From 10844cf82fe0c7dda1d5d09c750501799f8c2a19 Mon Sep 17 00:00:00 2001
From: Philippe Suter <philippe.suter@gmail.com>
Date: Fri, 26 Oct 2012 18:37:25 +0200
Subject: [PATCH] Basics of UninterpretedZ3Solver in place
---
.../leon/solvers/z3/AbstractZ3Solver.scala | 2 +-
.../scala/leon/solvers/z3/FairZ3Solver.scala | 287 +-----------------
.../solvers/z3/UninterpretedZ3Solver.scala | 86 ++++++
3 files changed, 99 insertions(+), 276 deletions(-)
create mode 100644 src/main/scala/leon/solvers/z3/UninterpretedZ3Solver.scala
diff --git a/src/main/scala/leon/solvers/z3/AbstractZ3Solver.scala b/src/main/scala/leon/solvers/z3/AbstractZ3Solver.scala
index a2a78f952..5c31961fb 100644
--- a/src/main/scala/leon/solvers/z3/AbstractZ3Solver.scala
+++ b/src/main/scala/leon/solvers/z3/AbstractZ3Solver.scala
@@ -375,7 +375,7 @@ trait AbstractZ3Solver {
}
}
- protected[leon] def toZ3Formula(z3: Z3Context, expr: Expr, initialMap: Map[Identifier,Z3AST] = Map.empty) : Option[Z3AST] = {
+ protected[leon] def toZ3Formula(expr: Expr, initialMap: Map[Identifier,Z3AST] = Map.empty) : Option[Z3AST] = {
class CantTranslateException extends Exception
val varsInformula: Set[Identifier] = variablesOf(expr)
diff --git a/src/main/scala/leon/solvers/z3/FairZ3Solver.scala b/src/main/scala/leon/solvers/z3/FairZ3Solver.scala
index b0d7ba9d2..9d654c88f 100644
--- a/src/main/scala/leon/solvers/z3/FairZ3Solver.scala
+++ b/src/main/scala/leon/solvers/z3/FairZ3Solver.scala
@@ -97,14 +97,14 @@ class FairZ3Solver(reporter: Reporter) extends Solver(reporter) with AbstractZ3S
assert(variablesOf(expr) -- argsAsIDs.toSet == Set.empty)
val axiom : Z3AST = if(args.isEmpty) {
val eq = Equals(FunctionInvocation(fd, Seq(cc)), expr)
- toZ3Formula(z3, eq).get
+ toZ3Formula(eq).get
} else {
val z3ArgSorts = argsAsIDs.map(i => typeToSort(i.getType))
val boundVars = z3ArgSorts.zipWithIndex.map(p => z3.mkBound(p._2, p._1))
val map : Map[Identifier,Z3AST] = (argsAsIDs zip boundVars).toMap
val eq = Equals(FunctionInvocation(fd, Seq(cc)), expr)
- val z3IzedEq = toZ3Formula(z3, eq, map).get
- val z3IzedCC = toZ3Formula(z3, cc, map).get
+ val z3IzedEq = toZ3Formula(eq, map).get
+ val z3IzedCC = toZ3Formula(cc, map).get
val pattern = z3.mkPattern(functionDefToDecl(fd)(z3IzedCC))
val nameTypePairs = z3ArgSorts.map(s => (z3.mkFreshIntSymbol, s))
z3.mkForAll(0, List(pattern), nameTypePairs, z3IzedEq)
@@ -121,7 +121,7 @@ class FairZ3Solver(reporter: Reporter) extends Solver(reporter) with AbstractZ3S
val argSort = typeToSort(fd.args(0).getType)
val bound = z3.mkBound(0, argSort)
val subst = replace(Map(ResultVariable() -> FunctionInvocation(fd, Seq(fd.args(0).toVariable))), cleaned)
- val z3IzedPost = toZ3Formula(z3, subst, Map(fd.args(0).id -> bound)).get
+ val z3IzedPost = toZ3Formula(subst, Map(fd.args(0).id -> bound)).get
val pattern = z3.mkPattern(functionDefToDecl(fd)(bound))
val nameTypePairs = Seq((z3.mkFreshIntSymbol, argSort))
val postAxiom = z3.mkForAll(0, List(pattern), nameTypePairs, z3IzedPost)
@@ -219,11 +219,11 @@ class FairZ3Solver(reporter: Reporter) extends Solver(reporter) with AbstractZ3S
Logger.debug("we're getting a new clause " + clause, 4, "z3solver")
}
- val cc = toZ3Formula(z3, And(clauses)).get
+ val cc = toZ3Formula(And(clauses)).get
z3.assertCnstr(cc)
// these are the optional sequence of assumption literals
- val assumptionsAsZ3: Option[Seq[Z3AST]] = assumptions.map(set => set.toSeq.map(toZ3Formula(z3, _).get))
