path: root/decoder/cfg.cc

#include "cfg.h"
#include "hg.h"
#include "cfg_format.h"
#include "cfg_binarize.h"
#include "hash.h"
#include "batched_append.h"
#include <limits>
#include "fast_lexical_cast.hpp"
//#include "indices_after.h"
#include "show.h"
#include "null_traits.h"

#define DUNIQ(x) x
#define DBIN(x)
#define DSP(x) x
//SP:binarize by splitting.
#define DCFG(x) IF_CFG_DEBUG(x)

#undef CFG_FOR_RULES
#define CFG_FOR_RULES(i,expr)                                    \
  for (CFG::NTs::const_iterator n=nts.begin(),nn=nts.end();n!=nn;++n) { \
    NT const& nt=*n; \
    for (CFG::Ruleids::const_iterator ir=nt.ruleids.begin(),er=nt.ruleids.end();ir!=er;++ir) {  \
      RuleHandle i=*ir; \
      expr; \
    } \
  }


using namespace std;

typedef CFG::Rule Rule;
typedef CFG::NTOrder NTOrder;
typedef CFG::RHS RHS;
typedef CFG::BinRhs BinRhs;

/////index ruleids:
void CFG::UnindexRules() {
  for (NTs::iterator n=nts.begin(),nn=nts.end();n!=nn;++n)
    n->ruleids.clear();
}

void CFG::ReindexRules() {
  UnindexRules();
  for (int i=0,e=rules.size();i<e;++i)
    if (!rules[i].is_null())
      nts[rules[i].lhs].ruleids.push_back(i);
}

//////topo order:
namespace {
typedef std::vector<char> Seen; // 0 = unseen, 1 = seen+finished, 2 = open (for cycle detection; seen but not finished)
enum { UNSEEN=0,SEEN,OPEN };

// bottom -> top topo order (rev head->tails topo)
template <class OutOrder>
struct CFGTopo {
// meaningless efficiency alternative: close over all the args except ni - so they're passed as a single pointer.  also makes visiting tail_nts simpler.
  CFG const& cfg;
  OutOrder outorder;
  std::ostream *cerrp;
  CFGTopo(CFG const& cfg,OutOrder const& outorder,std::ostream *cerrp=&std::cerr)
    : cfg(cfg),outorder(outorder),cerrp(cerrp) // closure over args
    , seen(cfg.nts.size()) {  }

  Seen seen;
  void operator()(CFG::NTHandle ni) {
    char &seenthis=seen[ni];
    if (seenthis==UNSEEN) {
      seenthis=OPEN;

      CFG::NT const& nt=cfg.nts[ni];
      for (CFG::Ruleids::const_iterator i=nt.ruleids.begin(),e=nt.ruleids.end();i!=e;++i) {
        Rule const& r=cfg.rules[*i];
        r.visit_rhs_nts(*this); // recurse.
      }

      *outorder++=ni; // dfs finishing time order = reverse topo.
      seenthis=SEEN;
    } else if (cerrp && seenthis==OPEN) {
      std::ostream &cerr=*cerrp;
      cerr<<"WARNING: CFG Topo order attempt failed: NT ";
      cfg.print_nt_name(cerr,ni);
      cerr<<" already reached from goal(top) ";
      cfg.print_nt_name(cerr,cfg.goal_nt);
      cerr<<".  Continuing to reorder, but it's not fully topological.\n";
    }
  }

};

template <class O>
void DoCFGTopo(CFG const& cfg,CFG::NTHandle goal,O const& o,std::ostream *w=0) {
  CFGTopo<O> ct(cfg,o,w);
  ct(goal);
}

}//ns

// you would need to do this only if you didn't build from hg, or you Binarize without bin_topo option.  note: this doesn't sort the list of rules; it's assumed that if you care about the topo order you'll iterate over nodes.
void CFG::OrderNTsTopo(NTOrder *o_,std::ostream *cycle_complain) {
  NTOrder &o=*o_;
  o.resize(nts.size());
  DoCFGTopo(*this,goal_nt,o.begin(),cycle_complain);
}


/////sort/uniq:
namespace {
RHS null_rhs(1,INT_MIN);

//sort
struct ruleid_best_first {
  CFG::Rules const* rulesp;
  bool operator()(int a,int b) const { // true if a >(prob for ruleid) b
    return (*rulesp)[b].p < (*rulesp)[a].p;
  }
};

