text: from typing import FrozenSet
  from collections import Iterable
  from math import log, ceil
  
  from mathsat import msat_term, msat_env
  from mathsat import msat_make_constant, msat_declare_function
  from mathsat import msat_get_integer_type, msat_get_rational_type,     msat_get_bool_type
  from mathsat import msat_make_and, msat_make_not, msat_make_or, msat_make_iff
  from mathsat import msat_make_leq, msat_make_equal, msat_make_true
  from mathsat import msat_make_number, msat_make_plus, msat_make_times
  
  from pysmt.environment import Environment as PysmtEnv
  import pysmt.typing as types
  
  from ltl.ltl import TermMap, LTLEncoder
  from utils import name_next, symb_to_next
  from hint import Hint, Location
  
  delta_name = "delta"
  
  
  def decl_consts(menv: msat_env, name: str, c_type) -> tuple:
      assert not name.startswith("_"), name
      s = msat_declare_function(menv, name, c_type)
      s = msat_make_constant(menv, s)
      x_s = msat_declare_function(menv, name_next(name), c_type)
      x_s = msat_make_constant(menv, x_s)
      return s, x_s
  
  
  def make_enum(menv, v_name: str, enum_size: int):
      bool_type = msat_get_bool_type(menv)
      num_bits = ceil(log(enum_size, 2))
      b_vars = []
      for idx in range(num_bits):
          c_name = "{}{}".format(v_name, idx)
          b_vars.append(tuple(decl_consts(menv, c_name, bool_type)))
      vals = []
      x_vals = []
      for enum_val in range(enum_size):
          bit_val = format(enum_val, '0{}b'.format(num_bits))
          assert len(bit_val) == num_bits
          assert all(c in {'0', '1'} for c in bit_val)
          assign = [b_vars[idx] if c == '1' else
                    (msat_make_not(menv, b_vars[idx][0]),
                     msat_make_not(menv, b_vars[idx][1]))
                    for idx, c in enumerate(reversed(bit_val))]
          pred = assign[0][0]
          x_pred = assign[0][1]
          for it in assign[1:]:
              pred = msat_make_and(menv, pred, it[0])
              x_pred = msat_make_and(menv, x_pred, it[1])
          vals.append(pred)
          x_vals.append(x_pred)
      assert len(vals) == enum_size
      assert len(x_vals) == enum_size
      return b_vars, vals, x_vals
  
  
  def msat_make_minus(menv: msat_env, arg0: msat_term, arg1: msat_term):
      m_one = msat_make_number(menv, "-1")
      arg1 = msat_make_times(menv, arg1, m_one)
      return msat_make_plus(menv, arg0, arg1)
  
  
  def msat_make_lt(menv: msat_env, arg0: msat_term, arg1: msat_term):
      geq = msat_make_geq(menv, arg0, arg1)
      return msat_make_not(menv, geq)
  
  
  def msat_make_geq(menv: msat_env, arg0: msat_term, arg1: msat_term):
      return msat_make_leq(menv, arg1, arg0)
  
  
  def msat_make_gt(menv: msat_env, arg0: msat_term, arg1: msat_term):
      leq = msat_make_leq(menv, arg0, arg1)
      return msat_make_not(menv, leq)
  
  
  def msat_make_impl(menv: msat_env, arg0: msat_term, arg1: msat_term):
      n_arg0 = msat_make_not(menv, arg0)
      return msat_make_or(menv, n_arg0, arg1)
  
  
  def diverging_symbs(menv: msat_env) -> frozenset:
      real_type = msat_get_rational_type(menv)
      delta = msat_declare_function(menv, delta_name, real_type)
      delta = msat_make_constant(menv, delta)
      return frozenset([delta])
  
