improvements to sets sharing

* Add TheorySets::getEqualityStatus(TNode, TNode)
* Add TheorySets::getModelValue(TNode)

9 files changed, 373 insertions, 16 deletions

diff --git a/src/theory/arith/theory_arith_private.cpp b/src/theory/arith/theory_arith_private.cpp
index 220737d2e..c657796ee 100644
--- a/src/theory/arith/theory_arith_private.cpp
+++ b/src/theory/arith/theory_arith_private.cpp
@@ -335,7 +335,7 @@ TheoryArithPrivate::Statistics::Statistics()
   , d_unsatPivots("theory::arith::pivots::unsat")
   , d_unknownPivots("theory::arith::pivots::unkown")
   , d_solveIntModelsAttempts("theory::arith::z::solveInt::models::attempts", 0)
-  , d_solveIntModelsSuccessful("zzz::solveInt::models::successful", 0)
+  , d_solveIntModelsSuccessful("theory::arith::zzz::solveInt::models::successful", 0)
   , d_mipTimer("theory::arith::z::approx::mip::timer")
   , d_lpTimer("theory::arith::z::approx::lp::timer")
   , d_mipProofsAttempted("theory::arith::z::mip::proofs::attempted", 0)
diff --git a/src/theory/sets/options b/src/theory/sets/options
index 1c95e78e4..7cb3eb677 100644
--- a/src/theory/sets/options
+++ b/src/theory/sets/options
@@ -11,4 +11,7 @@ option setsPropagate --sets-propagate bool :default true
 option setsEagerLemmas --sets-eager-lemmas bool :default true
  add lemmas even at regular effort
 
+option setsCare1 --sets-care1 bool :default false
+ generate one lemma at a time for care graph
+
 endmodule
diff --git a/src/theory/sets/theory_sets.cpp b/src/theory/sets/theory_sets.cpp
index b59beac8d..faba2aab1 100644
--- a/src/theory/sets/theory_sets.cpp
+++ b/src/theory/sets/theory_sets.cpp
@@ -54,6 +54,14 @@ Node TheorySets::explain(TNode node) {
   return d_internal->explain(node);
 }
 
+EqualityStatus TheorySets::getEqualityStatus(TNode a, TNode b) {
+  return d_internal->getEqualityStatus(a, b);
+}
+
+Node TheorySets::getModelValue(TNode node) {
+  return d_internal->getModelValue(node);
+}
+
 void TheorySets::preRegisterTerm(TNode node) {
   d_internal->preRegisterTerm(node);
 }
diff --git a/src/theory/sets/theory_sets.h b/src/theory/sets/theory_sets.h
index a16832389..6136fc8f8 100644
--- a/src/theory/sets/theory_sets.h
+++ b/src/theory/sets/theory_sets.h
@@ -58,6 +58,10 @@ public:
 
   Node explain(TNode);
 
+  EqualityStatus getEqualityStatus(TNode a, TNode b);
+
+  Node getModelValue(TNode);
+
   std::string identify() const { return "THEORY_SETS"; }
 
   void preRegisterTerm(TNode node);
diff --git a/src/theory/sets/theory_sets_private.cpp b/src/theory/sets/theory_sets_private.cpp
index 592b4bc37..a8f6dcc38 100644
--- a/src/theory/sets/theory_sets_private.cpp
+++ b/src/theory/sets/theory_sets_private.cpp
@@ -27,6 +27,8 @@
 #include "util/emptyset.h"
 #include "util/result.h"
 
+#include "util/partitions.h"
+
 using namespace std;
 using namespace CVC4::expr::pattern;
 
