Recent work has shown that forward-and reverse-mode automatic differentiation (AD) over
the reals is almost always correct in a mathematically precise sense. However, actual …

We give a simple, direct, and reusable logical relations technique for languages with term
and type recursion and partially defined differentiable functions. We demonstrate it by …

This thesis revolves around an area of computer science called" semantics". We work with
operational semantics, equational theories, and denotational semantics. The first …

We present a novel, yet rather simple construction within the traditional framework of Scott
domains to provide semantics to probabilistic programming, thus obtaining a solution to a …

Forward-or reverse-mode automatic differentiation (AD) is a popular algorithm for computing
the derivative of a function expressed by a program. AD always outputs the correct derivative …

This dissertation supports the broader thesis that categorical semantics is a powerful tool to
study and design programming languages. It focuses on the foundational aspects of …

Continuous computations, which involve continuous data and operations on them, are
ubiquitous in diverse areas such as machine learning and scientific computing. In theoretical …

Probabilistic programming is an innovative programming paradigm for posing and
automatically solving Bayesian inference problems. In this thesis, we study the foundations …