  
  def check_ltl(menv: msat_env, enc: LTLEncoder) -> (Iterable, msat_term,
                                                     msat_term, msat_term):
      assert menv
      assert isinstance(menv, msat_env)
      assert enc
      assert isinstance(enc, LTLEncoder)
      int_type = msat_get_integer_type(menv)
      real_type = msat_get_rational_type(menv)
      r2s, x_r2s = decl_consts(menv, "r2s", int_type)
      s2r, x_s2r = decl_consts(menv, "s2r", int_type)
      delta, x_delta = decl_consts(menv, delta_name, real_type)
      sender = Sender("s", menv, enc, r2s, x_r2s, s2r, x_s2r, delta)
      receiver = Receiver("r", menv, enc, s2r, x_s2r, r2s, x_r2s, delta)
  
      curr2next = {r2s: x_r2s, s2r: x_s2r, delta: x_delta}
      for comp in [sender, receiver]:
          for s, x_s in comp.symb2next.items():
              curr2next[s] = x_s
  
      zero = msat_make_number(menv, "0")
      init = msat_make_and(menv, receiver.init, sender.init)
      trans = msat_make_and(menv, receiver.trans, sender.trans)
  
      # invar delta >= 0
      init = msat_make_and(menv, init,
                           msat_make_geq(menv, delta, zero))
      trans = msat_make_and(menv, trans,
                            msat_make_geq(menv, x_delta, zero))
  
      # delta > 0 -> (r2s' = r2s & s2r' = s2r)
      lhs = msat_make_gt(menv, delta, zero)
      rhs = msat_make_and(menv,
                          msat_make_equal(menv, x_r2s, r2s),
                          msat_make_equal(menv, x_s2r, s2r))
      trans = msat_make_and(menv, trans,
                            msat_make_impl(menv, lhs, rhs))
  
      # (G F !s.stutter) -> G (s.wait_ack -> F s.send)
      lhs = enc.make_G(enc.make_F(msat_make_not(menv, sender.stutter)))
      rhs = enc.make_G(msat_make_impl(menv, sender.wait_ack,
                                      enc.make_F(sender.send)))
      ltl = msat_make_impl(menv, lhs, rhs)
      return TermMap(curr2next), init, trans, ltl
  
  
  class Module:
      def __init__(self, name: str, menv: msat_env, enc: LTLEncoder,
                   *args, **kwargs):
          self.name = name
          self.menv = menv
          self.enc = enc
          self.symb2next = {}
          true = msat_make_true(menv)
          self.init = true
          self.trans = true
  
      def _symb(self, v_name, v_type):
          v_name = "{}_{}".format(self.name, v_name)
          return decl_consts(self.menv, v_name, v_type)
  
      def _enum(self, v_name: str, enum_size: int):
          c_name = "{}_{}".format(self.name, v_name)
          return make_enum(self.menv, c_name, enum_size)
  
  
  class Sender(Module):
      def __init__(self, name: str, menv: msat_env, enc: LTLEncoder,
                   in_c, x_in_c, out_c, x_out_c, delta):
          super().__init__(name, menv, enc)
  
          bool_type = msat_get_bool_type(menv)
          int_type = msat_get_integer_type(menv)
          real_type = msat_get_rational_type(menv)
          loc, x_loc = self._symb("l", bool_type)
          evt, x_evt = self._symb("evt", bool_type)
          msg_id, x_msg_id = self._symb("msg_id", int_type)
          timeout, x_timeout = self._symb("timeout", real_type)
          c, x_c = self._symb("c", real_type)
  
          self.move = evt
          self.stutter = msat_make_not(menv, evt)
          self.x_move = x_evt
          self.x_stutter = msat_make_not(menv, x_evt)
  
          self.send = loc
          self.wait_ack = msat_make_not(menv, loc)
          self.x_send = x_loc
          self.x_wait_ack = msat_make_not(menv, x_loc)
  
          self.symb2next = {loc: x_loc, evt: x_evt, msg_id: x_msg_id,
                            timeout: x_timeout, c: x_c}
  
          zero = msat_make_number(menv, "0")
          one = msat_make_number(menv, "1")
          base_timeout = one
  
