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The treatment of equality as a type in type theory gives rise to an interesting type-theoretic structure known as `identity type'. The idea is that, given terms $a,b$ of a type $A$, one may form the type $Id_{A}(a,b)$, whose elements are…
This paper introduces an ML / Haskell like programming language with nested inductive and coinductive algebraic datatypes called \chariot. Functions are defined by arbitrary recursive definitions and can thus lead to non-termination and…
The quantum assembly language (QASM) is a popular intermediate representation used in many quantum compilation and simulation tools to describe quantum circuits. Currently, multiple different dialects of QASM are used in different quantum…
Quantum computing (QC) represents the future of computing systems, but the tools for reasoning about the quantum model of computation, in which the laws obeyed are those on the quantum mechanical scale, are still a mix of linear algebra and…
Competency Questions (CQs) are widely used in ontology development by guiding, among others, the scoping and validation stages. However, very limited guidance exists for formulating CQs and assessing whether they are good CQs, leading to…
Post-training quantization (PTQ) has emerged as a promising technique to reduce the cost of large language models (LLMs). Specifically, PTQ can effectively mitigate memory consumption and reduce computational overhead in LLMs. To meet the…
Recent research in information extraction (IE) focuses on utilizing code-style inputs to enhance structured output generation. The intuition behind this is that the programming languages (PLs) inherently exhibit greater structural…
Quantum computing leverages the principles of quantum mechanics to perform computations far beyond the capabilities of classical systems, particularly in fields such as cryptography and optimization. However, current quantum programming…
Customer-service question answering (QA) systems increasingly rely on conversational language understanding. While Large Language Models (LLMs) achieve strong performance, their high computational cost and deployment constraints limit…
We introduce a general theory of quantitative and metric rewriting systems, namely systems with a rewriting relation enriched over quantales modelling abstract quantities. We develop theories of abstract and term-based systems, refining…
Current Machine Translation (MT) systems achieve very good results on a growing variety of language pairs and datasets. However, they are known to produce fluent translation outputs that can contain important meaning errors, thus…
In this paper, we outline the prototype of an automated inference tool, called QUIP, which provides a uniform implementation for several nonmonotonic reasoning formalisms. The theoretical basis of QUIP is derived from well-known results…
Fine-tuning large language models (LLMs) is often constrained by the computational costs of processing massive datasets. We propose \textbf{QLESS} (Quantized Low-rank Gradient Similarity Search), which integrates gradient quantization with…
We develop synthetic notions of oracle computability and Turing reducibility in the Calculus of Inductive Constructions (CIC), the constructive type theory underlying the Coq proof assistant. As usual in synthetic approaches, we employ a…
Quantitative reasoning is a higher-order reasoning skill that any intelligent natural language understanding system can reasonably be expected to handle. We present EQUATE (Evaluating Quantitative Understanding Aptitude in Textual…
Machine Translation Quality Estimation (MTQE) is the task of estimating the quality of machine-translated text in real time without the need for reference translations, which is of great importance for the development of MT. After two…
We report on the development of the HoTT library, a formalization of homotopy type theory in the Coq proof assistant. It formalizes most of basic homotopy type theory, including univalence, higher inductive types, and significant amounts of…
We extract mathematical concepts from mathematical text using generative large language models (LLMs) like ChatGPT, contributing to the field of automatic term extraction (ATE) and mathematical text processing, and also to the study of LLMs…
The goal of this lecture is to show how modern theorem provers---in this case, the Coq proof assistant---can be used to mechanize the specification of programming languages and their semantics, and to reason over individual programs and…
Linear type theories, of various types and kinds, are of fundamental importance in most programming language research nowadays. In this paper we describe an extension of Benton's Linear-Non-Linear type theory and model for which we can…