main.cpp

#include "AlignmentUtil.h"
#include "Alignment.h"
#include "AlignmentApprox.h"
#include "AlignmentAeson.h"
#include "rapidjson/document.h"
#include "rapidjson/writer.h"
#include "rapidjson/reader.h"
#include "rapidjson/stringbuffer.h"
#include "rapidjson/filereadstream.h"
#include <iomanip>
#include <set>
#include <unordered_set>
#include <vector>
#include <iostream>
#include <sstream>
#include <fstream>
#include <cstdio>
#include <thread>
#include <chrono>
#include <ctime>
#include <math.h>

using namespace Alignment;
namespace js = rapidjson;
using namespace std;

double f(const int& i) { return 0.5*i; }


int main(int argc, char **argv)
{
	if (false)
	{
		Rational a, b;
		a = 5;
		cout << a << endl;
		b = a + 7;
		cout << b << endl;
		b = 0.75;
		cout << b << endl;
		a++;
		cout << a << endl;

		try
		{
			cout << Rational(2.0) << endl;
			cout << Rational(1.0/9.0) << endl;
		}
		catch (const std::exception& e)
		{
			cout << "caught exception: " << e.what() << endl << endl;
		}
	}

	if (false) 
	{
		Variable v1("aa");
		cout << v1 << endl;

		Variable v2(3);
		cout << v2 << endl;

		Variable v3(Variable("aa"), Variable(3));
		cout << v3 << endl;

		Variable v4(Variable("aa"), Variable(Variable("aa"), Variable(3)));
		cout << v4 << endl;

		Variable v5(Variable("aa"), Variable(Variable(3),Variable("aa")));
		cout << v5 << endl;

		cout << "v1 < v1 == " << (v1 < v1) << endl;
		cout << "v1 > v1 == " << (v1 > v1) << endl;
		cout << "v1 == v1 == " << (v1 == v1) << endl;

		cout << "v2 < v2 == " << (v2 < v2) << endl;
		cout << "v2 > v2 == " << (v2 > v2) << endl;
		cout << "v2 == v2 == " << (v2 == v2) << endl;

		cout << "v3 < v3 == " << (v3 < v3) << endl;
		cout << "v3 > v3 == " << (v3 > v3) << endl;
		cout << "v3 == v3 == " << (v3 == v3) << endl;

		cout << "v4 < v4 == " << (v4 < v4) << endl;
		cout << "v4 > v4 == " << (v4 > v4) << endl;
		cout << "v4 == v4 == " << (v4 == v4) << endl;

		cout << "v5 < v5 == " << (v5 < v5) << endl;
		cout << "v5 > v5 == " << (v5 > v5) << endl;
		cout << "v5 == v5 == " << (v5 == v5) << endl;

		cout << "v1 < v2 == " << (v1 < v2) << endl;
		cout << "v1 > v2 == " << (v1 > v2) << endl;
		cout << "v1 == v2 == " << (v1 == v2) << endl;

		cout << "v2 < v3 == " << (v2 < v3) << endl;
		cout << "v2 > v3 == " << (v2 > v3) << endl;
		cout << "v2 == v3 == " << (v2 == v3) << endl;

		cout << "v3 < v4 == " << (v3 < v4) << endl;
		cout << "v3 > v4 == " << (v3 > v4) << endl;
		cout << "v3 == v4 == " << (v3 == v4) << endl;

		cout << "v4 < v5 == " << (v4 < v5) << endl;
		cout << "v4 > v5 == " << (v4 > v5) << endl;
		cout << "v4 == v5 == " << (v4 == v5) << endl;

		set<Variable> vv1 = { v1,v2,v3,v4,v5 };
		cout << "vv1 =" << vv1 << endl;

		set<Variable> vv2 = { v5,v4,v3,v2,v1 };
		cout << "vv2 =" << vv2 << endl;

		cout << "v1.hash() == " << v1.hash() << endl;
		cout << "v2.hash() == " << v2.hash() << endl;
		cout << "v3.hash() == " << v3.hash() << endl;
		cout << "v4.hash() == " << v4.hash() << endl;
		cout << "v5.hash() == " << v5.hash() << endl;

		unordered_set<Variable> vv3 = { v5,v4,v3,v2,v1 };
		cout << "vv3 =" << vv3 << endl;
	}

	if (false) 
	{
		Value v1("aa");
		cout << v1 << endl;

		Value v2(3);
		cout << v2 << endl;

		Value v3(1.23);
		cout << v3 << endl;


		cout << "v1 < v1 == " << (v1 < v1) << endl;
		cout << "v1 > v1 == " << (v1 > v1) << endl;
		cout << "v1 == v1 == " << (v1 == v1) << endl;

		cout << "v2 < v2 == " << (v2 < v2) << endl;
		cout << "v2 > v2 == " << (v2 > v2) << endl;
		cout << "v2 == v2 == " << (v2 == v2) << endl;

		cout << "v3 < v3 == " << (v3 < v3) << endl;
		cout << "v3 > v3 == " << (v3 > v3) << endl;
		cout << "v3 == v3 == " << (v3 == v3) << endl;

		cout << "v1 < v2 == " << (v1 < v2) << endl;
		cout << "v1 > v2 == " << (v1 > v2) << endl;
		cout << "v1 == v2 == " << (v1 == v2) << endl;

		cout << "v2 < v3 == " << (v2 < v3) << endl;
		cout << "v2 > v3 == " << (v2 > v3) << endl;
		cout << "v2 == v3 == " << (v2 == v3) << endl;

		set<Value> vv1 = { v1,v2,v3 };
		cout << "vv1 =" << vv1 << endl;

		set<Value> vv2 = { v3,v2,v1 };
		cout << "vv2 =" << vv2 << endl;

		cout << "v1.hash() == " << v1.hash() << endl;
		cout << "v2.hash() == " << v2.hash() << endl;
		cout << "v3.hash() == " << v3.hash() << endl;

		unordered_set<Value> vv3 = { v3,v2,v1 };
		cout << "vv3 =" << vv3 << endl;
	}

	if (false)
	{
		Id v1("aa");
		cout << v1 << endl;

		Id v2(3);
		cout << v2 << endl;

		cout << "v1 < v1 == " << (v1 < v1) << endl;
		cout << "v1 > v1 == " << (v1 > v1) << endl;
		cout << "v1 == v1 == " << (v1 == v1) << endl;

		cout << "v2 < v2 == " << (v2 < v2) << endl;
		cout << "v2 > v2 == " << (v2 > v2) << endl;
		cout << "v2 == v2 == " << (v2 == v2) << endl;

		cout << "v1 < v2 == " << (v1 < v2) << endl;
		cout << "v1 > v2 == " << (v1 > v2) << endl;
		cout << "v1 == v2 == " << (v1 == v2) << endl;

		set<Id> vv1 = { v1,v2 };
		cout << "vv1 =" << vv1 << endl;

		set<Id> vv2 = { v2,v1 };
		cout << "vv2 =" << vv2 << endl;

		cout << "v1.hash() == " << v1.hash() << endl;
		cout << "v2.hash() == " << v2.hash() << endl;

		unordered_set<Id> vv3 = { v2,v1 };
		cout << "vv3 =" << vv3 << endl;
	}

	if (false)
	{
		auto suit = Variable("suit");
		auto rank = Variable("rank");

		auto vv = vector<Variable>{ suit, rank };

		cout << vv << endl;
	}

	if (false)
	{
		auto suit = Variable("suit");
		auto rank = Variable("rank");

		auto vv = VarUSet{ suit,rank };

		cout << "vv" << endl 
			<< sorted(vv) << endl << endl;

		auto hearts = Value("hearts");
		auto clubs = Value("clubs");
		auto diamonds = Value("diamonds");
		auto spades = Value("spades");

		auto wws = ValSet{hearts,clubs,diamonds,spades};

		cout << "wws" << endl 
			<< wws << endl << endl;

		auto jack = Value("J");
		auto queen = Value("Q");
		auto king = Value("K");
		auto ace = Value("A");

		auto wwr = ValSet{jack,queen,king,ace };
		for (int i = 2; i <= 10; i++)
			wwr.insert(Value(i));

		cout << "wwr" << endl 
			<< wwr << endl << endl;

		auto uu = listsSystem_u(std::vector<VarValSetPair> {VarValSetPair(suit,wws), VarValSetPair(rank,wwr)});

		cout << "uu" << endl 
			<< *uu << endl << endl;

		cout << "rpln(cout,systemsList(uu))" << endl;
		rpln(cout,*systemsList(*uu)); cout << endl;

		//auto uu1 = listsSystem_u(std::vector<VarValUSetPair> {VarValUSetPair(suit, wws)});
		//auto uu2 = listsSystem_u(std::vector<VarValUSetPair> {VarValUSetPair(rank, wwr)});

		//cout << pairSystemsUnion(uu1,uu2) << endl;

		auto uvars = systemsSetVar;
		cout << "uvars(uu)" << endl 
			<< sorted(*uvars(*uu)) << endl << endl;

		auto uat = systemsVarsSetValue;
		cout << "uat(uu,suit)" << endl
			<< uat(*uu,suit) << endl << endl;
		cout << "uat(uu,suit).size()" << endl
			<< uat(*uu,suit).size() << endl << endl;
		cout << "uat(uu,rank).size()" << endl
			<< uat(*uu,rank).size() << endl << endl;

		auto vol = systemsSetVarsVolume_u;
		cout << "vol(uu,vv)" << endl
			<< vol(*uu,vv) << endl << endl;
		cout << "vol(uu,VarUSet{suit})" << endl
			<< vol(*uu,VarUSet{suit}) << endl << endl;
		cout << "vol(uu,VarUSet{rank})" << endl
			<< vol(*uu,VarUSet{rank}) << endl << endl;

		auto sysreg = systemRegular_u;

		auto uu1 = sysreg(3, 2);
		cout << "uu1" << endl
			<< *uu1 << endl << endl;
		cout << "vol(uu1,uvars(uu1))" << endl
			<< vol(*uu1,*uvars(*uu1)) << endl << endl;

		auto llss = listsState;
		auto ssll = statesList;

		auto ss = llss(std::vector<VarValPair>{VarValPair(suit, spades), VarValPair(rank, ace)});
		cout << "ss" << endl
			<< *ss << endl << endl;
		cout << "rpln(cout,ssll(ss))" << endl;
		rpln(cout,*ssll(*ss)); cout << endl;

		auto svars = statesSetVar;
		cout << "svars(ss)" << endl
			<< sorted(*svars(*ss)) << endl << endl;

		auto sat = statesVarsValue;
		cout << "sat(ss,suit)" << endl
			<< sat(*ss,suit) << endl << endl;

		cout << "svars(stateEmpty())" << endl
			<< sorted(*svars(stateEmpty())) << endl << endl;

		auto cart = systemsSetVarsSetStateCartesian_u;
		cout << "rpln(cout,cart(uu,vv))" << endl;
		rpln(cout,sorted(*cart(*uu,vv))); cout << endl;
		cout << "cart(uu,vv).size()" << endl
			<< cart(*uu, vv)->size() << endl << endl;
		cout << "vol(uu,vv)" << endl
			<< vol(*uu,vv) << endl << endl;

		auto sred = [](const State& ss, const VarUSet& vv) 
		{
			return setVarsStatesStateFiltered(vv,ss);
		};
		cout << "sred(ss,svars(ss))" << endl
			<< *sred(*ss,*svars(*ss)) << endl << endl;
		cout << "sred(ss,set())" << endl
			<< *sred(*ss,VarUSet()) << endl << endl;
		cout << "sred(ss,set([suit]))" << endl
			<< *sred(*ss,VarUSet{suit}) << endl << endl;
		cout << "sred(ss,set([rank]))" << endl
			<< *sred(*ss,VarUSet{rank}) << endl << endl;

		auto ssplit = setVarsSetStatesSplit;
		cout << "rpln(ssplit(sset([suit]),cart(uu,vv)))" << endl;
		rpln(cout,*ssplit(VarUSet{suit},*cart(*uu,vv))); cout << endl;
	}

	if (false)
	{
		auto cart = systemsSetVarsSetStateCartesian_u;

		auto suit = Variable("suit");
		auto rank = Variable("rank");
		auto vv = VarUSet{suit,rank};
		auto hearts = Value("hearts");
		auto clubs = Value("clubs");
		auto diamonds = Value("diamonds");
		auto spades = Value("spades");
		auto wws = ValSet{hearts,clubs,diamonds,spades};
		auto jack = Value("J");
		auto queen = Value("Q");
		auto king = Value("K");
		auto ace = Value("A");
		auto wwr = ValSet{jack,queen,king,ace};
		for (int i = 2; i <= 10; i++)
			wwr.insert(Value(i));
		auto uu = listsSystem_u(std::vector<VarValSetPair>{VarValSetPair(suit,wws),VarValSetPair(rank,wwr)});

		auto llhh = listsHistory_u;
		auto hhll = historiesList;

		std::vector<IdStatePair> ll;
		{
			auto qq = cart(*uu,vv);
			int i = 1;
			for (auto ss : *qq)
				ll.push_back(IdStatePair(Id(i++),ss));
		}
		auto hh = llhh(ll);

		cout << "hh" << endl
			<< *hh << endl << endl;
		cout << "rpln(hhll(hh))" << endl;
		rpln(cout,*hhll(*hh)); cout << endl;

		auto hvars = historiesSetVar;
		cout << "hvars(hh)" << endl
			<< sorted(*hvars(*hh)) << endl << endl;

		auto hred = [](const History& hh, const VarUSet& vv)
		{
			return setVarsHistoriesReduce(vv, hh);
		};
		cout << "rpln(hhll(hred(hh,set([suit])))" << endl;
		rpln(cout, *hhll(*hred(*hh, VarUSet{ suit }))); cout << endl;
		cout << "rpln(hhll(hred(hh,set([rank])))" << endl;
		rpln(cout, *hhll(*hred(*hh, VarUSet{ rank }))); cout << endl;

		auto hsize = historiesSize;
		cout << "hsize(hh)" << endl
			<< hsize(*hh) << endl << endl;

		auto hsys = historiesSystemImplied;

		cout << "hsys(hh)" << endl
			<< *hsys(*hh) << endl << endl;
	}

	if (true)
	{
		auto cart = systemsSetVarsSetStateCartesian_u;

		auto suit = Variable("suit");
		auto rank = Variable("rank");
		auto vv = VarUSet{ suit,rank };
		auto hearts = Value("hearts");
		auto clubs = Value("clubs");
		auto diamonds = Value("diamonds");
		auto spades = Value("spades");
		auto wws = ValSet{ hearts,clubs,diamonds,spades };
		auto jack = Value("J");
		auto queen = Value("Q");
		auto king = Value("K");
		auto ace = Value("A");
		auto wwr = ValSet{ jack,queen,king,ace };
		for (int i = 2; i <= 10; i++)
			wwr.insert(Value(i));
		auto uu = listsSystem_u(std::vector<VarValSetPair>{VarValSetPair(suit, wws), VarValSetPair(rank, wwr)});

		auto llaa = listsHistogram_u;
		auto aall = histogramsList;

		std::vector<StateRationalPair> ll;
		{
			auto qq = cart(*uu, vv);
			for (auto ss : *qq)
				ll.push_back(StateRationalPair(ss,1.0));
		}
		auto aa = llaa(ll);

		cout << "aa" << endl
			<< *aa << endl << endl;
		cout << "rpln(aall(aa))" << endl;
		rpln(cout, sorted(*aall(*aa))); cout << endl;

