InvariantChecker.scala 7.98 KB
Newer Older
Christian Müller's avatar
Christian Müller committed
1 2
package de.tum.workflows.toz3

Christian Müller's avatar
Christian Müller committed
3
import java.util.HashMap
Christian Müller's avatar
Christian Müller committed
4

Christian Müller's avatar
Christian Müller committed
5 6 7
import scala.annotation.tailrec

// labeled directed edge
Christian Müller's avatar
Christian Müller committed
8 9 10
import com.microsoft.z3.Context
import com.microsoft.z3.Status
import com.typesafe.scalalogging.LazyLogging
Christian Müller's avatar
Christian Müller committed
11 12 13 14 15 16

import de.tum.workflows.Encoding
import de.tum.workflows.Implicits._
import de.tum.workflows.Preconditions
import de.tum.workflows.blocks._
import de.tum.workflows.foltl.FOLTL._
Christian Müller's avatar
Christian Müller committed
17
import de.tum.workflows.foltl.FormulaFunctions
Christian Müller's avatar
Christian Müller committed
18
import de.tum.workflows.ltl.FOTransformers
Christian Müller's avatar
Christian Müller committed
19
import de.tum.workflows.Utils
Christian Müller's avatar
Christian Müller committed
20
import de.tum.workflows.foltl.Properties
Christian Müller's avatar
Christian Müller committed
21

Christian Müller's avatar
Christian Müller committed
22 23 24 25 26
case class InvProperties(stubborn:Boolean, eliminateAux:Boolean) { }
object InvProperties {
  val DEFAULT = InvProperties(true, true)
}

Christian Müller's avatar
Christian Müller committed
27
object InvariantChecker extends LazyLogging {
Christian Müller's avatar
Christian Müller committed
28

Christian Müller's avatar
Christian Müller committed
29
  val TIMEOUT = 60000 // in milliseconds
Christian Müller's avatar
Christian Müller committed
30 31

  def checkOnZ3(f: Formula) = {
Christian Müller's avatar
Christian Müller committed
32
    
Christian Müller's avatar
Christian Müller committed
33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67
    val (time, res) = Utils.time {
      // Set up Z3
      val cfg = new HashMap[String, String]()
      cfg.put("timeout", TIMEOUT.toString())
      val ctx = new Context(cfg)
  
      //    val qe = ctx.mkTactic("qe")
      //    val default = ctx.mkTactic("smt")
      //    val t = ctx.andThen(qe, default)
      //    val s = ctx.mkSolver(t)
  
      val s = ctx.mkSolver()
      
      // Can only check universal things
      val neg = Neg(f).simplify()
  
      // univfree is now in E*, so can be solved as SAT Problem
      val stripped = FormulaFunctions.stripQuantifiers(neg)
  
      // val prefix = FormulaFunctions.collectQuantifiersSub(univfree)
      val satform = FOTransformers.eliminatePredicates(stripped)
  
      // Checking QFree
      s.add(Z3QFree.translate(satform, ctx))
  
      // Send to z3
      val c = s.check()
      if (c == Status.UNKNOWN) {
        logger.info(s"Z3 status unknown: ${s.getReasonUnknown()}")
      }
      if (c == Status.SATISFIABLE) {
//        logger.info(s"Z3 status satisfiable")
        //      logger.info(s"${s.getModel()}")
      }
      (c, s)
Christian Müller's avatar
Christian Müller committed
68
    }
Christian Müller's avatar
Christian Müller committed
69 70
    logger.info(s"Z3 call took $time ms")
    res
Christian Müller's avatar
Christian Müller committed
71
  }
Christian Müller's avatar
Christian Müller committed
72

Christian Müller's avatar
Christian Müller committed
73 74 75
  def checkBlockInvariant(spec:Spec, b: SimpleBlock, pre: Formula, post: Formula, isfirst: Boolean, properties:InvProperties) = {
    val precond = Preconditions.abstractPrecondition(post, b, spec, properties)
    
76
    // TODO: do we do this here?
77
    val firstprecond = if (isfirst) {
Christian Müller's avatar
Christian Müller committed
78
      precond.assumeEmpty(spec.w.sig.preds.map(_.name).toList)
Christian Müller's avatar
Christian Müller committed
79
    } else { precond }
Christian Müller's avatar
Christian Müller committed
80 81 82 83 84 85 86
    val noinfprecond = if (isfirst) {
      firstprecond.assumeEmpty(List(Properties.INFNAME))
    } else { firstprecond }
    
    val z3simpednewinv = Z3QFree.simplifyUniv(noinfprecond)
    val gained = noinfprecond.toString().length() - z3simpednewinv.toString().length()
    logger.info(s"Invariant shrunken by $gained chars")
87 88 89 90

