Multimethods for C++, example 1, calculus multidispatcher

multidispatcher.cpp

#include <iostream>
#include <stdexcept>
#define TRACE() \
  std::cout << __PRETTY_FUNCTION__ << std::endl;

namespace details {

template<class Parameter>
struct expected {
  template<class Argument>
  static constexpr bool matches(const Argument& argument) noexcept {
    return typeid(Parameter) == typeid(argument);
  }
};
template<auto Method>
struct entry;

template<class Return, class ... Parameter, Return (*Function)(Parameter...)>
struct entry<Function> {
  template<class ... Argument>
  static constexpr bool matches(const Argument& ... argument) noexcept {
    return (expected<Parameter>::matches(argument) and ...);
  }
  template<class ... Argument>
  static Return call(Argument& ... argument) noexcept(noexcept(Function)) {
    return (*Function)((Parameter)(argument)...);
  }
};
} //namespace details

template<auto Entry, auto ... Entries>
struct multidispatcher {
  template<class ... Arguments>
  static auto dispatch(Arguments& ... arguments) {
    if (details::entry<Entry>::matches(arguments...)) {
      return details::entry<Entry>::call(arguments...);
    }
    if constexpr (sizeof...(Entries)>0) {
      return multidispatcher<Entries...>::dispatch(arguments...);
    }
    throw std::logic_error("Dispatcher failure");
  }
};
namespace calculus {
struct Expression {
  virtual ~Expression() {}
};

struct Constant : Expression {};
struct Integer : Constant {};
struct Float : Constant {};

template<class A, class B>
Expression* add(const A&, const B&);
template<class A, class B>
Expression* sub(const A&, const B&);

template<>
inline Expression* add<Integer, Integer>(const Integer& a, const Integer& b) {	TRACE(); return nullptr; }
template<>
inline Expression* add<Float, Float>(const Float& a, const Float& b) { TRACE();	return nullptr; }
template<>
inline Expression* add<Float, Integer>(const Float& a, const Integer& b) { TRACE();	return nullptr; }
template<>
inline Expression* add<Integer, Float>(const Integer& a, const Float& b) { TRACE();	return nullptr; }

template<>
inline Expression* sub<Integer, Integer>(const Integer& a, const Integer& b) {  TRACE(); return nullptr; }
template<>
inline Expression* sub<Float, Float>(const Float& a, const Float& b) { TRACE(); return nullptr; }
template<>
inline Expression* sub<Float, Integer>(const Float& a, const Integer& b) { TRACE(); return nullptr; }
template<>
inline Expression* sub<Integer, Float>(const Integer& a, const Float& b) { TRACE(); return nullptr; }

template<>
inline Expression* add<Expression,Expression>(const Expression& a, const Expression& b) {
  return multidispatcher<
    add<Integer, Integer>,
    add<Float, Integer>,
    add<Integer, Float>,
    add<Float, Float>>::dispatch(a,b);
}

template<>
inline Expression* sub<Expression,Expression>(const Expression& a, const Expression& b) {
  return multidispatcher<
    sub<Integer, Integer>,
    sub<Float, Integer>,
    sub<Integer, Float>,
    sub<Float, Float>>::dispatch(a,b);
}

inline void test(const Expression& a, const Expression& b) {
  add(a, b);
  sub(a, b);
}


inline void test() {
  Integer a{};
  Integer b{};
  Float c{};
  test(a, b);
  test(c, b);
  test(a, c);
  test(c, c);
}

} // namespace calculus

int main() {
    calculus::test();
}