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    <p>The question is "what is the difference between covariance and contravariance?"</p> <p>Covariance and contravariance are properties of <em>a mapping function that associates one member of a set with another</em>. More specifically, a mapping can be covariant or contravariant with respect to a <em>relation</em> on that set.</p> <p>Consider the following two subsets of the set of all C# types. First:</p> <pre><code>{ Animal, Tiger, Fruit, Banana }. </code></pre> <p>And second, this clearly related set:</p> <pre><code>{ IEnumerable&lt;Animal&gt;, IEnumerable&lt;Tiger&gt;, IEnumerable&lt;Fruit&gt;, IEnumerable&lt;Banana&gt; } </code></pre> <p>There is a <em>mapping</em> operation from the first set to the second set. That is, for each T in the first set, the <em>corresponding</em> type in the second set is <code>IEnumerable&lt;T&gt;</code>. Or, in short form, the mapping is <code>T → IE&lt;T&gt;</code>. Notice that this is a "thin arrow".</p> <p>With me so far?</p> <p>Now let's consider a <em>relation</em>. There is an <em>assignment compatibility relationship</em> between pairs of types in the first set. A value of type <code>Tiger</code> can be assigned to a variable of type <code>Animal</code>, so these types are said to be "assignment compatible". Let's write "a value of type <code>X</code> can be assigned to a variable of type <code>Y</code>" in a shorter form: <code>X ⇒ Y</code>. Notice that this is a "fat arrow".</p> <p>So in our first subset, here are all the assignment compatibility relationships:</p> <pre><code>Tiger ⇒ Tiger Tiger ⇒ Animal Animal ⇒ Animal Banana ⇒ Banana Banana ⇒ Fruit Fruit ⇒ Fruit </code></pre> <p>In C# 4, which supports covariant assignment compatibility of certain interfaces, there is an assignment compatibility relationship between pairs of types in the second set:</p> <pre><code>IE&lt;Tiger&gt; ⇒ IE&lt;Tiger&gt; IE&lt;Tiger&gt; ⇒ IE&lt;Animal&gt; IE&lt;Animal&gt; ⇒ IE&lt;Animal&gt; IE&lt;Banana&gt; ⇒ IE&lt;Banana&gt; IE&lt;Banana&gt; ⇒ IE&lt;Fruit&gt; IE&lt;Fruit&gt; ⇒ IE&lt;Fruit&gt; </code></pre> <p>Notice that the mapping <code>T → IE&lt;T&gt;</code> <em>preserves the existence and direction of assignment compatibility</em>. That is, if <code>X ⇒ Y</code>, then it is also true that <code>IE&lt;X&gt; ⇒ IE&lt;Y&gt;</code>. </p> <p>If we have two things on either side of a fat arrow, then we can replace both sides with something on the right hand side of a corresponding thin arrow.</p> <p>A mapping which has this property with respect to a particular relation is called a "covariant mapping". This should make sense: a sequence of Tigers can be used where a sequence of Animals is needed, but the opposite is not true. A sequence of animals cannot necessarily be used where a sequence of Tigers is needed.</p> <p>That's covariance. Now consider this subset of the set of all types:</p> <pre><code>{ IComparable&lt;Tiger&gt;, IComparable&lt;Animal&gt;, IComparable&lt;Fruit&gt;, IComparable&lt;Banana&gt; } </code></pre> <p>now we have the mapping from the first set to the third set <code>T → IC&lt;T&gt;</code>.</p> <p>In C# 4:</p> <pre><code>IC&lt;Tiger&gt; ⇒ IC&lt;Tiger&gt; IC&lt;Animal&gt; ⇒ IC&lt;Tiger&gt; Backwards! IC&lt;Animal&gt; ⇒ IC&lt;Animal&gt; IC&lt;Banana&gt; ⇒ IC&lt;Banana&gt; IC&lt;Fruit&gt; ⇒ IC&lt;Banana&gt; Backwards! IC&lt;Fruit&gt; ⇒ IC&lt;Fruit&gt; </code></pre> <p>That is, the mapping <code>T → IC&lt;T&gt;</code> has <em>preserved the existence but reversed the direction</em> of assignment compatibility. That is, if <code>X ⇒ Y</code>, then <code>IC&lt;X&gt; ⇐ IC&lt;Y&gt;</code>.</p> <p>A mapping which <em>preserves but reverses</em> a relation is called a <em>contravariant</em> mapping.</p> <p>Again, this should be clearly correct. A device which can compare two Animals can also compare two Tigers, but a device which can compare two Tigers cannot necessarily compare any two Animals.</p> <p>So that's the difference between covariance and contravariance in C# 4. Covariance <em>preserves</em> the direction of assignability. Contravariance <em>reverses</em> it.</p>
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