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diff --git a/src/exp_semiring.h b/src/exp_semiring.h
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+++ b/src/exp_semiring.h
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+#ifndef _EXP_SEMIRING_H_
+#define _EXP_SEMIRING_H_
+
+#include <iostream>
+
+// 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 <typename PType, typename 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 <typename P, typename R>
+std::ostream& operator<<(std::ostream& o, const PRPair<P,R>& x) {
+  return o << '<' << x.p << ", " << x.r << '>';
+}
+
+template <typename P, typename 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 <typename P, typename 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 <typename P, typename PWeightFunction, typename R, typename RWeightFunction>
+struct PRWeightFunction {
+  explicit PRWeightFunction(const PWeightFunction& pwf = PWeightFunction(),
+                            const RWeightFunction& rwf = RWeightFunction()) :
+    pweight(pwf), rweight(rwf) {}
+  PRPair<P,R> operator()(const Hypergraph::Edge& e) const {
+    const P p = pweight(e);
+    const R r = rweight(e);
+    return PRPair<P,R>(p, r * p);
+  }
+  const PWeightFunction pweight;
+  const RWeightFunction rweight;
+};
+
+#endif