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Ability to use definitions occurring in the code directly in equational reasoning is one of the key strengths of functional programming. This is impossible in the case of Haskell type class methods unless a particular instance type is…

Recent advances in tracking sensors and pose estimation software enable smart systems to use trajectories of skeleton joint locations for supervised learning. We study the problem of accurately recognizing sign language words, which is key…

The challenge of automatically determining the correctness of test executions is referred to as the test oracle problem and is one of the key remaining issues for automated testing. The goal in this paper is to solve the test oracle problem…

Appel and McAllester's "step-indexed" logical relations have proven to be a simple and effective technique for reasoning about programs in languages with semantically interesting types, such as general recursive types and general reference…

Elaboration-based type class resolution, as found in languages like Haskell, Mercury and PureScript, is generally nondeterministic: there can be multiple ways to satisfy a wanted constraint in terms of global instances and locally given…

Recent advances in artificial intelligence have demonstrated the learnability of symbolic computation through end-to-end deep learning. Given a sufficient number of examples of symbolic expressions before and after the target computation,…

Proof assistants and programming languages based on type theories usually come in two flavours: one is based on the standard natural deduction presentation of type theory and involves eliminators, while the other provides a syntax in…

In previous work, we have introduced functional strategies, that is, first-class generic functions that can traverse into terms of any type while mixing uniform and type-specific behaviour. In the present paper, we give a detailed…

We present an approach to support partiality in type-level computation without compromising expressiveness or type safety. Existing frameworks for type-level computation either require totality or implicitly assume it. For example, type…

Hashing produces compact representations for documents, to perform tasks like classification or retrieval based on these short codes. When hashing is supervised, the codes are trained using labels on the training data. This paper first…

Elfe is an interactive system for teaching basic proof methods in discrete mathematics. The user inputs a mathematical text written in fair English which is converted to a special data-structure of first-order formulas. Certain proof…

This article is concerned with the application of the program extraction technique to a new class of problems: the synthesis of decision procedures for the classical satisfiability problem that are correct by construction. To this end, we…

We consider the problem of translating high-level textual descriptions to formal representations in technical documentation as part of an effort to model the meaning of such documentation. We focus specifically on the problem of learning…

Large transformer-based language models have been shown to be very effective in many classification tasks. However, their computational complexity prevents their use in applications requiring the classification of a large set of candidates.…

As a powerful tool of asynchronous event sequence analysis, point processes have been studied for a long time and achieved numerous successes in different fields. Among various point process models, Hawkes process and its variants attract…

We study machine learning formulations of inductive program synthesis; that is, given input-output examples, synthesize source code that maps inputs to corresponding outputs. Our key contribution is TerpreT, a domain-specific language for…

This document specifies a core version of the type theory implemented in the Cedille tool. Cedille is a language for dependently typed programming and computer-checked proof. Cedille can elaborate source programs down to Cedille Core, which…

Specification languages are essential in deductive program verification, but they are usually based on first-order logic, hence less expressive than the programs they specify. Recently, trace specification logics with fixed points that are…

We develop the operational semantics of an untyped probabilistic lambda-calculus with continuous distributions, as a foundation for universal probabilistic programming languages such as Church, Anglican, and Venture. Our first contribution…

Terms are a concise representation of tree structures. Since they can be naturally defined by an inductive type, they offer data structures in functional programming and mechanised reasoning with useful principles such as structural…