		auto vars = histogramsSetVar;
		cout << "vars(aa)" << endl
			<< sorted(*vars(*aa)) << endl << endl;

		auto reframe = histogramsMapVarsFrame_u;

		auto mm = VarVarUMap{{suit,Variable("S")},{rank,Variable("R")}};
		cout << "rpln(aall(reframe(aa,mm)))" << endl;
		rpln(cout, sorted(*aall(*reframe(*aa,mm)))); cout << endl;
		cout << "vars(reframe(aa,mm))" << endl
			<< sorted(*vars(*reframe(*aa, mm))) << endl << endl;

		auto states = histogramsStates;
		cout << "rpln(states(aa))" << endl;
		rpln(cout, sorted(*states(*aa))); cout << endl;

		auto aat = histogramsStatesCount;
		auto ss = State(std::vector<VarValPair>{VarValPair(suit,spades),VarValPair(rank,ace)});

		cout << "ss" << endl
			<< ss << endl << endl;
		cout << "aat(aa,ss)" << endl
			<< aat(*aa,ss) << endl << endl;

		auto size = histogramsSize;
		cout << "size(aa)" << endl
			<< size(*aa) << endl << endl;

		auto norm = [](const Histogram& aa)
		{
			return histogramsResize(1, aa);
		};
		cout << "rpln(aall(norm(aa)))" << endl;
		rpln(cout, sorted(*aall(*norm(*aa)))); cout << endl;
		cout << "size(norm(aa))" << endl
			<< size(*norm(*aa)) << endl << endl;

		auto scalar = histogramScalar_u;

		cout << "scalar(52)" << endl
			<< *scalar(52) << endl << endl;

		auto single = histogramSingleton_u;
		auto rr = State(std::vector<VarValPair>{VarValPair(suit, hearts), VarValPair(rank, queen)});

		cout << "single(ss,1)" << endl
			<< *single(ss, 1) << endl << endl;
		cout << "single(rr,1)" << endl
			<< *single(rr, 1) << endl << endl;

		auto unit = setStatesHistogramUnit_u;
		cout << "rpln(aall(unit(cart(uu,vv))))" << endl;
		rpln(cout, sorted(*aall(*unit(*cart(*uu, vv))))); cout << endl;
		cout << "rpln(aall(unit(StateUSet{rr,ss})))" << endl;
		rpln(cout, sorted(*aall(*unit(StateUSet{ rr,ss })))); cout << endl;

		auto trim = histogramsTrim;
		cout << "rpln(aall(trim(llaa([(ss, 3), (rr, 0)]))))" << endl;
		rpln(cout, sorted(*aall(*trim(*llaa(std::vector<StateRationalPair>{StateRationalPair(ss, 3), StateRationalPair(rr, 0)}))))); cout << endl;
		cout << "rpln(aall(trim(llaa([(ss, 3), (rr, 5)]))))" << endl;
		rpln(cout, sorted(*aall(*trim(*llaa(std::vector<StateRationalPair>{StateRationalPair(ss, 3), StateRationalPair(rr, 5)}))))); cout << endl;

		auto eff = histogramsEffective;
		cout << "rpln(aall(eff(llaa([(ss, 3), (rr, 0)]))))" << endl;
		rpln(cout, sorted(*aall(*eff(*llaa(std::vector<StateRationalPair>{StateRationalPair(ss, 3), StateRationalPair(rr, 0)}))))); cout << endl;
		cout << "rpln(aall(eff(llaa([(ss, 3), (rr, 5)]))))" << endl;
		rpln(cout, sorted(*aall(*eff(*llaa(std::vector<StateRationalPair>{StateRationalPair(ss, 3), StateRationalPair(rr, 5)}))))); cout << endl;

		auto regcart = histogramRegularCartesian_u;
		cout << "rpln(aall(regcart(3,2)))" << endl;
		rpln(cout, sorted(*aall(*regcart(3, 2)))); cout << endl;

		auto regsing = histogramRegularUnitSingleton_u;
		cout << "rpln(aall(regsing(3,2)))" << endl;
		rpln(cout, sorted(*aall(*regsing(3, 2)))); cout << endl;

		auto regdiag = histogramRegularUnitDiagonal_u;
		cout << "rpln(aall(regdiag(3,2)))" << endl;
		rpln(cout, sorted(*aall(*regdiag(3, 2)))); cout << endl;

		auto regpivot = histogramRegularUnitPivot_u;
		cout << "rpln(aall(regpivot(1,2)))" << endl;
		rpln(cout, sorted(*aall(*regpivot(1, 2)))); cout << endl;
		cout << "rpln(aall(regpivot(3,2)))" << endl;
		rpln(cout, sorted(*aall(*regpivot(3, 2)))); cout << endl;
		cout << "rpln(aall(regpivot(3,4)))" << endl;
		rpln(cout, sorted(*aall(*regpivot(3, 4)))); cout << endl;

		auto sys = histogramsSystemImplied;

		cout << "sys(regcart(3,2))" << endl
			<< *sys(*regcart(3, 2)) << endl << endl;

		cout << "sys(regsing(3,2))" << endl
			<< *sys(*regsing(3, 2)) << endl << endl;

		cout << "sys(regdiag(3,2))" << endl
			<< *sys(*regdiag(3, 2)) << endl << endl;

		auto hhll = historiesList;
		auto hhaa = historiesHistogram;
		auto aahh = histogramsHistory_u;

		cout << "rpln(hhll(aahh(aa)))" << endl;
		rpln(cout, *hhll(*aahh(*aa))); cout << endl;
		cout << "rpln(aall(hhaa(aahh(aa))))" << endl;
		rpln(cout, sorted(*aall(*hhaa(*aahh(*aa))))); cout << endl;

		auto ared = [](const Histogram& aa, const VarUSet& vv)
		{
			return setVarsHistogramsReduce(vv, aa);
		};
		cout << "rpln(aall(ared(aa,sset([suit]))))" << endl;
		rpln(cout, sorted(*aall(*ared(*aa, VarUSet{suit})))); cout << endl;
		cout << "rpln(aall(ared(aa,sset([rank]))))" << endl;
		rpln(cout, sorted(*aall(*ared(*aa, VarUSet{ rank })))); cout << endl;
		cout << "rpln(aall(ared(aa,sset([]))))" << endl;
		rpln(cout, sorted(*aall(*ared(*aa, VarUSet())))); cout << endl;
		cout << "rpln(aall(ared(aa,vars(aa))))" << endl;
		rpln(cout, sorted(*aall(*ared(*aa,*vars(*aa))))); cout << endl;

		auto bb = single(State(std::vector<VarValPair>{VarValPair(suit, spades), VarValPair(rank, ace)}),1);

		auto cc = llaa(std::vector<StateRationalPair>{StateRationalPair(State(std::vector<VarValPair>{VarValPair(suit, spades), VarValPair(rank, ace)}), 1), StateRationalPair(State(std::vector<VarValPair>{VarValPair(suit, hearts), VarValPair(rank, queen)}), 1)});

		auto dd = llaa(std::vector<StateRationalPair>{StateRationalPair(State(std::vector<VarValPair>{VarValPair(suit, spades), VarValPair(rank, ace)}), 1), StateRationalPair(State(std::vector<VarValPair>{VarValPair(suit, hearts), VarValPair(rank, queen)}), 2)});

		auto add = pairHistogramsAdd_u;

		cout << "bb" << endl
			<< *bb << endl << endl;
		cout << "cc" << endl
			<< *cc << endl << endl;
		cout << "dd" << endl
			<< *dd << endl << endl;
		cout << "add(bb,cc)" << endl
			<< *add(*bb, *cc) << endl << endl;
		cout << "add(cc,dd)" << endl
			<< *add(*cc, *dd) << endl << endl;
		cout << "add(bb,add(cc,dd))" << endl
			<< *add(*bb, *add(*cc, *dd)) << endl << endl;

		auto mul = pairHistogramsMultiply;

		auto colour = Variable("colour");
		auto red = Value("red");
		auto black = Value("black");

		bb = llaa(std::vector<StateRationalPair>{StateRationalPair(State(std::vector<VarValPair>{VarValPair(suit, hearts), VarValPair(colour, red)}), 1), StateRationalPair(State(std::vector<VarValPair>{VarValPair(suit, clubs), VarValPair(colour, black)}), 1), StateRationalPair(State(std::vector<VarValPair>{VarValPair(suit, diamonds), VarValPair(colour, red)}), 1), StateRationalPair(State(std::vector<VarValPair>{VarValPair(suit, spades), VarValPair(colour, black)}), 1)});

		cout << "rpln(aall(bb))" << endl;
		rpln(cout, sorted(*aall(*bb))); cout << endl;
		cout << "rpln(aall(mul(aa,bb)))" << endl;
		rpln(cout, sorted(*aall(*mul(*aa, *bb)))); cout << endl;
		cout << "rpln(aall(ared(mul(aa,bb),sset([rank,colour]))))" << endl;
		rpln(cout, sorted(*aall(*ared(*mul(*aa,*bb), VarUSet{ rank, colour })))); cout << endl;
		cout << "rpln(aall(ared(mul(aa,bb),sset([colour]))))" << endl;
		rpln(cout, sorted(*aall(*ared(*mul(*aa, *bb), VarUSet{ colour })))); cout << endl;

		auto coin = Variable("coin");
		auto heads = Value("heads");
		auto tails = Value("tails");

		cc = llaa(std::vector<StateRationalPair>{StateRationalPair(State(std::vector<VarValPair>{VarValPair(coin, heads)}), 1), StateRationalPair(State(std::vector<VarValPair>{VarValPair(coin, tails)}), 1)});

		cout << "rpln(aall(cc))" << endl;
		rpln(cout, sorted(*aall(*cc))); cout << endl;
		cout << "rpln(aall(mul(aa,cc)))" << endl;
		rpln(cout, sorted(*aall(*mul(*aa, *cc)))); cout << endl;
		cout << "rpln(aall(ared(mul(aa,cc),sset([coin]))))" << endl;
		rpln(cout, sorted(*aall(*ared(*mul(*aa, *cc), VarUSet{ coin })))); cout << endl;

		auto ind = histogramsIndependent;
		cout << "rpln(aall(ind(aa)))" << endl;
		rpln(cout, sorted(*aall(*ind(*aa)))); cout << endl;
		cout << "size(ind(aa))" << endl
			<< size(*ind(*aa)) << endl << endl;
		cout << "rpln(aall(ind(regdiag(2,2))))" << endl;
		rpln(cout, sorted(*aall(*ind(*regdiag(2, 2))))); cout << endl;
		cout << "rpln(aall(ind(regsing(2,2))))" << endl;
		rpln(cout, sorted(*aall(*ind(*regsing(2, 2))))); cout << endl;
		cout << "rpln(aall(ind(regcart(2,2))))" << endl;
		rpln(cout, sorted(*aall(*ind(*regcart(2, 2))))); cout << endl;
	}

	if (false)
	{
		auto uvars = systemsSetVar;
		auto cart = systemsSetVarsSetStateCartesian_u;
		auto vol = systemsSetVarsVolume_u;
		auto ssplit = [](const VarUSet& vv, const Histogram& aa)
		{
			return setVarsSetStatesSplit(vv, *histogramsStates(aa));
		};
		typedef std::pair<int, ValList> IntValListPair;
		typedef std::vector<IntValListPair> IntValListPairList;
		auto llhh = [](const VarList& vv, const IntValListPairList& ee)
		{
			std::vector<IdStatePair> ii;
			for (auto& pp : ee)
			{
				auto i = pp.first;
				auto& ll = pp.second;
				auto jj = std::vector<VarValPair>();
				for (int j = 0; j < ll.size(); j++)
					jj.push_back(VarValPair(vv[j], ll[j]));
				ii.push_back(IdStatePair(Id(i), *listsState(jj)));
			}
			return listsHistory_u(ii);
		};
		auto hhll = historiesList;
		auto hvars = historiesSetVar;
		auto hsize = historiesSize;
		auto hred = [](const History& hh, const VarUSet& vv)
		{
			return setVarsHistoriesReduce(vv, hh);
		};
		auto hhaa = historiesHistogram;
		auto aahh = histogramsHistory_u;
		auto aall = histogramsList;
		auto vars = histogramsSetVar;
		auto size = histogramsSize;
		auto unit = setStatesHistogramUnit_u;
		auto norm = [](const Histogram& aa)
		{
			return histogramsResize(1, aa);
		};
		auto ared = [](const Histogram& aa, const VarUSet& vv)
		{
			return setVarsHistogramsReduce(vv, aa);
		};
		auto ind = histogramsIndependent;

		auto pressure = Variable("pressure");
		auto cloud = Variable("cloud");
		auto wind = Variable("wind");
		auto rain = Variable("rain");
		auto low = Value("low");
		auto medium = Value("medium");
		auto high = Value("high");
		auto none = Value("none");
		auto light = Value("light");
		auto heavy = Value("heavy");
		auto strong = Value("strong");

		auto uu = listsSystem_u(std::vector<VarValSetPair>{
			VarValSetPair(pressure, ValSet{ low,medium,high }),
				VarValSetPair(cloud, ValSet{ none,light,heavy }),
				VarValSetPair(wind, ValSet{ none,light,strong }),
				VarValSetPair(rain, ValSet{ none,light,heavy })});

		cout << "uu" << endl
			<< *uu << endl << endl;

		cout << "uvars(uu)" << endl
			<< sorted(*uvars(*uu)) << endl << endl;

		auto vv = uvars(*uu);

		cout << "vol(uu,vv)" << endl
			<< vol(*uu, *vv) << endl << endl;

		auto hh = llhh(VarList{ pressure, cloud, wind, rain }, IntValListPairList{
			IntValListPair(1, ValList{high, none, none, none}),
			IntValListPair(2, ValList{medium, light, none, light}),
			IntValListPair(3, ValList{high, none, light, none}),
			IntValListPair(4, ValList{low, heavy, strong, heavy}),
			IntValListPair(5, ValList{low, none, light, light}),
			IntValListPair(6, ValList{medium, none, light, light}),
			IntValListPair(7, ValList{low, heavy, light, heavy}),
			IntValListPair(8, ValList{high, none, light, none}),
			IntValListPair(9, ValList{medium, light, strong, heavy}),
			IntValListPair(10, ValList{medium, light, light, light}),
			IntValListPair(11, ValList{high, light, light, heavy}),
			IntValListPair(12, ValList{medium, none, none, none}),
			IntValListPair(13, ValList{medium, light, none, none}),
			IntValListPair(14, ValList{high, light, strong, light}),
			IntValListPair(15, ValList{medium, none, light, light}),
			IntValListPair(16, ValList{low, heavy, strong, heavy}),
			IntValListPair(17, ValList{low, heavy, light, heavy}),
			IntValListPair(18, ValList{high, none, none, none}),
			IntValListPair(19, ValList{low, light, none, light}),
			IntValListPair(20, ValList{high, none, none, none})});

		cout << "rpln(hhll(hh))" << endl;
		rpln(cout, sorted(*hhll(*hh))); cout << endl;

		cout << "hvars(hh)" << endl
			<< sorted(*hvars(*hh)) << endl << endl;

		cout << "hsize(hh)" << endl
			<< hsize(*hh) << endl << endl;

		cout << "rpln(hhll(hred(hh,[pressure,rain])))" << endl;
		rpln(cout, *hhll(*hred(*hh, VarUSet{ pressure,rain }))); cout << endl;

		auto aa = hhaa(*hh);
		cout << "rpln(aall(aa))" << endl;
		rpln(cout, sorted(*aall(*aa))); cout << endl;

		cout << "vars(aa)" << endl
			<< sorted(*vars(*aa)) << endl << endl;

		cout << "size(aa)" << endl
			<< size(*aa) << endl << endl;

		cout << "size(unit(cart(uu,vv)))" << endl
			<< size(*unit(*cart(*uu, *vv))) << endl << endl;

		cout << "rpln(aall(norm(aa)))" << endl;
		rpln(cout, sorted(*aall(*norm(*aa)))); cout << endl;

		cout << "rpln(aall(red(aa,[pressure,rain])))" << endl;
		rpln(cout, sorted(*aall(*ared(*aa, VarUSet{ pressure,rain })))); cout << endl;

		cout << "rpln(ssplit([pressure],red(aa,[pressure,rain]))))" << endl;
		rpln(cout, *ssplit(VarUSet{ pressure }, *ared(*aa, VarUSet{ pressure,rain }))); cout << endl;

		cout << "rpln(aall(red(aa,[cloud,wind,rain])))" << endl;
		rpln(cout, sorted(*aall(*ared(*aa, VarUSet{ cloud,wind,rain })))); cout << endl;

		cout << "rpln(ssplit([cloud,wind],red(aa,[cloud,wind,rain])))" << endl;
		rpln(cout, *ssplit(VarUSet{ cloud,wind }, *ared(*aa, VarUSet{ cloud,wind,rain }))); cout << endl;

		cout << "rpln(aall(red(aa,[pressure])))" << endl;
		rpln(cout, sorted(*aall(*ared(*aa, VarUSet{ pressure })))); cout << endl;

		cout << "rpln(aall(red(aa,[cloud])))" << endl;
		rpln(cout, sorted(*aall(*ared(*aa, VarUSet{ cloud })))); cout << endl;

		cout << "rpln(aall(red(aa,[wind])))" << endl;
		rpln(cout, sorted(*aall(*ared(*aa, VarUSet{ wind })))); cout << endl;

		cout << "rpln(aall(red(aa,[rain])))" << endl;
		rpln(cout, sorted(*aall(*ared(*aa, VarUSet{ rain })))); cout << endl;

		cout << "rpln(aall(ind(aa)))" << endl;
		rpln(cout, sorted(*aall(*ind(*aa)))); cout << endl;

