// -*- coding: utf-8 -*-
// Copyright (C) 2014, 2015 Laboratoire de Recherche
// et Développement de l'Epita (LRDE).
//
// This file is part of Spot, a model checking library.
//
// Spot is free software; you can redistribute it and/or modify it
// under the terms of the GNU General Public License as published by
// the Free Software Foundation; either version 3 of the License, or
// (at your option) any later version.
//
// Spot is distributed in the hope that it will be useful, but WITHOUT
// ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
// or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public
// License for more details.
//
// You should have received a copy of the GNU General Public License
// along with this program.  If not, see <http://www.gnu.org/licenses/>.

#include "stutter.hh"
#include "twa/twa.hh"
#include "misc/hash.hh"
#include "misc/hashfunc.hh"
#include "tl/apcollect.hh"
#include "translate.hh"
#include "tl/remove_x.hh"
#include "twaalgos/product.hh"
#include "twaalgos/ltl2tgba_fm.hh"
#include "twaalgos/isdet.hh"
#include "twaalgos/complement.hh"
#include "twaalgos/remfin.hh"
#include "twa/twaproduct.hh"
#include "twa/bddprint.hh"
#include <deque>
#include <unordered_map>
#include <unordered_set>
#include <vector>

namespace spot
{
  namespace
  {
    class state_tgbasl: public state
    {
    public:
      state_tgbasl(const state* s, bdd cond) : s_(s), cond_(cond)
      {
      }

      virtual
      ~state_tgbasl()
      {
        s_->destroy();
      }

      virtual int
      compare(const state* other) const
      {
        const state_tgbasl* o =
          down_cast<const state_tgbasl*>(other);
        assert(o);
        int res = s_->compare(o->real_state());
        if (res != 0)
          return res;
        return cond_.id() - o->cond_.id();
      }

      virtual size_t
      hash() const
      {
        return wang32_hash(s_->hash()) ^ wang32_hash(cond_.id());
      }

      virtual
      state_tgbasl* clone() const
      {
        return new state_tgbasl(*this);
      }

      const state*
      real_state() const
      {
        return s_;
      }

      bdd
      cond() const
      {
        return cond_;
      }

    private:
      const state* s_;
      bdd cond_;
    };

    class twasl_succ_iterator : public twa_succ_iterator
    {
    public:
      twasl_succ_iterator(twa_succ_iterator* it, const state_tgbasl* state,
			   bdd_dict_ptr d, bdd atomic_propositions)
        : it_(it), state_(state), aps_(atomic_propositions), d_(d)
      {
      }

      virtual
      ~twasl_succ_iterator()
      {
        delete it_;
      }

      // iteration

      bool
      first()
      {
        loop_ = false;
        done_ = false;
        need_loop_ = true;
        if (it_->first())
          {
            cond_ = it_->cond();
            next_edge();
          }
        return true;
      }

      bool
      next()
      {
        if (cond_ != bddfalse)
          {
            next_edge();
            return true;
          }
        if (!it_->next())
          {
            if (loop_ || !need_loop_)
              done_ = true;
            loop_ = true;
            return !done_;
          }
        else
          {
            cond_ = it_->cond();
            next_edge();
            return true;
          }
      }

      bool
      done() const
      {
        return it_->done() && done_;
      }

      // inspection

      state_tgbasl*
      dst() const
      {
        if (loop_)
          return new state_tgbasl(state_->real_state(), state_->cond());
        return new state_tgbasl(it_->dst(), one_);
      }

      bdd
      cond() const
      {
        if (loop_)
          return state_->cond();
        return one_;
      }

      acc_cond::mark_t
      acc() const
      {
        if (loop_)
          return 0U;
        return it_->acc();
      }

    private:
      void
      next_edge()
      {
        one_ = bdd_satoneset(cond_, aps_, bddtrue);
        cond_ -= one_;
        if (need_loop_ && (state_->cond() == one_)
            && (state_ == it_->dst()))
          need_loop_ = false;
      }

      twa_succ_iterator* it_;
      const state_tgbasl* state_;
      bdd cond_;
      bdd one_;
      bdd aps_;
      bdd_dict_ptr d_;
      bool loop_;
      bool need_loop_;
      bool done_;
    };


