############################################
# Copyright (c) 2016 Microsoft Corporation
# 
# MSS enumeration based on maximal resolution.
#
# Author: Nikolaj Bjorner (nbjorner)
############################################

"""

The following is a procedure for enumerating maximal satisfying subsets.
It uses maximal resolution to eliminate cores from the state space.
Whenever the hard constraints are satisfiable, it finds a model that
satisfies the maximal number of soft constraints. 
During this process it collects the set of cores that are encountered.
It then reduces the set of soft constraints using max-resolution in
the style of [Narodytska & Bacchus, AAAI'14]. In other words, 
let F1, ..., F_k be a core among the soft constraints F1,...,F_n 
Replace F1,.., F_k by 
          F1 or F2, F3 or (F2 & F1), F4 or (F3 & (F2 & F1)), ..., 
          F_k or (F_{k-1} & (...))
Optionally, add the core ~F1 or ... or ~F_k to F
The current model M satisfies the new set F, F1,...,F_{n-1} if the core is minimal.
Whenever we modify the soft constraints by the core reduction any assignment
to the reduced set satisfies a k-1 of the original soft constraints.
    
"""

from z3 import *

def main():
    x, y = Reals('x y')
    soft_constraints = [x > 2, x < 1, x < 0, Or(x + y > 0, y < 0), Or(y >= 0, x >= 0), Or(y < 0, x < 0), Or(y > 0, x < 0)]
    hard_constraints = BoolVal(True)
    solver = MSSSolver(hard_constraints, soft_constraints)
    for lits in enumerate_sets(solver):
        print("%s" % lits)


def enumerate_sets(solver):
    while True:
        if sat == solver.s.check():
           MSS = solver.grow()
           yield MSS
        else:
           break

class CompareSetSize():
   def __call__(self, s1, s2):
       return len(s1) < len(s2) 


class MSSSolver:
   s = Solver()
   varcache = {}
   idcache = {}

   def __init__(self, hard, soft):
       self.n = len(soft)
       self.soft = soft
       self.s.add(hard)       
       self.soft_vars = set([self.c_var(i) for i in range(self.n)])
       self.orig_soft_vars = set([self.c_var(i) for i in range(self.n)])
       self.s.add([(self.c_var(i) == soft[i]) for i in range(self.n)])

   def c_var(self, i):
       if i not in self.varcache:
          v = Bool(str(self.soft[abs(i)]))
          self.idcache[v] = abs(i)
          if i >= 0:
             self.varcache[i] = v
          else:
             self.varcache[i] = Not(v)
       return self.varcache[i]

   def update_unknown(self):
       self.model = self.s.model()
       new_unknown = set([])
       for x in self.unknown:
           if is_true(self.model[x]):
              self.mss.append(x)
           else:
              new_unknown.add(x)
       self.unknown = new_unknown
      
   def relax_core(self, core):
       assert(core <= self.soft_vars)
       prev = BoolVal(True)
       core_list = [x for x in core]
       self.soft_vars -= core
       # replace x0, x1, x2, .. by
       # Or(x1, x0), Or(x2, And(x1, x0)), Or(x3, And(x2, And(x1, x0))), ...
       for i in range(len(core_list)-1):
           x = core_list[i]
           y = core_list[i+1]
           prevf = And(x, prev)
           prev = Bool("%s" % prevf)
           self.s.add(prev == prevf)
           zf = Or(prev, y)
           z = Bool("%s" % zf)
           self.s.add(z == zf)
           self.soft_vars.add(z)

   def resolve_core(self, core):
       new_core = set([])
       for x in core:
           if x in self.mcs_explain:
              new_core |= self.mcs_explain[x]
           else:
              new_core.add(x)
       return new_core


   def grow(self):
       self.mss = []
       self.mcs = []
       self.nmcs = []
       self.mcs_explain = {}
       self.unknown = self.soft_vars
       self.update_unknown()
       cores = []
       while len(self.unknown) > 0:
           x = self.unknown.pop()
           is_sat = self.s.check(self.mss + [x] + self.nmcs)
           if is_sat == sat:
              self.mss.append(x)
              self.update_unknown()
           elif is_sat == unsat:
              core = self.s.unsat_core()
              core = self.resolve_core(core)
              self.mcs_explain[Not(x)] = {y for y in core if not eq(x,y)}
              self.mcs.append(x)
              self.nmcs.append(Not(x)) 
              cores += [core]              
           else:
              print("solver returned %s" % is_sat)
              exit()
       mss = [x for x in self.orig_soft_vars if is_true(self.model[x])]
       mcs = [x for x in self.orig_soft_vars if not is_true(self.model[x])]
       self.s.add(Or(mcs))
       core_literals = set([])
       cores.sort(CompareSetSize()) 
       for core in cores:
           if len(core & core_literals) == 0:
              self.relax_core(core)
              core_literals |= core
       return mss


main()