Functional composition with variadic templates in C++11

Question

I'm a mathematician used to doing "old style" C++ programming for a long time now. I feel that some new syntactic constructions offerred by C++11 could help me achieve some better code regarding my professionnal projects. Yet as I'm no CS professionnal I must confess that I lack the knowledge to understand some examples I encounter in my self-learning process, altough I've been pretty lucky/succesful so far.

My impression is that variadic templates can be used to implement type-safe functions composition, as in this question. My concern is slightly more general since I'd like to compose functions with heterogeneous (but compatible) argument/return types. I've googled a lot and found another reference, but it seems utter "black magic" to me ;) and I won't pretend I can adapt the code in my context, although I feel I should find what I need in there.

I think the (most incomplete) code below is relatively self-explanatory as to what I'd like to achieve. In particular I believe the proper implementation will throw a compile-time error when one's trying to compose incompatible functions (Arrow here), and will need a piece of recursive template code.

template <typename Source , typename Target> class Arrow
{
  Target eval (const Source &);
};

template <typename ...Arrows> class Compositor
{
  template <typename ...Arrows>
  Compositor (Arrows... arrows)
  {
     // do/call what needs be here
  };

  auto arrow(); // gives a function performing the functionnal composition of arrows

};

// define some classes A, B and C

int main(int argc, char **argv)
{
  Arrow < A , B >  arrow1;
  Arrow < B , C >  arrow2;

  Compositor< Arrow < A , B > , Arrow < B , C > > compositor(arrow1 , arrow2);

  Arrow < A , C >  expected_result = compositor.arrow();
}

Ideally I'd like
    Compositor
to directly subclass
    Arrow < source_of_first_arrow , target_of_last_arrow>
and the method
   arrow()
be replaced by the corresponding
    eval()

but I felt the above code was more explanatory.

Any help will be greatly appreciated, even if it consists in a rough rebuke with a pointer to an existing (relatively basic) piece of example which will surely have escaped my search. Thanks!

Answer 1

If I got it correctly, you need no fancy template magic to do this composition. Here is the almost self-explanatory code:

#include <functional>
#include <string>
#include <iostream>

// it is just an std::function taking A and returning B
template <typename A, typename B>
using Arrow = std::function<B(const A&)>;

// composition operator: just create a new composed arrow
template <typename A, typename B, typename C>
Arrow<A, C> operator*(const Arrow<A, B>& arr1, const Arrow<B, C>& arr2)
{
    // arr1 and arr2 are copied into the lambda, so we won't lose track of them
    return [arr1, arr2](const A& a) { return arr2(arr1(a)); };
}

int main()
{
    Arrow<int, float> plusHalf([](int i){return i + 0.5;});
    Arrow<float, std::string> toString([](float f){return std::to_string(f);});

    auto composed = plusHalf * toString; // composed is Arrow<int, std::string>
    std::cout << composed(6) << std::endl; // 6.5

    //auto badComposed = toString * plusHalf; // compile time error
}

I mostly played with lambda functions here.

Using a single function call instead of a operator chain proved to be a more tricky problem. This time you got some templates:

#include <functional>
#include <string>
#include <iostream>

// it is just an std::function taking A and returning B
template <typename A, typename B>
using Arrow = std::function<B(const A&)>;

// A helper struct as template function can't get partial specialization
template <typename... Funcs>
struct ComposerHelper;

// Base case: a single arrow
template <typename A, typename B>
struct ComposerHelper<Arrow<A, B>>
{
    static Arrow<A, B> compose(const Arrow<A, B>& arr)
    {
        return arr;
    }
};

// Tail case: more arrows
template <typename A, typename B, typename... Tail>
struct ComposerHelper<Arrow<A, B>, Tail...>
{
    // hard to know the exact return type here. Let the compiler figure out
    static auto compose(const Arrow<A, B>& arr, const Tail&... tail)
    -> decltype(arr * ComposerHelper<Tail...>::compose(tail...))
    {
        return arr * ComposerHelper<Tail...>::compose(tail...);
    }
};

// A simple function to call our helper struct
// again, hard to write the return type
template <typename... Funcs>
auto compose(const Funcs&... funcs)
-> decltype(ComposerHelper<Funcs...>::compose(funcs...))
{
    return ComposerHelper<Funcs...>::compose(funcs...);
}

using namespace std;

int main()
{
    Arrow<int, float> plusHalf([](int i){return i + 0.5;});
    Arrow<float, string> toString([](float f){return to_string(f);});
    Arrow<string, int> firstDigit([](const string& s){return s[0]-'0';});

    auto composed = compose(plusHalf, toString, firstDigit);
    // composed is Arrow<int, int>

    std::cout << composed(61) << std::endl; // "6"

    //auto badComposed = compose(toString, plusHalf); // compile time error
}