from pysat.solvers import Solver
from pysat.card import ITotalizer
from pysat.formula import IDPool

import signal
import math
import argparse

### Gebruik:
# Stap 1: pip3 install python-sat
# Stap 2: python3 decompose_fsm.py -h

keep_log = True


def main():
  record_file = './results/log.txt' if keep_log else None

  parser = argparse.ArgumentParser(description='Decomposes a FSM into smaller components by remapping its outputs. Uses a SAT solver.')
  parser.add_argument('-c', '--components', type=int, default=2, help='number of components')
  parser.add_argument('-w', '--weak', default=False, action='store_true', help='look for weak decomposition')
  parser.add_argument('--add-state-trans', default=False, action='store_true', help='adds state transitivity constraints')
  parser.add_argument('-v', '--verbose', default=False, action='store_true', help='prints more info')
  parser.add_argument('-t', '--timeout', type=int, default=None, help='timeout (in seconds)')
  parser.add_argument('filename', help='path to .dot file')
  args = parser.parse_args()

  # Aantal componenten. c = 1 is zinloos, maar zou moeten werken
  c = args.components
  assert c >= 1

  with open(args.filename) as file:
    machine = parse_dot_file(file)
    if args.verbose:
      print(machine)

  print(f'Input FSM: {len(machine.states)} states, {len(machine.inputs)} inputs, and {len(machine.outputs)} outputs')

  if args.timeout:

    def timeout_handler(*_):
      with open(record_file, 'a') as file:
        last_two_comps = '/'.join(args.filename.split('/')[-2:])
        file.write(f'{last_two_comps}\t{len(machine.states)}\t{len(machine.inputs)}\t{len(machine.outputs)}\t{args.weak}\t{c}\tTIMEOUT\n')
      print('TIMEOUT')
      exit()

    signal.signal(signal.SIGALRM, timeout_handler)
    signal.alarm(args.timeout)

  encoder = Encoder(machine, args, record_file=record_file)
  encoder.solve()


###################################
# .dot file parser (heuristic)
class FSM:
  def __init__(self, initial_state, states, inputs, outputs, transition_map, output_map):
    self.initial_state = initial_state
    self.states = states
    self.inputs = inputs
    self.outputs = outputs
    self.transition_map = transition_map
    self.output_map = output_map

  def __str__(self):
    return f'FSM({self.initial_state}, {self.states}, {self.inputs}, {self.outputs}, {self.transition_map}, {self.output_map})'

  def transition(self, s, a):
    return self.transition_map[(s, a)]

  def output(self, s, a):
    return self.output_map[(s, a)]


def parse_dot_file(lines):
  def parse_transition(line):
    (l, _, r) = line.partition('->')
    s = l.strip()

    (l, _, r) = r.partition('[label="')
    t = l.strip()

    (l, _, _) = r.partition('"]')
    (i, _, o) = l.partition('/')

    return (s, i, o, t)

  initial_state = None
  states, inputs, outputs = set(), set(), set()
  transition_map, output_map = {}, {}

  for line in lines:
    (s, i, o, t) = parse_transition(line)
    if s and i and o and t:
      states.add(s)
      inputs.add(i)
      outputs.add(o)
      states.add(t)

      transition_map[(s, i)] = t
      output_map[(s, i)] = o

      if not initial_state:
        initial_state = s

  assert initial_state in states
  assert len(transition_map) == len(states) * len(inputs)
  assert len(output_map) == len(states) * len(inputs)

  return FSM(initial_state, states, inputs, outputs, transition_map, output_map)


###################################
# Utility functions
def print_table(cell, rs, cs):
  first_col_size = max([len(str(r)) for r in rs])
  col_size = 1 + max([len(str(c)) for c in cs] + [len(cell(r, c)) for c in cs for r in rs])

  print(''.rjust(first_col_size), end='')
  for c in cs:
    print(str(c).rjust(col_size), end='')
  print('')

  for r in rs:
    print(str(r).rjust(first_col_size), end='')
    for c in cs:
      print(cell(r, c).rjust(col_size), end='')
    print('')


def print_eqrel(rel, xs):
  print_table(lambda r, c: 'Y' if rel(r, c) else '·', xs, xs)


class Progress:
  def __init__(self, name, guess):
    self.reset(name, guess, show=False)

  def reset(self, name, guess, show=True):
    self.name = name
    self.guess = math.ceil(guess)
    self.count = 0
    self.percentage = None

    if show:
      print(name)

  def add(self, n=1):
    self.count += n
    percentage = math.floor(100 * self.count / self.guess)

    if percentage != self.percentage:
      self.percentage = percentage
      print(f'{self.percentage}%', end='', flush=True)
      print('\r', end='')


