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package hu.bme.mit.inf.dslreasoner.viatrasolver.logic2viatra.cardinality
import com.microsoft.z3.ArithExpr
import com.microsoft.z3.Context
import com.microsoft.z3.Expr
import com.microsoft.z3.IntNum
import com.microsoft.z3.Optimize
import com.microsoft.z3.Status
import com.microsoft.z3.Symbol
import java.util.Map
import org.eclipse.xtend.lib.annotations.FinalFieldsConstructor
class Z3PolyhedronSolver implements PolyhedronSolver {
val boolean lpRelaxation
@FinalFieldsConstructor
new() {
}
new() {
this(true)
}
override createSaturationOperator(Polyhedron polyhedron) {
new Z3SaturationOperator(polyhedron, lpRelaxation)
}
}
class Z3SaturationOperator extends AbstractPolyhedronSaturationOperator {
static val INFINITY_SYMBOL_NAME = "oo"
static val MULT_SYMBOL_NAME = "*"
extension val Context context
val Symbol infinitySymbol
val Symbol multSymbol
val Map<Dimension, ArithExpr> variables
new(Polyhedron polyhedron, boolean lpRelaxation) {
super(polyhedron)
context = new Context
infinitySymbol = context.mkSymbol(INFINITY_SYMBOL_NAME)
multSymbol = context.mkSymbol(MULT_SYMBOL_NAME)
variables = polyhedron.dimensions.toInvertedMap [ dimension |
val name = dimension.name
if (lpRelaxation) {
mkRealConst(name)
} else {
mkIntConst(name)
}
]
}
override doSaturate() {
val status = executeSolver()
convertStatusToSaturationResult(status)
}
private def convertStatusToSaturationResult(Status status) {
switch (status) {
case SATISFIABLE:
PolyhedronSaturationResult.SATURATED
case UNSATISFIABLE:
PolyhedronSaturationResult.EMPTY
case UNKNOWN:
PolyhedronSaturationResult.UNKNOWN
default:
throw new IllegalArgumentException("Unknown Status: " + status)
}
}
private def executeSolver() {
for (expressionToSaturate : polyhedron.expressionsToSaturate) {
val expr = expressionToSaturate.toExpr
val lowerResult = saturateLowerBound(expr, expressionToSaturate)
if (lowerResult != Status.SATISFIABLE) {
return lowerResult
}
val upperResult = saturateUpperBound(expr, expressionToSaturate)
if (upperResult != Status.SATISFIABLE) {
return upperResult
}
}
Status.SATISFIABLE
}
private def saturateLowerBound(ArithExpr expr, LinearBoundedExpression expressionToSaturate) {
val optimize = prepareOptimize
val handle = optimize.MkMinimize(expr)
val status = optimize.Check()
if (status == Status.SATISFIABLE) {
val value = switch (resultExpr : handle.lower) {
IntNum:
resultExpr.getInt()
default:
if (isNegativeInfinity(resultExpr)) {
null
} else {
throw new IllegalArgumentException("Integer result expected, got: " + resultExpr)
}
}
expressionToSaturate.lowerBound = value
}
status
}
private def saturateUpperBound(ArithExpr expr, LinearBoundedExpression expressionToSaturate) {
val optimize = prepareOptimize
val handle = optimize.MkMaximize(expr)
val status = optimize.Check()
if (status == Status.SATISFIABLE) {
val value = switch (resultExpr : handle.upper) {
IntNum:
resultExpr.getInt()
default:
if (isPositiveInfinity(resultExpr)) {
null
} else {
throw new IllegalArgumentException("Integer result expected, got: " + resultExpr)
}
}
expressionToSaturate.upperBound = value
}
status
}
private def isPositiveInfinity(Expr expr) {
expr.app && expr.getFuncDecl.name == infinitySymbol
}
private def isNegativeInfinity(Expr expr) {
// Negative infinity is represented as (* (- 1) oo)
if (!expr.app || expr.getFuncDecl.name != multSymbol || expr.numArgs != 2) {
return false
}
isPositiveInfinity(expr.args.get(1))
}
private def prepareOptimize() {
val optimize = mkOptimize()
assertConstraints(optimize)
optimize
}
private def assertConstraints(Optimize it) {
for (pair : variables.entrySet) {
assertBounds(pair.value, pair.key)
}
for (constraint : nonTrivialConstraints) {
val expr = createLinearCombination(constraint.coefficients)
assertBounds(expr, constraint)
}
}
private def assertBounds(Optimize it, ArithExpr expression, LinearBoundedExpression bounds) {
val lowerBound = bounds.lowerBound
val upperBound = bounds.upperBound
if (lowerBound == upperBound) {
if (lowerBound === null) {
return
}
Assert(mkEq(expression, mkInt(lowerBound)))
} else {
if (lowerBound !== null) {
Assert(mkGe(expression, mkInt(lowerBound)))
}
if (upperBound !== null) {
Assert(mkLe(expression, mkInt(upperBound)))
}
}
}
private def toExpr(LinearBoundedExpression linearBoundedExpression) {
switch (linearBoundedExpression) {
Dimension: variables.get(linearBoundedExpression)
LinearConstraint: createLinearCombination(linearBoundedExpression.coefficients)
default: throw new IllegalArgumentException("Unknown linear bounded expression:" + linearBoundedExpression)
}
}
private def createLinearCombination(Map<Dimension, Integer> coefficients) {
val size = coefficients.size
if (size == 0) {
return mkInt(0)
}
val array = newArrayOfSize(size)
var int i = 0
for (pair : coefficients.entrySet) {
val variable = variables.get(pair.key)
if (variable === null) {
throw new IllegalArgumentException("Unknown dimension: " + pair.key.name)
}
val coefficient = pair.value
val term = if (coefficient == 1) {
variable
} else {
mkMul(mkInt(coefficient), variable)
}
array.set(i, term)
i++
}
mkAdd(array)
}
override close() throws Exception {
context.close()
}
}
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