The Semantics of Dependent Type Theory

categorical semantics of dependent type theory in nLab

Dependent types (in dependent type theory) have categorical semantics given by morphisms which are the bundles whose fibers are the families indexed by the ...

Categories with families are category theoretical models of dependent type theories, which can be augmented with dependent right adjoints to ...

Syntax and Semantics of Dependent Types - IRIF

Then in order to obtain an interpretation of type theory one \only" needs to check that one has an instance of the semantic notion. The semantics is not ...

Categorical Semantics of Dependent Type Theory - Daniel Mroz

There is a syntax/semantics duality between type theory and category theory. We can think of type theories as being a formal syntactic system ...

dependent type theory in nLab

1. Idea ... Dependent type theory is the flavor of type theory that admits dependent types. ... is interpreted as a morphism E → X E \to X , hence ...

Syntax and Semantics of Dependent Type Theories

For dependent type theories, we need more a complex notion of arity, to account for variable binding operations, e.g. λ, Π, Σ. 7 / 54. Page 8. Signatures (II).

Syntax and Semantics of Dependent Types

Syntax and Semantics of Dependent Types ... HTML view is not available for this content. However, as you have access to this content, a full PDF is available via ...

What are the motivations for different variants of categorical models ...

I am new to the categorical semantics for dependent type theories, so it is surprising for me to see nLab introduces so many variants of ...

Categorical semantics of universe levels in dependent type theory

Categorical semantics of universe levels in dependent type theory ... I know that locally closed cartesian categories provide categorical ...

Dependent type - Wikipedia

In computer science and logic, a dependent type is a type whose definition depends on a value. It is an overlapping feature of type theory and type systems.

Semantics of Type Theory - SpringerLink

Thus by the "proposition-as-types" paradigm one obtains types whose elements are considered as proofs. Each of these proofs contains a program correct w.r.t. ...

Game semantics for dependent types - ScienceDirect.com

The simple type theory we use is a variant STT of the simply typed λ-calculus with finite product types and finite inductive types {ai | i} for any finite set ...

Dependent Type Theory for Programming and Proving*

extant programming languages are phase-separated in this sense. By contrast dependent type theories exhibit no such separation of types from ...

Categorical Semantics for Type Theories - Jason Hu

... Category Theory, Categorical Semantics, Type Theory, Logic, Dependent. Types. ACM Reference Format: Jason Z.S. Hu. 2020. Categorical Semantics for Type Theories ...

[1405.0033] Syntax and Semantics of Linear Dependent Types - arXiv

Abstract:A type theory is presented that combines (intuitionistic) linear types with type dependency, thus properly generalising both ...

Semantics of Type Theory

An exploration of the categorical semantics of theories of dependent and polymorphic types, using the example of Coquand and Huet's calculus of ...

A Dependent Type Theory with Abstractable Names

We will give a semantics to FreshMLTT using nominal sets with sorted atoms. Thus we assume there is a fixed set A of atoms, partitioned into countably ...

Denotational semantics for guarded dependent type theory - arXiv

Title:Denotational semantics for guarded dependent type theory ... Abstract:We present a new model of Guarded Dependent Type Theory (GDTT), a type ...

What's the categorical semantics of definitional equality?

What's the categorical semantics of definitional equality? ... The categorical semantics of a dependent type theory is normally described as a CwA ...

A graded dependent type system with a usage-aware semantics

Graded Type Theory provides a mechanism to track and reason about resource usage in type systems. In this paper, we develop GraD, a novel version of such a ...