	}

	if (false)
	{
		auto lluu = listsSystem_u;
		auto cart = systemsSetVarsSetStateCartesian_u;
		auto unit = setStatesHistogramUnit_u;
		auto aall = histogramsList;
		auto size = histogramsSize;
		auto resize = histogramsResize;
		auto norm = [](const Histogram& aa)
		{
			return histogramsResize(1, aa);
		};
		auto add = pairHistogramsAdd_u;
		auto scalar = histogramScalar_u;
		auto regsing = histogramRegularUnitSingleton_u;
		auto regdiag = histogramRegularUnitDiagonal_u;
		auto regcart = histogramRegularCartesian_u;
		auto ent = histogramsEntropy;
		auto ared = [](const Histogram& aa, const VarUSet& vv)
		{
			return setVarsHistogramsReduce(vv, aa);
		};
		auto lent = [size, ent, ared](const VarUSet& vv, const Histogram& aa)
		{
			return size(aa).getDouble() * (ent(aa) - ent(*ared(aa, vv)));
		};
		auto algn = histogramsAlignment;

		auto suit = Variable("suit");
		auto rank = Variable("rank");
		auto vv = VarUSet{ suit,rank };
		auto hearts = Value("hearts");
		auto clubs = Value("clubs");
		auto diamonds = Value("diamonds");
		auto spades = Value("spades");
		auto wws = ValSet{ hearts,clubs,diamonds,spades };
		auto jack = Value("J");
		auto queen = Value("Q");
		auto king = Value("K");
		auto ace = Value("A");
		auto wwr = ValSet{ jack,queen,king,ace };
		for (int i = 2; i <= 10; i++)
			wwr.insert(Value(i));
		auto uu = lluu(std::vector<VarValSetPair>{VarValSetPair(suit, wws), VarValSetPair(rank, wwr)});

		cout << "uu" << endl
			<< *uu << endl << endl;

		cout << "vv" << endl
			<< sorted(vv) << endl << endl;

		auto aa = unit(*cart(*uu, vv));
		cout << "rpln(aall(aa))" << endl;
		rpln(cout, sorted(*aall(*aa))); cout << endl;

		cout << "ent(aa)" << endl
			<< setprecision(17) << ent(*aa) << endl << endl;

		double z = size(*aa).getDouble();

		cout << "z * ent(aa)" << endl
			<< setprecision(17) << z * ent(*aa) << endl << endl;

		cout << "ent(regsing(2,2))" << endl
			<< setprecision(17) << ent(*regsing(2, 2)) << endl << endl;

		cout << "lent([suit, rank],aa)" << endl
			<< setprecision(17) << lent(VarUSet{ suit, rank }, *aa) << endl << endl;

		cout << "lent([],aa)" << endl
			<< setprecision(17) << lent(VarUSet{}, *aa) << endl << endl;

		cout << "lent([suit],aa)" << endl
			<< setprecision(17) << lent(VarUSet{ suit }, *aa) << endl << endl;

		cout << "lent([rank],aa)" << endl
			<< setprecision(17) << lent(VarUSet{ rank }, *aa) << endl << endl;

		aa = norm(*regsing(3, 2));
		aa = add(*aa, *norm(*regdiag(3, 2)));
		aa = add(*aa, *norm(*regcart(3, 2)));
		aa = resize(100, *aa);

		cout << "rpln(aall(aa))" << endl;
		rpln(cout, sorted(*aall(*aa))); cout << endl;

		cout << "algn(aa)" << endl
			<< setprecision(17) << algn(*aa) << endl << endl;

		cout << "algn(scalar(100))" << endl
			<< setprecision(17) << algn(*scalar(100)) << endl << endl;
		cout << "algn(resize(100,regdiag(3,1)))" << endl
			<< setprecision(17) << algn(*resize(100, *regdiag(3, 1))) << endl << endl;
		cout << "algn(resize(100,regcart(3,3)))" << endl
			<< setprecision(17) << algn(*resize(100, *regcart(3, 3))) << endl << endl;
		cout << "algn(resize(100,regsing(3,3)))" << endl
			<< setprecision(17) << algn(*resize(100, *regsing(3, 3))) << endl << endl;

		cout << "algn(resize(100,regdiag(3,2)))" << endl
			<< setprecision(17) << algn(*resize(100, *regdiag(3, 2))) << endl << endl;
	}

	if (false)
	{
		auto uvars = systemsSetVar;
		auto cart = systemsSetVarsSetStateCartesian_u;
		auto vol = systemsSetVarsVolume_u;
		auto ssplit = [](const VarUSet& vv, const Histogram& aa)
		{
			return setVarsSetStatesSplit(vv, *histogramsStates(aa));
		};

		auto llhh = [](const VarList& vv, const IntValListPairList& ee)
		{
			std::vector<IdStatePair> ii;
			for (auto& pp : ee)
			{
				auto i = pp.first;
				auto& ll = pp.second;
				auto jj = std::vector<VarValPair>();
				for (int j = 0; j < ll.size(); j++)
					jj.push_back(VarValPair(vv[j], ll[j]));
				ii.push_back(IdStatePair(Id(i), *listsState(jj)));
			}
			return listsHistory_u(ii);
		};
		auto hhll = historiesList;
		auto hvars = historiesSetVar;
		auto hsize = historiesSize;
		auto hred = [](const History& hh, const VarUSet& vv)
		{
			return setVarsHistoriesReduce(vv, hh);
		};
		auto hhaa = historiesHistogram;
		auto aahh = histogramsHistory_u;
		auto aall = histogramsList;
		auto vars = histogramsSetVar;
		auto size = histogramsSize;
		auto unit = setStatesHistogramUnit_u;
		auto norm = [](const Histogram& aa)
		{
			return histogramsResize(1, aa);
		};
		auto ared = [](const Histogram& aa, const VarUSet& vv)
		{
			return setVarsHistogramsReduce(vv, aa);
		};
		auto ind = histogramsIndependent;
		auto ent = histogramsEntropy;
		auto lent = [size, ent, ared](const VarUSet& vv, const Histogram& aa)
		{
			return size(aa).getDouble() * (ent(aa) - ent(*ared(aa, vv)));
		};
		auto algn = histogramsAlignment;

		auto pressure = Variable("pressure");
		auto cloud = Variable("cloud");
		auto wind = Variable("wind");
		auto rain = Variable("rain");
		auto low = Value("low");
		auto medium = Value("medium");
		auto high = Value("high");
		auto none = Value("none");
		auto light = Value("light");
		auto heavy = Value("heavy");
		auto strong = Value("strong");
		auto uu = listsSystem_u(std::vector<VarValSetPair>{
			VarValSetPair(pressure, ValSet{ low,medium,high }),
				VarValSetPair(cloud, ValSet{ none,light,heavy }),
				VarValSetPair(wind, ValSet{ none,light,strong }),
				VarValSetPair(rain, ValSet{ none,light,heavy })});
		auto vv = uvars(*uu);
		auto hh = llhh(VarList{ pressure, cloud, wind, rain }, IntValListPairList{
			IntValListPair(1, ValList{ high, none, none, none }),
			IntValListPair(2, ValList{ medium, light, none, light }),
			IntValListPair(3, ValList{ high, none, light, none }),
			IntValListPair(4, ValList{ low, heavy, strong, heavy }),
			IntValListPair(5, ValList{ low, none, light, light }),
			IntValListPair(6, ValList{ medium, none, light, light }),
			IntValListPair(7, ValList{ low, heavy, light, heavy }),
			IntValListPair(8, ValList{ high, none, light, none }),
			IntValListPair(9, ValList{ medium, light, strong, heavy }),
			IntValListPair(10, ValList{ medium, light, light, light }),
			IntValListPair(11, ValList{ high, light, light, heavy }),
			IntValListPair(12, ValList{ medium, none, none, none }),
			IntValListPair(13, ValList{ medium, light, none, none }),
			IntValListPair(14, ValList{ high, light, strong, light }),
			IntValListPair(15, ValList{ medium, none, light, light }),
			IntValListPair(16, ValList{ low, heavy, strong, heavy }),
			IntValListPair(17, ValList{ low, heavy, light, heavy }),
			IntValListPair(18, ValList{ high, none, none, none }),
			IntValListPair(19, ValList{ low, light, none, light }),
			IntValListPair(20, ValList{ high, none, none, none }) });
		auto aa = hhaa(*hh);

		cout << "size(aa)" << endl
			<< size(*aa) << endl << endl;

		double z = size(*aa).getDouble();

		cout << "z * ent(aa)" << endl
			<< setprecision(17) << z * ent(*aa) << endl << endl;

		cout << "z * ent(ind(aa))" << endl
			<< setprecision(17) << z * ent(*ind(*aa)) << endl << endl;

		cout << "algn(aa)" << endl
			<< setprecision(17) << algn(*aa) << endl << endl;

		cout << "algn(red(aa,[pressure,rain]))" << endl
			<< setprecision(17) << algn(*ared(*aa, VarUSet{ pressure, rain })) << endl << endl;

		cout << "algn(red(aa,[pressure,cloud]))" << endl
			<< setprecision(17) << algn(*ared(*aa, VarUSet{ pressure,cloud })) << endl << endl;

		cout << "lent([pressure],red(aa,[pressure,rain]))" << endl
			<< setprecision(17) << lent(VarUSet{ pressure }, *ared(*aa, VarUSet{ pressure, rain })) << endl << endl;

	}
	
	if (false)
	{
		auto lluu = listsSystem_u;
		auto cart = systemsSetVarsSetStateCartesian_u;
		auto llss = listsState;
		auto unit = setStatesHistogramUnit_u;
		auto aall = histogramsList;
		auto size = histogramsSize;
		auto resize = histogramsResize;
		auto norm = [](const Histogram& aa)
		{
			return histogramsResize(1, aa);
		};
		auto add = pairHistogramsAdd_u;
		auto scalar = histogramScalar_u;
		auto regsing = histogramRegularUnitSingleton_u;
		auto regdiag = histogramRegularUnitDiagonal_u;
		auto regcart = histogramRegularCartesian_u;
		auto ared = [](const Histogram& aa, const VarUSet& vv)
		{
			return setVarsHistogramsReduce(vv, aa);
		};
		auto llhh = [llss](const VarList& vv, const IntValListPairList& ee)
		{
			std::vector<IdStatePair> ii;
			for (auto& pp : ee)
			{
				auto i = pp.first;
				auto& ll = pp.second;
				auto jj = std::vector<VarValPair>();
				for (int j = 0; j < ll.size(); j++)
					jj.push_back(VarValPair(vv[j], ll[j]));
				ii.push_back(IdStatePair(Id(i), *llss(jj)));
			}
			return listsHistory_u(ii);
		};
		auto hhaa = historiesHistogram;
		auto trans = histogramsSetVarsTransform;
		auto ttaa = transformsHistogram;
		auto und = transformsUnderlying;
		auto der = transformsDerived;
		auto tmul = [](const Histogram& aa, const Transform& tt)
		{
			return transformsHistogramsApply(tt, aa);
		};

		auto suit = Variable("suit");
		auto rank = Variable("rank");
		auto vv = VarUSet{ suit,rank };
		auto hearts = Value("hearts");
		auto clubs = Value("clubs");
		auto diamonds = Value("diamonds");
		auto spades = Value("spades");
		auto wws = ValSet{ hearts,clubs,diamonds,spades };
		auto jack = Value("J");
		auto queen = Value("Q");
		auto king = Value("K");
		auto ace = Value("A");
		auto wwr = ValSet{ jack,queen,king,ace };
		for (int i = 2; i <= 10; i++)
			wwr.insert(Value(i));
		auto uu = lluu(std::vector<VarValSetPair>{VarValSetPair(suit, wws), VarValSetPair(rank, wwr)});

		cout << "uu" << endl
			<< *uu << endl << endl;

		cout << "vv" << endl
			<< sorted(vv) << endl << endl;

		auto aa = unit(*cart(*uu, vv));
		cout << "rpln(aall(aa))" << endl;
		rpln(cout, sorted(*aall(*aa))); cout << endl;

		auto colour = Variable("colour");
		auto red = Value("red");
		auto black = Value("black");

		auto xx = hhaa(*llhh(VarList{ suit, colour }, IntValListPairList{
			IntValListPair(1, ValList{ hearts, red }),
			IntValListPair(2, ValList{ clubs, black }),
			IntValListPair(3, ValList{ diamonds, red }),
			IntValListPair(4, ValList{ spades, black }) }));

		cout << "rpln(aall(xx))" << endl;
		rpln(cout, sorted(*aall(*xx))); cout << endl;

		auto ww = VarUSet{ colour };

		auto tt = trans(*xx, ww);

		cout << "trans(xx,ww)" << endl
			<< *tt << endl << endl;

		cout << "Transform(xx,ww)" << endl
			<< Transform(xx, ww) << endl << endl;

		cout << "xx" << endl
			<< (xx ? "set" : "reset") << endl << endl;

		cout << "rpln(aall(ttaa(tt)))" << endl;
		rpln(cout, sorted(*aall(ttaa(*tt)))); cout << endl;

		cout << "und(tt)" << endl
			<< sorted(*und(*tt)) << endl << endl;

		cout << "der(tt)" << endl
			<< sorted(der(*tt)) << endl << endl;

		cout << "rpln(aall(tmul(aa, tt)))" << endl;
		rpln(cout, sorted(*aall(*tmul(*aa,*tt)))); cout << endl;

