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Only a few object-oriented languages actually allow this (for example, Python when typechecked with mypy). C++, Java and most other languages that support overloading and/or shadowing would interpret this as a method with an overloaded or shadowed name. However, Sather supported both covariance and
In object-oriented programming, a covariant return type of a method is one that can be replaced by a "narrower" (derived) type when the method is overridden in a subclass. A notable language in which this is a fairly common paradigm is C++. C# supports return type covariance as of version 9.0. [1]
Contravariance of method parameter types in the subtype. Covariance of method return types in the subtype. New exceptions cannot be thrown by the methods in the subtype, except if they are subtypes of exceptions thrown by the methods of the supertype. In addition to the signature requirements, the subtype must meet a number of behavioural ...
Covariance and contravariance may refer to: Covariance and contravariance of vectors, in mathematics and theoretical physics; Covariance and contravariance of functors, in category theory; Covariance and contravariance (computer science), whether a type system preserves the ordering ≤ of types; An informal synonym for invariance (physics)
The duality between covariance and contravariance intervenes whenever a vector or tensor quantity is represented by its components, although modern differential geometry uses more sophisticated index-free methods to represent tensors. In tensor analysis, a covariant vector varies more or less reciprocally to a corresponding contravariant vector ...
A Newey–West estimator is used in statistics and econometrics to provide an estimate of the covariance matrix of the parameters of a regression-type model where the standard assumptions of regression analysis do not apply. [1] It was devised by Whitney K. Newey and Kenneth D. West in 1987, although there are a number of later variants.
Covariance/Contravariance are not properties of a type or a method (function, procedure) alone. Rather, they are relations between a method and its argument and result types. Whenever a contravariant type is mentioned, it must be clear from the context what method it is being related to and what position (argument v. result) in the method it is ...
In probability theory and statistics, the covariance function describes how much two random variables change together (their covariance) with varying spatial or temporal separation. For a random field or stochastic process Z ( x ) on a domain D , a covariance function C ( x , y ) gives the covariance of the values of the random field at the two ...