@@ -420,29 +422,213 @@ void TheorySetsPrivate::addSharedTerm(TNode n) {
 
 void TheorySetsPrivate::computeCareGraph() {
   Debug("sharing") << "Theory::computeCareGraph<" << d_external.identify() << ">()" << endl;
-  for (unsigned i = 0; i < d_external.d_sharedTerms.size(); ++ i) {
+
+  // dump our understanding of assertions
+  if(Trace.isOn("sets-assertions")
+     || Trace.isOn("sets-care-dump"))
+  {
+    std::string tag = "sets-assertions";
+    context::CDList<Assertion>::const_iterator it = d_external.facts_begin(), it_end = d_external.facts_end();
+
+    std::map<TNode, std::set<TNode> > equalities;
+    std::set< pair<TNode, TNode> > disequalities;
+    std::map<TNode, std::pair<std::set<TNode>, std::set<TNode> > > members;
+    static std::map<TNode, int> numbering;
+    static int number = 0;
+
+    for (unsigned i = 0; it != it_end; ++ it, ++i) {
+      TNode ass = (*it).assertion;
+      Trace("sets-care-dump") << AssertCommand(ass.toExpr()) << endl;
+      bool polarity = ass.getKind() != kind::NOT;
+      ass = polarity ? ass : ass[0];
+      Assert( ass.getNumChildren() == 2);
+      TNode left = d_equalityEngine.getRepresentative(ass[0]);
+      TNode right = d_equalityEngine.getRepresentative(ass[1]);
+      if(numbering[left] == 0) numbering[left] = ++number;
+      if(numbering[right] == 0) numbering[right] = ++number;
+      equalities[left].insert(ass[0]);
+      equalities[right].insert(ass[1]);
+      if(ass.getKind() == kind::EQUAL) {
+        if(polarity) {
+          Assert(left == right);
+        } else {
+          if(left > right) std::swap(left, right);
+          disequalities.insert(make_pair(left, right));
+        }
+      } else if(ass.getKind() == kind::MEMBER) {
+        (polarity ? members[right].first : members[right].second).insert(left);
+      }
+    }
+#define FORIT(it, container) for(typeof((container).begin()) it=(container).begin(); (it) != (container).end(); ++(it))
+    FORIT(kt, equalities) {
+      Trace(tag) << " Eq class of t" << numbering[(*kt).first] << ": " << std::endl;
+      FORIT(jt, (*kt).second) {
+        TNode S = (*jt);
+        if( S.getKind() != kind::UNION && S.getKind() != kind::INTERSECTION && S.getKind() != kind::SETMINUS) {
+          Trace(tag) << "    " << *jt << ((*jt).getType().isSet() ? "\n": " ");
+        } else {
+          Trace(tag) << "    ";
+          if(S[0].isConst() || numbering.find(d_equalityEngine.getRepresentative(S[0])) == numbering.end()) {
+            Trace(tag) << S[0];
+          } else {
+            Trace(tag) << "t" << numbering[d_equalityEngine.getRepresentative(S[0])];
+          }
+          Trace(tag) << " " << (S.getKind() == kind::UNION ? "|" : (S.getKind() == kind::INTERSECTION ? "&" : "-")) << " ";
+          if(S[1].isConst() || numbering.find(d_equalityEngine.getRepresentative(S[1])) == numbering.end()) {
+            Trace(tag) << S[1];
+          } else {
+            Trace(tag) << "t" << numbering[d_equalityEngine.getRepresentative(S[1])];
+          }
+          Trace(tag) << std::endl;
+        }
+      }
+      Trace(tag) << std::endl;
+    }
+    FORIT(kt, disequalities) Trace(tag) << "NOT(t"<<numbering[(*kt).first]<<" = t" <<numbering[(*kt).second] <<")"<< std::endl;
+    FORIT(kt, members) {
+      if( (*kt).second.first.size() > 0) {
+        Trace(tag) << "IN t" << numbering[(*kt).first] << ": ";
+        FORIT(jt, (*kt).second.first) {
+          TNode x = (*jt);
+          if(x.isConst() || numbering.find(d_equalityEngine.getRepresentative(x)) == numbering.end()) {
+            Trace(tag) << x;
+          } else {
+            Trace(tag) << "x" << numbering[d_equalityEngine.getRepresentative(x)] << ", ";
+          }
+        }
+        Trace(tag) << std::endl;
+      }
+      if( (*kt).second.second.size() > 0) {
+        Trace(tag) << "NOT IN t" << numbering[(*kt).first] << ": ";
+        FORIT(jt, (*kt).second.second) {
+          TNode x = (*jt);
+          if(x.isConst() || numbering.find(d_equalityEngine.getRepresentative(x)) == numbering.end()) {
+            Trace(tag) << x;
+          } else {
