- Does Homotopy Type Theory Provide a Foundation for Mathematics?🔍
- Homotopy Type Theory and Computing — Classical and Quantum🔍
- Homotopy Type Theory🔍
- Homotopy type theory🔍
- Logic Across Disciplines| Homotopy Type Theory🔍
- What is equality? From Leibniz to homotopy type theory🔍
- Modal Homotopy Type Theory. The Prospect of a New Logic for ...🔍
- Identity in Homotopy Type Theory🔍
Homotopy type theory
Does Homotopy Type Theory Provide a Foundation for Mathematics?
Homotopy Type Theory is a putative new foundation for mathematics grounded in constructive intensional type theory that offers an alternative to the ...
Homotopy Type Theory and Computing — Classical and Quantum
Homotopy Type Theory and Computing – Classical and Quantum ... The aim of this conference is to discuss Homotopy Type Theory Theory (HoTT) as a ...
Thorsten Altenkirch (Nottingham). Homotopy Type Theory is a new foundation of Mathematics which generalizes Martin-Löf Type Theory to higher ...
Homotopy type theory - Wikiwand
In mathematical logic and computer science, homotopy type theory (HoTT) refers to various lines of development of intuitionistic type theory, based on the ...
Ma 334: Homotopy Type Theory - IISc Math
This course introduces homotopy type theory, which provides alternative foundations for mathematics based on deep connections between type theory, from logic ...
Logic Across Disciplines- Homotopy Type Theory, the confluence of ...
University Seminar: Logic Across Disciplines- Homotopy Type Theory, the confluence of logic and space ... Abstract: In this talk we will learn how to express ...
Homotopy Type Theory: Unified Foundations of Mathematics and ...
At the conceptual center of these developments is the new homotopy-theoretic semantics for constructive type theories. The computational proof ...
What is equality? From Leibniz to homotopy type theory - Xavier Leroy
Equality as defined in type theory is perfect for purely inductive types, but does not allow us to identify object that we think are equal: two functions that ...
Modal Homotopy Type Theory. The Prospect of a New Logic for ...
Modal homotopy type theory, a field that uses modal dependent type theories to formalise arguments in areas of geometry related to homotopy ...
Homotopy Type Theory: Vladimir Voevodsky - Computerphile
Voevodsky took his knowledge of abstract geometry and applied it to Computer Science, then took Computer Science principles and applied them ...
Homotopy Type Theory - Ulrik Buchholtz
A gentle introduction to type theory and constructive mathematics for (mathematics and computer science) students with no previous exposure to either.
Identity in Homotopy Type Theory, Part I: The Justification of Path ...
An important rule for the treatment of identity in HoTT is path induction, which is commonly explained by appeal to the homotopy interpretation of the theory's ...
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):.
Homotopy Type Theory: Univalent Foundations of Mathematics
It is based on a recently discovered connection between homotopy the- ory and type theory. Homotopy theory is an outgrowth of algebraic topology and ...
Homotopy theory in type theory - Sandiego
We treat types as spaces/∞-groupoids/homotopy types, and we think of terms p: (x = y) as paths x y. • Reflexivity becomes the constant path reflx : x x. • ...
Expressing 'the structure of' in homotopy type theory | Synthese
Opportunities to express 'the structure of' within homotopy type theory are explored, and it is shown there is little or no need for this expression.
The Axiom of Choice and Homotopy Type Theory | ID: 5138jp65c ...
Honors College Thesis: The Axiom of Choice and Homotopy Type Theory. Public Deposited. Downloadable Content. Download PDF.
Homotopy type theory: unified foundations of mathematics and ...
Abstract. Homotopy type theory is a recently-developed unification of previously disparate frameworks, which can serve to advance the project of ...
Symmetry of equality is then interpreted as saying that if we have a path from a to b then we have a path from b to a , and transitivity is just ...
Homotopy Type Theory - Lehrstuhl für theoretische Informatik 8
Homotopy Type Theory. Homotopy Type Theory (HoTT) is a new approach to foundations of logic, programming and mathematics. It has an ...