+ val assumptionsAsZ3: Option[Seq[Z3AST]] = assumptions.map(set => set.toSeq.map(toZ3Formula(_).get))
blockingSet ++= Set(guards.map(p => if(p._2) Not(Variable(p._1)) else Variable(p._1)) : _*)
@@ -234,7 +234,7 @@ class FairZ3Solver(reporter: Reporter) extends Solver(reporter) with AbstractZ3S
iterationsLeft -= 1
blocking2Z3Stopwatch.start
- val blockingSetAsZ3 : Seq[Z3AST] = blockingSet.toSeq.map(toZ3Formula(z3, _).get)
+ val blockingSetAsZ3 : Seq[Z3AST] = blockingSet.toSeq.map(toZ3Formula(_).get)
// println("Blocking set : " + blockingSet)
blocking2Z3Stopwatch.stop
@@ -398,12 +398,12 @@ class FairZ3Solver(reporter: Reporter) extends Solver(reporter) with AbstractZ3S
for(ex <- blockingSet) ex match {
case Not(Variable(b)) => {
z3.push
- z3.assertCnstr(toZ3Formula(z3, Variable(b)).get)
+ z3.assertCnstr(toZ3Formula(Variable(b)).get)
z3.check match {
case Some(false) => {
//println("We had ~" + b + " in the blocking set. We now know it should stay there forever.")
z3.pop(1)
- z3.assertCnstr(toZ3Formula(z3, Not(Variable(b))).get)
+ z3.assertCnstr(toZ3Formula(Not(Variable(b))).get)
fixedForEver = fixedForEver + ex
}
case _ => z3.pop(1)
@@ -411,12 +411,12 @@ class FairZ3Solver(reporter: Reporter) extends Solver(reporter) with AbstractZ3S
}
case Variable(b) => {
z3.push
- z3.assertCnstr(toZ3Formula(z3, Not(Variable(b))).get)
+ z3.assertCnstr(toZ3Formula(Not(Variable(b))).get)
z3.check match {
case Some(false) => {
//println("We had " + b + " in the blocking set. We now know it should stay there forever.")
z3.pop(1)
- z3.assertCnstr(toZ3Formula(z3, Variable(b)).get)
+ z3.assertCnstr(toZ3Formula(Variable(b)).get)
fixedForEver = fixedForEver + ex
}
case _ => z3.pop(1)
@@ -446,7 +446,7 @@ class FairZ3Solver(reporter: Reporter) extends Solver(reporter) with AbstractZ3S
}
for(ncl <- newClauses) {
- z3.assertCnstr(toZ3Formula(z3, ncl).get)
+ z3.assertCnstr(toZ3Formula(ncl).get)
}
blockingSet = blockingSet ++ Set(newBlockers.map(p => if(p._2) Not(Variable(p._1)) else Variable(p._1)) : _*)
}
@@ -544,269 +544,6 @@ class FairZ3Solver(reporter: Reporter) extends Solver(reporter) with AbstractZ3S
}
}
-
- // the last return value is a map binding ite values to boolean switches
- private def clausifyITE(formula : Expr) : (Expr, List[Expr], Map[Identifier,Identifier]) = {
- var newClauses : List[Expr] = Nil
- var ite2Bools : Map[Identifier,Identifier] = Map.empty
-
- def clausify(ex : Expr) : Option[Expr] = ex match {
- case ie @ IfExpr(cond, then, elze) => {
- val switch = FreshIdentifier("path", true).setType(BooleanType).toVariable
- val placeHolder = FreshIdentifier("iteval", true).setType(ie.getType).toVariable
- newClauses = Iff(switch, cond) :: newClauses
- newClauses = Implies(switch, Equals(placeHolder, then)) :: newClauses
- newClauses = Implies(Not(switch), Equals(placeHolder, elze)) :: newClauses
- // newBools = newBools + switch.id
- ite2Bools = ite2Bools + (placeHolder.id -> switch.id)
- Some(placeHolder)
- }
- case _ => None
- }
-
- val cleanedUp = searchAndReplaceDFS(clausify)(formula)
-
- (cleanedUp, newClauses.reverse, ite2Bools)
- }
-
- protected[leon] override def toZ3Formula(z3: Z3Context, expr: Expr, initialMap: Map[Identifier,Z3AST] = Map.empty) : Option[Z3AST] = {
- class CantTranslateException extends Exception
-
- val varsInformula: Set[Identifier] = variablesOf(expr)
-
- var z3Vars: Map[Identifier,Z3AST] = if(!initialMap.isEmpty) {
- initialMap
- } else {
- // FIXME TODO pleeeeeeeease make this cleaner. Ie. decide what set of
- // variable has to remain in a map etc.