//uniq
struct prob_pos {
  prob_pos() {}
  prob_pos(prob_t prob,int pos) : prob(prob),pos(pos) {}
  prob_t prob;
  int pos;
  bool operator <(prob_pos const& o) const { return prob<o.prob; }
};
}//ns

int CFG::UniqRules(NTHandle ni) {
  typedef HASH_MAP<RHS,prob_pos,boost::hash<RHS> > BestRHS; // faster to use trie? maybe.
  BestRHS bestp; // once inserted, the position part (output index) never changes.  but the prob may be improved (overwrite ruleid at that position).
  HASH_MAP_EMPTY(bestp,null_rhs);
  Ruleids &adj=nts[ni].ruleids;
  Ruleids oldadj=adj;
  int newpos=0;
  for (int i=0,e=oldadj.size();i!=e;++i) { // this beautiful complexity is to ensure that adj' is a subsequence of adj (without duplicates)
    int ri=oldadj[i];
    Rule const& r=rules[ri];
    prob_pos pi(r.p,newpos);
    prob_pos &oldpi=get_default(bestp,r.rhs,pi);
    if (oldpi.pos==newpos) {// newly inserted
      adj[newpos++]=ri;
    } else {
      SHOWP(DUNIQ,"Uniq duplicate: ") SHOW4(DUNIQ,oldpi.prob,pi.prob,oldpi.pos,newpos);
      SHOW(DUNIQ,ShowRule(ri));
      SHOW(DUNIQ,ShowRule(adj[oldpi.pos]));
      if (oldpi.prob<pi.prob) { // we improve prev. best (overwrite it @old pos)
        oldpi.prob=pi.prob;
        adj[oldpi.pos]=ri; // replace worse rule w/ better
      }
    }

  }
  // post: newpos = number of new adj
  adj.resize(newpos);
  return newpos;
}

void CFG::SortLocalBestFirst(NTHandle ni) {
  ruleid_best_first r;
  r.rulesp=&rules;
  Ruleids &adj=nts[ni].ruleids;
  std::stable_sort(adj.begin(),adj.end(),r);
}


/////binarization:
namespace {

BinRhs null_bin_rhs(std::numeric_limits<int>::min(),std::numeric_limits<int>::min());

// index i >= N.size()?  then it's in M[i-N.size()]
//WordID first,WordID second,
string BinStr(BinRhs const& b,CFG::NTs const& N,CFG::NTs const& M)
{
  int nn=N.size();
  ostringstream o;
#undef BinNameOWORD
#define BinNameOWORD(w)                                 \
  do {                                                  \
    int n=w; if (n>0) o << TD::Convert(n);              \
    else {                                              \
      int i=-n;                                         \
      if (i<nn) o<<N[i].from<<i; else o<<M[i-nn].from;  \
    }                                                   \
  } while(0)

  BinNameOWORD(b.first);
  o<<'+';
  BinNameOWORD(b.second);
  return o.str();
}

string BinStr(RHS const& r,CFG::NTs const& N,CFG::NTs const& M)
{
  int nn=N.size();
  ostringstream o;
  for (int i=0,e=r.size();i!=e;++i) {
    if (i)
      o<<'+';
    BinNameOWORD(r[i]);
  }
  return o.str();
}


WordID BinName(BinRhs const& b,CFG::NTs const& N,CFG::NTs const& M)
{
  return TD::Convert(BinStr(b,N,M));
}

WordID BinName(RHS const& b,CFG::NTs const& N,CFG::NTs const& M)
{
  return TD::Convert(BinStr(b,N,M));
}

/*
template <class Rhs>
struct null_for;


template <>
struct null_for<BinRhs> {
  static BinRhs null;
};

template <>
struct null_for<RHS> {
  static RHS null;
};
*/

template <>
BinRhs null_traits<BinRhs>::null(std::numeric_limits<int>::min(),std::numeric_limits<int>::min());

template <>
RHS null_traits<RHS>::null(1,std::numeric_limits<int>::min());

