My general research interests are in the study of programming languages, including their theory, semantics, design, and implementation. In particular, I am interested in the foundations of programming languages and their relation to logic and duality. I'm also interested in understanding aspects of practical languages including computational effects (like mutable state, exceptions, and first-class continuations) and evaluation strategies (strict versus lazy evaluation and memoization), as well as ways for languages to sensibly bridge between high-level abstractions and low-level details.
I am interested in an alternative model for computation based on the connection between programming languages and formal logic (known as the Curry-Howard correspondence or proofs-as-programs interpretation). With a single stroke in 1935, Gentzen laid out the basis for the modern study of formalized logic: natural deduction and the sequent calculus. On the one hand, natural deduction is the logic of the lambda calculus, which serves as the bedrock for functional programming languages (like Scheme, Haskell, and OCaml) and proof assistants (like Coq). On the other hand, the sequent calculus has only recently been connected with a lower-level model for programs that highlights the dualities present in programming languages and details such as evaluation strategies (like strict or lazy evaluation) and control-flow effects (like exceptions). I am interested in developing this view of computation to get another view of programs and languages from different angles:
- A high-level calculus for reasoning about the behavior of programs (in a similar style as the lambda calculus) while also accounting for low-level details such as evaluation strategy and control flow.
- A contextual representation of programs that allows for performing context-sensitive analysis and transformation of programs, as done by optimizing compilers like GHC.
- A dualized framework that gives a symmetric and unified view of programming concepts, as a way to understand differences and similarities in language design, including types and abstraction mechanisms from both functional and object-oriented languages.
Some of these ideas have implemented in the form of a practical intermediate language for GHC, analogous to its Core representation, that can be used for analyzing and optimizing Haskell programs. The current version of Sequent Core can be found on Hackage as a plugin for GHC.