Covariance andContravariance.

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Alin Pandichi

Alin Pandichi

Open spaceCoding DojoBucharest Java User GroupGlobal Day of Coderetreat

Alin Pandichi

Open spaceCoding DojoBucharest Java User GroupGlobal Day of Coderetreat

Software developer @Mozaic LabsBuilding eventriX

Covariance = the property of a function of retaining its form when the variables 

are linearly transformed.

Covariance = changing the input moves the function in the same direction.

Contravariance = The basis and the vector transform in an opposite way.

Contravariance = changing the input moves the function in the opposite direction.

Cov

aria

nce

Contravariance

Cov

aria

nce

Variance refers to how subtyping between complex types (lists, arrays) relates to 

subtyping between their components (individual items).

Depending on variance, the subtyping relation may be either preserved, reversed, or ignored.

Integer is a subtype of  Number Integer i = 1;Number n = i;

Number  <  Integer Number  ← Integer

< means “is a subtype of”← means “can be assigned to”*read from right to the left

Integer[] is a subtype of  Number[]  Integer[] ints = {1, 2, 3};Number[] nums = ints;

Number[]  <  Integer[] Number[]    ← Integer[]

< means “is a subtype of”← means “can be assigned to”*read from right to the left

Number     ←  Integer  Number[]  ←  Integer[] 

A   B←  means “B can be assigned to A”

Array types can be assigned in the same order.Arrays are covariant.

ArrayList<Integer> ints = new ArrayList<Integer>();ArrayList<? extends Number> nums = ints;

Number   ←  IntegerNumber[]    ← Integer[]

<? extends Number>   ←  <Integer>  

Can be assigned in the same order.This generic list is covariant.

A   B←  means “B can be assigned to A”

ArrayList<Object> objs = new ArrayList<Object>();ArrayList<? super Number> nums = objs;

Object      ←  NumberObject[]       ← Number[]<Object>     → <? super Number>  

Can be assigned in the reverse order.This generic list is contravariant.

A   B←  means “B can be assigned to A”

Interesting properties of covariance and contravariance:

With covariance you can only take values out.

With contravariance you can only put values in.

With covariance you can only take values out.

ArrayList<? extends Error> errs = new ArrayList<StackOverflowError>();

Error e = errs.get(0);

errs.add(new Error("")); // compiler errorerrs.add(new StackOverflowError("")); // compiler error

With contravariance you can only put values in.

ArrayList<? super StackOverflowError> errs = new ArrayList<Error>();

errs.add(new StackOverflowError("w00t"));

Error e = errs.get(0); //compiler-error

StackOverflowError soe = errs.get(0); //compiler-error

public void copy(List<? extends Number> source,List<? super Number> destination) {

for(Number number : source) {destination.add(number);

}}

…

List<Integer> myInts = asList(1,2,3,4);List<Integer> myDoubles = asList(3.14, 6.28);List<Object> myObjs = new ArrayList<Object>();copy(myInts, myObjs);copy(myDoubles, myObjs);

In C#, covariant generic interfaces are annotated with out:

interface IMessageRecieved <out T>{

T RecievedData();}

Covariance ­ take values out.

In C#, contravariant generic interfaces are annotated with in:

interface IMessageSend <in T>{

void SendData(T data);}

Contravariance – put values in.

Covariance

Enables you to use a more derived type than originally specified.

You can assign an instance of IEnumerable<Derived> to a variable of type IEnumerable<Base>.

Contravariance

Enables you to use a more generic (less derived) type than originally specified.

You can assign an instance of IEnumerable<Base> to a variable of type IEnumerable<Derived>.

class A { Object getSomething(){}}

class B extends A { String getSomething() {}}

Covariance because it returns a String  which extends Object (more derived)

class A { void doSomething(String param){}}

class B extends A { void doSomething(Object param){}}

Contravariance because it takes an Object which is a super class of String (less derived)

Type systems that support subtyping.

Programming language designers devising typing rules for arrays, inheritance, and 

generic datatypes

Programmers who use inheritance and override methods.

Programmers who develop generic interfaces, methods and code.

Subtyping relation

Data access

Overriding methods

Wildcard generics

Covariance

Keep the order

Take values 

out

More derived return type

extends

Contravariance

Reverse the order

Put values in

Less derived 

parameter type

super

Resources

http://www.i­programmer.info/programming/theory/1632­covariance­and­contravariance­a­simple­guide.htmlhttps://dzone.com/articles/covariance­and­contravariancehttps://msdn.microsoft.com/en­us/library/dd799517(v=vs.110).aspxhttps://en.wikipedia.org/wiki/Covariance_and_contravariance_(computer_science)#Covariant_arrays_in_Java_and_C.23https://www.codeproject.com/articles/86419/variance­in­c­net­covariance­and­contravarianchttp://stackoverflow.com/questions/8481301/covariance­invariance­and­contravariance­explained­in­plain­englishhttp://stackoverflow.com/questions/2501023/demonstrate­covariance­and­contravariance­in­java#2501513

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