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Polymorphism.html
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<!DOCTYPE html>
<html>
<head><meta charset="utf-8" />
<title>Polymorphism</title>
<script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.1.10/require.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/2.0.3/jquery.min.js"></script>
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<h1 id="다형성-(Polymorphism)">다형성 (Polymorphism)<a class="anchor-link" href="#다형성-(Polymorphism)">¶</a></h1><p>프로그래밍에서 활용되는 다형성은 크게 두 가지로 분류할 수 있다.</p>
<ul>
<li>인자 다형성 (parametric polymorphism)</li>
<li>ad-hoc polymorpism (주로 함수/연산자 오버로딩 해당)<ul>
<li>클래스와 상속을 지원하는 OOP 언어에서는 subtype polymorphism (주로 동적 디스패치, 오버라이딩 해당)을 따로 구분하기도 한다.</li>
</ul>
</li>
</ul>
<p>인자 다형성이란 넘어오는 인자의 타입이나 내용에 관계없이 일관된 동작을 하는 경우를 뜻한다.
대표적인 예로 넘어온 값을 그대로 돌려주는 항등함수를 들 수 있다.</p>
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<div class=" highlight hl-haskell"><pre><span class="nf">f</span> <span class="n">x</span> <span class="ow">=</span> <span class="n">x</span>
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<div class=" highlight hl-haskell"><pre><span class="kt">:</span><span class="kr">type</span> <span class="n">f</span>
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</style><span class='get-type'>f :: forall t. t -> t</span>
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<div class=" highlight hl-haskell"><pre><span class="nf">f</span> <span class="s">"hello"</span>
<span class="nf">f</span> <span class="mi">153</span>
<span class="nf">f</span> <span class="mf">3.141592</span>
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<p>다른 언어에서도 인자 다형성을 지원한다.
예를 들어 C++ 에서 항등함수 f를 정의하는 방법:
<a href="http://cpp.sh/8avlb">http://cpp.sh/8avlb</a>
(C++ template 사용)</p>
<p>Java, C# 등에서도 제너릭(generic)이라는 기능을 통해 인자 다형성 기능을 지원
(Java 등에서 제너릭은 C++의 템플릿과 비슷한 문법을 사용하지만 기능이 미묘하게 다르다)</p>
<p>C++, Java, C# 등에서 인자 다형성을 활용하기 위한 문법이 Haskell과 같은 함수형 언어들보다 복잡한 이유는, 처음에는 이걸 필요없다고 생각해서 또는 만들기 어렵다고 생각해서 인자 다형성 없이 언어를 구현해 사용하다가 나중에 보니 없으면 안되겠다 싶어서 추가하느라 문법이 복잡해져 버린 것이다.</p>
<h2 id="polymorphic-리스트">polymorphic 리스트<a class="anchor-link" href="#polymorphic-리스트">¶</a></h2><p>인자 다형성은 함수 정의에서 뿐 아니라 리스트와 같은 데이타 구조 정의에서도 매우 유용하다.
