Basic building blocks of dependent type theory

Basic building blocks of dependent type theory - LessWrong

In contrast to set theory, functions are a fundamental concept in type theory, and are not defined in terms of other things. There are three ...

Basic building blocks of dependent type theory - Reddit

Dependent types work great to automatically propagate invariants attached to data structures (standard); In conjunction with monads (new!).

Introduction to Dependent Type Theory - LessWrong

48Basic building blocks of dependent type theory · 8 ; 15Recreating logic in type theory · 0 ; logic based on propositions-as-subsingleton-types · 0.

2. Dependent Type Theory - Lean

When β doesn't depend on x , Π x : α, β is no different from the type α → β . Indeed, in dependent type theory (and in Lean), the Pi construction is fundamental ...

An Interactive Introduction to Dependent Types with Idris

Type theory and programming languages research in recent decades has produced this incredibly interesting extension to ordinary types in ...

TypeDB Fundamentals: How Type Theory Powers Formal Languages

In this paradigm, classical predicates become so-called dependent types: while predicates R(x,y) describe when a relation is true depending on the given x and y ...

The Semantics of Dependent Type Theory

The fundamental building blocks of type theory are types and terms, with each term inhabiting exactly one type. In dependent type theory one ...

dependent type theory in nLab

is interpreted as a morphism E → X E \to X , hence an object in the slice category C / X C_{/X} . Then change of context corresponds to base ...

Series “Introduction to dependent type theory”

15 Dec 2022. Basic building blocks of dependent type theory · 21 Dec 2022. Recreating logic in type theory · 28 Dec 2022. Classical logic based on propositions-as ...

Foundations of Path-Dependent Types

ful building blocks: traits, mixin composition / refinements, path ... A nominal theory of objects with dependent types. In ECOOP, 2003 ...

Resources for implementing dependent type theory

This paper is my go-to for implementing dependent types. It starts from the basics, uses bidirectional types, and has accompanying code in ...

Formal mathematics, dependent type theory, and the Topos Institute

4th of November, 2021. Part of the Topos Institute Colloquium. ----- Abstract: Modern logic tells us that mathematics can be formalized, ...

An Introduction to Programming and Proving with Dependent Types ...

The semicolon is one of the most fundamental building blocks of effective proof automation. The period terminator is very useful for exploratory proving ...

Dependent Communication in Type Theory - Nicolas Pouillard

... type theory, building on the similarity of ... As a way to present and demonstrate the expressiveness of our system we define the essential building blocks and ...

Short and Mechanized Logical Relation for Dependent Type Theories

a boolean base type, and dependent elimination forms. Our ... While not without limitations, our simple proof demonstrates the core building blocks of more.

Native Type Theory (Part 3) | The n-Category Café

Hence the two basic entities are predicates and (dependent) types. ... kind of dependent type theory, and it's always true in a topos model.

(Homotopy) Type Theory Musings, informal and intuitive (hopefully)

(In type theory language, this means that the recursor, through which pattern matching and elimination are defined, requires proofs that the functions for each ...

Introduction to Dependent Type Theory - GreaterWrong.com

Basic building blocks of dependent type theory · 12/15/2022, 6:54 AM. 48 ; Recreating logic in type theory · 12/21/2022, 7:19 AM. 15 ; Classical ...

Simple Type Theory is not too Simple: Grothendieck's Schemes ...

1 Introduction · 2 A World Without Dependent Types: Problems and solutions · 3 Schemes in Isabelle/HOL · 3.2 Elements of Algebraic Geometry · 4 ...

4.2: Building Blocks of a Theory - Social Sci LibreTexts

David Whetten (1989) suggests that there are four building blocks of a theory: constructs, propositions, logic, and boundary conditions/assumptions.