scholarly journals A Mechanized Theory of Regular Trees in Dependent Type Theory

2015 ◽  
pp. 405-420
Author(s):  
Régis Spadotti
Keyword(s):  
Type Theory ◽  
Dependent Type Theory ◽  
Dependent Type

scholarly journals A relationally parametric model of dependent type theory

2014 ◽  
Vol 49 (1) ◽  
pp. 503-515 ◽  
Author(s):  
Robert Atkey ◽  
Neil Ghani ◽  
Patricia Johann
Keyword(s):  
Type Theory ◽  
Parametric Model ◽  
Dependent Type Theory ◽  
Dependent Type

scholarly journals Implementing a modal dependent type theory

2019 ◽  
Vol 3 (ICFP) ◽  
pp. 1-29 ◽  
Author(s):  
Daniel Gratzer ◽  
Jonathan Sterling ◽  
Lars Birkedal
Keyword(s):  
Type Theory ◽  
Dependent Type Theory ◽  
Dependent Type

scholarly journals Guarded Dependent Type Theory with Coinductive Types

2016 ◽  
pp. 20-35 ◽  
Author(s):  
Aleš Bizjak ◽  
Hans Bugge Grathwohl ◽  
Ranald Clouston ◽  
Rasmus E. Møgelberg ◽  
Lars Birkedal
Keyword(s):  
Type Theory ◽  
Dependent Type Theory ◽  
Dependent Type

scholarly journals Parametric quantifiers for dependent type theory

2017 ◽  
Vol 1 (ICFP) ◽  
pp. 1-29 ◽  
Author(s):  
Andreas Nuyts ◽  
Andrea Vezzosi ◽  
Dominique Devriese
Keyword(s):  
Type Theory ◽  
Dependent Type Theory ◽  
Dependent Type

Introduction to the Special Issue on Dependent Type Theory Meets Practical Programming

2004 ◽  
Vol 14 (1) ◽  
pp. 1-2
Author(s):  
GILLES BARTHE ◽  
PETER DYBJEN ◽  
PETER THIEMANN
Keyword(s):  
Programming Languages ◽  
Type Theory ◽  
Type System ◽  
Type Systems ◽  
Special Issue ◽  
Dependent Type Theory ◽  
Dependent Type

Modern programming languages rely on advanced type systems that detect errors at compile-time. While the benefits of type systems have long been recognized, there are some areas where the standard systems in programming languages are not expressive enough. Language designers usually trade expressiveness for decidability of the type system. Some interesting programs will always be rejected (despite their semantical soundness) or be assigned uninformative types.

scholarly journals Univalent categories and the Rezk completion

2015 ◽  
Vol 25 (5) ◽  
pp. 1010-1039 ◽  
Author(s):  
BENEDIKT AHRENS ◽  
KRZYSZTOF KAPULKIN ◽  
MICHAEL SHULMAN
Keyword(s):  
Category Theory ◽  
Type Theory ◽  
Dependent Type Theory ◽  
Equivalence Of Categories ◽  
Segal Spaces ◽  
Definition Of ◽  
Categorical Semantics ◽  
Univalent Foundations ◽  
Dependent Type

We develop category theory within Univalent Foundations, which is a foundational system for mathematics based on a homotopical interpretation of dependent type theory. In this system, we propose a definition of ‘category’ for which equality and equivalence of categories agree. Such categories satisfy a version of the univalence axiom, saying that the type of isomorphisms between any two objects is equivalent to the identity type between these objects; we call them ‘saturated’ or ‘univalent’ categories. Moreover, we show that any category is weakly equivalent to a univalent one in a universal way. In homotopical and higher-categorical semantics, this construction corresponds to a truncated version of the Rezk completion for Segal spaces, and also to the stack completion of a prestack.

scholarly journals A Multi-Modal Dependent Type Theory for Representing Data Accessibility in a Network

10.29007/vm4p ◽  
2018 ◽  
Author(s):  
Giuseppe Primiero
Keyword(s):  
Type Theory ◽  
Partial Evaluation ◽  
Distributed Processing ◽  
Program Structure ◽  
Data Accessibility ◽  
Dependent Type Theory ◽  
Modal Type ◽  
Dependent Type

In the present paper we explore the use of a newly formulated polymorphic modal type theory for a computational interpretation of programs in the context of distributed processing. The initial language define judgemental modalities with a the standard constructor for necessity interpreted as the presentation of instructions for a program terminating at runtime and an independent constructor for the possibility judgement as a representation of a process of partial evaluation. In order to interpret distributed and localised computing, we propose an extension in terms of multi-modalities, to express programs equipped with locations and data accessibility. Besides localised accessibility formalised by the different signed modalities, we develop further the language by prioritising these modalities, which implement seriality or staging annotations in the program structure.

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