###################################
# Main logic
class Encoder:
  def __init__(self, machine, args, record_file=None, progress=None):
    self.machine = machine
    self.args = args
    self.record_file = record_file
    self.progress = progress if progress else Progress('', 1)

    self.c = self.args.components
    self.N = len(self.machine.states)
    self.os = list(machine.outputs)  # outputs
    self.rids = [i for i in range(self.c)]  # components
    self.vpool = IDPool()
    self.solver = Solver()

    self.encode()

  def add_clause(self, cls, no_return=True):
    self.solver.add_clause(cls, no_return)

  def add_clauses(self, clss, no_return=True):
    self.solver.append_formula(clss, no_return)

  # Een hulp variabele voor False en True, maakt de andere variabelen eenvoudiger
  def var_const(self, b):
    return self.vpool.id(('const', b))

  # Voor elke relatie en elke twee elementen o1 en o2, is er een variabele die
  # aangeeft of o1 en o2 gerelateerd zijn. Er is 1 variabele voor xRy en yRx, dus
  # symmetrie is al ingebouwd. Reflexiviteit is ook ingebouwd.
  def var_rel(self, rid, o1, o2):
    if o1 == o2:
      return self.var_const(True)

    [so1, so2] = sorted([o1, o2])
    return self.vpool.id(('rel', rid, so1, so2))

  # De relatie op outputs geeft een relaties op states. Deze relatie moet ook een
  # bisimulatie zijn.
  def var_state_rel(self, rid, s1, s2):
    if s1 == s2:
      return self.var_const(True)

    [ss1, ss2] = sorted([s1, s2])
    return self.vpool.id(('state_rel', rid, ss1, ss2))

  # Voor elke relatie, en elke equivalentie-klasse, kiezen we precies 1 state
  # als representant. Deze variabele geeft aan welk element.
  def var_state_rep(self, rid, s):
    return self.vpool.id(('state_rep', rid, s))

  def encode(self):
    print('===============')
    print('Start encoding')
    self.add_clause([self.var_const(True)])
    self.add_clause([-self.var_const(False)])

    # Contraints zodat de relatie een equivalentie relatie is. We hoeven alleen
    # maar transitiviteit te encoderen, want refl en symm zijn ingebouwd in de var.
    self.progress.reset('transitivity (o)', guess=len(self.rids) * len(self.os) ** 3)
    for rid in self.rids:
      for xo in self.os:
        for yo in self.os:
          for zo in self.os:
            # als xo R yo en yo R zo dan xo R zo
            self.add_clause([-self.var_rel(rid, xo, yo), -self.var_rel(rid, yo, zo), self.var_rel(rid, xo, zo)])
            self.progress.add()

    if self.args.add_state_trans:
      self.progress.reset('transitivity (s)', guess=len(self.rids) * len(self.machine.states) ** 3)
      for rid in self.rids:
        for sx in self.machine.states:
          for sy in self.machine.states:
            for sz in self.machine.states:
              # als sx R sy en sy R sz dan sx R sz
              self.add_clause([-self.var_state_rel(rid, sx, sy), -self.var_state_rel(rid, sy, sz), self.var_state_rel(rid, sx, sz)])
              self.progress.add()

    # Constraint zodat de relaties samen alle elementen kunnen onderscheiden.
    # (Aka: the bijbehorende quotienten zijn joint-injective.)
    self.progress.reset('injectivity', guess=len(self.os) * (len(self.os) - 1) / 2)
    for xi, xo in enumerate(self.os):
      for yo in self.os[xi + 1 :]:
        # Tenminste een rid moet een verschil maken
        self.add_clause([-self.var_rel(rid, xo, yo) for rid in self.rids])
        self.progress.add()

    # sx ~ sy => for each input: (1) outputs equivalent AND (2) successors related
    # Momenteel hebben we niet de inverse implicatie, is misschien ook niet nodig?
    self.progress.reset('bisimulation modulo rel', guess=len(self.rids) * len(self.machine.states) * len(self.machine.states) * len(self.machine.inputs))
    for rid in self.rids:
      for sx in self.machine.states:
        for sy in self.machine.states:
          for i in self.machine.inputs:
            # sx ~ sy => output(sx, i) ~ output(sy, i)
            ox = self.machine.output(sx, i)
            oy = self.machine.output(sy, i)
            self.add_clause([-self.var_state_rel(rid, sx, sy), self.var_rel(rid, ox, oy)])

            # sx ~ sy => delta(sx, i) ~ delta(sy, i)
            tx = self.machine.transition(sx, i)
            ty = self.machine.transition(sy, i)
            self.add_clause([-self.var_state_rel(rid, sx, sy), self.var_state_rel(rid, tx, ty)])

            self.progress.add()

    # De constraints die zorgen dat representanten ook echt representanten zijn.
    states = list(self.machine.states)
    self.progress.reset('representatives', guess=len(self.rids) * len(states))
    for rid in self.rids:
      for ix, sx in enumerate(states):
        # Belangrijkste: een element is een representant, of equivalent met een
        # eerder element. We forceren hiermee dat de solver representanten moet
        # kiezen (voor aan de lijst).
        self.add_clause([self.var_state_rep(rid, sx)] + [self.var_state_rel(rid, sx, sy) for sy in states[:ix]])

        for sy in states[:ix]:
          # rx en ry kunnen niet beide een representant zijn, tenzij ze
          # niet gerelateerd zijn.
          self.add_clause([-self.var_state_rep(rid, sx), -self.var_state_rep(rid, sy), -self.var_state_rel(rid, sx, sy)])

        self.progress.add()