template <class Rhs>
struct add_virtual_rules {
  typedef CFG::RuleHandle RuleHandle;
  typedef CFG::NTHandle NTHandle;
  CFG::NTs &nts,new_nts;
  CFG::Rules &rules, new_rules;
// above will be appended at the end, so we don't have to worry about iterator invalidation
  WordID newnt; //negative of NTHandle, or positive => unary lexical item (not to binarize).  fit for rhs of a rule
  RuleHandle newruleid;
  typedef HASH_MAP<Rhs,WordID,boost::hash<Rhs> > R2L;
  R2L rhs2lhs; // an rhs maps to this -virtntid, or original id if length 1
  bool name_nts;
  add_virtual_rules(CFG &cfg,bool name_nts=false) : nts(cfg.nts),rules(cfg.rules),newnt(-nts.size()),newruleid(rules.size()),name_nts(name_nts) {
    HASH_MAP_EMPTY(rhs2lhs,null_traits<Rhs>::null);
  }
  NTHandle get_virt(Rhs const& r) {
    NTHandle nt=get_default(rhs2lhs,r,newnt);
    SHOW(DBIN,newnt) SHOWP(DBIN,"bin="<<BinStr(r,nts,new_nts)<<"=>") SHOW(DBIN,nt);
    if (newnt==nt) {
      create(r);
    }
    return nt;
  }
  inline void set_nt_name(Rhs const& r) {
    if (name_nts)
      new_nts.back().from.nt=BinName(r,nts,new_nts);
  }
  inline void create_nt(Rhs const& rhs) {
    new_nts.push_back(CFG::NT(newruleid++));
    set_nt_name(rhs);
  }
  inline void create_rule(Rhs const& rhs) {
    new_rules.push_back(CFG::Rule(-newnt,rhs));
    --newnt;
  }
  inline void create_adding(Rhs const& rhs) {
    NTHandle nt=get_default(rhs2lhs,rhs,newnt);
    assert(nt==newnt);
    create(rhs);
  }
  inline void create(Rhs const& rhs) {
    SHOWP(DSP,"Create ") SHOW3(DSP,newnt,newruleid,BinStr(rhs,nts,new_nts))
    create_nt(rhs);
    create_rule(rhs);
    assert(newruleid==rules.size()+new_rules.size());assert(-newnt==nts.size()+new_nts.size());
  }

  ~add_virtual_rules() {
    append_rules();
  }
  void append_rules() {
    // marginally more efficient
    batched_append_swap(nts,new_nts);
    batched_append_swap(rules,new_rules);
  }
  inline bool have(Rhs const& rhs,NTHandle &h) const {
    if (rhs.size()==1) {     // stop creating virtual unary rules.
      h=rhs[0];
      return true;
    }
    typename R2L::const_iterator i=rhs2lhs.find(rhs);
    if (i==rhs2lhs.end())
      return false;
    h=i->second;
    return true;
  }
  //HACK: prevent this for instantiating for BinRhs.  we need to use rule index because we'll be adding rules before we can update.
  // returns 1 per replaced NT (0,1, or 2)
  inline std::string Str(Rhs const& rhs) const {
    return BinStr(rhs,nts,new_nts);
  }

  template <class RHSi>
  int split_rhs(RHSi &rhs,bool only_free=false,bool only_reusing_1=false) {
    typedef WordID const* WP;
    //TODO: don't actually build substrings of rhs; define key type that stores ref to rhs in new_nts by index (because it may grow), and also allows an int* [b,e) range to serve as key (i.e. don't insert the latter type of key).
    int n=rhs.size();
    if (n<=2) return 0;
    int longest1=1; // all this other stuff is not uninitialized when used, based on checking this and other things (it's complicated, learn to prove theorems, gcc)
    int mid=n/2;
    int best_k;
    enum {HAVE_L=-1,HAVE_NONE=0,HAVE_R=1};
    int have1=HAVE_NONE; // will mean we already have some >1 length prefix or suffix as a virt. (it's free).  if we have both we use it immediately and return.
    NTHandle ntr,ntl;
    NTHandle bestntr,bestntl;
    WP b=&rhs.front(),e=b+n;
    WP wk=b;
    SHOWM3(DSP,"Split",Str(rhs),only_free,only_reusing_1);
    int rlen=n;
    for (int k=1;k<n-1;++k) {
      //TODO: handle length 1 l and r parts without explicitly building Rhs?
      ++wk; assert(k==wk-b);
      --rlen; assert(rlen==n-k);
      Rhs l(b,wk);
      if (have(l,ntl)) {
        if (k>1) { SHOWM3(DSP,"Have l",k,n,Str(l)) }
        Rhs r(wk,e);
        if (have(r,ntr)) {
          SHOWM3(DSP,"Have r too",k,n,Str(r))
          rhs.resize(2);
          rhs[0]=ntl;
          rhs[1]=ntr;
          return 2;
        } else if (k>longest1) {
          longest1=k;
          have1=HAVE_L;
          bestntl=ntl;
          best_k=k;
        }
      } else if (rlen>longest1) { // > or >= favors l or r branching, maybe.  who cares.
        Rhs r(wk,e);
        if (have(r,ntr)) {
          longest1=rlen;
          if (rlen>1) { SHOWM3(DSP,"Have r (only) ",k,n,Str(r)) }
          have1=HAVE_R;
          bestntr=ntr;
          best_k=k;
        }
      }
      //TODO: swap order of consideration (l first or r?) depending on pre/post midpoint?  one will be useless to check for beating the longest single match so far.  check that second