- exprToZ3Id.filter(p => p._1.isInstanceOf[Variable]).map(p => (p._1.asInstanceOf[Variable].id -> p._2))
- }
- // exprToZ3Id = Map.empty
- // z3IdToExpr = Map.empty
-
- // for((k, v) <- initialMap) {
- // exprToZ3Id += (k.toVariable -> v)
- // z3IdToExpr += (v -> k.toVariable)
- // }
-
- def rec(ex: Expr): Z3AST = {
- //println("Stacking up call for:")
- //println(ex)
- val recResult = (ex match {
- case tu@Tuple(args) => {
- // This call is required, because the Z3 sort may not have been generated yet.
- // If it has, it's just a map lookup and instant return.
- typeToSort(tu.getType)
- val constructor = tupleConstructors(tu.getType)
- constructor(args.map(rec(_)): _*)
- }
- case ts@TupleSelect(tu, i) => {
- // See comment above for similar code.
- typeToSort(tu.getType)
- val selector = tupleSelectors(tu.getType)(i-1)
- selector(rec(tu))
- }
- case Let(i, e, b) => {
- val re = rec(e)
- z3Vars = z3Vars + (i -> re)
- val rb = rec(b)
- z3Vars = z3Vars - i
- rb
- }
- case Waypoint(_, e) => rec(e)
- case e @ Error(_) => {
- val tpe = e.getType
- val newAST = z3.mkFreshConst("errorValue", typeToSort(tpe))
- exprToZ3Id += (e -> newAST)
- z3IdToExpr += (newAST -> e)
- newAST
- }
- case v@Variable(id) => z3Vars.get(id) match {
- case Some(ast) => ast
- case None => {
- // if (id.isLetBinder) {
- // scala.sys.error("Error in formula being translated to Z3: identifier " + id + " seems to have escaped its let-definition")
- // }
- val newAST = z3.mkFreshConst(id.uniqueName/*name*/, typeToSort(v.getType))
- z3Vars = z3Vars + (id -> newAST)
- exprToZ3Id += (v -> newAST)
- z3IdToExpr += (newAST -> v)
- newAST
- }
- }
-
- case ite @ IfExpr(c, t, e) => {
- z3.mkITE(rec(c), rec(t), rec(e))
- }
- // case ite @ IfExpr(c, t, e) => {
- // val switch = z3.mkFreshConst("path", z3.mkBoolSort)
- // val placeHolder = z3.mkFreshConst("ite", typeToSort(ite.getType))
- // val clause1 = z3.mkIff(switch, rec(c))
- // val clause2 = z3.mkImplies(switch, z3.mkEq(placeHolder, rec(t)))
- // val clause3 = z3.mkImplies(z3.mkNot(switch), z3.mkEq(placeHolder, rec(e)))
-
- // accumulatedClauses = clause3 :: clause2 :: clause1 :: accumulatedClauses
-
- // placeHolder
- // }
- case And(exs) => z3.mkAnd(exs.map(rec(_)): _*)
- case Or(exs) => z3.mkOr(exs.map(rec(_)): _*)
- case Implies(l, r) => z3.mkImplies(rec(l), rec(r))
- case Iff(l, r) => {
- val rl = rec(l)
- val rr = rec(r)
- z3.mkAnd(z3.mkImplies(rl, rr), z3.mkImplies(rr, rl))
- }
- case Not(Iff(l, r)) => z3.mkXor(rec(l), rec(r))
- case Not(Equals(l, r)) => z3.mkDistinct(rec(l), rec(r))
- case Not(e) => z3.mkNot(rec(e))
- case IntLiteral(v) => z3.mkInt(v, intSort)
- case BooleanLiteral(v) => if (v) z3.mkTrue() else z3.mkFalse()
- case UnitLiteral => unitValue
- case Equals(l, r) => z3.mkEq(rec(l), rec(r))