+            Trace(tag) << "x" << numbering[d_equalityEngine.getRepresentative(x)] << ", ";
+          }
+        }
+        Trace(tag) << std::endl;
+      }
+    }
+    Trace(tag) << std::endl;
+
+  }
+
+  std::map<TypeNode, std::set<TNode> > careGraphVertices;
+
+  for (unsigned i = d_ccg_i; i < d_external.d_sharedTerms.size(); ++ i) {
     TNode a = d_external.d_sharedTerms[i];
     TypeNode aType = a.getType();
-    for (unsigned j = i + 1; j < d_external.d_sharedTerms.size(); ++ j) {
+    // if(a.getType().isSet()) {
+    //   int sizeMem = d_termInfoManager->getMembers(d_equalityEngine.getRepresentative(a))->size();
+    //   int sizeNonMem = d_termInfoManager->getNonMembers(d_equalityEngine.getRepresentative(a))->size();
+    //   Debug("sets-care") << "[sets-care] " << a << " : " << sizeMem << " " << sizeNonMem << std::endl;
+    //   if(sizeMem == 0 && sizeNonMem == 0) continue;
+    // }
+    unsigned j_st;
+    if(i == d_ccg_i) j_st = d_ccg_j + 1;
+    else j_st = i + 1;
+    for (unsigned j = j_st; j < d_external.d_sharedTerms.size(); ++ j) {
       TNode b = d_external.d_sharedTerms[j];
       if (b.getType() != aType) {
         // We don't care about the terms of different types
         continue;
       }
+      // if(b.getType().isSet()) {
+      //   int sizeMem = d_termInfoManager->getMembers(d_equalityEngine.getRepresentative(b))->size();
+      //   int sizeNonMem = d_termInfoManager->getNonMembers(d_equalityEngine.getRepresentative(b))->size();
+      //   Debug("sets-care") << "[sets-care] " << a << " : " << sizeMem << " " << sizeNonMem << std::endl;
+      //   if(sizeMem == 0 && sizeNonMem == 0) continue;
+      // }
       switch (d_external.d_valuation.getEqualityStatus(a, b)) {
       case EQUALITY_TRUE_AND_PROPAGATED:
+        // If we know about it, we should have propagated it, so we can skip
+        Trace("sets-care") << "[sets-care] Know: " << EQUAL(a, b) << std::endl;
+        break;
       case EQUALITY_FALSE_AND_PROPAGATED:
         // If we know about it, we should have propagated it, so we can skip
+        Trace("sets-care") << "[sets-care] Know: " << NOT(EQUAL(a, b)) << std::endl;
         break;
-      default:
+      case EQUALITY_FALSE:
+      case EQUALITY_TRUE:
+        Assert(false, "ERROR: Equality status true/false but not propagated (sets care graph computation).");
+        break;
+      case EQUALITY_TRUE_IN_MODEL:
+        d_external.addCarePair(a, b);
+      case EQUALITY_FALSE_IN_MODEL:
+        if(Trace.isOn("sets-care-performance-test")) {
+          // TODO: delete these lines, only for performance testing for now
+          d_external.addCarePair(a, b);
+        }
+        break;
+      case EQUALITY_UNKNOWN:
         // Let's split on it
         d_external.addCarePair(a, b);
+        if(options::setsCare1()) {
+          d_ccg_i = i;
+          d_ccg_j = j;
+          return;
+        }
+        if(Trace.isOn("sets-care-dump")) {
+          careGraphVertices[a.getType()].insert(a);
+          careGraphVertices[a.getType()].insert(b);
+        }
         break;
+      default:
+	Unreachable();
       }
     }
   }
+
+  if(Trace.isOn("sets-care-dump")) {
+    FORIT(it, careGraphVertices) {
+      // Trace("sets-care-dump") << "For " << (*it).first << ": " << std::endl;
+      std::set<TNode>& S = (*it).second;
+      for(util::partition::iterator subsets(S.size());
+          !subsets.isFinished(); ++subsets) {
+        Trace("sets-care-dump") << ";---split---" << std::endl;
+        Trace("sets-care-dump") << ";";
+        for(unsigned i = 0; i < S.size(); ++i) Trace("sets-care-dump") << subsets.get(i);
+        Trace("sets-care-dump") << std::endl;
+        int j = 0;
+        FORIT(jt, (*it).second) {
+          int k = 0;
+          FORIT(kt, (*it).second) {
+            if(j == k) continue;
+            Node n = EQUAL( (*jt), (*kt) );
+            if(!subsets.equal(j, k)) n = NOT(n);
+            Trace("sets-care-dump") << AssertCommand(n.toExpr()) << std::endl;
+            ++k;
+          }
+          ++j;
+        }
+      }
+    }
+    Trace("sets-care-dump") << ";---split---" << std::endl;
+#undef FORIT
+  }
 }
 