    //      val test1 = inv.toPrenex()
    //      val test2 = stubprecond.toPrenex()

Christian Müller's avatar
Christian Müller committed
91
    val f = Implies(pre, z3simpednewinv)
92 93 94

    logger.info(s"Checking invariant implication for $b")

Christian Müller's avatar
Christian Müller committed
95
    (checkOnZ3(f.simplify()), z3simpednewinv)
96
  }
97

Christian Müller's avatar
Christian Müller committed
98
  def checkInvariantFP(spec: Spec, inv: Formula, properties:InvProperties = InvProperties.DEFAULT) = {
99
    val graph = Encoding.toGraph(spec.w)
100 101 102 103
    type Node = graph.NodeT
    type Edge = graph.EdgeT

    @tailrec
104
    def checkInvariantRec(labellist: List[Map[Node, Formula]], provenlist: List[Set[Edge]]): (Boolean, List[Map[Node, Formula]], List[Set[Edge]]) = {
105

106 107
      val labels = labellist.head
      val proven = provenlist.head
108 109 110
      // check if done, i.e. all edges proven
      val toProve = (graph.edges -- proven)
      if (toProve.isEmpty) {
Christian Müller's avatar
Christian Müller committed
111
        logger.info("Everything proven. Terminating.")
112
        (true, labellist, provenlist)
113 114 115
      } else {

        // take one edge to prove
116 117 118 119 120 121
//        val next = toProve.head
        // take the edge with a minimum of following unproven edges excluding selfloops
//        val next = toProve.minBy(edge => ((edge.target.outgoing.filter(t => t.target != t.source) -- proven).size))
        // take the edge with maximum source node first
        val next = toProve.maxBy(edge => edge.source.value)
        
122 123 124
        // try to prove
        val pre = labels(next._1)
        val post = labels(next._2)
Christian Müller's avatar
Christian Müller committed
125
        val isfirst = !next._1.hasPredecessors
Christian Müller's avatar
Christian Müller committed
126
        val ((status, solver), strengthened) = checkBlockInvariant(spec, next, pre, post, isfirst, properties)
127 128 129

        if (status == Status.UNSATISFIABLE) {
          // Negation of implication unsat
Christian Müller's avatar
Christian Müller committed
130 131
          // --> safe, continue with larger proven set.
          logger.info(s"Proven inductiveness for (${next._1} -> ${next._2}).")
132
          checkInvariantRec(labels :: labellist, (proven + next) :: provenlist)
133 134 135 136
        } else {
          // Negation of implication sat
          // --> unsafe, relabel incoming node, invalidate all proven guarantees for that node
          // check if relabelled invariant still satisfiable
Christian Müller's avatar
Christian Müller committed
137
          // never relabel initial node
Christian Müller's avatar
Christian Müller committed
138
          logger.info(s"Invariant not inductive, strengthening")
Christian Müller's avatar
Christian Müller committed
139
          if (!isfirst) {
Christian Müller's avatar
Christian Müller committed
140
            // check if strengthened -> old_inv else use conjunction
Christian Müller's avatar
Christian Müller committed
141
//            val strengthened = Preconditions.abstractPrecondition(post, next, spec, properties)
Christian Müller's avatar
Christian Müller committed
142
            val newinv = And(labels(next._1), strengthened).simplify()
Christian Müller's avatar
Christian Müller committed
143
            
Christian Müller's avatar
Christian Müller committed
144 145 146 147 148
            val nostrangebindings = FormulaFunctions.checkBindings(newinv)
            if (!nostrangebindings) {
              logger.error("New invariant binds variables more than once")
              logger.error(s"Invariant would be $newinv")
            }
Christian Müller's avatar
Christian Müller committed
149 150

            val newlabels = labels.updated(next._1, strengthened)
Christian Müller's avatar
Christian Müller committed
151 152 153 154
            val invalidated = proven.filter(_._2 == next._1)
            