	}

	if (false)
	{
		auto uvars = systemsSetVar;
		auto cart = systemsSetVarsSetStateCartesian_u;
		auto llss = listsState;
		auto vol = systemsSetVarsVolume_u;
		auto ssplit = [](const VarUSet& vv, const Histogram& aa)
		{
			return setVarsSetStatesSplit(vv, *histogramsStates(aa));
		};
		auto unit = setStatesHistogramUnit_u;
		auto aall = histogramsList;
		auto size = histogramsSize;
		auto resize = histogramsResize;
		auto norm = [](const Histogram& aa)
		{
			return histogramsResize(1, aa);
		};
		auto add = pairHistogramsAdd_u;
		auto scalar = histogramScalar_u;
		auto regsing = histogramRegularUnitSingleton_u;
		auto regdiag = histogramRegularUnitDiagonal_u;
		auto regcart = histogramRegularCartesian_u;
		auto ared = [](const Histogram& aa, const VarUSet& vv)
		{
			return setVarsHistogramsReduce(vv, aa);
		};
		auto llhh = [llss](const VarList& vv, const IntValListPairList& ee)
		{
			std::vector<IdStatePair> ii;
			for (auto& pp : ee)
			{
				auto i = pp.first;
				auto& ll = pp.second;
				auto jj = std::vector<VarValPair>();
				for (int j = 0; j < ll.size(); j++)
					jj.push_back(VarValPair(vv[j], ll[j]));
				ii.push_back(IdStatePair(Id(i), *llss(jj)));
			}
			return listsHistory_u(ii);
		};
		auto hhll = historiesList;
		auto hvars = historiesSetVar;
		auto hsize = historiesSize;
		auto hred = [](const History& hh, const VarUSet& vv)
		{
			return setVarsHistoriesReduce(vv, hh);
		};
		auto hhaa = historiesHistogram;
		auto aahh = histogramsHistory_u;
		auto ind = histogramsIndependent;
		auto ent = histogramsEntropy;
		auto lent = [size, ent, ared](const VarUSet& vv, const Histogram& aa)
		{
			return size(aa).getDouble() * (ent(aa) - ent(*ared(aa, vv)));
		};
		auto algn = histogramsAlignment;
		auto trans = histogramsSetVarsTransform;
		auto ttaa = transformsHistogram;
		auto und = transformsUnderlying;
		auto der = transformsDerived;
		auto tmul = [](const Histogram& aa, const Transform& tt)
		{
			return transformsHistogramsApply(tt, aa);
		};
		auto lltt = [llss, trans](const VarList& kk, const VarList& ww, const ValListList& qq)
		{
			VarList vv(kk.begin(),kk.end());
			vv.insert(vv.end(), ww.begin(), ww.end());
			std::vector<StateRationalPair> ii;
			for (auto& ll : qq)
			{
				auto jj = std::vector<VarValPair>();
				for (int j = 0; j < ll.size(); j++)
					jj.push_back(VarValPair(vv[j], ll[j]));
				ii.push_back(StateRationalPair(*llss(jj),1));
			}
			return trans(Histogram(ii), VarUSet(ww.begin(), ww.end()));
		};

		auto pressure = Variable("pressure");
		auto cloud = Variable("cloud");
		auto wind = Variable("wind");
		auto rain = Variable("rain");
		auto cloud_and_wind = Variable("cloud_and_wind");
		auto low = Value("low");
		auto medium = Value("medium");
		auto high = Value("high");
		auto none = Value("none");
		auto light = Value("light");
		auto heavy = Value("heavy");
		auto strong = Value("strong");
		auto uu = listsSystem_u(std::vector<VarValSetPair>{
			VarValSetPair(pressure, ValSet{ low,medium,high }),
				VarValSetPair(cloud, ValSet{ none,light,heavy }),
				VarValSetPair(wind, ValSet{ none,light,strong }),
				VarValSetPair(rain, ValSet{ none,light,heavy })});
		auto vv = uvars(*uu);
		auto hh = llhh(VarList{ pressure, cloud, wind, rain }, IntValListPairList{
			IntValListPair(1, ValList{ high, none, none, none }),
			IntValListPair(2, ValList{ medium, light, none, light }),
			IntValListPair(3, ValList{ high, none, light, none }),
			IntValListPair(4, ValList{ low, heavy, strong, heavy }),
			IntValListPair(5, ValList{ low, none, light, light }),
			IntValListPair(6, ValList{ medium, none, light, light }),
			IntValListPair(7, ValList{ low, heavy, light, heavy }),
			IntValListPair(8, ValList{ high, none, light, none }),
			IntValListPair(9, ValList{ medium, light, strong, heavy }),
			IntValListPair(10, ValList{ medium, light, light, light }),
			IntValListPair(11, ValList{ high, light, light, heavy }),
			IntValListPair(12, ValList{ medium, none, none, none }),
			IntValListPair(13, ValList{ medium, light, none, none }),
			IntValListPair(14, ValList{ high, light, strong, light }),
			IntValListPair(15, ValList{ medium, none, light, light }),
			IntValListPair(16, ValList{ low, heavy, strong, heavy }),
			IntValListPair(17, ValList{ low, heavy, light, heavy }),
			IntValListPair(18, ValList{ high, none, none, none }),
			IntValListPair(19, ValList{ low, light, none, light }),
			IntValListPair(20, ValList{ high, none, none, none }) });
		auto aa = hhaa(*hh);

		cout << "size(aa)" << endl
			<< size(*aa) << endl << endl;

		auto tt = lltt(VarList{ cloud, wind }, VarList{ cloud_and_wind }, ValListList{
			ValList{none, none, none},
			ValList{none, light, light},
			ValList{none, strong, light},
			ValList{light, none, light},
			ValList{light, light, light},
			ValList{light, strong, light},
			ValList{heavy, none, strong},
			ValList{heavy, light, strong},
			ValList{heavy, strong, strong}});

		cout << "rpln(aall(ttaa(tt)))" << endl;
		rpln(cout, sorted(*aall(ttaa(*tt)))); cout << endl;

		cout << "rpln(ssplit([cloud, wind], ttaa(tt)))" << endl;
		rpln(cout, *ssplit(VarUSet{ cloud, wind }, ttaa(*tt))); cout << endl;

		cout << "und(tt)" << endl
			<< sorted(*und(*tt)) << endl << endl;

		cout << "der(tt)" << endl
			<< sorted(der(*tt)) << endl << endl;

		cout << "rpln(aall(tmul(aa, tt)))" << endl;
		rpln(cout, sorted(*aall(*tmul(*aa, *tt)))); cout << endl;
	}

	if (false)
	{
		auto lluu = listsSystem_u;
		auto cart = systemsSetVarsSetStateCartesian_u;
		auto llss = listsState;
		auto unit = setStatesHistogramUnit_u;
		auto aall = histogramsList;
		auto size = histogramsSize;
		auto resize = histogramsResize;
		auto norm = [](const Histogram& aa)
		{
			return histogramsResize(1, aa);
		};
		auto add = pairHistogramsAdd_u;
		auto scalar = histogramScalar_u;
		auto regsing = histogramRegularUnitSingleton_u;
		auto regdiag = histogramRegularUnitDiagonal_u;
		auto regcart = histogramRegularCartesian_u;
		auto ared = [](const Histogram& aa, const VarUSet& vv)
		{
			return setVarsHistogramsReduce(vv, aa);
		};
		auto llhh = [llss](const VarList& vv, const IntValListPairList& ee)
		{
			std::vector<IdStatePair> ii;
			for (auto& pp : ee)
			{
				auto i = pp.first;
				auto& ll = pp.second;
				auto jj = std::vector<VarValPair>();
				for (int j = 0; j < ll.size(); j++)
					jj.push_back(VarValPair(vv[j], ll[j]));
				ii.push_back(IdStatePair(Id(i), *llss(jj)));
			}
			return listsHistory_u(ii);
		};
		auto hhaa = historiesHistogram;
		auto trans = [](std::unique_ptr<Histogram>& xx, const VarUSet& ww)
		{
			return std::make_shared<Transform>(xx, ww);
		};
		auto ttaa = transformsHistogram;
		auto und = transformsUnderlying;
		auto der = transformsDerived;
		auto tmul = [](const Histogram& aa, const Transform& tt)
		{
			return transformsHistogramsApply(tt, aa);
		};
		auto lltt = [llss, trans](const VarList& kk, const VarList& ww, const ValListList& qq)
		{
			VarList vv(kk.begin(), kk.end());
			vv.insert(vv.end(), ww.begin(), ww.end());
			std::vector<StateRationalPair> ii;
			for (auto& ll : qq)
			{
				auto jj = std::vector<VarValPair>();
				for (int j = 0; j < ll.size(); j++)
					jj.push_back(VarValPair(vv[j], ll[j]));
				ii.push_back(StateRationalPair(*llss(jj), 1));
			}
			auto aa = std::make_unique<Histogram>(ii);
			return trans(aa, VarUSet(ww.begin(), ww.end()));
		};
		auto llff = setTransformsFud_u;
		auto fhis = fudsSetHistogram;
		auto fvars = fudsSetVar;
		auto fder = fudsDerived;
		auto fund = fudsUnderlying;
		auto fftt = fudsTransform;
		auto dep = fudsSetVarsDepends_u;

		auto suit = Variable("suit");
		auto rank = Variable("rank");
		auto vv = VarUSet{ suit,rank };
		auto hearts = Value("hearts");
		auto clubs = Value("clubs");
		auto diamonds = Value("diamonds");
		auto spades = Value("spades");
		auto wws = ValSet{ hearts,clubs,diamonds,spades };
		auto jack = Value("J");
		auto queen = Value("Q");
		auto king = Value("K");
		auto ace = Value("A");
		auto wwr = ValSet{ jack,queen,king,ace };
		for (int i = 2; i <= 10; i++)
			wwr.insert(Value(i));
		auto uu = lluu(std::vector<VarValSetPair>{VarValSetPair(suit, wws), VarValSetPair(rank, wwr)});

		cout << "uu" << endl
			<< *uu << endl << endl;

		cout << "vv" << endl
			<< sorted(vv) << endl << endl;

		auto aa = unit(*cart(*uu, vv));
		cout << "rpln(aall(aa))" << endl;
		rpln(cout, sorted(*aall(*aa))); cout << endl;

		auto colour = Variable("colour");
		auto red = Value("red");
		auto black = Value("black");

		auto ttc = lltt(VarList{ suit }, VarList{ colour }, ValListList{
			ValList{ hearts, red },
			ValList{ clubs, black },
			ValList{ diamonds, red },
			ValList{ spades, black } });

		cout << "rpln(aall(ttaa(ttc)))" << endl;
		rpln(cout, sorted(*aall(ttaa(*ttc)))); cout << endl;

		cout << "und(ttc)" << endl
			<< sorted(*und(*ttc)) << endl << endl;

		cout << "der(ttc)" << endl
			<< sorted(der(*ttc)) << endl << endl;

		auto pip_or_face = Variable("pip_or_face");
		auto pip = Value("pip");
		auto face = Value("face");

		auto xxt = ValListList{
			ValList{ ace, pip },
			ValList{ king, face },
			ValList{ queen, face },
			ValList{ jack, face } };
		for (int i = 2; i <= 10; i++)
			xxt.push_back(ValList{Value(i),pip});

		auto ttt = lltt(VarList{ rank }, VarList{ pip_or_face }, xxt);

		cout << "rpln(aall(ttaa(ttt)))" << endl;
		rpln(cout, sorted(*aall(ttaa(*ttt)))); cout << endl;

		cout << "und(ttt)" << endl
			<< sorted(*und(*ttt)) << endl << endl;

		cout << "der(ttt)" << endl
			<< sorted(der(*ttt)) << endl << endl;

		auto ff = llff(TransformPtrList{ ttc, ttt });

		cout << "ff" << endl
			<< *ff << endl << endl;

		cout << "rpln(fhis(ff))" << endl;
		rpln(cout, *fhis(*ff)); cout << endl;

		cout << "fvars(ff)" << endl
			<< sorted(*fvars(*ff)) << endl << endl;

		cout << "fund(ff)" << endl
			<< sorted(*fund(*ff)) << endl << endl;

		cout << "fder(ff)" << endl
			<< sorted(*fder(*ff)) << endl << endl;

		cout << "rpln(aall(ttaa(fftt(ff))))" << endl;
		rpln(cout, sorted(*aall(ttaa(*fftt(*ff))))); cout << endl;

		auto red_face = Variable("red_face");
		auto yes = Value("yes");
		auto no = Value("no");

		auto ttrf = lltt(VarList{ colour,pip_or_face }, VarList{ red_face }, ValListList{
			ValList{ red, face, yes },
			ValList{ red, pip, no },
			ValList{ black, face, no },
			ValList{ black, pip, no } });

		auto gg = llff(TransformPtrList{ ttc, ttt, ttrf });

		cout << "gg" << endl
			<< *gg << endl << endl;

		cout << "rpln(fhis(gg))" << endl;
		rpln(cout, *fhis(*gg)); cout << endl;

		cout << "fvars(gg)" << endl
			<< sorted(*fvars(*gg)) << endl << endl;

		cout << "fund(gg)" << endl
			<< sorted(*fund(*gg)) << endl << endl;

		cout << "fder(gg)" << endl
			<< sorted(*fder(*gg)) << endl << endl;

		cout << "dep(gg,colour)" << endl
			<< *dep(*gg, VarUSet{ colour }) << endl << endl;
		cout << "dep(gg,pip_or_face)" << endl
			<< *dep(*gg, VarUSet{ pip_or_face }) << endl << endl;
		cout << "dep(gg,red_face)" << endl
			<< *dep(*gg, VarUSet{ red_face }) << endl << endl;
	}

