2. Dependent Type Theory
2. Dependent Type Theory - Lean
One way in which Lean's dependent type theory extends simple type theory is that types themselves — entities like nat and bool — are first-class citizens, which ...
2. In the foundations of mathematics · One can add a cumulative hierarchy to the dependent type theory and work entirely in the cumulative ...
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.
2. Dependent types — Logic in computer science lecture notes
2.4. The identity type¶ ... The identity type is a dependent type which represents the equality relation. It is also an inductive type whose only constructor is ...
Dependent Type Theory - Theorem Proving in Lean 4
Dependent type theory is a powerful and expressive language, allowing you to express complex mathematical assertions, write complex hardware and software ...
Basic building blocks of dependent type theory - LessWrong
There are three basic building blocks in type theory: values, functions, and types. (And then you can additionally construct ordered pairs out ...
2-Dimensional Directed Type Theory
These connections suggest a gen- eralization of dependent type theory to account for computationally relevant proofs of propositional equality—for example ...
Two-level type theory (2LTT) refers to versions of Martin-Lof type theory that combine two type theories: one level as a homotopy type theory.
Type Theory - Lecture 2: Dependent Types
2 Dependent Type Theory. Expressions and judgements. Dependent function type. 3 The Logical Framework. A type of types. Type conversion. Andreas ...
Dependent Type theory — What is mathematics? 1.0 documentation
Dependent type theory is a way to set up the foundations of mathematics. What does that even mean? Some mathematicians perhaps learn in a logic course that ZFC ...
Intuitionistic type theory - Wikipedia
There are multiple versions of the type theory: Martin-Löf proposed both intensional and extensional variants of the theory and early impredicative versions, ...
Admissible rules in dependent type theory
From the nlab article on Martin-Löf dependent type theory: The weakening and substitution rules are admissible rules: they do not need to be ...
Why dependent type theory? - Miscellaneous - Coq's discourse
In the HOL type system there are no dependent types, nor is there any form of subtyping. (Mizar and Coq both have dependent types and some form ...
How to implement dependent type theory II
How to implement dependent type theory II · Spiff up the syntax by allowing more flexible syntax for bindings in functions and products. · Keep ...
Staged Compilation with Two-Level Type Theory - András Kovács
In Section 2 we present an informal syntax of two-level type theory, a dependent type theory with support for two-stage compilation. We look at basic use ...
Computational Higher Type Theory II: Dependent Cubical Realizability
Title:Computational Higher Type Theory II: Dependent Cubical Realizability ... Abstract:This is the second in a series of papers extending Martin- ...
An Introduction to Dependent Type Theory
This is in contrast with type theories whose λ-abstractions are not explicitly typed, see Subsection. 2.2. 2. Pure Type Systems are minimal. The minimality of ...
Dependent vs. polymorphic types in modern type theories
From λ→ there are three directions (axes) we can go. We can add the ability for terms to depend on types producing λ2, the polymorphic lambda ...
A Dependent Type Theory with Abstractable Names
2. We call this delegation of freshness to definitional equality definitional fresh- ness. It means that equality judgements get intertwined with typing ...
David McAllester - Dependent Type Theory from the Perspective of ...
Dependent type theory imposes a type system on Zemelo-Fraenkel set theory (ZFC). From a mathematics and physics perspective dependent type ...