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Type system covariance and contravariance

Полагаю, многие разработчики не знают, что такое ковариантность/контравариарность системы типов. К примеру, в версии 1.5 языка Java появилась возможность использовать тип класса-наследника в объявлении замещающей функции:

 0: /**
 1:  *
 2:  */
 3: package com.chabster.covariance;
 5: /**
 6:  * @author Chabster
 7:  */
 8: public class Container
 9: {
10:   class A
11:   {
12:      A some() {
13:         return (this);
14:      }
15:   }
17:   class B extends A
18:   {
19:      @Override
20:      B some() {
21:         return (this);
22:      }
23:   }
25: }

В С++ такая возможность существует уже давно, а вот в C# все еще отсутствует. Полагаю, это связано с нестыковкой сигнатур методов в C# и IL. Вот, что говорит по этому поводу Standard ECMA-335 Common Language Infrastructure (CLI) 4th edition (June 2006):

A method signatures is composed of

  • a calling convention,
  • the number of generic parameters, if the method is generic,
  • a list of zero or more parameter signatures—one for each parameter of the method—and,
  • a type signature for the result value, if one is produced.

Получается, что IL код различает методы, которые отличаются лишь типом возврата, а C# - нет. Как и любой существующий на данный момент управляемый .NET-язык. С другой стороны этот недостаток можно элементарно восполнить. Вариант реализации предлогаю расценивать, как домашнее задание для читателя :).

В некоторых моментах C#, все же, поддерживает ковариантность и контравариантнось. Но для начала выясним что это такое.

Ковариантность (covariance) и контравариантнось (contravariance)

Ковариантностью называют сохранение формы при преобразовании. Соответсвенно, ковариантным называется преобразование, сохраняющее форму (свойства).

Например, оператор F(x) = x*2 является ковариантным касательно отношения % (делимость). Т.е. из x%y следует, что F(x)%F(y).

Контравариантностью называют обращение формы при преобразовании. Соответсвенно, контравариантным называется преобразование, обращающее форму.

Например, оператор F(x) = -x является контравариантным касательно отношения > (больше). Т.е. из x>y следует, что F(x)<F(y).

Оба этих понятия нельзя правильно обобщить поскольку в каждой науке оно выглядит по-своему. Рассмотрим их в самой интересной для нас области - программирование!

Ковариантность и контравариантнось в системе типов языков программирования

Рассмотрим пример C# кода:

class A {
    A[] aArr = new B[] { };

class B : A {

Пусть « обозначает отношение is a для типов. Поэтому B«A. Оператор Arrize({T}) = {T[]} является ковариантным касательно отношения is a для ссылочных типов т.к. из B«A следует B[]«A[].

Возвращаясь к первому Java примеру можно сказать, что оператор Methodize({SuperT virtMethod(T1,T2,...)}) = {SubT virtMethod(T1,T2,...)} является ковариантным касательно отношения override между методами.

Ковариантность и контравариантнось в системе типов C#

В C# есть ковариация, связанная с делегатами:

class A {

class B : A {

delegate A SomeDelegate();

static B SomeMethod() { return (null); }

static SomeDelegate sd = SomeMethod;

Типы возвращаемых значений метода и делегата различны, но совместимы.

В C# есть и контравариация, связанная с делегатами:

class A {

class B : A {

delegate void SomeDelegate(B b);

static void SomeMethod(A a) { }

static SomeDelegate sd = SomeMethod;

Сигнатуры метода и делегата различны, но совместимы, правда, уже в обратном направлении.

Это все, конечно, хорошо, вот только...

class A {

class B : A {

delegate T SomeDelegate<T>();

static B SomeMethod() { return (null); }

static SomeDelegate<B> sdB = SomeMethod;

static SomeDelegate<A> sdA = sdB;

... последняя строчка вызывает ошибку компиляции.

В целом, вариантность - очень полезный механизм, если им правильно пользоваться.

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