- case Plus(l, r) => if(USEBV) z3.mkBVAdd(rec(l), rec(r)) else z3.mkAdd(rec(l), rec(r))
- case Minus(l, r) => if(USEBV) z3.mkBVSub(rec(l), rec(r)) else z3.mkSub(rec(l), rec(r))
- case Times(l, r) => if(USEBV) z3.mkBVMul(rec(l), rec(r)) else z3.mkMul(rec(l), rec(r))
- case Division(l, r) => if(USEBV) z3.mkBVSdiv(rec(l), rec(r)) else z3.mkDiv(rec(l), rec(r))
- case Modulo(l, r) => if(USEBV) sys.error("I don't know what to do here!") else z3.mkMod(rec(l), rec(r))
- case UMinus(e) => if(USEBV) z3.mkBVNeg(rec(e)) else z3.mkUnaryMinus(rec(e))
- case LessThan(l, r) => if(USEBV) z3.mkBVSlt(rec(l), rec(r)) else z3.mkLT(rec(l), rec(r))
- case LessEquals(l, r) => if(USEBV) z3.mkBVSle(rec(l), rec(r)) else z3.mkLE(rec(l), rec(r))
- case GreaterThan(l, r) => if(USEBV) z3.mkBVSgt(rec(l), rec(r)) else z3.mkGT(rec(l), rec(r))
- case GreaterEquals(l, r) => if(USEBV) z3.mkBVSge(rec(l), rec(r)) else z3.mkGE(rec(l), rec(r))
- case c@CaseClass(cd, args) => {
- val constructor = adtConstructors(cd)
- constructor(args.map(rec(_)): _*)
- }
- case c@CaseClassSelector(_, cc, sel) => {
- val selector = adtFieldSelectors(sel)
- selector(rec(cc))
- }
- case c@CaseClassInstanceOf(ccd, e) => {
- val tester = adtTesters(ccd)
- tester(rec(e))
- }
- case f@FunctionInvocation(fd, args) => {
- z3.mkApp(functionDefToDecl(fd), args.map(rec(_)): _*)
- }
- case e@EmptySet(_) => z3.mkEmptySet(typeToSort(e.getType.asInstanceOf[SetType].base))
-
- case SetEquals(s1, s2) => z3.mkEq(rec(s1), rec(s2))
- case ElementOfSet(e, s) => z3.mkSetSubset(z3.mkSetAdd(z3.mkEmptySet(typeToSort(e.getType)), rec(e)), rec(s))
- case SubsetOf(s1, s2) => z3.mkSetSubset(rec(s1), rec(s2))
- case SetIntersection(s1, s2) => z3.mkSetIntersect(rec(s1), rec(s2))
- case SetUnion(s1, s2) => z3.mkSetUnion(rec(s1), rec(s2))
- case SetDifference(s1, s2) => z3.mkSetDifference(rec(s1), rec(s2))
- case f@FiniteSet(elems) => elems.foldLeft(z3.mkEmptySet(typeToSort(f.getType.asInstanceOf[SetType].base)))((ast, el) => z3.mkSetAdd(ast, rec(el)))
- case SetCardinality(s) => {
- val rs = rec(s)
- setCardFuns(s.getType.asInstanceOf[SetType].base)(rs)
- }
- case SetMin(s) => intSetMinFun(rec(s))
- case SetMax(s) => intSetMaxFun(rec(s))
- case s @ SingletonMap(from,to) => s.getType match {
- case MapType(fromType, toType) =>
- val fromSort = typeToSort(fromType)
- val toSort = typeToSort(toType)
- val constArray = z3.mkConstArray(fromSort, mapRangeNoneConstructors(toType)())
- z3.mkStore(constArray, rec(from), mapRangeSomeConstructors(toType)(rec(to)))
- case errorType => scala.sys.error("Unexpected type for singleton map: " + (ex, errorType))
- }
- case e @ EmptyMap(fromType, toType) => {
- typeToSort(e.getType) //had to add this here because the mapRangeNoneConstructors was not yet constructed...