지금까지는 원소가 정수인 리스트만 다루었지만 경우에 따라서는 문자열의 리스트도 필요할 것이고 또 부동소수점수의 리스트도 필요할 것이고 또 다른 타입의 리스트도 필요할 것이다.</p>
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<div class=" highlight hl-haskell"><pre><span class="c1">-- 타입마다 새로운 리스트 타입을 계속 정의하는 것은 좀 아니다</span>
<span class="kr">data</span> <span class="kt">ListI</span> <span class="ow">=</span> <span class="kt">NilI</span> <span class="o">|</span> <span class="kt">ConsI</span> <span class="kt">Int</span> <span class="kt">ListI</span> <span class="kr">deriving</span> <span class="kt">Show</span>
<span class="kr">data</span> <span class="kt">ListS</span> <span class="ow">=</span> <span class="kt">NilS</span> <span class="o">|</span> <span class="kt">ConsS</span> <span class="kt">String</span> <span class="kt">ListS</span> <span class="kr">deriving</span> <span class="kt">Show</span>
<span class="kr">data</span> <span class="kt">ListD</span> <span class="ow">=</span> <span class="kt">NilD</span> <span class="o">|</span> <span class="kt">ConsD</span> <span class="kt">Double</span> <span class="kt">ListD</span> <span class="kr">deriving</span> <span class="kt">Show</span>
<span class="c1">-- ...</span>
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<div class=" highlight hl-haskell"><pre><span class="c1">-- 인자 다형성을 활용한 일반적인 리스트 정의</span>
<span class="c1">-- (이거 하나면 위에것들 다 커버한다!)</span>
<span class="kr">data</span> <span class="kt">List</span> <span class="n">a</span> <span class="ow">=</span> <span class="kt">Nil</span> <span class="o">|</span> <span class="kt">Cons</span> <span class="n">a</span> <span class="p">(</span><span class="kt">List</span> <span class="n">a</span><span class="p">)</span> <span class="kr">deriving</span> <span class="kt">Show</span>
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<div class=" highlight hl-haskell"><pre><span class="nf">x1</span><span class="p">,</span> <span class="n">x2</span> <span class="ow">::</span> <span class="kt">Int</span>
<span class="nf">x1</span> <span class="ow">=</span> <span class="mi">1</span>
<span class="nf">x2</span> <span class="ow">=</span> <span class="mi">2</span>
<span class="kt">:</span><span class="kr">type</span> <span class="p">(</span><span class="kt">Cons</span> <span class="n">x1</span> <span class="p">(</span><span class="kt">Cons</span> <span class="n">x2</span> <span class="kt">Nil</span><span class="p">))</span>
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</style><span class='get-type'>(Cons x1 (Cons x2 Nil)) :: List Int</span>
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<div class=" highlight hl-haskell"><pre><span class="nf">s1</span><span class="p">,</span> <span class="n">s2</span> <span class="ow">::</span> <span class="kt">String</span>
<span class="nf">s1</span> <span class="ow">=</span> <span class="s">"hello"</span>
<span class="nf">s2</span> <span class="ow">=</span> <span class="s">"world"</span>
<span class="kt">:</span><span class="kr">type</span> <span class="p">(</span><span class="kt">Cons</span> <span class="n">s1</span> <span class="p">(</span><span class="kt">Cons</span> <span class="n">s2</span> <span class="kt">Nil</span><span class="p">))</span>
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</style><span class='get-type'>(Cons s1 (Cons s2 Nil)) :: List String</span>
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<p>전에 작성했던 <code>append</code> 함수도 사실은 polymorphic 함수이다.
똑같은 등식으로 된 함수 정의가 polymorphic 리스트 타입 <code>(List a)</code>에 대해서도 그대로 동작한다.</p>
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<div class=" highlight hl-haskell"><pre><span class="nf">append</span> <span class="kt">Nil</span> <span class="n">ys</span> <span class="ow">=</span> <span class="n">ys</span>
<span class="nf">append</span> <span class="p">(</span><span class="kt">Cons</span> <span class="n">x</span> <span class="n">xs</span><span class="p">)</span> <span class="n">ys</span> <span class="ow">=</span> <span class="kt">Cons</span> <span class="n">x</span> <span class="p">(</span><span class="n">append</span> <span class="n">xs</span> <span class="n">ys</span><span class="p">)</span>
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<div class=" highlight hl-haskell"><pre><span class="kt">:</span><span class="kr">type</span> <span class="n">append</span>
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</style><span class='get-type'>append :: forall a. List a -> List a -> List a</span>
