efficiency of inference. Compiler optimizations help make inference run more efficiently.
My recent focus is on probabilistic programming languages that support higher-order functions. Their denotational semantics steps outside the traditional measure-theoretic formalization of probability theory. To that end, I am now investigating a new category-theoretic foundation of probability theory using mathematical structures called quasi-Borel spaces. Surprisingly, this has close connections to name generation and logical relations. Keywords: Probability monads, Functional programming, Type theory, Category theory, Descriptive set theory, ν-calculus