A unifying cartesian cubical type theory
Cubical — Agda 2.8.0 documentation
The Cubical mode extends Agda with a variety of features from Cubical Type Theory. In particular, it adds computational univalence and higher inductive types.
Dependent type theories are a family of logical systems employed by philosophers as foun- dations of constructive mathematics, and by computer scientists as ...
A PROTOTYPE IMPLEMENTATION OF CUBICAL TYPE THEORY ...
Cubical type theory gives a constructive interpretation of the univalence axiom, which has been one of the central problems in homotopy type theory. In this.
Transpension: The Right Adjoint to the Pi-Type - Lirias
... cartesian cubical models of HoTT and/or parametricity, the sort of names ... Guarded cubical type theory. Journal of Automated Reasoning, 63(2):211–253 ...
Homotopy Type Theory Electronic Seminar Talks
Dependently typed algebraic theories are a generalisation of ordinary multisorted algebraic theories (finite-product theories). When it comes to models valued ...
Translations between Type Theories - GtR - UKRI
Inspired by this, the last decade has seen a plethora of new type theories including cubical, cartesian cubical, modal, spatial, cohesive, directed, and two- ...
Internal Parametricity, without an Interval - ACM Digital Library
In this paper we present a type theory with internal parametricity which is a simple extension of Martin-Löf type theory.
The thesis contains two papers. The first paper presents a type theory with a family of Fitch-style later modalities indexed over an object of clocks, called.
Cubical Agda: A Dependently Typed Programming Language with ...
Cubical type theory provides a solution by giving computational meaning to Homotopy. Type Theory and Univalent Foundations, in particular to the univalence ...
Type theory is the academic study of type systems. Some type theories serve as alternatives to set theory as a foundation of mathematics. Two influential type ...
Cartesian versus Symmetric Monoidal | The n-Category Café
It is obvious, still thinking in this cubical way, that one can freely make any category cartesian monoidal by just chucking in a square with ...
Proof Search in Cartesian Cubical Type Theory - Zhuyang Wang
def refl≡p∘p¯¹ (A : type) (p : I → A). : path {path A {p 0} {p 0}}. {refl A {p 0}}. {trans A p {symm A p}} = k i => hcom A 0 1 {i=0 ∨ i=1 ∨ k=0 ∨ k=1} {j =>.
Controlling unfolding in type theory - Department of Computer Science
cooltt proof assistant [29]; cooltt is an implementation of cartesian cubical type theory [2], a computational version of homotopy type theory whose syntactic.
What kind of category is generated by Cubical type theory?
Or one could take a more restricted notion of weak equivalences that see the cubical aspect and say that cubical type theory is the internal ...
... Sterling cartesian cubical proof assistant. Page 2. 2 type theory. Γ ⊦ A type. Γ ⊦ A = B type. Γ ⊦ M : A. Γ ⊦ M = N : A. Page 3. 3 cubical type ...
A Cubical Language for Bishop Sets - Daniel Gratzer
We present XTT, a version of Cartesian cubical type theory specialized for. Bishop sets `a la Coquand, in which every type enjoys a definitional ...
Cubical Type Theory – Synthetic
Unifying Cubical Models of Univalent Type Theory. Evan Cavallo, Anders Mörtberg, Andrew W Swan. 2020. Axioms for Modelling Cubical Type Theory in a Topos. Ian ...
Mathematical Structures in Computer Science, Volume 31 - DBLP
Formalising nominal C-unification generalised with protected variables. 286 ... Syntax and models of Cartesian cubical type theory. 424-468. Volume 31 ...
Internal and Observational Parametricity for Cubical Agda - Lirias
We observe that the SRP is harder to prove than the SIP and provide in Agda --bridges a shallowly embedded type theory to compose types that satisfy the SRP.
Homotopy type theory - Wikiwand
It was originally used by Vladimir Voevodsky to refer to his vision of a foundational system for mathematics in which the basic objects are homotopy types, ...