    }
    // now we know how we're going to split the rule; what follows is just doing the actual splitting:

    if (only_free) {
      if (have1==HAVE_NONE)
        return 0;
      if (have1==HAVE_L) {
        rhs.erase(rhs.begin()+1,rhs.begin()+best_k); //erase [1..best_k)
        rhs[0]=bestntl;
      } else {
        assert(have1==HAVE_R);
        rhs.erase(rhs.begin()+best_k+1,rhs.end()); // erase (best_k..)
        rhs[best_k]=bestntr;
      }
      return 1;
    }
    /* now we have to add some new virtual rules.
       some awkward constraints:

       1. can't resize rhs until you save copy of l or r split portion

       2. can't create new rule until you finished modifying rhs (this is why we store newnt then create).  due to vector push_back invalidation.  perhaps we could bypass this by reserving sufficient space first before a splitting pass (# rules and nts created is <= 2 * # of rules being passed over)

    */
    if (have1==HAVE_NONE) { // default: split down middle.
      DSP(assert(longest1==1));
      WP m=b+mid;
      if (n%2==0) {
        WP i=b;
        WP j=m;
        for (;i!=m;++i,++j)
          if (*i!=*j) goto notleqr;
        // [...mid]==[mid...]!
        RHS l(b,m); // 1. // this is equal to RHS(m,e).
        rhs.resize(2);
        rhs[0]=rhs[1]=newnt; //2.
        create_adding(l);
        return 1; // only had to create 1 total when splitting down middle when l==r
      }
    notleqr:
      if (only_reusing_1) return 0;
      best_k=mid; // rounds down
      if (mid==1) {
        RHS r(m,e); //1.
        rhs.resize(2);
        rhs[1]=newnt; //2.
        create_adding(r);
        return 1;
      } else {
        Rhs l(b,m);
        Rhs r(m,e); // 1.
        rhs.resize(2);
        rhs[0]=newnt;
        rhs[1]=newnt-1; // 2.
        create_adding(l);
        create_adding(r);
        return 2;
      }
    }
    WP best_wk=b+best_k;
    //we build these first because adding rules may invalidate the underlying pointers (we end up binarizing already split virt rules)!.
    //wow, that decision (not to use index into new_nts instead of pointer to rhs), while adding new nts to it really added some pain.
    if (have1==HAVE_L) {
      Rhs r(best_wk,e); //1.
      rhs.resize(2);
      rhs[0]=bestntl;
      DSP(assert(best_wk<e-1)); // because we would have returned having both if rhs was singleton
      rhs[1]=newnt; //2.
      create_adding(r);
    } else {
      DSP(assert(have1==HAVE_R));
      DSP(assert(best_wk>b+1)); // because we would have returned having both if lhs was singleton
      Rhs l(b,best_wk); //1.
      rhs.resize(2);
      rhs[0]=newnt; //2.
      rhs[1]=bestntr;
      create_adding(l);
    }
    return 1;
  }
};

}//ns

void CFG::BinarizeSplit(CFGBinarize const& b) {
  add_virtual_rules<RHS> v(*this,b.bin_name_nts);
  CFG_FOR_RULES(i,v.split_rhs(rules[i].rhs,false,false));
  Rules &newr=v.new_rules;
#undef CFG_FOR_VIRT
#define CFG_FOR_VIRT(r,expr)                                                 \
  for (int i=0,e=newr.size();i<e;++i) { \
    Rule &r=newr[i];expr;  } // NOTE: must use indices since we'll be adding rules as we iterate.

