Examples of using Type theory in English and their translations into Vietnamese
{-}
-
Colloquial
-
Ecclesiastic
-
Computer
Homotopy type theory is being researched.
For a theoretical formulation, see type theory.
Cover of Homotopy Type Theory: Univalent Foundations of Mathematics.
The fundamental concept of homotopy type theory is the path.
Type theory is consistent with the mathematical axioms, but couched in the language of computers.
The basic premise of the film comes from the Japanese blood type theory of….
The fundamental problem addressed by a type theory is to insure that programs have meaning.
The formal design andstudy of type systems is known as type theory.
The fundamental problem caused by a type theory is that meaningful programs may not have meanings ascribed to them.
They attributed the paradox to"vicious circularity" andbuilt up what they called ramified type theory to deal with it.
Therefore, in homotopy type theory, when applying the substitution property, it is necessary to state which path is being used.
Calculus of constructions Curry- Howard correspondence Intuitionistic type theory Homotopy hypothesis Univalent foundations.
But it does work in New Foundations(and in related systems known to be relatively consistent)and in some systems of type theory.
In the terms of type theory, a class is an implementation- a concrete data structure and collection of subroutines- while a type is an interface.
Two well-known such theories areAlonzo Church's typed λ-calculus and Per Martin-Löf's intuitionistic type theory.
In type theory and programming language theory, the colon sign after a term is used to indicate its type, sometimes as a replacement to the"∈" symbol.
Simply typed lambda calculus which is ahigher-order logic; intuitionistic type theory; system F; LF is often used to define other type theories; calculus of constructions and its derivatives.
In type theory, product types(with no field names) are generally preferred due to their simplicity, but proper record types are studied in languages such as System F-sub.
HoTT uses a modifiedversion of the"propositions as types" interpretation of type theory, according to which types can also represent propositions and terms can then represent proofs.
Three years ago, Vladimir Voevodsky, one of the organizers of a new program on the foundations of mathematics at the Institute for Advanced Study in Princeton, N.J., discovered that a formal logic system that was developed by computer scientists,called“type theory,” could be used to re-create the entire mathematical universe from scratch.
The first higher-dimensional models of intensional type theory were constructed by Steve Awodey and his student Michael Warren in 2005 using Quillen model categories.
These results were first presented in public at the conference FMCS 2006[4]at which Warren gave a talk titled"Homotopy models of intensional type theory", which also served as his thesis prospectus(the dissertation committee present were Awodey, Nicola Gambino and Alex Simpson).
In mathematical logic and computer science, homotopy type theory(HoTT/hɒt/) refers to various lines of development of intuitionistic type theory, based on the interpretation of types as objects to which the intuition of(abstract) homotopy theory applies.
The paradox drove Russell to develop type theory and Ernst Zermelo to develop an axiomatic set theory, which evolved into the now-canonical Zermelo- Fraenkel set theory. .
Dependent type theories appear mostly in computer programs that use such theories as their foundation.
He was working on new foundations ofmathematics based on homotopy-theoretic semantics of Martin-Löf type theories.
As Carl Jung said,each individual is ultimately a unique crystal, but type theories can be helpful for navigating social life.
Voevodsky said that the main goal of his most recent workwas“to advance the mathematical theory of dependent type theories to the level where it can be used for rigorous study of the complex type theories that are in use today and of the even more complex ones that will appear in the future.”.
Inasmuch as there are 5 seemingly separate supersymmetric string theory candidates:Type I theory, Type IIA, Type IIB, the Heterotic Type O(32) theory, and the Heterotic type E8 X E8 theory.