#ifndef EXP_SEMIRING_H_
#define EXP_SEMIRING_H_

#include <iostream>
#include "star.h"

// this file implements the first-order expectation semiring described
// in Li & Eisner (EMNLP 2009)

// requirements:
//   RType * RType ==> RType
//   PType * PType ==> PType
//   RType * PType ==> RType
// good examples:
//   PType scalar, RType vector
// BAD examples:
//   PType vector, RType scalar
template <class PType, class RType>
struct PRPair {
  PRPair() : p(), r() {}
  // Inside algorithm requires that T(0) and T(1)
  // return the 0 and 1 values of the semiring
  explicit PRPair(double x) : p(x), r() {}
  PRPair(const PType& p, const RType& r) : p(p), r(r) {}
  PRPair& operator+=(const PRPair& o) {
    p += o.p;
    r += o.r;
    return *this;
  }
  PRPair& operator*=(const PRPair& o) {
    r = (o.r * p) + (o.p * r);
    p *= o.p;
    return *this;
  }
  PType p;
  RType r;
};

template <class P, class R>
std::ostream& operator<<(std::ostream& o, const PRPair<P,R>& x) {
  return o << '<' << x.p << ", " << x.r << '>';
}

template <class P, class R>
const PRPair<P,R> operator+(const PRPair<P,R>& a, const PRPair<P,R>& b) {
  PRPair<P,R> result = a;
  result += b;
  return result;
}

template <class P, class R>
const PRPair<P,R> operator*(const PRPair<P,R>& a, const PRPair<P,R>& b) {
  PRPair<P,R> result = a;
  result *= b;
  return result;
}

template <class P, class R>
inline const PRPair<P,R> star(const PRPair<P,R>& x) {
  const P pstar = star(x.p);
  return PRPair<P,R>(pstar, pstar * x.r * pstar);
}

#endif