  int n_changed_total=0;
  int n_changed=0; // quiets a warning
#define CFG_SPLIT_PASS(N,free,just1) \
  for (int pass=0;pass<b.N;++pass) { \
    n_changed=0; \
    CFG_FOR_VIRT(r,n_changed+=v.split_rhs(r.rhs,free,just1)); \
    if (!n_changed) { \
      break; \
    } n_changed_total+=n_changed; }

  CFG_SPLIT_PASS(split_passes,false,false)
    if (n_changed==0) return;
  CFG_SPLIT_PASS(split_share1_passes,false,true)
  CFG_SPLIT_PASS(split_free_passes,true,false)

}

void CFG::Binarize(CFGBinarize const& b) {
  if (!b.Binarizing()) return;
  cerr << "Binarizing "<<b<<endl;
  if (b.bin_thresh>0)
    BinarizeThresh(b);
  if (b.bin_split)
    BinarizeSplit(b);
  if (b.bin_l2r)
    BinarizeL2R(false,b.bin_name_nts);
  if (b.bin_topo) //TODO: more efficient (at least for l2r) maintenance of order?
    OrderNTsTopo();

}

namespace {
}

void CFG::BinarizeThresh(CFGBinarize const& b) {
  throw runtime_error("TODO: some fancy linked list thing - see NOTES.partial.binarize");
}


void CFG::BinarizeL2R(bool bin_unary,bool name) {
  add_virtual_rules<BinRhs> v(*this,name);
cerr << "Binarizing left->right " << (bin_unary?"real to unary":"stop at binary") <<endl;
  HASH_MAP<BinRhs,NTHandle,boost::hash<BinRhs> > bin2lhs; // we're going to hash cons rather than build an explicit trie from right to left.
  HASH_MAP_EMPTY(bin2lhs,null_bin_rhs);
  // iterate using indices and not iterators because we'll be adding to both nts and rules list?  we could instead pessimistically reserve space for both, but this is simpler.  also: store original end of nts since we won't need to reprocess newly added ones.
  int rhsmin=bin_unary?0:1;
  //NTs new_nts;
  //Rules new_rules;
  //TODO: this could be factored easily into in-place (append to new_* like below) and functional (nondestructive copy) versions (copy orig to target and append to target)
//  int newnt=nts.size(); // we're going to store binary rhs with -nt to keep distinct from words (>=0)
//  int newruleid=rules.size();
  BinRhs bin;
  CFG_FOR_RULES(ruleid,
/*  for (NTs::const_iterator n=nts.begin(),nn=nts.end();n!=nn;++n) {
    NT const& nt=*n;
    for (Ruleids::const_iterator ir=nt.ruleids.begin(),er=nt.ruleids.end();ir!=er;++ir) {
    RuleHandle ruleid=*ir;*/
//      SHOW2(DBIN,ruleid,ShowRule(ruleid));
                Rule & rule=rules[ruleid];
      RHS &rhs=rule.rhs; // we're going to binarize this while adding newly created rules to new_...
      if (rhs.empty()) continue;
      int r=rhs.size()-2; // loop below: [r,r+1) is to be reduced into a (maybe new) binary NT
      if (rhsmin<=r) { // means r>=0 also
        bin.second=rhs[r+1];
        int bin_to; // the replacement for bin
//        assert(newruleid==rules.size()+new_rules.size());assert(newnt==nts.size()+new_nts.size());
        // also true at start/end of loop:
        for (;;) { // pairs from right to left (normally we leave the last pair alone)
          bin.first=rhs[r];
          bin_to=v.get_virt(bin);
/*          bin_to=get_default(bin2lhs,bin,v.newnt);
//          SHOW(DBIN,r) SHOW(DBIN,newnt) SHOWP(DBIN,"bin="<<BinStr(bin,nts,new_nts)<<"=>") SHOW(DBIN,bin_to);
          if (v.newnt==bin_to) { // it's new!
            new_nts.push_back(NT(newruleid++));
            //now newnt is the index of the last (after new_nts is appended) nt.  bin is its rhs.  bin_to is its lhs
            new_rules.push_back(Rule(newnt,bin));
            ++newnt;
            if (name) new_nts.back().from.nt=BinName(bin,nts,new_nts);
          }
*/
          bin.second=bin_to;
          --r;
          if (r<rhsmin) {
            rhs[rhsmin]=bin_to;
            rhs.resize(rhsmin+1);
            break;
          }
        }
      })
                /*
    }
  }
                */
#if 0
  // marginally more efficient
  batched_append_swap(nts,new_nts);
  batched_append_swap(rules,new_rules);
//#else
  batched_append(nts,new_nts);
  batched_append(rules,new_rules);
#endif
}