            val newproven = (proven -- invalidated) + next
  
Christian Müller's avatar
Christian Müller committed
155
            val (status2, solver2) = checkOnZ3(Implies(newinv, False))
Christian Müller's avatar
Christian Müller committed
156
            if (status2 == Status.SATISFIABLE) {
Christian Müller's avatar
Christian Müller committed
157
              // Negation of newinv still sat, newinv does not imply false)
Christian Müller's avatar
Christian Müller committed
158
              logger.info(s"Relabeling ${next._1}. Continuing.")
159
              checkInvariantRec(newlabels :: labellist, newproven :: provenlist)
Christian Müller's avatar
Christian Müller committed
160 161
            } else {
              logger.info(s"New invariant for ${next._1} not satisfiable. Terminating.")
162
              (false, newlabels :: labellist, newproven :: provenlist)
Christian Müller's avatar
Christian Müller committed
163
            }
164
          } else {
Christian Müller's avatar
Christian Müller committed
165
            logger.info("Would have to relabel initial node. Terminating.")
166
            (false, labellist, provenlist)
167 168 169
          }
        }
      }
170 171
    }

Christian Müller's avatar
Christian Müller committed
172 173
    // create labelling - FIXME: maybe use inv only for last
    val labels = (for (n <- graph.nodes) yield { n -> inv }).toMap
174 175 176
    val (result, afterlabels, proven) = checkInvariantRec(labels, List(Set()))
    
    val dot1 = afterlabels.zip(proven).reverse
177

178 179 180
    val dot2 = dot1.map((tup) => Encoding.toDot(graph)(tup._1.map(t => (t._1, t._2.pretty())), tup._2))
    
    (result, dot2)
181
  }
Christian Müller's avatar
Christian Müller committed
182
  
Christian Müller's avatar
Christian Müller committed
183
  def checkInvariantOnce(spec: Spec, inv: Formula, properties: InvProperties) = {
Christian Müller's avatar
Christian Müller committed
184

Christian Müller's avatar
Christian Müller committed
185
    // Build graph
186
    val graph = Encoding.toGraph(spec.w)
Christian Müller's avatar
Christian Müller committed
187

Christian Müller's avatar
Christian Müller committed
188
    val msg = new StringBuilder()
189
    msg ++= s"Trying to prove safe with invariant:\n\n${inv.pretty()}\n\n"
Christian Müller's avatar
Christian Müller committed
190

191
    // Check all edges
Christian Müller's avatar
Christian Müller committed
192
    val list = for (e <- graph.edges) yield {
Christian Müller's avatar
Christian Müller committed
193

Christian Müller's avatar
Christian Müller committed
194
      // Check I -> WP[w](inv)
Christian Müller's avatar
Christian Müller committed
195
      val b: SimpleBlock = e
196

197 198 199
      // Special handling for first block
      // TODO: Replace by iteration
      val isfirst = !e.from.hasPredecessors
200

Christian Müller's avatar
Christian Müller committed
201
      val ((res, solver), strengthened) = checkBlockInvariant(spec, b, inv, inv, isfirst, properties)
202

Christian Müller's avatar
Christian Müller committed
203
      if (res != Status.UNSATISFIABLE) {
Christian Müller's avatar
Christian Müller committed
204 205 206
        msg ++= s"Possibly unsafe: Block may not uphold invariant:\n\n${e.label}\n\n"
        if (res == Status.SATISFIABLE) {
          msg ++= "Satisfying model:\n"
Christian Müller's avatar
Christian Müller committed
207
          msg ++= Z3.printModel(solver.getModel()).lines.map("  " + _).mkString("\n")
Christian Müller's avatar
Christian Müller committed
208 209
        } else if (res == Status.UNKNOWN) {
          msg ++= s"Z3 result: $res (${solver.getReasonUnknown()})\n"
Christian Müller's avatar
Christian Müller committed
210 211
        }
        msg ++= "\n"
Christian Müller's avatar
Christian Müller committed
212 213 214 215 216 217
        logger.info(s"Could not prove invariant $inv")
        logger.info(s"Z3 status $res")
        logger.info(s"Block ${e.label} may not uphold it")
      }
      res == Status.UNSATISFIABLE
    }
Christian Müller's avatar
Christian Müller committed
218

Christian Müller's avatar
Christian Müller committed
219 220
    val safe = list.reduceLeft(_ && _)
    if (safe) {
221
      msg ++= s"Proven safe.\n"
222
      logger.info(s"Workflow ${spec.w}\n proven safe for invariant:\n${inv.pretty()}")
Christian Müller's avatar
Christian Müller committed
223
    }
Christian Müller's avatar
Christian Müller committed
224
    (safe, msg)
Christian Müller's avatar
Christian Müller committed
225 226
  }
}