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  class Arrow
{
  Target eval (const Source &);
};

template  class Compositor
{
  template 
  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!

Functional composition with variadic templates in C++11

2 Answers