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/**
* This file is part of Ostrich, an SMT solver for strings.
* Copyright (c) 2018-2021 Matthew Hague, Philipp Ruemmer. All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
*
* * Redistributions of source code must retain the above copyright notice, this
* list of conditions and the following disclaimer.
*
* * Redistributions in binary form must reproduce the above copyright notice,
* this list of conditions and the following disclaimer in the documentation
* and/or other materials provided with the distribution.
*
* * Neither the name of the authors nor the names of their
* contributors may be used to endorse or promote products derived from
* this software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
* COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT,
* INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
* (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
* SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
* STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
* OF THE POSSIBILITY OF SUCH DAMAGE.
*/
package ostrich.automata
import ap.parser._
import IExpression._
import ap.SimpleAPI
import ap.basetypes.IdealInt
import SimpleAPI.ProverStatus
import ap.theories.ModuloArithmetic
import ap.theories.strings.{StringTheory, StringTheoryBuilder}
import scala.collection.mutable.{HashMap => MHashMap, HashSet => MHashSet,
ArrayBuffer}
/**
* Helper methods to translate transducers in symbolic representation
* (an arbitrary formula associated with each transition) to the
* Brics representation.
*
* TODO: check that transducers are deterministic!
*/
object TransducerTranslator {
import StringTheoryBuilder._
import Transducer._
def toBricsTransducer(transducer : SymTransducer,
alphabetSize : Int,
transducerStringTheory : StringTheory) : Transducer = {
val SymTransducer(transitions, accepting) = transducer
val states =
(for (TransducerTransition(from, to, _, _, _) <- transitions.iterator;
s <- Iterator(from, to))
yield s).toSet ++ accepting ++ List(0)
if (!(transitions forall {
case TransducerTransition(_, _, epsilons, _,_) => epsilons.size == 2
}))
throw new Exception(
"Can only handle 2-track transducers")
val usePriorities =
transducer.transitions exists { t => !t.blockedTransitions.isEmpty }
val builder =
if (usePriorities)
BricsPrioTransducer.getBuilder
else
BricsTransducer.getBuilder
val states2Brics =
(for (s <- states.toList.sorted) yield (s -> builder.getNewState)).toMap
for (s <- accepting)
builder.setAccept(states2Brics(s), true)
val epsTransitions =
new MHashMap[Int, ArrayBuffer[TransducerTransition]]
SimpleAPI.withProver { p =>
p.addTheory(transducerStringTheory)
val inputC, outputC =
p.createConstant(ModuloArithmetic.ModSort(IdealInt.ZERO,
IdealInt(alphabetSize - 1)))
val OutputInputOffsetEq =
OffsetEq(outputC, inputC)
for (transition@
TransducerTransition(fromState, toState, epsilons, constraint,
blockedTransitions) <- transitions) {
val bvLabel =
VariableSubstVisitor(constraint, (List(inputC, outputC), 0))
epsilons match {
case Seq(true, false) => p.scope {
if (!blockedTransitions.isEmpty)
throw new Exception(
"Priorities can only be use for epsilon-transitions")
for (out <- enumLabelSolutions(bvLabel, outputC,
p, transducerStringTheory)) {
val op = OutputOp(out.intValueSafe.toChar.toString, NOP, "")
Console.err.println("" + fromState + "- -> " +
toState + ": \t" + op)
builder.addETransition(states2Brics(fromState), op,
states2Brics(toState))
}
}
case Seq(true, true) =>
epsTransitions.getOrElseUpdate(fromState, new ArrayBuffer) +=
transition
case Seq(false, outEps) => {
if (!blockedTransitions.isEmpty)
throw new Exception(
"Priorities can only be use for epsilon-transitions")
val presLabel =
IntCastEliminator(
PartialEvaluator(
simplifyLabel(bvLabel, p, transducerStringTheory)))
if (!ContainsSymbol.isPresburger(presLabel))
throw new Exception(
"Could not translate constraint: " + p.pp(constraint))
val splitLabel = NegEqSplitter(Transform2NNF(presLabel))
for (disjunct <- DNFConverter mbDNF splitLabel) {
var inputOp : Option[InputOp] = None
var lBound : Option[Char] = None
var uBound : Option[Char] = None
var outputChars : List[Char] = List()
for (c <- LineariseVisitor(disjunct, IBinJunctor.And)) c match {
case IBoolLit(true) =>
// nothing
case OutputInputOffsetEq(offset) =>
inputOp = Some(Plus(offset.intValueSafe))
case EqLit(`outputC`, value) => {
inputOp = Some(NOP)
outputChars = List(value.intValueSafe.toChar)
}
case Geq(`inputC`, Const(bound)) =>
lBound = Some(bound.intValueSafe.toChar)
case Geq(Const(bound), `inputC`) =>
uBound = Some(bound.intValueSafe.toChar)
case INot(Geq(`inputC`, Const(bound))) => // inputC < bound
uBound = Some((bound.intValueSafe - 1).toChar)