          # send & c = 0 & msg_id = 0
          self.init = msat_make_and(menv,
                                    msat_make_and(menv, self.send,
                                                  msat_make_equal(menv, c,
                                                                  zero)),
                                    msat_make_equal(menv, msg_id, zero))
          # invar: wait_ack -> c <= timeout
          self.init = msat_make_and(
              menv, self.init,
              msat_make_impl(menv, self.wait_ack,
                             msat_make_leq(menv, c, timeout)))
          self.trans = msat_make_impl(menv, self.x_wait_ack,
                                      msat_make_leq(menv, x_c, x_timeout))
  
          # delta > 0 | stutter -> l' = l & msg_id' = msg_id & timeout' = timeout &
          # c' = c + delta & out_c' = out_c
          lhs = msat_make_or(menv, msat_make_gt(menv, delta, zero), self.stutter)
          rhs = msat_make_and(
              menv,
              msat_make_and(menv,
                            msat_make_iff(menv, x_loc, loc),
                            msat_make_equal(menv, x_msg_id, msg_id)),
              msat_make_and(menv,
                            msat_make_equal(menv, x_timeout, timeout),
                            msat_make_equal(menv, x_c,
                                            msat_make_plus(menv, c, delta))))
          rhs = msat_make_and(menv, rhs,
                              msat_make_equal(menv, x_out_c, out_c))
          self.trans = msat_make_and(menv, self.trans,
                                     msat_make_impl(menv, lhs, rhs))
  
          disc_t = msat_make_and(menv, self.move,
                                 msat_make_equal(menv, delta, zero))
          # (send & send') ->
          # (msg_id' = msg_id & timeout' = base_timeout & c' = 0 & out_c' = out_c)
          lhs = msat_make_and(menv, disc_t,
                              msat_make_and(menv, self.send, self.x_send))
          rhs = msat_make_and(
              menv,
              msat_make_and(menv,
                            msat_make_equal(menv, x_msg_id, msg_id),
                            msat_make_equal(menv, x_timeout, base_timeout)),
              msat_make_and(menv,
                            msat_make_equal(menv, x_c, zero),
                            msat_make_equal(menv, x_out_c, out_c)))
          self.trans = msat_make_and(menv, self.trans,
                                     msat_make_impl(menv, lhs, rhs))
          # (send & wait_ack') ->
          # (msg_id' = msg_id + 1 & timeout' = base_timeout & c' = 0 & out_c' = out_c)
          lhs = msat_make_and(menv, disc_t,
                              msat_make_and(menv, self.send, self.x_wait_ack))
          rhs = msat_make_and(
              menv,
              msat_make_and(menv,
                            msat_make_equal(menv, x_msg_id,
                                            msat_make_plus(menv, msg_id, one)),
                            msat_make_equal(menv, x_timeout, base_timeout)),
              msat_make_and(menv,
                            msat_make_equal(menv, x_c, zero),
                            msat_make_equal(menv, x_out_c, out_c)))
          self.trans = msat_make_and(menv, self.trans,
                                     msat_make_impl(menv, lhs, rhs))
          # (wait_ack) -> (c' = 0 & out_c' = out_c &
          # (wait_ack' <-> (in_c != msg_id & c > timeout))
          lhs = msat_make_and(menv, disc_t, self.wait_ack)
          rhs_iff = msat_make_and(menv,
                                  msat_make_not(menv,
                                                msat_make_equal(menv, in_c,
                                                                msg_id)),
                                  msat_make_geq(menv, c, timeout))
          rhs_iff = msat_make_iff(menv, self.x_wait_ack, rhs_iff)
          rhs = msat_make_and(menv,
                              msat_make_and(menv,
                                            msat_make_equal(menv, x_c, zero),
                                            msat_make_equal(menv, x_out_c,
                                                            out_c)),
                              rhs_iff)
          self.trans = msat_make_and(menv, self.trans,
                                     msat_make_impl(menv, lhs, rhs))
          # (wait_ack & wait_ack') -> (timeout' > timeout)
          lhs = msat_make_and(menv, disc_t,
                              msat_make_and(menv, self.wait_ack,
                                            self.x_wait_ack))
          rhs = msat_make_gt(menv, x_timeout, timeout)
          self.trans = msat_make_and(menv, self.trans,
                                     msat_make_impl(menv, lhs, rhs))
          # (wait_ack) -> (send' <-> (in_c = msg_id & c < timeout))
          lhs = msat_make_and(menv, disc_t, self.wait_ack)
          rhs = msat_make_iff(menv, self.x_send,
                              msat_make_and(menv,
                                            msat_make_equal(menv, in_c, msg_id),
                                            msat_make_lt(menv, c, timeout)))
          self.trans = msat_make_and(menv, self.trans,
                                     msat_make_impl(menv, lhs, rhs))
          # (wait_ack & send') -> (timeout' = base_timeout)
          lhs = msat_make_and(menv, disc_t,
                              msat_make_and(menv, self.wait_ack, self.x_send))
          rhs = msat_make_equal(menv, x_timeout, base_timeout)
          self.trans = msat_make_and(menv, self.trans,
                                     msat_make_impl(menv, lhs, rhs))
  