	if (false)
	{
		auto uvars = systemsSetVar;
		auto cart = systemsSetVarsSetStateCartesian_u;
		auto llss = listsState;
		auto vol = systemsSetVarsVolume_u;
		auto ssplit = [](const VarUSet& vv, const Histogram& aa)
		{
			return setVarsSetStatesSplit(vv, *histogramsStates(aa));
		};
		auto unit = setStatesHistogramUnit_u;
		auto aall = histogramsList;
		auto size = histogramsSize;
		auto resize = histogramsResize;
		auto norm = [](const Histogram& aa)
		{
			return histogramsResize(1, aa);
		};
		auto add = pairHistogramsAdd_u;
		auto scalar = histogramScalar_u;
		auto regsing = histogramRegularUnitSingleton_u;
		auto regdiag = histogramRegularUnitDiagonal_u;
		auto regcart = histogramRegularCartesian_u;
		auto ared = [](const Histogram& aa, const VarUSet& vv)
		{
			return setVarsHistogramsReduce(vv, aa);
		};
		auto llhh = [llss](const VarList& vv, const IntValListPairList& ee)
		{
			std::vector<IdStatePair> ii;
			for (auto& pp : ee)
			{
				auto i = pp.first;
				auto& ll = pp.second;
				auto jj = std::vector<VarValPair>();
				for (int j = 0; j < ll.size(); j++)
					jj.push_back(VarValPair(vv[j], ll[j]));
				ii.push_back(IdStatePair(Id(i), *llss(jj)));
			}
			return listsHistory_u(ii);
		};
		auto hhll = historiesList;
		auto hvars = historiesSetVar;
		auto hsize = historiesSize;
		auto hred = [](const History& hh, const VarUSet& vv)
		{
			return setVarsHistoriesReduce(vv, hh);
		};
		auto hhaa = historiesHistogram;
		auto aahh = histogramsHistory_u;
		auto ind = histogramsIndependent;
		auto ent = histogramsEntropy;
		auto lent = [size, ent, ared](const VarUSet& vv, const Histogram& aa)
		{
			return size(aa).getDouble() * (ent(aa) - ent(*ared(aa, vv)));
		};
		auto algn = histogramsAlignment;
		auto trans = [](std::unique_ptr<Histogram>& xx, const VarUSet& ww)
		{
			return std::make_shared<Transform>(xx, ww);
		};
		auto ttaa = transformsHistogram;
		auto und = transformsUnderlying;
		auto der = transformsDerived;
		auto tmul = [](const Histogram& aa, const Transform& tt)
		{
			return transformsHistogramsApply(tt, aa);
		};
		auto lltt = [llss, trans](const VarList& kk, const VarList& ww, const ValListList& qq)
		{
			VarList vv(kk.begin(), kk.end());
			vv.insert(vv.end(), ww.begin(), ww.end());
			std::vector<StateRationalPair> ii;
			for (auto& ll : qq)
			{
				auto jj = std::vector<VarValPair>();
				for (int j = 0; j < ll.size(); j++)
					jj.push_back(VarValPair(vv[j], ll[j]));
				ii.push_back(StateRationalPair(*llss(jj), 1));
			}
			auto aa = std::make_unique<Histogram>(ii);
			return trans(aa, VarUSet(ww.begin(), ww.end()));
		};
		auto llff = setTransformsFud_u;
		auto fhis = fudsSetHistogram;
		auto fvars = fudsSetVar;
		auto fder = fudsDerived;
		auto fund = fudsUnderlying;
		auto fftt = fudsTransform;
		auto fsys = fudsSystemImplied;
		auto dep = fudsSetVarsDepends_u;

		auto pressure = Variable("pressure");
		auto cloud = Variable("cloud");
		auto wind = Variable("wind");
		auto rain = Variable("rain");
		auto cloud_and_wind = Variable("cloud_and_wind");
		auto cloud_and_pressure = Variable("cloud_and_pressure");
		auto cloud_wind_pressure = Variable("cloud_wind_pressure");
		auto low = Value("low");
		auto medium = Value("medium");
		auto high = Value("high");
		auto none = Value("none");
		auto light = Value("light");
		auto heavy = Value("heavy");
		auto strong = Value("strong");
		auto uu = listsSystem_u(std::vector<VarValSetPair>{
			VarValSetPair(pressure, ValSet{ low,medium,high }),
				VarValSetPair(cloud, ValSet{ none,light,heavy }),
				VarValSetPair(wind, ValSet{ none,light,strong }),
				VarValSetPair(rain, ValSet{ none,light,heavy })});
		auto vv = uvars(*uu);
		auto hh = llhh(VarList{ pressure, cloud, wind, rain }, IntValListPairList{
			IntValListPair(1, ValList{ high, none, none, none }),
			IntValListPair(2, ValList{ medium, light, none, light }),
			IntValListPair(3, ValList{ high, none, light, none }),
			IntValListPair(4, ValList{ low, heavy, strong, heavy }),
			IntValListPair(5, ValList{ low, none, light, light }),
			IntValListPair(6, ValList{ medium, none, light, light }),
			IntValListPair(7, ValList{ low, heavy, light, heavy }),
			IntValListPair(8, ValList{ high, none, light, none }),
			IntValListPair(9, ValList{ medium, light, strong, heavy }),
			IntValListPair(10, ValList{ medium, light, light, light }),
			IntValListPair(11, ValList{ high, light, light, heavy }),
			IntValListPair(12, ValList{ medium, none, none, none }),
			IntValListPair(13, ValList{ medium, light, none, none }),
			IntValListPair(14, ValList{ high, light, strong, light }),
			IntValListPair(15, ValList{ medium, none, light, light }),
			IntValListPair(16, ValList{ low, heavy, strong, heavy }),
			IntValListPair(17, ValList{ low, heavy, light, heavy }),
			IntValListPair(18, ValList{ high, none, none, none }),
			IntValListPair(19, ValList{ low, light, none, light }),
			IntValListPair(20, ValList{ high, none, none, none }) });
		auto aa = hhaa(*hh);

		cout << "size(aa)" << endl
			<< size(*aa) << endl << endl;

		auto ttcw = lltt(VarList{ cloud, wind }, VarList{ cloud_and_wind }, ValListList{
			ValList{ none, none, none },
			ValList{ none, light, light },
			ValList{ none, strong, light },
			ValList{ light, none, light },
			ValList{ light, light, light },
			ValList{ light, strong, light },
			ValList{ heavy, none, strong },
			ValList{ heavy, light, strong },
			ValList{ heavy, strong, strong } });

		auto ttcp = lltt(VarList{ cloud, pressure }, VarList{ cloud_and_pressure }, ValListList{
			ValList{none, high, none},
			ValList{none, medium, light},
			ValList{none, low, light},
			ValList{light, high, light},
			ValList{light, medium, light},
			ValList{light, low, light},
			ValList{heavy, high, strong},
			ValList{heavy, medium, strong},
			ValList{heavy, low, strong} });

		auto ff = llff(TransformPtrList{ ttcw, ttcp });

		cout << "fder(ff)" << endl
			<< sorted(*fder(*ff)) << endl << endl;

		cout << "fund(ff)" << endl
			<< sorted(*fund(*ff)) << endl << endl;

		cout << "fsys(ff)" << endl
			<< *fsys(*ff) << endl << endl;

		cout << "der(fftt(ff))" << endl
			<< sorted(der(*fftt(*ff))) << endl << endl;

		cout << "und(fftt(ff))" << endl
			<< sorted(*und(*fftt(*ff))) << endl << endl;

		auto ttcwp = lltt(VarList{ cloud_and_wind,cloud_and_pressure }, VarList{ cloud_wind_pressure }, ValListList{
			ValList{ none, none, none },
			ValList{ none, light, none },
			ValList{ none, strong, none },
			ValList{ light, none, none },
			ValList{ light, light, light },
			ValList{ light, strong, light },
			ValList{ strong, none, none },
			ValList{ strong, light, light },
			ValList{ strong, strong, strong } });

		auto gg = llff(TransformPtrList{ ttcw, ttcp, ttcwp });

		cout << "fder(gg)" << endl
			<< sorted(*fder(*gg)) << endl << endl;

		cout << "fund(gg)" << endl
			<< sorted(*fund(*gg)) << endl << endl;

		cout << "fsys(gg)" << endl
			<< *fsys(*gg) << endl << endl;

		cout << "der(fftt(gg))" << endl
			<< sorted(der(*fftt(*gg))) << endl << endl;

		cout << "und(fftt(gg))" << endl
			<< sorted(*und(*fftt(*gg))) << endl << endl;

		cout << "len(dep(gg,fder(gg)))" << endl
			<< dep(*gg, *fder(*gg))->list_u().size() << endl << endl;

		cout << "len(dep(gg,fder(ff)))" << endl
			<< dep(*gg, *fder(*ff))->list_u().size() << endl << endl;

		cout << "len(dep(gg,[cloud_and_pressure]))" << endl
			<< dep(*gg, VarUSet{ cloud_and_pressure })->list_u().size() << endl << endl;

	}

	if (false)
	{
		auto x = std::shared_ptr<Tree<int>>(new Tree<int>());
		x->_list.push_back(std::pair<int, std::shared_ptr<Tree<int>>>(3, std::shared_ptr<Tree<int>>()));

		cout << "x" << endl
			<< *x << endl << endl;

		cout << "treesPaths(x)" << endl
			<< *treesPaths(*x) << endl << endl;

		auto y = std::shared_ptr<Tree<int>>(new Tree<int>());
		y->_list.push_back(std::pair<int, std::shared_ptr<Tree<int>>>(2, x));
		y->_list.push_back(std::pair<int, std::shared_ptr<Tree<int>>>(1, std::shared_ptr<Tree<int>>()));

		cout << "y" << endl
			<< *y << endl << endl;

		cout << "treesPaths(y)" << endl
			<< *treesPaths(*y) << endl << endl;

		auto z = std::shared_ptr<Tree<int>>(new Tree<int>());
		z->_list.push_back(std::pair<int, std::shared_ptr<Tree<int>>>(3, y));
		z->_list.push_back(std::pair<int, std::shared_ptr<Tree<int>>>(2, x));
		z->_list.push_back(std::pair<int, std::shared_ptr<Tree<int>>>(1, std::shared_ptr<Tree<int>>()));

		cout << "z" << endl
			<< *z << endl << endl;

		cout << "treesPaths(z)" << endl
			<< *treesPaths(*z) << endl << endl;

		cout << "y.sort()" << endl;
		y->sort();

		cout << "y" << endl
			<< *y << endl << endl;


		cout << "z.sort()" << endl;
		z->sort();

		cout << "z" << endl
			<< *z << endl << endl;

		cout << "treesPaths(z)" << endl
			<< *treesPaths(*z) << endl << endl;

		cout << "pairTreesUnion(x,x)" << endl
			<< *pairTreesUnion(*x, *x) << endl << endl;

		cout << "pairTreesUnion(x,y)" << endl
			<< *pairTreesUnion(*x, *y) << endl << endl;

		cout << "pairTreesUnion(x,z)" << endl
			<< *pairTreesUnion(*x, *z) << endl << endl;

		cout << "pairTreesUnion(y,y)" << endl
			<< *pairTreesUnion(*y, *y) << endl << endl;

		cout << "pairTreesUnion(y,z)" << endl
			<< *pairTreesUnion(*y, *z) << endl << endl;

		cout << "pairTreesUnion(z,z)" << endl
			<< *pairTreesUnion(*z, *z) << endl << endl;

		auto tt = pathsTree(std::vector<std::vector<int>>{
			std::vector<int>{9},
			std::vector<int>{1, 3, 4, 5, 6, 7},
			std::vector<int>{1, 2},
			std::vector<int>{1, 3},
			std::vector<int>{1},
			std::vector<int>{1, 8},
			std::vector<int>{1, 3, 4}});

		cout << "rpln(treesPaths(tt))" << endl;
		rpln(cout, *treesPaths(*tt)); cout << endl;

		cout << "tt.sort()" << endl;
		tt->sort();

		cout << "rpln(treesPaths(tt))" << endl;
		rpln(cout, *treesPaths(*tt)); cout << endl;

		cout << "tt" << endl
			<< *tt << endl << endl;

		auto tt1 = treesEnumeratePreOrder(0, *tt);
		cout << "tt1 = treesEnumeratePreOrder(0,tt)" << endl;
		cout << "rpln(treesPaths(tt1))" << endl;
		rpln(cout, *treesPaths(*tt1.first)); cout << endl;

		auto ss = funcsTreesMap(f, *tt);
		cout << "ss = funcsTreesMap(f, *tt)" << endl
			<< *ss << endl << endl;
		cout << "rpln(treesPaths(ss))" << endl;
		rpln(cout, *treesPaths(*ss)); cout << endl;
	}

	if (false)
	{
		auto lluu = listsSystem_u;
		auto cart = systemsSetVarsSetStateCartesian_u;
		auto llss = listsState;
		auto unit = setStatesHistogramUnit_u;
		auto aall = histogramsList;
		auto size = histogramsSize;
		auto resize = histogramsResize;
		auto norm = [](const Histogram& aa)
		{
			return histogramsResize(1, aa);
		};
		auto add = pairHistogramsAdd_u;
		auto scalar = histogramScalar_u;
		auto regsing = histogramRegularUnitSingleton_u;
		auto regdiag = histogramRegularUnitDiagonal_u;
		auto regcart = histogramRegularCartesian_u;
		auto ared = [](const Histogram& aa, const VarUSet& vv)
		{
			return setVarsHistogramsReduce(vv, aa);
		};
		auto llhh = [llss](const VarList& vv, const IntValListPairList& ee)
		{
			std::vector<IdStatePair> ii;
			for (auto& pp : ee)
			{
				auto i = pp.first;
				auto& ll = pp.second;
				auto jj = std::vector<VarValPair>();
				for (int j = 0; j < ll.size(); j++)
					jj.push_back(VarValPair(vv[j], ll[j]));
				ii.push_back(IdStatePair(Id(i), *llss(jj)));
			}
			return listsHistory_u(ii);
		};
		auto hhaa = historiesHistogram;
		auto trans = [](std::unique_ptr<Histogram>& xx, const VarUSet& ww)
		{
			return std::make_shared<Transform>(xx, ww);
		};
		auto ttaa = transformsHistogram;
		auto und = transformsUnderlying;
		auto der = transformsDerived;
		auto tmul = [](const Histogram& aa, const Transform& tt)
		{
			return transformsHistogramsApply(tt, aa);
		};
		auto lltt = [llss, trans](const VarList& kk, const VarList& ww, const ValListList& qq)
		{
			VarList vv(kk.begin(), kk.end());
			vv.insert(vv.end(), ww.begin(), ww.end());
			std::vector<StateRationalPair> ii;
			for (auto& ll : qq)
			{
				auto jj = std::vector<VarValPair>();
				for (int j = 0; j < ll.size(); j++)
					jj.push_back(VarValPair(vv[j], ll[j]));
				ii.push_back(StateRationalPair(*llss(jj), 1));
			}
			auto aa = std::make_unique<Histogram>(ii);
			return trans(aa, VarUSet(ww.begin(), ww.end()));
		};
		auto llff = setTransformsFud_u;
		auto fhis = fudsSetHistogram;
		auto fvars = fudsSetVar;
		auto fder = fudsDerived;
		auto fund = fudsUnderlying;
		auto fftt = fudsTransform;
		auto dep = fudsSetVarsDepends_u;
		typedef std::pair<VarValPairList, TransformPtrList> VarValPairListTransformPtrListPair;
		typedef std::vector<VarValPairListTransformPtrListPair> VarValPairListTransformPtrListPairList;
		typedef std::vector<VarValPairListTransformPtrListPairList> VarValPairListTransformPtrListPairListList;
		auto lldf = [llss, llff](const VarValPairListTransformPtrListPairListList& zz)
		{
			auto jj = std::vector<std::vector<StatePtrFudPtrPair>>();
			jj.reserve(zz.size());
			for (auto& ll : zz)
			{
				auto kk = std::vector<StatePtrFudPtrPair>();
				kk.reserve(ll.size());
				for (auto& pp : ll)
				{
					StatePtrFudPtrPair qq(std::move(llss(pp.first)), std::move(llff(pp.second)));
					kk.push_back(qq);
				}
				jj.push_back(kk);
			}
			auto tt = std::make_unique<DecompFud>();
			tt->tree_u() = *pathsTree(jj);
			return tt;
		};
		auto dfll = [](const DecompFud& df)
		{
			return treesPaths(df.tree_u());
		};
		auto dfund = decompFudsUnderlying;


		auto suit = Variable("suit");
		auto rank = Variable("rank");
		auto vv = VarUSet{ suit,rank };
		auto hearts = Value("hearts");
		auto clubs = Value("clubs");
		auto diamonds = Value("diamonds");
		auto spades = Value("spades");
		auto wws = ValSet{ hearts,clubs,diamonds,spades };
		auto jack = Value("J");
		auto queen = Value("Q");
		auto king = Value("K");
		auto ace = Value("A");
		auto wwr = ValSet{ jack,queen,king,ace };
		for (int i = 2; i <= 10; i++)
			wwr.insert(Value(i));
		auto uu = lluu(std::vector<VarValSetPair>{VarValSetPair(suit, wws), VarValSetPair(rank, wwr)});