    class tgbasl final : public twa
    {
    public:
      tgbasl(const const_twa_ptr& a, bdd atomic_propositions)
	: twa(a->get_dict()), a_(a), aps_(atomic_propositions)
      {
	get_dict()->register_all_propositions_of(&a_, this);
	assert(acc_.num_sets() == 0);
	acc_.add_sets(a_->num_sets());
	acc_.set_generalized_buchi();
      }

      virtual ~tgbasl()
      {
	get_dict()->unregister_all_my_variables(this);
      }

      virtual const state* get_init_state() const override
      {
	return new state_tgbasl(a_->get_init_state(), bddfalse);
      }

      virtual twa_succ_iterator* succ_iter(const state* state) const override
      {
	const state_tgbasl* s = down_cast<const state_tgbasl*>(state);
	assert(s);
	return new twasl_succ_iterator(a_->succ_iter(s->real_state()), s,
					a_->get_dict(), aps_);
      }

      virtual std::string format_state(const state* state) const override
      {
	const state_tgbasl* s = down_cast<const state_tgbasl*>(state);
	assert(s);
	return (a_->format_state(s->real_state())
		+ ", "
		+ bdd_format_formula(a_->get_dict(), s->cond()));
      }

    protected:
      virtual bdd compute_support_conditions(const state*) const override
      {
	return bddtrue;
      }

    private:
      const_twa_ptr a_;
      bdd aps_;
    };

    typedef std::shared_ptr<tgbasl> tgbasl_ptr;

    inline tgbasl_ptr make_tgbasl(const const_twa_ptr& aut, bdd ap)
    {
      return std::make_shared<tgbasl>(aut, ap);
    }



    typedef std::pair<unsigned, bdd> stutter_state;

    struct stutter_state_hash
    {
      size_t
      operator()(const stutter_state& s) const
      {
	return wang32_hash(s.first) ^ wang32_hash(s.second.id());
      }
    };

    // Associate the stutter state to its number.
    typedef std::unordered_map<stutter_state, unsigned,
			       stutter_state_hash> ss2num_map;

    // Queue of state to be processed.
    typedef std::deque<stutter_state> queue_t;
  }

  twa_graph_ptr
  sl(const twa_graph_ptr& a)
  {
    return sl(a, a->ap_var());
  }

  twa_graph_ptr
  sl2(const twa_graph_ptr& a)
  {
    return sl2(a, a->ap_var());
  }

  twa_graph_ptr
  sl(const const_twa_graph_ptr& a, bdd atomic_propositions)
  {
    // The result automaton uses numbered states.
    twa_graph_ptr res = make_twa_graph(a->get_dict());
    // We use the same BDD variables as the input.
    res->copy_ap_of(a);
    res->copy_acceptance_of(a);
    // These maps make it possible to convert stutter_state to number
    // and vice-versa.
    ss2num_map ss2num;

    queue_t todo;

    unsigned s0 = a->get_init_state_number();
    stutter_state s(s0, bddfalse);
    ss2num[s] = 0;
    res->new_state();
    todo.push_back(s);

    while (!todo.empty())
      {
	s = todo.front();
	todo.pop_front();
	unsigned src = ss2num[s];

	bool self_loop_needed = true;

	for (auto& t : a->out(s.first))
	  {
	    bdd all = t.cond;
	    while (all != bddfalse)
	      {
		bdd one = bdd_satoneset(all, atomic_propositions, bddtrue);
		all -= one;

		stutter_state d(t.dst, one);

		auto r = ss2num.emplace(d, ss2num.size());
		unsigned dest = r.first->second;

		if (r.second)
		  {
		    todo.push_back(d);
		    unsigned u = res->new_state();
		    assert(u == dest);
		    (void)u;
		  }

		// Create the edge.
		res->new_edge(src, dest, one, t.acc);

		if (src == dest)
		  self_loop_needed = false;
	      }
	  }

	if (self_loop_needed && s.second != bddfalse)
	  res->new_edge(src, src, s.second, 0U);
      }
    res->merge_edges();
    return res;
  }

  twa_graph_ptr
  sl2(twa_graph_ptr&& a, bdd atomic_propositions)
  {
    if (atomic_propositions == bddfalse)
      atomic_propositions = a->ap_var();
    unsigned num_states = a->num_states();
    unsigned num_edges = a->num_edges();
    std::vector<bdd> selfloops(num_states, bddfalse);
    std::map<std::pair<unsigned, int>, unsigned> newstates;
    // Record all the conditions for which we can selfloop on each
    // state.
    for (auto& t: a->edges())
      if (t.src == t.dst)
	selfloops[t.src] |= t.cond;
    for (unsigned t = 1; t <= num_edges; ++t)
      {
	auto& td = a->edge_storage(t);
	if (a->is_dead_edge(td))
	  continue;