    # Tot slot willen we weinig representanten. Dit doen we met een "atmost"
    # formule. We gaan een binaire zoek doen met incremental sat solving.
    self.rhs = None
    if self.args.weak:
      self.lower_bound = int(math.floor((self.N - 1) ** (1 / self.c)))
      self.upper_bound = int(self.N)
      print(f'weak size constraints {self.lower_bound} {self.upper_bound}')
      self.rhs = []
      for rid in self.rids:
        with ITotalizer([self.var_state_rep(rid, sx) for sx in self.machine.states], ubound=self.upper_bound, top_id=self.vpool.top) as cnf_optim:
          self.vpool.occupy(self.vpool.top + 1, cnf_optim.top_id)
          self.vpool.top = cnf_optim.top_id
          self.add_clauses(cnf_optim.cnf.clauses)
          self.rhs.append(cnf_optim.rhs)
    else:
      self.lower_bound = int(math.floor(self.c * (self.N - 1) ** (1 / self.c)))
      self.upper_bound = int(self.N + self.c - 1)
      print(f'size constraints {self.lower_bound} {self.upper_bound}')
      with ITotalizer([self.var_state_rep(rid, sx) for rid in self.rids for sx in self.machine.states], ubound=self.upper_bound, top_id=self.vpool.top) as cnf_optim:
        self.add_clauses(cnf_optim.cnf.clauses)
        self.rhs = cnf_optim.rhs

  def solve(self):
    print('===============')
    print('Start solving')
    sat = None
    while self.upper_bound - self.lower_bound >= 2:
      self.mid_size = int((self.lower_bound + self.upper_bound) / 2)
      print(f'Trying {self.lower_bound} < {self.mid_size} < {self.upper_bound}', end='', flush=True)
      if self.args.weak:
        assumptions = [-self.rhs[rid][self.mid_size] for rid in self.rids]
        sat = self.solver.solve(assumptions=assumptions)
      else:
        sat = self.solver.solve(assumptions=[-self.rhs[self.mid_size]])
      if sat:
        print('\tdown')
        self.upper_bound = self.mid_size
        continue
      else:
        print('\tup')
        self.lower_bound = self.mid_size
        continue

    self.bound = self.upper_bound
    print(f'done searching, found bound = {self.bound}')

    if self.args.weak:
      assumptions = [-self.rhs[rid][self.bound] for rid in self.rids]
      sat = self.solver.solve(assumptions=assumptions)
    else:
      sat = self.solver.solve(assumptions=[-self.rhs[self.bound]])
    assert sat

    # Even omzetten in een makkelijkere data structuur
    m = self.solver.get_model()
    model = {abs(l): l > 0 for l in m}

    if self.args.verbose:
      for rid in self.rids:
        print(f'Relation {rid}:')
        print_eqrel(lambda x, y: model[self.var_rel(rid, x, y)], self.os)

      for rid in self.rids:
        print(f'State relation {rid}:')
        print_eqrel(lambda x, y: model[self.var_state_rel(rid, x, y)], self.machine.states)

    # Precieze groottes van elk component tellen
    counts = []
    for rid in self.rids:
      count = 0
      # Eerst verzamelen we de representanten
      for s in self.machine.states:
        if model[self.var_state_rep(rid, s)]:
          count += 1
          if self.args.verbose:
            print(f'comp {rid} -> representative state {s}')
      counts.append(count)

    print(f'Reduced sizes = {counts} = {sum(counts)}')
    if self.record_file:
      with open(self.record_file, 'a') as file:
        last_two_comps = '/'.join(self.args.filename.split('/')[-2:])
        file.write(f'{last_two_comps}\t{self.N}\t{len(self.machine.inputs)}\t{len(self.machine.outputs)}\t{self.args.weak}\t{self.c}\t{sum(counts)}\t{sorted(counts, reverse=True)}\n')

    projections = {}
    for rid in self.rids:
      local_outputs = self.machine.outputs.copy()
      projections[rid] = {}
      count = 0

      while local_outputs:
        repr = local_outputs.pop()
        if repr in projections[rid]:
          continue

        projections[rid][repr] = f'cls_{rid}_{count}'
        others = False

        for o in local_outputs:
          if model[self.var_rel(rid, o, repr)]:
            others = True
            projections[rid][o] = f'cls_{rid}_{count}'

        if not others:
          # Aangeven dat het een unieke output is
          projections[rid][repr] = f'cls_{rid}_{count}_u'

        count += 1

    print('===============')
    print('Output mapping:')
    print_table(lambda o, rid: projections[rid][o], self.machine.outputs, self.rids)


###################################
# Run script
if __name__ == '__main__':
  main()