		cout << "uu" << endl
			<< *uu << endl << endl;

		cout << "vv" << endl
			<< sorted(vv) << endl << endl;

		auto colour = Variable("colour");
		auto red = Value("red");
		auto black = Value("black");

		auto ttc = lltt(VarList{ suit }, VarList{ colour }, ValListList{
			ValList{ hearts, red },
			ValList{ clubs, black },
			ValList{ diamonds, red },
			ValList{ spades, black } });

		auto pip_or_face = Variable("pip_or_face");
		auto pip = Value("pip");
		auto face = Value("face");

		auto xxt = ValListList{
			ValList{ ace, pip },
			ValList{ king, face },
			ValList{ queen, face },
			ValList{ jack, face } };
		for (int i = 2; i <= 10; i++)
			xxt.push_back(ValList{ Value(i),pip });

		auto ttt = lltt(VarList{ rank }, VarList{ pip_or_face }, xxt);

		auto odd_pip = Variable("odd_pip");
		auto yes = Value("yes");
		auto no = Value("no");

		auto xxop = ValListList{
			ValList{ ace, yes },
			ValList{ king, no },
			ValList{ queen, no },
			ValList{ jack, no } };
		for (int i = 2; i <= 10; i += 2)
			xxop.push_back(ValList{ Value(i),no });
		for (int i = 3; i <= 9; i += 2)
			xxop.push_back(ValList{ Value(i),yes });

		auto ttop = lltt(VarList{ rank }, VarList{ odd_pip }, xxop);

		auto df = lldf(VarValPairListTransformPtrListPairListList{
			VarValPairListTransformPtrListPairList{
				VarValPairListTransformPtrListPair(VarValPairList{},TransformPtrList{ttop}),
				VarValPairListTransformPtrListPair(VarValPairList{VarValPair(odd_pip, no)},TransformPtrList{ ttc, ttt})},
			VarValPairListTransformPtrListPairList{
				VarValPairListTransformPtrListPair(VarValPairList{},TransformPtrList{ ttop }),
				VarValPairListTransformPtrListPair(VarValPairList{VarValPair(odd_pip, yes)},TransformPtrList{ttc})} });

		cout << "df" << endl
			<< *df << endl << endl;

		cout << "treesSize(dfzz(df))" << endl
			<< treesSize(df->tree_u()) << endl << endl;

		cout << "dfund(df)" << endl
			<< sorted(*dfund(*df)) << endl << endl;

		cout << "rpln(dfll(df))" << endl;
		rpln(cout, *dfll(*df)); cout << endl;

		cout << "decompFudsPersistent(df,cout)" << endl;
		decompFudsPersistent(*df, cout); cout << endl << endl;

		cout << "decompFudsPersistentPretty(df,cout)" << endl;
		decompFudsPersistentPretty(*df, cout); cout << endl << endl;

		std::stringstream str1;
		decompFudsPersistentPretty(*df, str1);
		auto df1 = persistentsDecompFud(str1);
		cout << "df1 = persistentsDecompFud(str1)" << endl;
		cout << "rpln(dfll(df1))" << endl;
		rpln(cout, *dfll(*df1)); cout << endl;
		cout << "decompFudsPersistentPretty(df1,cout)" << endl;
		decompFudsPersistentPretty(*df1, cout); cout << endl << endl;
		cout << "treesSize(dfzz(df1))" << endl
			<< treesSize(df1->tree_u()) << endl << endl;
		cout << "dfund(df1)" << endl
			<< sorted(*dfund(*df1)) << endl << endl;

	}

	if (false)
	{
		const char* json = "{\"project\":\"rapidjson\",\"stars\":10}";
		js::Document d;
		d.Parse(json);

		js::Value& s = d["stars"];
		s.SetInt(s.GetInt() + 1);

		js::StringBuffer buffer;
		js::Writer<js::StringBuffer> writer(buffer);
		d.Accept(writer);

		std::cout << buffer.GetString() << std::endl;
	}

	if (false)
	{
		FILE* fp = std::fopen("../NISTPy/NIST_model1.json", "rb");
		assert(fp);
		char readBuffer[65536];
		js::FileReadStream is(fp, readBuffer, sizeof(readBuffer));

		js::Document d;
		d.ParseStream(is);

		cout << "d.IsObject()" << endl
			<< d.IsObject() << endl << endl;

		cout << "d.HasMember(\"paths\")" << endl
			<< d.HasMember("paths") << endl << endl;

		cout << "d.HasMember(\"nodes\")" << endl
			<< d.HasMember("nodes") << endl << endl;
	}

	if (false)
	{
		auto v1 = stringsVariable("aa");
		cout << v1 << endl;
		v1 = stringsVariable("1");
		cout << v1 << endl;
		v1 = stringsVariable("123");
		cout << v1 << endl;
		v1 = stringsVariable("<5,2>");
		cout << v1 << endl;
		v1 = stringsVariable("<<7,1>,2>");
		cout << v1 << endl;
	}

	if (false)
	{
		StrVarPtrMap m;
		auto v1 = stringsVariable("aa",m);
		cout << *v1 << endl;
		v1 = stringsVariable("1", m);
		cout << *v1 << endl;
		v1 = stringsVariable("123", m);
		cout << *v1 << endl;
		v1 = stringsVariable("<5,2>", m);
		cout << *v1 << endl;
		v1 = stringsVariable("<<7,1>,2>", m);
		cout << *v1 << endl;
		cout << "m" << endl
			<< m << endl << endl;
	}

	if (false)
	{
		auto v1 = stringsValue("aa");
		cout << v1 << endl;
		v1 = stringsValue("1");
		cout << v1 << endl;
		v1 = stringsValue("1.23");
		cout << v1 << endl;
		v1 = stringsValue("9	");
		cout << v1 << endl;
		v1 = stringsValue("  4.56   ");
		cout << v1 << endl;

	}

	if (false)
	{
		auto v1 = stringsRational("123 % 456");
		cout << v1 << endl;
		v1 = stringsRational("1");
		cout << v1 << endl;
		v1 = stringsRational(" % 456");
		cout << v1 << endl;
		v1 = stringsRational("123 % ");
		cout << v1 << endl;
		v1 = stringsRational("");
		cout << v1 << endl;

	}

	if (false)
	{
		cout << rationalsString(Rational(123, 456)) << endl;
		cout << rationalsString(Rational(123, 1)) << endl;
		cout << rationalsString(Rational(123.456)) << endl;

	}

	if (false)
	{
		auto uvars = systemsSetVar;
		auto cart = systemsSetVarsSetStateCartesian_u;
		auto llss = listsState;
		auto vol = systemsSetVarsVolume_u;
		auto ssplit = [](const VarUSet& vv, const Histogram& aa)
		{
			return setVarsSetStatesSplit(vv, *histogramsStates(aa));
		};
		auto unit = setStatesHistogramUnit_u;
		auto aall = histogramsList;
		auto size = histogramsSize;
		auto resize = histogramsResize;
		auto norm = [](const Histogram& aa)
		{
			return histogramsResize(1, aa);
		};
		auto add = pairHistogramsAdd_u;
		auto scalar = histogramScalar_u;
		auto regsing = histogramRegularUnitSingleton_u;
		auto regdiag = histogramRegularUnitDiagonal_u;
		auto regcart = histogramRegularCartesian_u;
		auto ared = [](const Histogram& aa, const VarUSet& vv)
		{
			return setVarsHistogramsReduce(vv, aa);
		};
		auto llhh = [llss](const VarList& vv, const IntValListPairList& ee)
		{
			std::vector<IdStatePair> ii;
			for (auto& pp : ee)
			{
				auto i = pp.first;
				auto& ll = pp.second;
				auto jj = std::vector<VarValPair>();
				for (int j = 0; j < ll.size(); j++)
					jj.push_back(VarValPair(vv[j], ll[j]));
				ii.push_back(IdStatePair(Id(i), *llss(jj)));
			}
			return listsHistory_u(ii);
		};
		auto hhll = historiesList;
		auto hvars = historiesSetVar;
		auto hsize = historiesSize;
		auto hred = [](const History& hh, const VarUSet& vv)
		{
			return setVarsHistoriesReduce(vv, hh);
		};
		auto hhaa = historiesHistogram;
		auto aahh = histogramsHistory_u;
		auto ind = histogramsIndependent;
		auto ent = histogramsEntropy;
		auto lent = [size, ent, ared](const VarUSet& vv, const Histogram& aa)
		{
			return size(aa).getDouble() * (ent(aa) - ent(*ared(aa, vv)));
		};
		auto algn = histogramsAlignment;
		auto trans = [](std::unique_ptr<Histogram>& xx, const VarUSet& ww)
		{
			return std::make_shared<Transform>(xx, ww);
		};
		auto ttaa = transformsHistogram;
		auto und = transformsUnderlying;
		auto der = transformsDerived;
		auto tmul = [](const Histogram& aa, const Transform& tt)
		{
			return transformsHistogramsApply(tt, aa);
		};
		auto lltt = [llss, trans](const VarList& kk, const VarList& ww, const ValListList& qq)
		{
			VarList vv(kk.begin(), kk.end());
			vv.insert(vv.end(), ww.begin(), ww.end());
			std::vector<StateRationalPair> ii;
			for (auto& ll : qq)
			{
				auto jj = std::vector<VarValPair>();
				for (int j = 0; j < ll.size(); j++)
					jj.push_back(VarValPair(vv[j], ll[j]));
				ii.push_back(StateRationalPair(*llss(jj), 1));
			}
			auto aa = std::make_unique<Histogram>(ii);
			return trans(aa, VarUSet(ww.begin(), ww.end()));
		};
		auto llff = setTransformsFud_u;
		auto fhis = fudsSetHistogram;
		auto fvars = fudsSetVar;
		auto fder = fudsDerived;
		auto fund = fudsUnderlying;
		auto fftt = fudsTransform;
		auto dep = fudsSetVarsDepends_u;

		auto pressure = Variable("pressure");
		auto cloud = Variable("cloud");
		auto wind = Variable("wind");
		auto rain = Variable("rain");
		auto cloud_and_wind = Variable("cloud_and_wind");
		auto cloud_and_pressure = Variable("cloud_and_pressure");
		auto cloud_wind_pressure = Variable("cloud_wind_pressure");
		auto low = Value("low");
		auto medium = Value("medium");
		auto high = Value("high");
		auto none = Value("none");
		auto light = Value("light");
		auto heavy = Value("heavy");
		auto strong = Value("strong");
		auto uu = listsSystem_u(std::vector<VarValSetPair>{
			VarValSetPair(pressure, ValSet{ low,medium,high }),
				VarValSetPair(cloud, ValSet{ none,light,heavy }),
				VarValSetPair(wind, ValSet{ none,light,strong }),
				VarValSetPair(rain, ValSet{ none,light,heavy })});
		auto vv = uvars(*uu);
		auto hh = llhh(VarList{ pressure, cloud, wind, rain }, IntValListPairList{
			IntValListPair(1, ValList{ high, none, none, none }),
			IntValListPair(2, ValList{ medium, light, none, light }),
			IntValListPair(3, ValList{ high, none, light, none }),
			IntValListPair(4, ValList{ low, heavy, strong, heavy }),
			IntValListPair(5, ValList{ low, none, light, light }),
			IntValListPair(6, ValList{ medium, none, light, light }),
			IntValListPair(7, ValList{ low, heavy, light, heavy }),
			IntValListPair(8, ValList{ high, none, light, none }),
			IntValListPair(9, ValList{ medium, light, strong, heavy }),
			IntValListPair(10, ValList{ medium, light, light, light }),
			IntValListPair(11, ValList{ high, light, light, heavy }),
			IntValListPair(12, ValList{ medium, none, none, none }),
			IntValListPair(13, ValList{ medium, light, none, none }),
			IntValListPair(14, ValList{ high, light, strong, light }),
			IntValListPair(15, ValList{ medium, none, light, light }),
			IntValListPair(16, ValList{ low, heavy, strong, heavy }),
			IntValListPair(17, ValList{ low, heavy, light, heavy }),
			IntValListPair(18, ValList{ high, none, none, none }),
			IntValListPair(19, ValList{ low, light, none, light }),
			IntValListPair(20, ValList{ high, none, none, none }) });
		auto aa = hhaa(*hh);
		auto ttcw = lltt(VarList{ cloud, wind }, VarList{ cloud_and_wind }, ValListList{
			ValList{ none, none, none },
			ValList{ none, light, light },
			ValList{ none, strong, light },
			ValList{ light, none, light },
			ValList{ light, light, light },
			ValList{ light, strong, light },
			ValList{ heavy, none, strong },
			ValList{ heavy, light, strong },
			ValList{ heavy, strong, strong } });
		auto ttcp = lltt(VarList{ cloud, pressure }, VarList{ cloud_and_pressure }, ValListList{
			ValList{ none, high, none },
			ValList{ none, medium, light },
			ValList{ none, low, light },
			ValList{ light, high, light },
			ValList{ light, medium, light },
			ValList{ light, low, light },
			ValList{ heavy, high, strong },
			ValList{ heavy, medium, strong },
			ValList{ heavy, low, strong } });
		auto ff = llff(TransformPtrList{ ttcw, ttcp });
		auto ttcwp = lltt(VarList{ cloud_and_wind,cloud_and_pressure }, VarList{ cloud_wind_pressure }, ValListList{
			ValList{ none, none, none },
			ValList{ none, light, none },
			ValList{ none, strong, none },
			ValList{ light, none, none },
			ValList{ light, light, light },
			ValList{ light, strong, light },
			ValList{ strong, none, none },
			ValList{ strong, light, light },
			ValList{ strong, strong, strong } });
		auto gg = llff(TransformPtrList{ ttcw, ttcp, ttcwp });

		cout << "uu" << endl
			<< *uu << endl << endl;

		cout << "systemsPersistent(uu,cout)" << endl;
		systemsPersistent(*uu, cout); cout << endl << endl;

		cout << "systemsPersistentSorted(uu,cout)" << endl;
		systemsPersistentSorted(*uu, cout); cout << endl << endl;

		std::stringstream str;
		systemsPersistent(*uu, str);
		auto uu1 = persistentsSystem(str);
		cout << "uu1 = persistentsSystem(str)" << endl
			<< *uu1 << endl << endl;

		std::stringstream str2;
		systemsPersistentSorted(*uu, str2);
		auto uu2 = persistentsSystem(str2);
		cout << "uu2 = persistentsSystem(str2)" << endl
			<< *uu2 << endl << endl;

		cout << "historiesPersistent(hh,cout)" << endl;
		historiesPersistent(*hh, cout); cout << endl << endl;

		std::stringstream str3;
		historiesPersistent(*hh, str3);
		auto hh2 = persistentsHistory(str3);
		cout << "hh2 = persistentsHistory(str3)" << endl
			<< *hh2 << endl << endl;

		cout << "rpln(aall(aa))" << endl;
		rpln(cout, sorted(*aall(*aa))); cout << endl;

		cout << "rpln(aall(hhaa(hh2)))" << endl;
		rpln(cout, sorted(*aall(*hhaa(*hh2)))); cout << endl;

		cout << "historiesPersistentPretty(1,hh,cout)" << endl;
		historiesPersistentPretty(1,*hh, cout); cout << endl << endl;

