Related papers: A Dependent Dependency Calculus (Extended Version)
This short note presents a new formal language, lambda dependency-based compositional semantics (lambda DCS) for representing logical forms in semantic parsing. By eliminating variables and making existential quantification implicit, lambda…
This paper brings mathematical tools to bear on the study of package dependencies in software systems. We introduce structures known as Dependency Structures with Choice (DSC) that provide a mathematical account of such dependencies,…
The article proposes formulating and codifying a set of applied numerical methods, coined as Deep Learning Discrete Calculus (DLDC), that uses the knowledge from discrete numerical methods to interpret the deep learning algorithms through…
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…
Prompt programming treats large language model prompts as software components with typed interfaces. Based on a literature survey of 15 recent works from 2023 to 2025, we observe a consistent trend: type systems are central to emerging…
Dependently typed programming languages allow sophisticated properties of data to be expressed within the type system. Of particular use in dependently typed programming are indexed types that refine data by computationally useful…
The defunctionalization translation that eliminates higher-order functions from programs forms a key part of many compilers. However, defunctionalization for dependently-typed languages has not been formally studied. We present the first…
In this tutorial I will present how a combination of linear and dependent type can be useful to describe different properties about higher order programs. Linear types have been proved particularly useful to express properties of functions;…
Probabilistic programming languages have recently gained a lot of attention, in particular due to their applications in domains such as machine learning and differential privacy. To establish invariants of interest, many such languages…
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…
The patterns in which the syntax of different languages converges and diverges are often used to inform work on cross-lingual transfer. Nevertheless, little empirical work has been done on quantifying the prevalence of different syntactic…
Deploying machine learning models in safety-related do-mains (e.g. autonomous driving, medical diagnosis) demands for approaches that are explainable, robust against adversarial attacks and aware of the model uncertainty. Recent deep…
Passive documents and active programs now widely comingle. Document languages include Turing-complete programming elements, and programming languages include sophisticated document notations. However, there are no formal foundations that…
This paper proposes a novel model-based approach to combine the quantitative dependability (safety, reliability, availability, maintainability and IT security) analysis and trade-off analysis. The proposed approach is called DPN…
In this article, we survey the main models, techniques, concepts, and results centered on the design and performance evaluation of engineered systems that rely on a utilization-dependent component (UDC) whose operation may depend on its…
We present a deductive approach for the analysis of secure information flows with support for fine-grained policies that include declassifications in the form of delimited information release. By explicitly tracking the dependencies of…
We develop a novel form of differentiable predictive control (DPC) with safety and robustness guarantees based on control barrier functions. DPC is an unsupervised learning-based method for obtaining approximate solutions to explicit model…
Automatic parallelization improves the performance of serial program by automatically converting to parallel program. Automatic parallelization typically works in three phases: check for data dependencies in the input program, perform…
The calculus of constructions (CC) is a core theory for dependently typed programming and higher-order constructive logic. Originally introduced in Coquand's 1985 thesis, CC has inspired 25 years of research in programming languages and…
Dependency parsing aims to extract syntactic dependency structure or semantic dependency structure for sentences. Existing methods suffer the drawbacks of lacking universality or highly relying on the auxiliary decoder. To remedy these…