Semantics for two-dimensional type theory

by   Benedikt Ahrens, et al.

In this work, we propose a general notion of model for two-dimensional type theory, in the form of comprehension bicategories. Examples of comprehension bicategories are plentiful; they include interpretations of directed type theory previously studied in the literature. From comprehension bicategories, we extract a core syntax, that is, judgment forms and structural inference rules, for a two-dimensional type theory. We prove soundness of the rules by giving an interpretation in any comprehension bicategory. The semantic aspects of our work are fully checked in the Coq proof assistant, based on the UniMath library. This work is the first step towards a theory of syntax and semantics for higher-dimensional directed type theory.



page 1

page 2

page 3

page 4


On Higher Inductive Types in Cubical Type Theory

Cubical type theory provides a constructive justification to certain asp...

Syntax and Typing for Cedille Core

This document specifies a core version of the type theory implemented in...

The RedPRL Proof Assistant (Invited Paper)

RedPRL is an experimental proof assistant based on Cartesian cubical com...

General Semantic Construction of Dependent Refinement Type Systems, Categorically

Refinement types are types equipped with predicates that specify precond...

The geometry of syntax and semantics for directed file transformations

We introduce a conceptual framework that associates syntax and semantics...

Transpension: The Right Adjoint to the Pi-type

Presheaf models of dependent type theory have been successfully applied ...

Towards Measuring and Quantifying the Comprehensibility of Process Models – The Process Model Comprehension Framework

Process models constitute crucial artifacts in modern information system...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.