		std::stringstream str4;
		historiesPersistentPretty(1,*hh, str4);
		auto hh3 = persistentsHistory(str4);
		cout << "hh3 = persistentsHistory(str4)" << endl
			<< *hh3 << endl << endl;

		cout << "rpln(aall(aa))" << endl;
		rpln(cout, sorted(*aall(*aa))); cout << endl;

		cout << "rpln(aall(hhaa(hh3)))" << endl;
		rpln(cout, sorted(*aall(*hhaa(*hh3)))); cout << endl;

		cout << "transformsPersistent(ttcw,cout)" << endl;
		transformsPersistent(*ttcw, cout); cout << endl << endl;

		cout << "transformsPersistent(ttcp,cout)" << endl;
		transformsPersistent(*ttcp, cout); cout << endl << endl;

		cout << "transformsPersistent(ttcwp,cout)" << endl;
		transformsPersistent(*ttcwp, cout); cout << endl << endl;

		cout << "transformsPersistent(fftt(ff),cout)" << endl;
		transformsPersistent(*fftt(*ff), cout); cout << endl << endl;

		cout << "transformsPersistentPretty(1,ttcwp,cout)" << endl;
		transformsPersistentPretty(1, *ttcwp, cout); cout << endl << endl;

		cout << "transformsPersistentPretty(1,fftt(ff),cout)" << endl;
		transformsPersistentPretty(1, *fftt(*ff), cout); cout << endl << endl;

		std::stringstream str5;
		transformsPersistentPretty(1, *ttcwp, str5);
		auto tt5 = persistentsTransform(str5);
		cout << "tt5 = persistentsTransform(str5)" << endl
			<< *tt5 << endl << endl;

		cout << "rpln(aall(ttaa(ttcwp)))" << endl;
		rpln(cout, sorted(*aall(ttcwp->histogram_u()))); cout << endl;

		cout << "rpln(aall(ttaa(tt5)))" << endl;
		rpln(cout, sorted(*aall(tt5->histogram_u()))); cout << endl;

		std::stringstream str6;
		transformsPersistentPretty(1, *fftt(*ff), str6);
		auto tt6 = persistentsTransform(str6);
		cout << "tt6 = persistentsTransform(str6)" << endl
			<< *tt6 << endl << endl;

		cout << "fudsPersistent(ff,cout)" << endl;
		fudsPersistent(*ff, cout); cout << endl << endl;

		cout << "fudsPersistentPretty(1,ff,cout)" << endl;
		fudsPersistentPretty(1, *ff, cout); cout << endl << endl;

		std::stringstream str7;
		fudsPersistentPretty(1, *ff, str7);
		auto ff7 = persistentsFud(str7);
		cout << "ff7 = persistentsFud(str7)" << endl
			<< *ff7 << endl << endl;

		cout << "rpln(aall(ttaa(fftt(ff))))" << endl;
		rpln(cout, sorted(*aall(fftt(*ff)->histogram_u()))); cout << endl;

		cout << "rpln(aall(ttaa(fftt(ff7))))" << endl;
		rpln(cout, sorted(*aall(fftt(*ff7)->histogram_u()))); cout << endl;

		cout << "fudsPersistent(gg,cout)" << endl;
		fudsPersistent(*gg, cout); cout << endl << endl;

		cout << "fudsPersistentPretty(1,gg,cout)" << endl;
		fudsPersistentPretty(1, *gg, cout); cout << endl << endl;

		std::stringstream str8;
		fudsPersistentPretty(1, *gg, str8);
		auto ff8 = persistentsFud(str8);
		cout << "ff8 = persistentsFud(str8)" << endl
			<< *ff8 << endl << endl;

		cout << "rpln(aall(ttaa(fftt(gg))))" << endl;
		rpln(cout, sorted(*aall(fftt(*gg)->histogram_u()))); cout << endl;

		cout << "rpln(aall(ttaa(fftt(ff8))))" << endl;
		rpln(cout, sorted(*aall(fftt(*ff8)->histogram_u()))); cout << endl;
	}

	if (false)
	{
		auto uvars = systemsSetVar;
		auto cart = systemsSetVarsSetStateCartesian_u;
		auto llss = listsState;
		auto vol = systemsSetVarsVolume_u;
		auto ssplit = [](const VarUSet& vv, const Histogram& aa)
		{
			return setVarsSetStatesSplit(vv, *histogramsStates(aa));
		};
		auto unit = setStatesHistogramUnit_u;
		auto aall = histogramsList;
		auto size = histogramsSize;
		auto resize = histogramsResize;
		auto norm = [](const Histogram& aa)
		{
			return histogramsResize(1, aa);
		};
		auto add = pairHistogramsAdd_u;
		auto scalar = histogramScalar_u;
		auto regsing = histogramRegularUnitSingleton_u;
		auto regdiag = histogramRegularUnitDiagonal_u;
		auto regcart = histogramRegularCartesian_u;
		auto ared = [](const Histogram& aa, const VarUSet& vv)
		{
			return setVarsHistogramsReduce(vv, aa);
		};
		auto llhh = [llss](const VarList& vv, const IntValListPairList& ee)
		{
			std::vector<IdStatePair> ii;
			for (auto& pp : ee)
			{
				auto i = pp.first;
				auto& ll = pp.second;
				auto jj = std::vector<VarValPair>();
				for (int j = 0; j < ll.size(); j++)
					jj.push_back(VarValPair(vv[j], ll[j]));
				ii.push_back(IdStatePair(Id(i), *llss(jj)));
			}
			return listsHistory_u(ii);
		};
		auto hhll = historiesList;
		auto hvars = historiesSetVar;
		auto hsize = historiesSize;
		auto hred = [](const History& hh, const VarUSet& vv)
		{
			return setVarsHistoriesReduce(vv, hh);
		};
		auto hhaa = historiesHistogram;
		auto aahh = histogramsHistory_u;
		auto ind = histogramsIndependent;
		auto ent = histogramsEntropy;
		auto lent = [size, ent, ared](const VarUSet& vv, const Histogram& aa)
		{
			return size(aa).getDouble() * (ent(aa) - ent(*ared(aa, vv)));
		};
		auto algn = histogramsAlignment;
		auto trans = [](std::unique_ptr<Histogram>& xx, const VarUSet& ww)
		{
			return std::make_shared<Transform>(xx, ww);
		};
		auto ttaa = transformsHistogram;
		auto und = transformsUnderlying;
		auto der = transformsDerived;
		auto tmul = [](const Histogram& aa, const Transform& tt)
		{
			return transformsHistogramsApply(tt, aa);
		};
		auto lltt = [llss, trans](const VarList& kk, const VarList& ww, const ValListList& qq)
		{
			VarList vv(kk.begin(), kk.end());
			vv.insert(vv.end(), ww.begin(), ww.end());
			std::vector<StateRationalPair> ii;
			for (auto& ll : qq)
			{
				auto jj = std::vector<VarValPair>();
				for (int j = 0; j < ll.size(); j++)
					jj.push_back(VarValPair(vv[j], ll[j]));
				ii.push_back(StateRationalPair(*llss(jj), 1));
			}
			auto aa = std::make_unique<Histogram>(ii);
			return trans(aa, VarUSet(ww.begin(), ww.end()));
		};
		auto llff = setTransformsFud_u;
		auto fhis = fudsSetHistogram;
		auto fvars = fudsSetVar;
		auto fder = fudsDerived;
		auto fund = fudsUnderlying;
		auto fftt = fudsTransform;
		auto dep = fudsSetVarsDepends_u;

		auto pressure = Variable("pressure");
		auto cloud = Variable("cloud");
		auto wind = Variable("wind");
		auto rain = Variable("rain");
		auto cloud_and_wind = Variable("cloud_and_wind");
		auto cloud_and_pressure = Variable("cloud_and_pressure");
		auto cloud_wind_pressure = Variable("cloud_wind_pressure");
		auto low = Value("low");
		auto medium = Value("medium");
		auto high = Value("high");
		auto none = Value("none");
		auto light = Value("light");
		auto heavy = Value("heavy");
		auto strong = Value("strong");
		auto uu = listsSystem_u(std::vector<VarValSetPair>{
			VarValSetPair(pressure, ValSet{ low,medium,high }),
				VarValSetPair(cloud, ValSet{ none,light,heavy }),
				VarValSetPair(wind, ValSet{ none,light,strong }),
				VarValSetPair(rain, ValSet{ none,light,heavy })});
		auto vv = uvars(*uu);
		auto hh = llhh(VarList{ pressure, cloud, wind, rain }, IntValListPairList{
			IntValListPair(1, ValList{ high, none, none, none }),
			IntValListPair(2, ValList{ medium, light, none, light }),
			IntValListPair(3, ValList{ high, none, light, none }),
			IntValListPair(4, ValList{ low, heavy, strong, heavy }),
			IntValListPair(5, ValList{ low, none, light, light }),
			IntValListPair(6, ValList{ medium, none, light, light }),
			IntValListPair(7, ValList{ low, heavy, light, heavy }),
			IntValListPair(8, ValList{ high, none, light, none }),
			IntValListPair(9, ValList{ medium, light, strong, heavy }),
			IntValListPair(10, ValList{ medium, light, light, light }),
			IntValListPair(11, ValList{ high, light, light, heavy }),
			IntValListPair(12, ValList{ medium, none, none, none }),
			IntValListPair(13, ValList{ medium, light, none, none }),
			IntValListPair(14, ValList{ high, light, strong, light }),
			IntValListPair(15, ValList{ medium, none, light, light }),
			IntValListPair(16, ValList{ low, heavy, strong, heavy }),
			IntValListPair(17, ValList{ low, heavy, light, heavy }),
			IntValListPair(18, ValList{ high, none, none, none }),
			IntValListPair(19, ValList{ low, light, none, light }),
			IntValListPair(20, ValList{ high, none, none, none }) });
		auto aa = hhaa(*hh);
		auto ttcw = lltt(VarList{ cloud, wind }, VarList{ cloud_and_wind }, ValListList{
			ValList{ none, none, none },
			ValList{ none, light, light },
			ValList{ none, strong, light },
			ValList{ light, none, light },
			ValList{ light, light, light },
			ValList{ light, strong, light },
			ValList{ heavy, none, strong },
			ValList{ heavy, light, strong },
			ValList{ heavy, strong, strong } });
		auto ttcp = lltt(VarList{ cloud, pressure }, VarList{ cloud_and_pressure }, ValListList{
			ValList{ none, high, none },
			ValList{ none, medium, light },
			ValList{ none, low, light },
			ValList{ light, high, light },
			ValList{ light, medium, light },
			ValList{ light, low, light },
			ValList{ heavy, high, strong },
			ValList{ heavy, medium, strong },
			ValList{ heavy, low, strong } });
		auto ff = llff(TransformPtrList{ ttcw, ttcp });
		auto ttcwp = lltt(VarList{ cloud_and_wind,cloud_and_pressure }, VarList{ cloud_wind_pressure }, ValListList{
			ValList{ none, none, none },
			ValList{ none, light, none },
			ValList{ none, strong, none },
			ValList{ light, none, none },
			ValList{ light, light, light },
			ValList{ light, strong, light },
			ValList{ strong, none, none },
			ValList{ strong, light, light },
			ValList{ strong, strong, strong } });
		auto gg = llff(TransformPtrList{ ttcw, ttcp, ttcwp });

		cout << "uu" << endl
			<< *uu << endl << endl;

		StrVarPtrMap m;

		cout << "systemsPersistent(uu,cout)" << endl;
		systemsPersistent(*uu, cout); cout << endl << endl;

		cout << "systemsPersistentSorted(uu,cout)" << endl;
		systemsPersistentSorted(*uu, cout); cout << endl << endl;

		std::stringstream str;
		systemsPersistent(*uu, str);
		auto uu1 = persistentsSystem(str,m);
		cout << "uu1 = persistentsSystem(str)" << endl
			<< *uu1 << endl << endl;

		std::stringstream str2;
		systemsPersistentSorted(*uu, str2);
		auto uu2 = persistentsSystem(str2,m);
		cout << "uu2 = persistentsSystem(str2)" << endl
			<< *uu2 << endl << endl;

		cout << "historiesPersistent(hh,cout)" << endl;
		historiesPersistent(*hh, cout); cout << endl << endl;

		std::stringstream str3;
		historiesPersistent(*hh, str3);
		auto hh2 = persistentsHistory(str3,m);
		cout << "hh2 = persistentsHistory(str3)" << endl
			<< *hh2 << endl << endl;

		cout << "rpln(aall(aa))" << endl;
		rpln(cout, sorted(*aall(*aa))); cout << endl;

		cout << "rpln(aall(hhaa(hh2)))" << endl;
		rpln(cout, sorted(*aall(*hhaa(*hh2)))); cout << endl;

		cout << "historiesPersistentPretty(1,hh,cout)" << endl;
		historiesPersistentPretty(1, *hh, cout); cout << endl << endl;

		std::stringstream str4;
		historiesPersistentPretty(1, *hh, str4);
		auto hh3 = persistentsHistory(str4,m);
		cout << "hh3 = persistentsHistory(str4)" << endl
			<< *hh3 << endl << endl;

		cout << "rpln(aall(aa))" << endl;
		rpln(cout, sorted(*aall(*aa))); cout << endl;

		cout << "rpln(aall(hhaa(hh3)))" << endl;
		rpln(cout, sorted(*aall(*hhaa(*hh3)))); cout << endl;

		cout << "transformsPersistent(ttcw,cout)" << endl;
		transformsPersistent(*ttcw, cout); cout << endl << endl;

		cout << "transformsPersistent(ttcp,cout)" << endl;
		transformsPersistent(*ttcp, cout); cout << endl << endl;

		cout << "transformsPersistent(ttcwp,cout)" << endl;
		transformsPersistent(*ttcwp, cout); cout << endl << endl;

		cout << "transformsPersistent(fftt(ff),cout)" << endl;
		transformsPersistent(*fftt(*ff), cout); cout << endl << endl;

		cout << "transformsPersistentPretty(1,ttcwp,cout)" << endl;
		transformsPersistentPretty(1, *ttcwp, cout); cout << endl << endl;

		cout << "transformsPersistentPretty(1,fftt(ff),cout)" << endl;
		transformsPersistentPretty(1, *fftt(*ff), cout); cout << endl << endl;

		std::stringstream str5;
		transformsPersistentPretty(1, *ttcwp, str5);
		auto tt5 = persistentsTransform(str5,m);
		cout << "tt5 = persistentsTransform(str5)" << endl
			<< *tt5 << endl << endl;

		cout << "rpln(aall(ttaa(ttcwp)))" << endl;
		rpln(cout, sorted(*aall(ttcwp->histogram_u()))); cout << endl;

		cout << "rpln(aall(ttaa(tt5)))" << endl;
		rpln(cout, sorted(*aall(tt5->histogram_u()))); cout << endl;

		std::stringstream str6;
		transformsPersistentPretty(1, *fftt(*ff), str6);
		auto tt6 = persistentsTransform(str6,m);
		cout << "tt6 = persistentsTransform(str6)" << endl
			<< *tt6 << endl << endl;

		cout << "fudsPersistent(ff,cout)" << endl;
		fudsPersistent(*ff, cout); cout << endl << endl;

		cout << "fudsPersistentPretty(1,ff,cout)" << endl;
		fudsPersistentPretty(1, *ff, cout); cout << endl << endl;

		std::stringstream str7;
		fudsPersistentPretty(1, *ff, str7);
		auto ff7 = persistentsFud(str7,m);
		cout << "ff7 = persistentsFud(str7)" << endl
			<< *ff7 << endl << endl;