- val fromSort = typeToSort(fromType)
- val toSort = typeToSort(toType)
- z3.mkConstArray(fromSort, mapRangeNoneConstructors(toType)())
- }
- case f @ FiniteMap(elems) => f.getType match {
- case MapType(fromType, toType) =>
- val fromSort = typeToSort(fromType)
- val toSort = typeToSort(toType)
- elems.foldLeft(z3.mkConstArray(fromSort, mapRangeNoneConstructors(toType)())){ case (ast, SingletonMap(k,v)) => z3.mkStore(ast, rec(k), mapRangeSomeConstructors(toType)(rec(v))) }
- case errorType => scala.sys.error("Unexpected type for finite map: " + (ex, errorType))
- }
- case mg @ MapGet(m,k) => m.getType match {
- case MapType(fromType, toType) =>
- val selected = z3.mkSelect(rec(m), rec(k))
- mapRangeValueSelectors(toType)(selected)
- case errorType => scala.sys.error("Unexpected type for map: " + (ex, errorType))
- }
- case MapUnion(m1,m2) => m1.getType match {
- case MapType(ft, tt) => m2 match {
- case FiniteMap(ss) =>
- ss.foldLeft(rec(m1)){
- case (ast, SingletonMap(k, v)) => z3.mkStore(ast, rec(k), mapRangeSomeConstructors(tt)(rec(v)))
- }
- case SingletonMap(k, v) => z3.mkStore(rec(m1), rec(k), mapRangeSomeConstructors(tt)(rec(v)))
- case _ => scala.sys.error("map updates can only be applied with concrete map instances")
- }
- case errorType => scala.sys.error("Unexpected type for map: " + (ex, errorType))
- }
- case MapIsDefinedAt(m,k) => m.getType match {
- case MapType(ft, tt) => z3.mkDistinct(z3.mkSelect(rec(m), rec(k)), mapRangeNoneConstructors(tt)())
- case errorType => scala.sys.error("Unexpected type for map: " + (ex, errorType))
- }
- case fill@ArrayFill(length, default) => {
- val at@ArrayType(base) = fill.getType
- typeToSort(at)
- val cons = arrayTupleCons(at)
- val ar = z3.mkConstArray(typeToSort(base), rec(default))
- val res = cons(ar, rec(length))
- res
- }
- case ArraySelect(a, index) => {
- typeToSort(a.getType)
- val ar = rec(a)
- val getArray = arrayTupleSelectorArray(a.getType)
- val res = z3.mkSelect(getArray(ar), rec(index))
- res
- }
- case ArrayUpdated(a, index, newVal) => {
- typeToSort(a.getType)
- val ar = rec(a)
- val getArray = arrayTupleSelectorArray(a.getType)
- val getLength = arrayTupleSelectorLength(a.getType)
- val cons = arrayTupleCons(a.getType)
- val store = z3.mkStore(getArray(ar), rec(index), rec(newVal))
- val res = cons(store, getLength(ar))
- res
- }
- case ArrayLength(a) => {
- typeToSort(a.getType)
- val ar = rec(a)
- val getLength = arrayTupleSelectorLength(a.getType)
- val res = getLength(ar)
- res
- }
- case AnonymousFunctionInvocation(id, args) => id.getType match {
- case ft @ FunctionType(fts, tt) => {
- val consFD = funDomainConstructors(ft)
- val rid = rec(Variable(id))
- val rargs = args map rec
- z3.mkSelect(rid, consFD(rargs: _*))
- }
- case errorType => scala.sys.error("Unexpected type for function: " + (ex, errorType))
- }
-
- case Distinct(exs) => z3.mkDistinct(exs.map(rec(_)): _*)
-
- case _ => {
- reporter.warning("Can't handle this in translation to Z3: " + ex)
- throw new CantTranslateException
- }
- })
- recResult
- }
-
- try {
- val res = Some(rec(expr))
- res
- } catch {
- case e: CantTranslateException => None
- }
- }
-
-
class UnrollingBank {
private val blockMap : MutableMap[(Identifier,Boolean),Set[FunctionInvocation]] = MutableMap.empty
private def registerBlocked(id: Identifier, pol: Boolean, fi: FunctionInvocation) : Boolean =
diff --git a/src/main/scala/leon/solvers/z3/UninterpretedZ3Solver.scala b/src/main/scala/leon/solvers/z3/UninterpretedZ3Solver.scala
new file mode 100644
index 000000000..10162c266
--- /dev/null
+++ b/src/main/scala/leon/solvers/z3/UninterpretedZ3Solver.scala
@@ -0,0 +1,86 @@
+package leon
+package solvers.z3
+
+import z3.scala._
+import purescala.Common._
+import purescala.Definitions._
+import purescala.Trees._
+import purescala.Extractors._
+import purescala.TreeOps._
+import purescala.TypeTrees._
+import Extensions._
+
+/** This is a rather direct mapping to Z3, where all functions are left uninterpreted.