+EqualityStatus TheorySetsPrivate::getEqualityStatus(TNode a, TNode b) {
+  Assert(d_equalityEngine.hasTerm(a) && d_equalityEngine.hasTerm(b));
+  if (d_equalityEngine.areEqual(a, b)) {
+    // The terms are implied to be equal
+    return EQUALITY_TRUE;
+  }
+  if (d_equalityEngine.areDisequal(a, b, false)) {
+    // The terms are implied to be dis-equal
+    return EQUALITY_FALSE;
+  }
+  if( d_external.d_valuation.getModelValue(a) == d_external.d_valuation.getModelValue(b) ) {
+    // Ther term are true in current model
+    return EQUALITY_TRUE_IN_MODEL;
+  }
+  return EQUALITY_FALSE_IN_MODEL;
+  // }
+  // //TODO: can we be more precise sometimes?
+  // return EQUALITY_UNKNOWN;
+}
 
 /******************** Model generation ********************/
 /******************** Model generation ********************/
@@ -578,6 +764,21 @@ Node TheorySetsPrivate::elementsToShape(Elements elements, TypeNode setType) con
     return cur;
   }
 }
+Node TheorySetsPrivate::elementsToShape(set<Node> elements, TypeNode setType) const
+{
+  NodeManager* nm = NodeManager::currentNM();
+
+  if(elements.size() == 0) {
+    return nm->mkConst(EmptySet(nm->toType(setType)));
+  } else {
+    typeof(elements.begin()) it = elements.begin();
+    Node cur = SINGLETON(*it);
+    while( ++it != elements.end() ) {
+      cur = nm->mkNode(kind::UNION, cur, SINGLETON(*it));
+    }
+    return cur;
+  }
+}
 
 void TheorySetsPrivate::collectModelInfo(TheoryModel* m, bool fullModel)
 {
@@ -684,6 +885,11 @@ void TheorySetsPrivate::collectModelInfo(TheoryModel* m, bool fullModel)
 #endif
 }
 
+Node TheorySetsPrivate::getModelValue(TNode n)
+{
+  CodeTimer codeTimer(d_statistics.d_getModelValueTime);
+  return d_termInfoManager->getModelValue(n);
+}
 
 /********************** Helper functions ***************************/
 /********************** Helper functions ***************************/
@@ -730,14 +936,17 @@ Node mkAnd(const std::vector<TNode>& conjunctions) {
 
 
 TheorySetsPrivate::Statistics::Statistics() :
-  d_checkTime("theory::sets::time") {
-
+  d_checkTime("theory::sets::time")
+  , d_getModelValueTime("theory::sets::getModelValueTime")
+{
   StatisticsRegistry::registerStat(&d_checkTime);
+  StatisticsRegistry::registerStat(&d_getModelValueTime);
 }
 
 
 TheorySetsPrivate::Statistics::~Statistics() {
   StatisticsRegistry::unregisterStat(&d_checkTime);
+  StatisticsRegistry::unregisterStat(&d_getModelValueTime);
 }
 
 
@@ -876,6 +1085,9 @@ TheorySetsPrivate::TheorySetsPrivate(TheorySets& external,
   d_pending(c),
   d_pendingDisequal(c),
   d_pendingEverInserted(u),
+  d_modelCache(c),
+  d_ccg_i(c),
+  d_ccg_j(c),
   d_scrutinize(NULL)
 {
   d_termInfoManager = new TermInfoManager(*this, c, &d_equalityEngine);
@@ -1106,6 +1318,8 @@ void TheorySetsPrivate::TermInfoManager::notifyMembership(TNode fact) {
 
   d_info[S]->addToElementList(x, polarity);
   d_info[x]->addToSetList(S, polarity);
+
+  d_theory.d_modelCache.clear();
 }
 
 const CDTNodeList* TheorySetsPrivate::TermInfoManager::getParents(TNode x) {
@@ -1259,8 +1473,35 @@ void TheorySetsPrivate::TermInfoManager::mergeTerms(TNode a, TNode b) {
               (*itb).second->setsContainingThisElement );
   mergeLists( (*ita).second->setsNotContainingThisElement,
               (*itb).second->setsNotContainingThisElement );
+
+  d_theory.d_modelCache.clear();
 }
 