  
  class Receiver(Module):
      def __init__(self, name: str, menv: msat_env, enc: LTLEncoder,
                   in_c, x_in_c, out_c, x_out_c, delta):
          super().__init__(name, menv, enc)
  
          bool_type = msat_get_bool_type(menv)
          loc, x_loc = self._symb("l", bool_type)
  
          self.wait = loc
          self.work = msat_make_not(menv, loc)
          self.x_wait = x_loc
          self.x_work = msat_make_not(menv, x_loc)
  
          self.symb2next = {loc: x_loc}
  
          zero = msat_make_number(menv, "0")
          # wait
          self.init = self.wait
  
          # delta > 0 -> loc' = loc & out_c' = out_c
          lhs = msat_make_gt(menv, delta, zero)
          rhs = msat_make_and(menv,
                              msat_make_iff(menv, x_loc, loc),
                              msat_make_equal(menv, x_out_c, out_c))
          self.trans = msat_make_impl(menv, lhs, rhs)
  
          disc_t = msat_make_equal(menv, delta, zero)
          # wait -> (wait' <-> in_c = out_c)
          lhs = msat_make_and(menv, disc_t, self.wait)
          rhs = msat_make_iff(menv, self.x_wait,
                              msat_make_equal(menv, in_c, out_c))
          self.trans = msat_make_and(menv, self.trans,
                                     msat_make_impl(menv, lhs, rhs))
          # (wait & wait') -> (out_c' = out_c)
          lhs = msat_make_and(menv, disc_t,
                              msat_make_and(menv, self.wait, self.x_wait))
          rhs = msat_make_equal(menv, x_out_c, out_c)
          self.trans = msat_make_and(menv, self.trans,
                                     msat_make_impl(menv, lhs, rhs))
          # (wait & work') -> out_c' = in_c
          lhs = msat_make_and(menv, disc_t,
                              msat_make_and(menv, self.wait, self.x_work))
          rhs = msat_make_equal(menv, x_out_c, in_c)
          self.trans = msat_make_and(menv, self.trans,
                                     msat_make_impl(menv, lhs, rhs))
          # work -> out_c' = out_c
          lhs = msat_make_and(menv, disc_t, self.work)
          rhs = msat_make_equal(menv, x_out_c, out_c)
          self.trans = msat_make_and(menv, self.trans,
                                     msat_make_impl(menv, lhs, rhs))
  
  
  def hints(env: PysmtEnv) -> FrozenSet[Hint]:
      assert isinstance(env, PysmtEnv)
  
      mgr = env.formula_manager
      delta = mgr.Symbol(delta_name, types.REAL)
      r2s = mgr.Symbol("r2s", types.INT)
      s2r = mgr.Symbol("r2s", types.INT)
      s_l = mgr.Symbol("s_l", types.BOOL)
      s_evt = mgr.Symbol("s_evt", types.BOOL)
      s_msg_id = mgr.Symbol("s_msg_id", types.INT)
      s_timeout = mgr.Symbol("s_timeout", types.REAL)
      s_c = mgr.Symbol("s_c", types.REAL)
      r_l = mgr.Symbol("r_l", types.BOOL)
      symbs = frozenset([delta, r2s, s2r, s_l, s_evt, s_msg_id, s_timeout, s_c,
                         r_l])
  