case INot(Geq(Const(bound), `inputC`)) => // bound < inputC
lBound = Some((bound.intValueSafe + 1).toChar)
case EqLit(`inputC`, value) => {
lBound = Some(value.intValueSafe.toChar)
uBound = Some(value.intValueSafe.toChar)
}
case _ =>
throw new Exception(
"cannot handle transducer constraint " + c)
}
val lb = lBound getOrElse Char.MinValue
val ub = uBound getOrElse Char.MaxValue
if (outEps)
inputOp = Some(NOP)
val op = OutputOp("", inputOp.get, outputChars)
Console.err.println("" + fromState +
"- [" + lb + ", " + ub + "] -> " +
toState + ": \t" + op)
builder.addTransition(states2Brics(fromState),
(lb, ub), op,
states2Brics(toState))
}
}
}
}
}
val nop = OutputOp("", NOP, "")
for (fromState <- epsTransitions.keys.toVector.sorted) {
val transitions = epsTransitions(fromState)
if (transitions exists {
case TransducerTransition(_, _, _, _, blocked) =>
blocked exists {
case BlockedTransition(_, Seq(false, true)) => false
case _ => true
}
})
throw new Exception (
"Priority guards can only quantify the second track of a transducer")
val allTransitions =
for (TransducerTransition(_, toState, _, _, blockedTransitions) <-
transitions) yield {
val blockedStates =
for (BlockedTransition(s, _) <- blockedTransitions) yield s
(toState, blockedStates.toSet)
}
var remTransitions = allTransitions
val finishedStates = new MHashSet[Int]
var curPriority = 10
while (!remTransitions.isEmpty) {
val (chosen, rem) = remTransitions partition {
case (_, blocked) => blocked == finishedStates
}
if (chosen.isEmpty)
throw new Exception(
"Epsilon transitions are not correctly prioritised")
remTransitions = rem
for ((toState, _) <- chosen) {
if (usePriorities) {
builder.asInstanceOf[BricsPrioTransducerBuilder]
.addETransition(states2Brics(fromState), nop, curPriority,
states2Brics(toState))
Console.err.println("" + fromState +
"- -> " +
"" + toState + ": \t" + nop)
} else {
builder.addETransition(states2Brics(fromState), nop,
states2Brics(toState))
Console.err.println("" + fromState +
"- -> " +
"" + toState + ": \t" + nop)
}
finishedStates += toState
}
curPriority = curPriority - 1
}
}
builder setInitialState states2Brics(0)
builder.getTransducer
}
/**
* Enumerate the solutions of a label that contains outputC
* as the only variable.
*/
private def enumLabelSolutions(f : IFormula,
outputC : ITerm,
p : SimpleAPI,
tdST : StringTheory) : Iterator[IdealInt] ={
import IExpression._
import tdST._
f match {
case Eq(`outputC`,
IFunApp(`str_to_code`,
Seq(IFunApp(`str_cons`,
Seq(IFunApp(ModuloArithmetic.mod_cast,
Seq(IIntLit(lower),IIntLit(upper),
Const(value))),
IFunApp(`str_empty`, Seq())))))) =>
Iterator single ModuloArithmetic.evalModCast(lower, upper, value)
case f => {
import p._
!! (f)
new Iterator[IdealInt] {
def hasNext : Boolean =
(??? == ProverStatus.Sat)
def next : IdealInt = {
???
val res = eval(outputC)
!! (outputC =/= res)
res
}
}
}
}
}
/**
* Simplify the label of a transition, with some optimisations for
* simple/common labels.
*/
private def simplifyLabel(f : IFormula,
p : SimpleAPI,
tdST : StringTheory) : IFormula = {
import IExpression._
import tdST._
f match {
case f : IBoolLit =>
f
case f @ Eq(_ : IConstant, _ : IConstant) =>
f
case Eq(c : IConstant,
IFunApp(`str_to_code`,
Seq(IFunApp(`str_cons`,
Seq(IFunApp(ModuloArithmetic.mod_cast,
Seq(IIntLit(lower),IIntLit(upper),
Const(value))),
IFunApp(`str_empty`, Seq())))))) =>
c === ModuloArithmetic.evalModCast(lower, upper, value)
case f =>
p.simplify(f)
}
}
/**
* Visitor that splits negated equations into two inequalities.
*/
private object NegEqSplitter extends CollectingVisitor[Unit, IExpression] {
import IExpression._
def apply(f : IFormula) : IFormula =
visit(f, ()).asInstanceOf[IFormula]
def postVisit(t : IExpression, arg : Unit,
subres : Seq[IExpression]) : IExpression =
(t update subres) match {
case INot(EqLit(t, value)) => t <= (value-1) | t >= (value+1)
case s => s
}
}
/**
* Visitor that eliminates the ModuloArithmetic.int_cast
* function.
*/
private object IntCastEliminator extends CollectingVisitor[Unit, IExpression]{
def apply(f : IFormula) : IFormula =
visit(f, ()).asInstanceOf[IFormula]
def postVisit(t : IExpression, arg : Unit,
subres : Seq[IExpression]) : IExpression =
t match {
case IFunApp(ModuloArithmetic.int_cast, _) => subres.head
case _ => t update subres
}
}
/**
* Extractor that matches equations equivalent to
* sym1 = sym2 + offset.
*/
private case class OffsetEq(sym1 : ITerm, sym2 : ITerm) {
private val Sym1Eq = SymbolEquation(sym1)
private val Sym2Sum = SymbolSum(sym2)
def unapply(f : IFormula) : Option[IdealInt] = f match {
case Sym1Eq(sym1Coeff, Sym2Sum(sym2Coeff, Const(offset))) =>
(sym1Coeff, sym2Coeff) match {
case (IdealInt.ONE, IdealInt.ONE) => Some(offset)
case (IdealInt.MINUS_ONE, IdealInt.MINUS_ONE) => Some(-offset)
case _ => None
}
case _ =>
None
}
}
}