高级类型与C ++ [英] Higher-kinded Types with C++

问题描述

这个问题是对于知道Haskell（或任何其他功能语言，支持高级类型）和C ++ ...的人。

使用C ++模板的更高类型的类型？如果是，那么如何？

编辑：

http://www.blumenfeld-maso.com/2010/01/what-does-monad-mean-by-tony-morris/\">此由Tony Morris介绍：

高阶多态性：

• C＃有
  一阶多态性，因为他们
  允许我们在类型上抽象。例如
  List< A> 可以有一个 reverse 函数
  ，更实用的编程语言
  和类型系统（
  A ）


<允许我们将类型构造函数的
抽象为
。



• 此功能称为高阶
  -kinded）多态性。

b $ b

具有用于高阶多态性的发明符号的伪Java

  interface Transformer< X，Y& {
 Y transform（X x）; 
} 
 
 interface Monad< M> {// M :: *  - > * 
< A> M A纯（A a）; 
< A，B> M B bind（Transformer< A，M B> t，M A a）; 
} 
  

解决方案

模板参数？ / p>

 模板< template< typename>类m> 
 struct Monad {
 template< typename a> 
 static m< a> mreturn（const a&）; 
 
 template< typename a，typename b> 
 static m< b> mbind（const m a& m b（*）（const a&））; 
}; 
 
 template< typename a> 
 struct Maybe {
 bool isNothing; 
 a value; 
}; 
 
模板<> 
 struct Monad< Maybe> {
 template< typename a> 
 static Maybe< a> mreturn（const a& v）{
 Maybe< a> X; 
 x.isNothing = false; 
 x.value = v; 
 return x; 
} 
 
 template< typename a，typename b> 
 static Maybe< b> mbind（const Maybe< a& action，Maybe< b>（* function）（const a&））{
 if（action.isNothing）
 return action; 
 else 
 return function（action.value）; 
} 
}; 
  

This question is for the people who know both Haskell (or any other functional language that supports Higher-kinded Types) and C++...

Is it possible to model higher kinded types using C++ templates? If yes, then how?

EDIT :

From this presentation by Tony Morris:

Higher-order Polymorphism :

• Languages such as Java and C# have first-order polymorphism because they allow us to abstract on types. e.g. List<A> can have a reverse function that works on any element type (the A).

• More practical programming languages and type systems allow us to abstract on type constructors as well.

• This feature is called higher-order (or higher-kinded) polymorphism.

Example :

Pseudo-Java with an invented notation for higher-order polymorphism

interface Transformer<X, Y> {
  Y transform(X x);
}

interface Monad<M> { // M :: * -> *
  <A> M<A> pure(A a);
  <A, B> M<B> bind(Transformer<A, M<B>> t, M<A> a);
}

解决方案

Template-template parameters?

template <template <typename> class m>
struct Monad {
    template <typename a>
    static m<a> mreturn(const a&);

    template <typename a, typename b>
    static m<b> mbind(const m<a>&, m<b>(*)(const a&));
};

template <typename a>
struct Maybe {
    bool isNothing;
    a value;
};

template <>
struct Monad<Maybe> {
    template <typename a>
    static Maybe<a> mreturn(const a& v) {
        Maybe<a> x;
        x.isNothing = false;
        x.value = v;
        return x;
    }

    template <typename a, typename b>
    static Maybe<b> mbind(const Maybe<a>& action, Maybe<b>(*function)(const a&)) {
        if (action.isNothing)
            return action;
        else
            return function(action.value);
    }
};

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