	unsigned src = td.src;
	unsigned dst = td.dst;
	if (src != dst)
	  {
	    bdd all = td.cond;
	    // If there is a self-loop with the whole condition on
	    // either end of the edge, do not bother with it.
	    if (bdd_implies(all, selfloops[src])
		|| bdd_implies(all, selfloops[dst]))
	      continue;
	    // Do not use td in the loop because the new_edge()
	    // might invalidate it.
	    auto acc = td.acc;
	    while (all != bddfalse)
	      {
		bdd one = bdd_satoneset(all, atomic_propositions, bddtrue);
		all -= one;
		// Skip if there is a loop for this particular letter.
		if (bdd_implies(one, selfloops[src])
		    || bdd_implies(one, selfloops[dst]))
		  continue;
		auto p = newstates.emplace(std::make_pair(dst, one.id()), 0);
		if (p.second)
		  p.first->second = a->new_state();
		unsigned tmp = p.first->second; // intermediate state
		unsigned i = a->new_edge(src, tmp, one, acc);
		assert(i > num_edges);
		i = a->new_edge(tmp, tmp, one, 0U);
		assert(i > num_edges);
		// No acceptance here to preserve the state-based property.
		i = a->new_edge(tmp, dst, one, 0U);
		assert(i > num_edges);
		(void)i;
	      }
	  }
      }
    if (num_states != a->num_states())
      a->prop_keep({true,	// state_based
	            false,	// inherently_weak
	            false,	// deterministic
	            false,      // stutter inv.
	           });
    a->merge_edges();
    return a;
  }

  twa_graph_ptr
  sl2(const const_twa_graph_ptr& a, bdd atomic_propositions)
  {
    return sl2(make_twa_graph(a, twa::prop_set::all()),
	       atomic_propositions);
  }


  twa_graph_ptr
  closure(twa_graph_ptr&& a)
  {
    a->prop_keep({false,	// state_based
	          false,	// inherently_weak
	          false,	// deterministic
	          false,        // stutter inv.
	         });

    unsigned n = a->num_states();
    std::vector<unsigned> todo;
    std::vector<std::vector<unsigned> > dst2trans(n);

    for (unsigned state = 0; state < n; ++state)
      {
	auto trans = a->out(state);

	for (auto it = trans.begin(); it != trans.end(); ++it)
	  {
	    todo.push_back(it.trans());
	    dst2trans[it->dst].push_back(it.trans());
	  }

	while (!todo.empty())
	  {
	    auto t1 = a->edge_storage(todo.back());
	    todo.pop_back();

	    for (auto& t2 : a->out(t1.dst))
	      {
		bdd cond = t1.cond & t2.cond;
		if (cond != bddfalse)
		  {
                    bool need_new_trans = true;
		    acc_cond::mark_t acc = t1.acc | t2.acc;
                    for (auto& t: dst2trans[t2.dst])
                      {
                        auto& ts = a->edge_storage(t);
                        if (acc == ts.acc)
                          {
                            if (!bdd_implies(cond, ts.cond))
                              {
                                ts.cond |= cond;
                                if (std::find(todo.begin(), todo.end(), t)
                                    == todo.end())
                                  todo.push_back(t);
                              }
                            need_new_trans = false;
			    break;
                          }
			else if (cond == ts.cond)
			  {
			    acc |= ts.acc;
			    if (ts.acc != acc)
			      {
				ts.acc = acc;
				if (std::find(todo.begin(), todo.end(), t)
				    == todo.end())
				  todo.push_back(t);
			      }
                            need_new_trans = false;
			    break;
			  }
                      }
                    if (need_new_trans)
                      {
			// Load t2.dst first, because t2 can be
			// invalidated by new_edge().
			auto dst = t2.dst;
                        auto i = a->new_edge(state, dst, cond, acc);
                        dst2trans[dst].push_back(i);
                        todo.push_back(i);
                      }
		  }
	      }
	  }
        for (auto& it: dst2trans)
          it.clear();
      }
    return a;
  }

  twa_graph_ptr
  closure(const const_twa_graph_ptr& a)
  {
    return closure(make_twa_graph(a, {true, true, true, false}));
  }