+Node TheorySetsPrivate::TermInfoManager::getModelValue(TNode n)
+{
+  Assert(n.getType().isSet());
+  set<Node> elements, elements_const;
+  Node S = d_eqEngine->getRepresentative(n);
+  typeof(d_theory.d_modelCache.begin()) it = d_theory.d_modelCache.find(S);
+  if(it != d_theory.d_modelCache.end()) {
+    return (*it).second;
+  }
+  const CDTNodeList* l = getMembers(S);
+  for(typeof(l->begin()) it = l->begin(); it != l->end(); ++it) {
+    TNode n = *it;
+    elements.insert(d_eqEngine->getRepresentative(n));
+  }
+  BOOST_FOREACH(TNode e, elements) {
+    if(e.isConst()) {
+      elements_const.insert(e);
+    } else {
+      elements_const.insert(d_theory.d_external.d_valuation.getModelValue(e));
+    }
+  }
+  Node v = d_theory.elementsToShape(elements_const, n.getType());
+  d_theory.d_modelCache[n] = v;
+  return v;
+}
 
 }/* CVC4::theory::sets namespace */
 }/* CVC4::theory namespace */
diff --git a/src/theory/sets/theory_sets_private.h b/src/theory/sets/theory_sets_private.h
index 78a415529..b293c63e6 100644
--- a/src/theory/sets/theory_sets_private.h
+++ b/src/theory/sets/theory_sets_private.h
@@ -60,6 +60,10 @@ public:
 
   Node explain(TNode);
 
+  EqualityStatus getEqualityStatus(TNode a, TNode b);
+
+  Node getModelValue(TNode);
+
   void preRegisterTerm(TNode node);
 
   void propagate(Theory::Effort) { /* we don't depend on this call */ }
@@ -70,6 +74,7 @@ private:
   class Statistics {
   public:
     TimerStat d_checkTime;
+    TimerStat d_getModelValueTime;
 
     Statistics();
     ~Statistics();
@@ -123,6 +128,7 @@ private:
     void notifyMembership(TNode fact);
     const CDTNodeList* getParents(TNode x);
     const CDTNodeList* getMembers(TNode S);
+    Node getModelValue(TNode n);
     const CDTNodeList* getNonMembers(TNode S);
     void addTerm(TNode n);
     void mergeTerms(TNode a, TNode b);
@@ -174,8 +180,15 @@ private:
   typedef std::hash_map<TNode, Elements, TNodeHashFunction> SettermElementsMap;
   const Elements& getElements(TNode setterm, SettermElementsMap& settermElementsMap) const;
   Node elementsToShape(Elements elements, TypeNode setType) const;
+  Node elementsToShape(std::set<Node> elements, TypeNode setType) const;
   bool checkModel(const SettermElementsMap& settermElementsMap, TNode S) const;
 
+  context::CDHashMap <Node, Node, NodeHashFunction> d_modelCache;
+
+
+  // sharing related
+  context::CDO<unsigned>  d_ccg_i, d_ccg_j;
+
   // more debugging stuff
   friend class TheorySetsScrutinize;
   TheorySetsScrutinize* d_scrutinize;
diff --git a/src/theory/sets/theory_sets_type_rules.h b/src/theory/sets/theory_sets_type_rules.h
index eb270202a..6754bbb9e 100644
--- a/src/theory/sets/theory_sets_type_rules.h
+++ b/src/theory/sets/theory_sets_type_rules.h
@@ -100,7 +100,7 @@ struct MemberTypeRule {
       }
       TypeNode elementType = n[0].getType(check);
       if(elementType != setType.getSetElementType()) {
-        throw TypeCheckingExceptionPrivate(n, "set in operating on sets of different types");
+        throw TypeCheckingExceptionPrivate(n, "member operating on sets of different types");
       }
     }
     return nodeManager->booleanType();
diff --git a/src/theory/theory_engine.cpp b/src/theory/theory_engine.cpp
index 53a529325..19409faf7 100644
--- a/src/theory/theory_engine.cpp
+++ b/src/theory/theory_engine.cpp
@@ -155,7 +155,7 @@ TheoryEngine::TheoryEngine(context::Context* context,
   d_sharedTermsVisitor(d_sharedTerms),
   d_unconstrainedSimp(new UnconstrainedSimplifier(context, logicInfo)),
   d_bvToBoolPreprocessor(),
-  d_arithSubstitutionsAdded("zzz::arith::substitutions", 0)
+  d_arithSubstitutionsAdded("theory::arith::zzz::arith::substitutions", 0)
 {
   for(TheoryId theoryId = theory::THEORY_FIRST; theoryId != theory::THEORY_LAST; ++ theoryId) {
     d_theoryTable[theoryId] = NULL;
@@ -453,7 +453,7 @@ void TheoryEngine::check(Theory::Effort effort) {
 
 void TheoryEngine::combineTheories() {
 
-  Debug("sharing") << "TheoryEngine::combineTheories()" << endl;
+  Trace("sharing") << "TheoryEngine::combineTheories()" << endl;
 
