It has been a busy year for me so far, and it's nice to be able to tell the world about some of the fruits of that labour. In the next few months my coauthors and I will be presenting a few papers at PLDI and ECOOP. All of these papers will probably change a bit more before assuming their final forms, but I'd like to circulate their existence to give non-reviewers a chance to say their bit.

*A Typed, Algebraic Approach to Parsing*, Neel Krishnaswami and Jeremy Yallop. Draft, accepted for publication at PLDI 2019.In this paper, we recall the definition of the context-free expressions (or µ-regular expressions), an algebraic presentation of the context-free languages. Then, we define a core type system for the context-free expressions which gives a compositional criterion for identifying those context-free expressions which can be parsed unambiguously by predictive algorithms in the style of recursive descent or LL(1).

Next, we show how these typed grammar expressions can be used to derive a parser combinator library which both guarantees linear-time parsing with no backtracking and single-token lookahead, and which respects the natural denotational semantics of context-free expressions. Finally, we show how to exploit the type information to write a staged version of this library, which produces dramatic increases in performance, even outperforming code generated by the standard parser generator tool ocamlyacc.

In this paper we redo some classical results in parsing theory using the tools of type theory and semantics, and the results is very satisfying. Partly, this is due to the fact that the techniques we used are actually all known, but merely by chance happened to fall out of fashion.

It was also nice seeing just how big a win staging is, and how comprehensively it erases the costs of using combinators. I'd really like to take another look at using staged type systems as the basis of a macro system a la MacroML.

*NumLin: Linear Types for Linear Algebra*, Dhruv Makwana and Neel Krishnaswmi. Draft, conditionally accepted for publication at ECOOP 2019.We present NumLin, a functional programming language designed to express the APIs of low-level linear algebra libraries (such as BLAS/LAPACK) safely and explicitly, through a brief description of its key features and several illustrative examples. We show that NumLin’s type system is sound and that its implementation improves upon naïve implementations of linear algebra programs, almost towards C-levels of performance. Lastly, we contrast it to other recent developments in linear types and show that using linear types and fractional permissions to express the APIs of low-level linear algebra libraries is a simple and effective idea.

One of the things that has always surprised me about linear types is that it has always seemed to me like they would be a natural fit for working with array/matrix programs, and yet if you look around there is surprisingly little work on this. In this paper Dhruv Makwana and I decided to try it to see if it could actually worked, and we learned two things:

- Linear types are indeed a good fit for array programming.
- But really making it work calls for
*fractional permissions*, and to date the type systems for working with fractions have been surprisingly complicated. - However, we came up with a trick for drastically reducing the implementation complexity of fractions, to the point that it's barely more complicated than standard HM type inference.

*A Program Logic for First-Order Encapsulated WebAssembly*, Conrad Watt, Petar Maksimov, Neel Krishnaswami, Phillipa Gardner. Draft, accepted for publication at ECOOP 2019.We introduce Wasm Logic, a sound program logic for first-order, encapsulated WebAssembly.

We design a novel assertion syntax, tailored to WebAssembly's stack-based semantics and the strong guarantees given by WebAssembly's type system, and show how to adapt the standard separation logic triple and proof rules in a principled way to capture WebAssembly's uncommon structured control flow. Using Wasm Logic, we specify and verify a simple WebAssembly B-tree library, giving abstract specifications independent of the underlying implementation.

We mechanise Wasm Logic and its soundness proof in full in Isabelle/HOL. As part of the soundness proof, we formalise and fully mechanise a novel, big-step semantics of WebAssembly, which we prove equivalent, up to transitive closure, to the original WebAssembly small-step semantics.

For me, there was a bit of nostalgia in this paper: I started out my research career working on separation logic, and it was nice to be able to do that stuff again. Also, it was nice to find out what the heck Webassembly actually is!