		cout << "rpln(aall(ttaa(fftt(ff))))" << endl;
		rpln(cout, sorted(*aall(fftt(*ff)->histogram_u()))); cout << endl;

		cout << "rpln(aall(ttaa(fftt(ff7))))" << endl;
		rpln(cout, sorted(*aall(fftt(*ff7)->histogram_u()))); cout << endl;

		cout << "fudsPersistent(gg,cout)" << endl;
		fudsPersistent(*gg, cout); cout << endl << endl;

		cout << "fudsPersistentPretty(1,gg,cout)" << endl;
		fudsPersistentPretty(1, *gg, cout); cout << endl << endl;

		std::stringstream str8;
		fudsPersistentPretty(1, *gg, str8);
		auto ff8 = persistentsFud(str8,m);
		cout << "ff8 = persistentsFud(str8)" << endl
			<< *ff8 << endl << endl;

		cout << "rpln(aall(ttaa(fftt(gg))))" << endl;
		rpln(cout, sorted(*aall(fftt(*gg)->histogram_u()))); cout << endl;

		cout << "rpln(aall(ttaa(fftt(ff8))))" << endl;
		rpln(cout, sorted(*aall(fftt(*ff8)->histogram_u()))); cout << endl;
	}

	if (false)
	{
		unsigned int n = std::thread::hardware_concurrency();
		std::cout << n << " concurrent threads are supported.\n";
	}

	if (false)
	{
		auto dfund = decompFudsUnderlying;
		auto dfff = decompFudsFud;
		auto fvars = fudsSetVar;

		ifstream istrm("../NISTPy/NIST_model2.json");

		auto start = chrono::system_clock::now();
		auto df = persistentsDecompFud(istrm);
		auto end = chrono::system_clock::now();
		chrono::duration<double> elapsed_seconds = end - start;
		cout << "df = persistentsDecompFud(istrm) " << elapsed_seconds.count() << "s" << endl;

		cout << "len(dfund(df))" << endl
			<< dfund(*df)->size() << endl << endl;

		cout << "len(fvars(dfff(df)))" << endl
			<< fvars(*dfff(*df))->size() << endl << endl;

		std::stringstream str1;
		start = chrono::system_clock::now();
		decompFudsPersistentPretty(*df, str1);
		end = chrono::system_clock::now();
		elapsed_seconds = end - start;
		cout << "decompFudsPersistentPretty(*df, str1) " << elapsed_seconds.count() << "s" << endl;

		start = chrono::system_clock::now();
		auto df1 = persistentsDecompFud(str1);
		end = std::chrono::system_clock::now();
		elapsed_seconds = end - start;
		cout << "df1 = persistentsDecompFud(str1) " << elapsed_seconds.count() << "s" << endl;

		cout << "len(dfund(df1))" << endl
			<< dfund(*df1)->size() << endl << endl;

		cout << "len(fvars(dfff(df1)))" << endl
			<< fvars(*dfff(*df1))->size() << endl << endl;


		/*
		df = persistentsDecompFud(istrm) 0.187205s
		len(dfund(df))
		134

		len(fvars(dfff(df)))
		515

		decompFudsPersistentPretty(*df, str1) 0.140404s
		df1 = persistentsDecompFud(str1) 0.156004s
		len(dfund(df1))
		134

		len(fvars(dfff(df1)))
		515
		*/
	}

	if (false)
	{
		auto dfund = decompFudsUnderlying;
		auto dfff = decompFudsFud;
		auto fvars = fudsSetVar;

		ifstream istrm("../NISTPy/NIST_model2.json");

		StrVarPtrMap m;

		auto start = chrono::system_clock::now();
		auto df = persistentsDecompFud(istrm,m);
		auto end = chrono::system_clock::now();
		chrono::duration<double> elapsed_seconds = end - start;
		cout << "df = persistentsDecompFud(istrm) " << elapsed_seconds.count() << "s" << endl;

		cout << "len(dfund(df))" << endl
			<< dfund(*df)->size() << endl << endl;

		cout << "len(fvars(dfff(df)))" << endl
			<< fvars(*dfff(*df))->size() << endl << endl;

		std::stringstream str1;
		start = chrono::system_clock::now();
		decompFudsPersistentPretty(*df, str1);
		end = chrono::system_clock::now();
		elapsed_seconds = end - start;
		cout << "decompFudsPersistentPretty(*df, str1) " << elapsed_seconds.count() << "s" << endl;

		StrVarPtrMap m2;

		start = chrono::system_clock::now();
		auto df1 = persistentsDecompFud(str1,m2);
		end = std::chrono::system_clock::now();
		elapsed_seconds = end - start;
		cout << "df1 = persistentsDecompFud(str1) " << elapsed_seconds.count() << "s" << endl;

		cout << "len(dfund(df1))" << endl
			<< dfund(*df1)->size() << endl << endl;

		cout << "len(fvars(dfff(df1)))" << endl
			<< fvars(*dfff(*df1))->size() << endl << endl;


		/*
		df = persistentsDecompFud(istrm) 0.156007s
		len(dfund(df))
		134

		len(fvars(dfff(df)))
		515

		decompFudsPersistentPretty(*df, str1) 0.156007s
		df1 = persistentsDecompFud(str1) 0.171608s
		len(dfund(df1))
		134

		len(fvars(dfff(df1)))
		515
		*/
	}


	if (false)
	{
		auto dfund = decompFudsUnderlying;
		auto dfff = decompFudsFud;
		auto fvars = fudsSetVar;

		ifstream istrm("../NISTPy/NIST_model35.json");

		auto start = chrono::system_clock::now();
		auto df = persistentsDecompFud(istrm);
		auto end = chrono::system_clock::now();
		chrono::duration<double> elapsed_seconds = end - start;
		cout << "df = persistentsDecompFud(istrm) " << elapsed_seconds.count() << "s" << endl;

		cout << "len(dfund(df))" << endl
			<< dfund(*df)->size() << endl << endl;

		cout << "len(fvars(dfff(df)))" << endl
			<< fvars(*dfff(*df))->size() << endl << endl;

		std::stringstream str1;
		start = chrono::system_clock::now();
		decompFudsPersistentPretty(*df, str1);
		end = chrono::system_clock::now();
		elapsed_seconds = end - start;
		cout << "decompFudsPersistentPretty(*df, str1) " << elapsed_seconds.count() << "s" << endl;

		start = chrono::system_clock::now();
		auto df1 = persistentsDecompFud(str1);
		end = std::chrono::system_clock::now();
		elapsed_seconds = end - start;
		cout << "df1 = persistentsDecompFud(str1) " << elapsed_seconds.count() << "s" << endl;

		cout << "len(dfund(df1))" << endl
			<< dfund(*df1)->size() << endl << endl;

		cout << "len(fvars(dfff(df1)))" << endl
			<< fvars(*dfff(*df1))->size() << endl << endl;


		/*
		df = persistentsDecompFud(istrm) 3.05768s
		len(dfund(df))
		488

		len(fvars(dfff(df)))
		4040

		decompFudsPersistentPretty(*df, str1) 2.60527s
		df1 = persistentsDecompFud(str1) 2.87047s
		len(dfund(df1))
		488

		len(fvars(dfff(df1)))
		4040
		*/
	}

	if (false)
	{
		auto dfund = decompFudsUnderlying;
		auto dfff = decompFudsFud;
		auto fvars = fudsSetVar;

		ifstream istrm("../NISTPy/NIST_model35.json");

		StrVarPtrMap m;

		auto start = chrono::system_clock::now();
		auto df = persistentsDecompFud(istrm,m);
		auto end = chrono::system_clock::now();
		chrono::duration<double> elapsed_seconds = end - start;
		cout << "df = persistentsDecompFud(istrm) " << elapsed_seconds.count() << "s" << endl;

		cout << "len(dfund(df))" << endl
			<< dfund(*df)->size() << endl << endl;

		cout << "len(fvars(dfff(df)))" << endl
			<< fvars(*dfff(*df))->size() << endl << endl;

		std::stringstream str1;
		start = chrono::system_clock::now();
		decompFudsPersistentPretty(*df, str1);
		end = chrono::system_clock::now();
		elapsed_seconds = end - start;
		cout << "decompFudsPersistentPretty(*df, str1) " << elapsed_seconds.count() << "s" << endl;

		StrVarPtrMap m2;

		start = chrono::system_clock::now();
		auto df1 = persistentsDecompFud(str1,m2);
		end = std::chrono::system_clock::now();
		elapsed_seconds = end - start;
		cout << "df1 = persistentsDecompFud(str1) " << elapsed_seconds.count() << "s" << endl;

		cout << "len(dfund(df1))" << endl
			<< dfund(*df1)->size() << endl << endl;

		cout << "len(fvars(dfff(df1)))" << endl
			<< fvars(*dfff(*df1))->size() << endl << endl;


		/*
		df = persistentsDecompFud(istrm) 2.96406s
		len(dfund(df))
		488

		len(fvars(dfff(df)))
		4040

		decompFudsPersistentPretty(*df, str1) 2.46485s
		df1 = persistentsDecompFud(str1) 2.84025s
		len(dfund(df1))
		488

		len(fvars(dfff(df1)))
		4040
		*/
	}


	if (false)
	{
		auto dfund = decompFudsUnderlying;
		auto dfff = decompFudsFud;
		auto fvars = fudsSetVar;

		ifstream istrm("../NISTPy/NIST_model24.json");

		auto start = chrono::system_clock::now();
		auto df = persistentsDecompFud(istrm);
		auto end = chrono::system_clock::now();
		chrono::duration<double> elapsed_seconds = end - start;
		cout << "df = persistentsDecompFud(istrm) " << elapsed_seconds.count() << "s" << endl;

		cout << "len(dfund(df))" << endl
			<< dfund(*df)->size() << endl << endl;

		cout << "len(fvars(dfff(df)))" << endl
			<< fvars(*dfff(*df))->size() << endl << endl;

		std::stringstream str1;
		start = chrono::system_clock::now();
		decompFudsPersistentPretty(*df, str1);
		end = chrono::system_clock::now();
		elapsed_seconds = end - start;
		cout << "decompFudsPersistentPretty(*df, str1) " << elapsed_seconds.count() << "s" << endl;

		start = chrono::system_clock::now();
		auto df1 = persistentsDecompFud(str1);
		end = std::chrono::system_clock::now();
		elapsed_seconds = end - start;
		cout << "df1 = persistentsDecompFud(str1) " << elapsed_seconds.count() << "s" << endl;

		cout << "len(dfund(df1))" << endl
			<< dfund(*df1)->size() << endl << endl;

		cout << "len(fvars(dfff(df1)))" << endl
			<< fvars(*dfff(*df1))->size() << endl << endl;


		/*
		df = persistentsDecompFud(istrm) 11.4663s
		len(dfund(df))
		639

		len(fvars(dfff(df)))
		5966

		decompFudsPersistentPretty(*df, str1) 9.26664s
		df1 = persistentsDecompFud(str1) 10.889s
		len(dfund(df1))
		639

		len(fvars(dfff(df1)))
		5966
		*/
	}

	if (false)
	{
		auto dfund = decompFudsUnderlying;
		auto dfff = decompFudsFud;
		auto fvars = fudsSetVar;

		ifstream istrm("../NISTPy/NIST_model24.json");

		StrVarPtrMap m;

		auto start = chrono::system_clock::now();
		auto df = persistentsDecompFud(istrm,m);
		auto end = chrono::system_clock::now();
		chrono::duration<double> elapsed_seconds = end - start;
		cout << "df = persistentsDecompFud(istrm) " << elapsed_seconds.count() << "s" << endl;

		cout << "len(dfund(df))" << endl
			<< dfund(*df)->size() << endl << endl;

		cout << "len(fvars(dfff(df)))" << endl
			<< fvars(*dfff(*df))->size() << endl << endl;

		std::stringstream str1;
		start = chrono::system_clock::now();
		decompFudsPersistentPretty(*df, str1);
		end = chrono::system_clock::now();
		elapsed_seconds = end - start;
		cout << "decompFudsPersistentPretty(*df, str1) " << elapsed_seconds.count() << "s" << endl;

		StrVarPtrMap m2;

		start = chrono::system_clock::now();
		auto df1 = persistentsDecompFud(str1,m2);
		end = std::chrono::system_clock::now();
		elapsed_seconds = end - start;
		cout << "df1 = persistentsDecompFud(str1) " << elapsed_seconds.count() << "s" << endl;

		cout << "len(dfund(df1))" << endl
			<< dfund(*df1)->size() << endl << endl;

		cout << "len(fvars(dfff(df1)))" << endl
			<< fvars(*dfff(*df1))->size() << endl << endl;


		/*
		df = persistentsDecompFud(istrm) 10.6394s
		len(dfund(df))
		639

		len(fvars(dfff(df)))
		5966

		decompFudsPersistentPretty(*df, str1) 8.92337s
		df1 = persistentsDecompFud(str1) 9.79699s
		len(dfund(df1))
		639

		len(fvars(dfff(df1)))
		5966
		*/
	}

	if (false)
	{
		auto fsys = fudsSystemImplied;
		auto dfund = decompFudsUnderlying;
		auto dfff = decompFudsFud;
		auto fvars = fudsSetVar;

		ifstream istrm("../NISTPy/NIST_model24.json");

		StrVarPtrMap m;

		auto start = chrono::system_clock::now();
		auto df = persistentsDecompFud(istrm,m);
		auto end = chrono::system_clock::now();
		cout << "df = persistentsDecompFud(istrm) " << ((chrono::duration<double>)(end - start)).count() << "s" << endl;

		auto ff = dfff(*df);
		auto uu = fsys(*ff);
		cout << "len(uu)" << endl
			<< uu->map_u().size() << endl << endl;

		std::stringstream str1;
		start = chrono::system_clock::now();
		systemsPersistent(*uu, str1);
		end = chrono::system_clock::now();
		cout << "systemsPersistent(*uu, str1) " << ((chrono::duration<double>)(end - start)).count() << "s" << endl;

		StrVarPtrMap m2;

		start = chrono::system_clock::now();
		auto uu1 = persistentsSystem(str1, m2);
		end = std::chrono::system_clock::now();
		cout << "uu1 = persistentsSystem(str1) " << ((chrono::duration<double>)(end - start)).count() << "s" << endl;

		cout << "len(uu1)" << endl
			<< uu1->map_u().size() << endl << endl;


		/*
		df = persistentsDecompFud(istrm) 10.3273s
		len(uu)
		5966

		systemsPersistent(*uu, str1) 0.0624004s
		uu1 = persistentsSystem(str1) 0.109201s
		len(uu1)
		5966
		*/
	}

	if (true)
	{
		auto start = chrono::system_clock::now();
		double r = 0.0;
		for (double a = 0.0; a < 1e7; a += 0.1)
			r = alngam(a);
		auto end = chrono::system_clock::now();
		cout.precision(16);
		cout << "r = " << r  << " " << ((chrono::duration<double>)(end - start)).count() << "s" << endl;
	}

	if (true)
	{
		auto start = chrono::system_clock::now();
		double r = 0.0;
		for (double a = 0.0; a < 1e7; a += 0.1)
			r = lgamma(a);
		auto end = chrono::system_clock::now();
		cout.precision(16);
		cout << "r = " << r << " " << ((chrono::duration<double>)(end - start)).count() << "s" << endl;
		/*
		r = 151180949.0653166 6.397066s
		r = 151180949.0653166 14.8991726s
		*/
	}

	return 0;
}