  // The stutter check algorithm to use can be overridden via an
  // environment variable.
  static int default_stutter_check_algorithm()
  {
    static const char* stutter_check = getenv("SPOT_STUTTER_CHECK");
    if (stutter_check)
      {
	char* endptr;
	long res = strtol(stutter_check, &endptr, 10);
	if (*endptr || res < 0 || res > 9)
	  throw
	    std::runtime_error("invalid value for SPOT_STUTTER_CHECK.");
	return res;
      }
    else
      {
	return 8;     // The best variant, according to our benchmarks.
      }
  }

  bool
  is_stutter_invariant(formula f)
  {
    if (f.is_ltl_formula() && f.is_syntactic_stutter_invariant())
      return true;

    int algo = default_stutter_check_algorithm();

    if (algo == 0 || algo == 9)
      // Etessami's check via syntactic transformation.
      {
	if (!f.is_ltl_formula())
	  throw std::runtime_error("Cannot use the syntactic "
				   "stutter-invariance check "
				   "for non-LTL formulas");
	formula g = remove_x(f);
	bool res;
	if (algo == 0)		// Equivalence check
	  {
	    tl_simplifier ls;
	    res = ls.are_equivalent(f, g);
	  }
	else
	  {
	    formula h = formula::Xor(f, g);
	    res = ltl_to_tgba_fm(h, make_bdd_dict())->is_empty();
	  }
	return res;
      }

    // Prepare for an automata-based check.
    translator trans;
    auto aut_f = trans.run(f);
    auto aut_nf = trans.run(formula::Not(f));
    bdd aps = atomic_prop_collect_as_bdd(f, aut_f);
    return is_stutter_invariant(std::move(aut_f), std::move(aut_nf), aps, algo);
  }

  bool
  is_stutter_invariant(twa_graph_ptr&& aut_f,
                       twa_graph_ptr&& aut_nf, bdd aps, int algo)
  {
    if (algo == 0)
      algo = default_stutter_check_algorithm();

    switch (algo)
      {
      case 1: // sl(aut_f) x sl(aut_nf)
	return product(sl(std::move(aut_f), aps),
		       sl(std::move(aut_nf), aps))->is_empty();
      case 2: // sl(cl(aut_f)) x aut_nf
	return product(sl(closure(std::move(aut_f)), aps),
		       std::move(aut_nf))->is_empty();
      case 3: // (cl(sl(aut_f)) x aut_nf
	return product(closure(sl(std::move(aut_f), aps)),
		       std::move(aut_nf))->is_empty();
      case 4: // sl2(aut_f) x sl2(aut_nf)
	return product(sl2(std::move(aut_f), aps),
		       sl2(std::move(aut_nf), aps))->is_empty();
      case 5: // sl2(cl(aut_f)) x aut_nf
	return product(sl2(closure(std::move(aut_f)), aps),
		       std::move(aut_nf))->is_empty();
      case 6: // (cl(sl2(aut_f)) x aut_nf
	return product(closure(sl2(std::move(aut_f), aps)),
		       std::move(aut_nf))->is_empty();
      case 7: // on-the-fly sl(aut_f) x sl(aut_nf)
	return otf_product(make_tgbasl(aut_f, aps),
			   make_tgbasl(aut_nf, aps))->is_empty();
      case 8: // cl(aut_f) x cl(aut_nf)
	return product(closure(std::move(aut_f)),
		       closure(std::move(aut_nf)))->is_empty();
      default:
	throw std::runtime_error("invalid algorithm number for "
				 "is_stutter_invariant()");
	SPOT_UNREACHABLE();
      }
  }

  bool
  check_stutter_invariance(const twa_graph_ptr& aut, formula f)
  {
    bool is_stut = aut->prop_stutter_invariant();
    if (is_stut)
      return is_stut;

    twa_graph_ptr neg = nullptr;
    if (f)
      {
	neg = translator(aut->get_dict()).run(formula::Not(f));
      }
    else
      {
	// If the automaton is deterministic, we
	// know how to complement it.
	aut->prop_deterministic(is_deterministic(aut));
	if (!aut->prop_deterministic())
	  return false;
	neg = remove_fin(dtwa_complement(aut));
      }

    is_stut = is_stutter_invariant(make_twa_graph(aut, twa::prop_set::all()),
				   std::move(neg), aut->ap_var());
    aut->prop_stutter_invariant(is_stut);
    aut->prop_stutter_sensitive(!is_stut);
    return is_stut;
  }
}