+ * It reports the results as follows (based on the negation of the formula):
+ * - if Z3 reports UNSAT, it reports VALID
+ * - if Z3 reports SAT and the formula contained no function invocation, it returns INVALID with the counter-example/model
+ * - otherwise it returns UNKNOWN
+ * Results should come back very quickly.
+ */
+class UninterpretedZ3Solver(reporter : Reporter) extends Solver(reporter) with AbstractZ3Solver with Z3ModelReconstruction {
+ val description = "Uninterpreted Z3 Solver"
+ override val shortDescription = "Z3-u"
+
+ // this is fixed
+ protected[leon] val z3cfg = new Z3Config(
+ "MODEL" -> true,
+ "MBQI" -> false,
+ "TYPE_CHECK" -> true,
+ "WELL_SORTED_CHECK" -> true
+ )
+ toggleWarningMessages(true)
+
+ private var functionMap: Map[FunDef, Z3FuncDecl] = Map.empty
+ private var reverseFunctionMap: Map[Z3FuncDecl, FunDef] = Map.empty
+ protected[leon] def prepareFunctions : Unit = {
+ functionMap = Map.empty
+ reverseFunctionMap = Map.empty
+ for(funDef <- program.definedFunctions) {
+ val sortSeq = funDef.args.map(vd => typeToSort(vd.tpe))
+ val returnSort = typeToSort(funDef.returnType)
+
+ val z3Decl = z3.mkFreshFuncDecl(funDef.id.name, sortSeq, returnSort)
+ functionMap = functionMap + (funDef -> z3Decl)
+ reverseFunctionMap = reverseFunctionMap + (z3Decl -> funDef)
+ }
+ }
+ protected[leon] def functionDefToDecl(funDef: FunDef) : Z3FuncDecl = functionMap(funDef)
+ protected[leon] def functionDeclToDef(decl: Z3FuncDecl) : FunDef = reverseFunctionMap(decl)
+ protected[leon] def isKnownDecl(decl: Z3FuncDecl) : Boolean = reverseFunctionMap.isDefinedAt(decl)
+
+ override def solve(expression: Expr) : Option[Boolean] = solveOrGetCounterexample(expression)._1
+
+ // Where the solving occurs
+ override def solveOrGetCounterexample(expression : Expr) : (Option[Boolean],Map[Identifier,Expr]) = {
+ val emptyModel = Map.empty[Identifier,Expr]
+ val unknownResult = (None, emptyModel)
+ val validResult = (Some(true), emptyModel)
+
+ containedInvocations = false
+ val result = toZ3Formula(expression).map { asZ3 =>
+ z3.assertCnstr(z3.mkNot(asZ3))
+ z3.checkAndGetModel() match {
+ case (Some(false), _) => validResult
+ case (Some(true), model) if !containedInvocations => {
+ val variables = variablesOf(expression)
+ val r = (Some(false), modelToMap(model, variables))
+ model.delete
+ r
+ }
+ case _ => unknownResult
+ }
+ } getOrElse unknownResult
+
+ result
+ }
+
+ private var containedInvocations : Boolean = _
+
+ override def toZ3Formula(expr : Expr, m : Map[Identifier,Z3AST] = Map.empty) : Option[Z3AST] = {
+ expr match {
+ case FunctionInvocation(_, _) => containedInvocations = true
+ case _ => ;
+ }
+ super.toZ3Formula(expr,m)
+ }
+}
--
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