   TimerStat::CodeTimer combineTheoriesTimer(d_combineTheoriesTime);
 
@@ -471,7 +471,7 @@ void TheoryEngine::combineTheories() {
   // Call on each parametric theory to give us its care graph
   CVC4_FOR_EACH_THEORY;
 
-  Debug("sharing") << "TheoryEngine::combineTheories(): care graph size = " << careGraph.size() << endl;
+  Trace("sharing") << "TheoryEngine::combineTheories(): care graph size = " << careGraph.size() << endl;
 
   // Now add splitters for the ones we are interested in
   CareGraph::const_iterator care_it = careGraph.begin();
@@ -1394,16 +1394,10 @@ theory::LemmaStatus TheoryEngine::lemma(TNode node, bool negated, bool removable
   }
 
   // WARNING: Below this point don't assume additionalLemmas[0] to be not negated.
-  // WARNING: Below this point don't assume additionalLemmas[0] to be not negated.
   if(negated) {
-    // Can't we just get rid of passing around this 'negated' stuff?
-    // Is it that hard for the propEngine to figure that out itself?
-    // (I like the use of triple negation <evil laugh>.) --K
     additionalLemmas[0] = additionalLemmas[0].notNode();
     negated = false;
   }
-  // WARNING: Below this point don't assume additionalLemmas[0] to be not negated.
-  // WARNING: Below this point don't assume additionalLemmas[0] to be not negated.
 
   // assert to decision engine
   if(!removable) {
diff --git a/src/util/partitions.h b/src/util/partitions.h
new file mode 100644
index 000000000..eaf29932b
--- /dev/null
+++ b/src/util/partitions.h
@@ -0,0 +1,94 @@
+#include <vector>
+#include <algorithm>
+
+namespace CVC4 {
+namespace util {
+
+class partition
+{
+public:
+  class iterator
+  {
+  public:
+    /** 
+     * iterate over all partitions of [0, 1, ... n-1] (same as
+     * generating equivalence relations)
+     * 
+     * corresponds to n-th bell number (A000110 in OEIS)
+     */
+    iterator(unsigned n, bool first = true);
+
+    unsigned  size()     const { return kappa.size();      }
+
+    /** How many partitions does the current paritioning use */
+    unsigned  subsets()  const { return M[size() - 1] + 1; }
+
+    /** Which partition is 'i' in? Numbering starts with 0. */
+    int get(int i) { return kappa[i]; }
+
+    /** Are 'i' and 'j' in the same partition */
+    bool equal(int i, int j) { return kappa[i] == kappa[j]; }
+
+    /** go to next partitioning */
+    iterator& operator++();
+
+    bool isFinished() { return d_finished; }
+  protected:
+    std::vector<unsigned> kappa, M;
+    bool d_finished;
+  };
+};
+
+/**
+   Implementation from
+   https://www.cs.bgu.ac.il/~orlovm/papers/partitions-source.tar.gz
+
+   Released in public domain by Michael Orlov <orlovm@cs.bgu.ac.il>,
+   according to the accompaning paper (Efficient Generation of Set
+   Partitions, Appendix A).
+
+   --Kshitij Bansal, Tue Aug  5 15:57:20 EDT 2014
+*/
+
+partition::iterator::
+iterator(unsigned n, bool first)
+  : kappa(n), M(n), d_finished(false)
+{
+  if (n <= 0)
+    throw std::invalid_argument
+      ("partition::iterator: n must be positive");
+
+  if (! first)
+    for (unsigned i = 1; i < n; ++i) {
+      kappa[i] = i;
+      M[i] = i;
+    }
+}
+
+partition::iterator&
+partition::iterator::
+operator++()
+{
+  const unsigned n = size();
+
+  for (unsigned i = n-1; i > 0; --i)
+    if (kappa[i] <= M[i-1]) {
+      ++kappa[i];
+
+      const unsigned new_max = std::max(M[i], kappa[i]);
+      M[i] = new_max;
+      for (unsigned j = i + 1; j < n; ++j) {
+        kappa[j] = 0;
+        M[j] = new_max;
+      }
+
+      // integrityCheck();
+      return *this;
+    }
+
+  d_finished = true;
+  return *this;
+}
+
+}
+}