namespace {
inline int nt_index(int nvar,Hypergraph::TailNodeVector const& t,bool target_side,int w) {
  assert(w<0 || (target_side&&w==0));
  return t[target_side?-w:nvar];
}
}

void CFG::Init(Hypergraph const& hg,bool target_side,bool copy_features,bool push_weights) {
  uninit=false;
  hg_=&hg;
  Hypergraph::NodeProbs np;
  goal_inside=hg.ComputeNodeViterbi(&np);
  pushed_inside=push_weights ? goal_inside : prob_t(1);
  int nn=hg.nodes_.size(),ne=hg.edges_.size();
  nts.resize(nn);
  goal_nt=nn-1;
  rules.resize(ne);
  for (int i=0;i<nn;++i) {
    nts[i].ruleids=hg.nodes_[i].in_edges_;
    hg.SetNodeOrigin(i,nts[i].from);
  }
  for (int i=0;i<ne;++i) {
    Rule &cfgr=rules[i];
    Hypergraph::Edge const& e=hg.edges_[i];
    prob_t &crp=cfgr.p;
    crp=e.edge_prob_;
    cfgr.lhs=e.head_node_;
    IF_CFG_TRULE(cfgr.rule=e.rule_;)
    if (copy_features) cfgr.f=e.feature_values_;
    if (push_weights) crp /=np[e.head_node_];
    TRule const& er=*e.rule_;
    vector<WordID> const& rule_rhs=target_side?er.e():er.f();
    int nr=rule_rhs.size();
    RHS &rhs_out=cfgr.rhs;
    rhs_out.resize(nr);
    Hypergraph::TailNodeVector const& tails=e.tail_nodes_;
    int nvar=0;
    //split out into separate target_side, source_side loops?
    for (int j=0;j<nr;++j) {
      WordID w=rule_rhs[j];
      if (w>0)
        rhs_out[j]=w;
      else {
        int n=nt_index(nvar,tails,target_side,w);
        ++nvar;
        if (push_weights) crp*=np[n];
        rhs_out[j]=-n;
      }
    }
    assert(nvar==er.Arity());
    assert(nvar==tails.size());
  }
}

void CFG::Clear() {
  rules.clear();
  nts.clear();
  goal_nt=-1;
  hg_=0;
}

namespace {
CFGFormat form;
}

void CFG::PrintRule(std::ostream &o,RuleHandle rulei,CFGFormat const& f) const {
  Rule const& r=rules[rulei];
  f.print_lhs(o,*this,r.lhs);
  f.print_rhs(o,*this,r.rhs.begin(),r.rhs.end());
  f.print_features(o,r.p,r.f);
  IF_CFG_TRULE(if (r.rule) o<<f.partsep<<*r.rule;)
}
void CFG::PrintRule(std::ostream &o,RuleHandle rulei) const {
  PrintRule(o,rulei,form);
}
string CFG::ShowRule(RuleHandle i) const {
  ostringstream o;PrintRule(o,i);return o.str();
}

void CFG::Print(std::ostream &o,CFGFormat const& f) const {
  assert(!uninit);
  if (!f.goal_nt_name.empty()) {
    o << '['<<f.goal_nt_name <<']';
    WordID rhs=-goal_nt;
    f.print_rhs(o,*this,&rhs,&rhs+1);
    if (pushed_inside!=prob_t::One())
      f.print_features(o,pushed_inside);
    o<<'\n';
  }
  CFG_FOR_RULES(i,PrintRule(o,i,f);o<<'\n';)
}

void CFG::Print(std::ostream &o) const {
  Print(o,form);
}

std::ostream &operator<<(std::ostream &o,CFG const &x) {
  x.Print(o);
  return o;
}