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<div class=" highlight hl-haskell"><pre><span class="nf">append</span> <span class="p">(</span><span class="kt">Cons</span> <span class="mi">1</span> <span class="p">(</span><span class="kt">Cons</span> <span class="mi">2</span> <span class="kt">Nil</span><span class="p">))</span> <span class="p">(</span><span class="kt">Cons</span> <span class="mi">3</span> <span class="p">(</span><span class="kt">Cons</span> <span class="mi">4</span> <span class="kt">Nil</span><span class="p">))</span>
<span class="nf">append</span> <span class="p">(</span><span class="kt">Cons</span> <span class="s">"hello"</span> <span class="p">(</span><span class="kt">Cons</span> <span class="s">"world"</span> <span class="kt">Nil</span><span class="p">))</span> <span class="p">(</span><span class="kt">Cons</span> <span class="s">"hi"</span> <span class="p">(</span><span class="kt">Cons</span> <span class="s">"sky"</span> <span class="kt">Nil</span><span class="p">))</span>
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<pre>Cons 1 (Cons 2 (Cons 3 (Cons 4 Nil)))</pre>
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<pre>Cons "hello" (Cons "world" (Cons "hi" (Cons "sky" Nil)))</pre>
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<h2 id="polymorphic-이진트리">polymorphic 이진트리<a class="anchor-link" href="#polymorphic-이진트리">¶</a></h2><p>리스트와 마찬가지로 이진트리도 polymophic하게 정의할 수 있다. 리스트에 대한 <code>append</code>를 polymorphic 타입을 갖는 함수로 정의될 수 있는 것과 마찬가지로, 이전에 정의한 <code>sumTree</code>, <code>height</code> 같은 함수들도 똑같은 등식으로 polymorphic 이진트리에 대해서 정의할 수 있다.</p>
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<div class=" highlight hl-haskell"><pre><span class="kr">data</span> <span class="kt">Tree</span> <span class="n">a</span> <span class="ow">=</span> <span class="kt">Null</span> <span class="o">|</span> <span class="kt">Node</span> <span class="n">a</span> <span class="p">(</span><span class="kt">Tree</span> <span class="n">a</span><span class="p">)</span> <span class="p">(</span><span class="kt">Tree</span> <span class="n">a</span><span class="p">)</span> <span class="kr">deriving</span> <span class="kt">Show</span>
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<h1 id="하스켈에서-제공하는-리스트-라이브러리">하스켈에서 제공하는 리스트 라이브러리<a class="anchor-link" href="#하스켈에서-제공하는-리스트-라이브러리">¶</a></h1><ul>
<li><code>List a</code> 대신에 <code>[a]</code></li>
<li><code>Nil</code> 대신에 <code>[]</code></li>
<li><code>Cons</code> 대신에 <code>(:)</code></li>
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<p>라이브러리 함수로 <code>append</code>의 기능을 하는 <code>(++)</code> 연산자.</p>
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<div class=" highlight hl-haskell"><pre><span class="kt">:</span><span class="n">info</span> <span class="kt">[]</span>
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<div class=" highlight hl-haskell"><pre><span class="mi">1</span> <span class="kt">:</span> <span class="kt">[]</span>
<span class="mi">1</span> <span class="kt">:</span> <span class="mi">2</span> <span class="kt">:</span> <span class="mi">3</span> <span class="kt">:</span> <span class="mi">4</span> <span class="kt">:</span> <span class="kt">[]</span>
<span class="p">[</span><span class="mi">1</span><span class="p">]</span>
<span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">]</span>
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</style><div class="suggestion-name" style="clear:both;">Use list literal</div><div class="suggestion-row" style="float: left;"><div class="suggestion-warning">Found:</div><div class="highlight-code" id="haskell">1 : []</div></div><div class="suggestion-row" style="float: left;"><div class="suggestion-warning">Why Not:</div><div class="highlight-code" id="haskell">[1]</div></div><div class="suggestion-name" style="clear:both;">Use list literal</div><div class="suggestion-row" style="float: left;"><div class="suggestion-warning">Found:</div><div class="highlight-code" id="haskell">1 : 2 : 3 : 4 : []</div></div><div class="suggestion-row" style="float: left;"><div class="suggestion-warning">Why Not:</div><div class="highlight-code" id="haskell">[1, 2, 3, 4]</div></div>
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<pre>[1]</pre>
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