      x_delta = symb_to_next(mgr, delta)
      x_r2s = symb_to_next(mgr, r2s)
      x_s2r = symb_to_next(mgr, s2r)
      x_s_l = symb_to_next(mgr, s_l)
      x_s_evt = symb_to_next(mgr, s_evt)
      x_s_msg_id = symb_to_next(mgr, s_msg_id)
      x_s_timeout = symb_to_next(mgr, s_timeout)
      x_s_c = symb_to_next(mgr, s_c)
      x_r_l = symb_to_next(mgr, r_l)
  
      res = []
  
      r0 = mgr.Real(0)
      r1 = mgr.Real(1)
      i0 = mgr.Int(0)
      i1 = mgr.Int(1)
  
      loc0 = Location(env, mgr.Equals(s2r, i0))
      loc0.set_progress(0, mgr.Equals(x_s2r, i0))
      hint = Hint("h_s2r0", env, frozenset([s2r]), symbs)
      hint.set_locs([loc0])
      res.append(hint)
  
  
      loc0 = Location(env, mgr.Equals(r2s, i0))
      loc0.set_progress(0, mgr.Equals(x_r2s, i0))
      hint = Hint("h_r2s0", env, frozenset([r2s]), symbs)
      hint.set_locs([loc0])
      res.append(hint)
  
  
      loc0 = Location(env, s_evt)
      loc0.set_progress(0, x_s_evt)
      hint = Hint("h_s_evt0", env, frozenset([s_evt]), symbs)
      hint.set_locs([loc0])
      res.append(hint)
  
  
      loc0 = Location(env, mgr.Equals(s_msg_id, i0))
      loc0.set_progress(0, mgr.Equals(x_s_msg_id, i0))
      hint = Hint("h_s_msg_id0", env, frozenset([s_msg_id]), symbs)
      hint.set_locs([loc0])
      res.append(hint)
  
  
      loc0 = Location(env, r_l)
      loc0.set_progress(0, x_r_l)
      hint = Hint("h_r_l0", env, frozenset([r_l]), symbs)
      hint.set_locs([loc0])
      res.append(hint)
  
  
      loc0 = Location(env, mgr.GE(s2r, i0))
      loc0.set_progress(0, mgr.Equals(x_s2r, i1))
      hint = Hint("h_s2r1", env, frozenset([s2r]), symbs)
      hint.set_locs([loc0])
      res.append(hint)
  
  
      loc0 = Location(env, mgr.GE(s_timeout, r0))
      loc0.set_progress(0, mgr.Equals(x_s_timeout, mgr.Plus(s_timeout, r1)))
      hint = Hint("h_s_timeout1", env, frozenset([s_timeout]), symbs)
      hint.set_locs([loc0])
      res.append(hint)
  
  
      loc0 = Location(env, mgr.GE(s_c, r0))
      loc0.set_progress(0, mgr.Equals(x_s_c, mgr.Plus(s_c, r1)))
      hint = Hint("h_s_c1", env, frozenset([s_c]), symbs)
      hint.set_locs([loc0])
      res.append(hint)
  
  
      loc0 = Location(env, r_l)
      loc0.set_progress(1, mgr.Not(x_r_l))
      loc1 = Location(env, mgr.Not(r_l))
      loc1.set_progress(0, x_r_l)
      hint = Hint("h_r_l1", env, frozenset([r_l]), symbs)
      hint.set_locs([loc0, loc1])
      res.append(hint)
  
  
      loc0 = Location(env, mgr.GE(delta, r0))
      loc0.set_progress(0, mgr.Equals(x_delta, mgr.Plus(delta, r1)))
      hint = Hint("h_delta2", env, frozenset([delta]), symbs)
      hint.set_locs([loc0])
      res.append(hint)
  
      return frozenset(res)
  