Simon Peyton Jones

Functional logic languages have a rich literature, but it is tricky to give them a satisfying semantics. In this paper we describe the Verse calculus, VC, a new core calculus for deterministic functional logic programming. Our main contribution is to equip VC with a small-step rewrite semantics, so that we can reason about a VC program in the same way as one does with lambda calculus; that is, by applying successive rewrites to it. We also show that the rewrite system is confluent for well-behaved terms.

In this paper, we give a simple and efficient implementation of reverse-mode automatic differentiation, which both extends easily to higher-order functions, and has run time and memory consumption linear in the run time of the original program. In addition to a formal description of the translation, we also describe an implementation of this algorithm, and prove its correctness by means of a logical relations argument.

Digital technologies are becoming increasingly prevalent in education, enabling personalized, high quality education resources to be accessible by students across the world. Importantly, among these resources are diagnostic questions: the answers that the students give to these questions reveal key information about the specific nature of misconceptions that the students may hold. Analyzing the massive quantities of data stemming from students' interactions with these diagnostic questions can help us more accurately understand the students' learning status and thus allow us to automate learning curriculum recommendations. In this competition, participants will focus on the students' answer records to these multiple-choice diagnostic questions, with the aim of 1) accurately predicting which answers the students provide; 2) accurately predicting which questions have high quality; and 3) determining a personalized sequence of questions for each student that best predicts the student's answers. These tasks closely mimic the goals of a real-world educational platform and are highly representative of the educational challenges faced today. We provide over 20 million examples of students' answers to mathematics questions from Eedi, a leading educational platform which thousands of students interact with daily around the globe. Participants to this competition have a chance to make a lasting, real-world impact on the quality of personalized education for millions of students across the world.

Online education platforms enable teachers to share a large number of educational resources such as questions to form exercises and quizzes for students. With large volumes of available questions, it is important to have an automated way to quantify their properties and intelligently select them for students, enabling effective and personalized learning experiences. In this work, we propose a framework for mining insights from educational questions at scale. We utilize the state-of-the-art Bayesian deep learning method, in particular partial variational auto-encoders (p-VAE), to analyze real students' answers to a large collection of questions. Based on p-VAE, we propose two novel metrics that quantify question quality and difficulty, respectively, and a personalized strategy to adaptively select questions for students. We apply our proposed framework to a real-world dataset with tens of thousands of questions and tens of millions of answers from an online education platform. Our framework not only demonstrates promising results in terms of statistical metrics but also obtains highly consistent results with domain experts' evaluation.

Sheet-defined functions (SDFs) bring modularity and abstraction to the world of spreadsheets. Alas, end users naturally write SDFs that work over fixed-size arrays, which limits their reusability. To help end user programmers write more reusable SDFs, we describe a principled approach to generalising such functions to become elastic SDFs that work over inputs of arbitrary size. We prove that under natural, checkable conditions, our algorithm returns the principal generalisation of an input SDF. We describe a formal semantics and several efficient implementation strategies for elastic SDFs. A user study with spreadsheet users compares the human experience of programming with elastic SDFs to the alternative of relying on array-processing combinators. Our user study finds that the cognitive load of elastic SDFs is lower than for SDFs with map/reduce array combinators, the closest alternative solution.

Build systems are awesome, terrifying – and unloved. They are used by every developer around the world, but are rarely the object of study. In this paper, we offer a systematic, and executable, framework for developing and comparing build systems, viewing them as related points in a landscape rather than as isolated phenomena. By teasing apart existing build systems, we can recombine their components, allowing us to prototype new build systems with desired properties.

For many years, GHC has implemented an extension to Haskell that allows type variables to be bound in type signatures and patterns, and to scope over terms. This extension was never properly specified. We rectify that oversight here. With the formal specification in hand, the otherwise-labyrinthine path toward a design for binding type variables in patterns becomes blindingly clear. We thus extend ScopedTypeVariables to bind type variables explicitly, obviating the Proxy workaround to the dustbin of history.