Constructive Type Theory and Homotopy
constructive type theory and homotopy - andrew.cmu.ed
CONSTRUCTIVE TYPE THEORY AND HOMOTOPY. STEVE AWODEY. CARNEGIE MELLON UNIVERSITY. The purpose of this survey talk is to introduce a new and ...
[1010.1810] Type theory and homotopy - arXiv
Abstract:The purpose of this survey article is to introduce the reader to a connection between Logic, Geometry, and Algebra which has ...
Type Theory and Homotopy - andrew.cmu.ed
tion of the constructive type theory of Per Martin-Löf into homotopy theory, resulting in new examples of certain algebraic structures which are important ...
Homotopy Type Theory: What is it? - MathOverflow
Topologists are seeing type theory as a concise and convenient ways to reason about topology, where equalities are interpreted as paths (and ...
Constructivity in Homotopy Type Theory
In the seminal HoTT Book (2013), it is maintained that constructive reasoning is not necessary when formalizing mathematics in homotopy type theory. (HoTT):.
Constructive Type Theory and Homotopy - Institute for Advanced Study
In recent research it has become clear that there are fascinating connections between constructive mathematics, especially as formulated in ...
About constructive mathematics and Homotopy type theory
I am a CSer and I am reading the HoTT book and found that doing math with computer is fascinating. I found that constructive math compared with classical math ...
Homotopy type theory - Wikipedia
In mathematical logic and computer science, homotopy type theory (HoTT) refers to various lines of development of intuitionistic type theory, based on the ...
Intuitionistic Type Theory - Stanford Encyclopedia of Philosophy
Intuitionistic type theory (also constructive type theory or Martin-Löf type theory) is a formal logical system and philosophical foundation for constructive ...
What is Homotopy Type Theory, and what implications does it hold?
Homotopy theory is an advanced branch of topology which studies a weak notion of equivalence between spaces called homotopy equivalence.
[1201.3898] Inductive types in homotopy type theory - arXiv
There results a link between constructive mathematics and algebraic topology, providing topological semantics for intensional systems of type ...
Homotopy Type Theory - Steve Awodey
▷ Martin-Löf type theory (a formal system of constructive foundations) can be interpreted into abstract homotopy theory. (the mathematics of continuous space).
Homotopy Type Theory refers to a new field of study relating Martin-Löf's system of intensional, constructive type theory with abstract homotopy theory.
homotopy type theory FAQ in nLab
Homotopy type theory is a refinement of constructive set theory that takes fully seriously the constructive nature also of identity. (As with ...
Intuitionistic type theory - Wikipedia
Intuitionistic type theory (also known as constructive type theory, or Martin-Löf type theory (MLTT)) is a type theory and an alternative foundation of ...
Homotopy Type Theory, I | The n-Category Café - Welcome
Last week I was at a mini-workshop at Oberwolfach entitled “The Homotopy Interpretation of Constructive Type Theory.” Some aspects of this ...
The Homotopy Interpretation of Constructive Type Theory - EMS Press
Over the past few years it has become apparent that there is a surprising and deep connection between constructive logic and higherdimensional ...
A Primer on Homotopy Type Theory Part 1 - PhilSci-Archive
The use of constructive logic also enables us to give a firmer philosophical basis for the resulting foundation for mathematics, and eliminates ...
Eric Finster : Homotopy Theory and Constructive Mathematics
Constructive mathematicians and computer scientists have long been interested in logical theories in which all mathematical statements have ...
CS6180: Introduction to Constructive Type Theory - Cornell CS
A related topic would be to apply a result from homotopy theory to a practical geometric algorithm. The PRL group researcher Ariel Kellison is ...