相关论文: Presheaf Models of Relational Modalities in Depend…

The purpose of this text is to prove all technical aspects of our model for dependent type theory with parametric quantifiers [Nuyts, Vezzosi and Devriese, 2017]. It is well-known that any presheaf category constitutes a model of dependent…

The purpose of these notes is to give a categorical semantics for the transpension type (Nuyts and Devriese, Transpension: The Right Adjoint to the Pi-type, Accepted at LMCS, 2024), which is right adjoint to a potentially substructural…

We introduce MTT, a dependent type theory which supports multiple modalities. MTT is parametrized by a mode theory which specifies a collection of modes, modalities, and transformations between them. We show that different choices of mode…

In this paper, we analyze and compare three of the many algebraic structures that have been used for modeling dependent type theories: categories with families, split type-categories, and representable maps of presheaves. We study these in…

The first part of this dissertation defines "dependently typed algebraic theories", which are a strict subclass of the generalised algebraic theories (GATs) of Cartmell. We characterise dependently typed algebraic theories as finitary…

This paper presents preliminary work on a general system for integrating dependent types into substructural type systems such as linear logic and linear type theory. Prior work on this front has generally managed to deliver type systems…

We develop normalisation by evaluation (NBE) for dependent types based on presheaf categories. Our construction is formulated in the metalanguage of type theory using quotient inductive types. We use a typed presentation hence there are no…

Graded type theories are an emerging paradigm for augmenting the reasoning power of types with parameterizable, fine-grained analyses of program properties. There have been many such theories in recent years which equip a type theory with…

We define a computational type theory combining the contentful equality structure of cartesian cubical type theory with internal parametricity primitives. The combined theory supports both univalence and its relational equivalent, which we…

Parametricity is a key metatheoretic property of type systems, which implies strong uniformity & modularity properties of the structure of types within systems possessing it. In recent years, various systems of dependent type theory have…

Presheaf models provide a formulation of labelled transition systems that is useful for, among other things, modelling concurrent computation. This paper aims to extend such models further to represent stochastic dynamics such as shown in…

This paper proposes the use of dependent types for pragmatic phenomena such as pronoun binding and presupposition resolution as a type-theoretic alternative to formalisms such as Discourse Representation Theory and Dynamic Semantics.

A type theory is presented that combines (intuitionistic) linear types with type dependency, thus properly generalising both intuitionistic dependent type theory and full linear logic. A syntax and complete categorical semantics are…

This article is the first in a series of articles that explain the formalization of a constructive model of cubical type theory in Nuprl. In this document we discuss only the parts of the formalization that do not depend on the choice of…

We exhibit a computational type theory which combines the higher-dimensional structure of cartesian cubical type theory with the internal parametricity primitives of parametric type theory, drawing out the similarities and distinctions…

A type theory is presented that combines (intuitionistic) linear types with type dependency, thus properly generalising both intuitionistic dependent type theory and full linear logic. A syntax and complete categorical semantics are…

Dependency pairs are a key concept at the core of modern automated termination provers for first-order term rewriting systems. In this paper, we introduce an extension of this technique for a large class of dependently-typed higher-order…

This is the second in a series of papers extending Martin-L\"{o}f's meaning explanation of dependent type theory to account for higher-dimensional types. We build on the cubical realizability framework for simple types developed in Part I,…

Presheaf models of dependent type theory have been successfully applied to model HoTT, parametricity, and directed, guarded and nominal type theory. There has been considerable interest in internalizing aspects of these presheaf models,…

The problem of comparing concepts of dependence in general rough sets with those in probability theory had been initiated by the present author in some of her recent papers. This problem relates to the identification of the limitations of…