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Commit 14b736c7 authored by Christian Müller's avatar Christian Müller
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leaders

parent 2c08691d
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Showing with 271 additions and 143 deletions
src/main/scala/de/tum/workflows/MainLTL.scala
View file @ 14b736c7
......@@ -32,7 +32,7 @@ object MainLTL extends App with LazyLogging {
logger.info("Embedding FOLTL formula in LTL")
val (agents, res) = FOTransformers.eliminateExistentials(prop)
val universe = agents.map(_.withType()).mkString(", ")
val universe = agents.map(_.withType).mkString(", ")
logger.info(s"Using universe $universe")
if (agents.groupBy(_.typ).exists(_._2.size > MAX_AGENTS)) {
......
src/main/scala/de/tum/workflows/Preconditions.scala
View file @ 14b736c7
......@@ -18,10 +18,10 @@ object Preconditions extends LazyLogging {
for (s <- b.steps) yield {
val first = s.tuple.head
val inner = if (first.typ == spec.target.params.head.typ) {
val inf = Fun(INFNAME, List(b.agents.head))
if (properties.stubborn) {
choice.in(T1)
} else {
val inf = Fun(INFNAME, List(b.agents.head))
Or(And(Neg(inf.in(T1)), choice.in(T1)), And(inf.in(T1), choice))
}
} else {
......@@ -34,16 +34,23 @@ object Preconditions extends LazyLogging {
b.steps
}
val newsteps = for (
val newb = b.updateSteps(guardfix)
// for causality, add informedness updates
if (properties.stubborn) {
List(newb)
} else {
val newsteps = for (
stmt <- b.steps
if spec.causals.map(_.typ).contains(stmt.tuple.head.typ) ||
stmt.tuple.head.typ == spec.target.params.head.typ) yield {
val fun = Fun(stmt.fun, stmt.tuple)
// TODO
val guard = Neg(Equiv(fun.in(T1), fun.in(T2)))
ForallBlock(stmt.tuple, List(Add(guard, INFNAME, List(stmt.tuple.head))))
val fun = Fun(stmt.fun, stmt.tuple)
// TODO
val guard = Neg(Equiv(fun.in(T1), fun.in(T2)))
ForallBlock(stmt.tuple, List(Add(guard, INFNAME, List(stmt.tuple.head))))
}
newb :: newsteps
}
b :: newsteps
}
// For oracly blocks, remove O from guard and add to ForallMay choice predicate
......@@ -54,7 +61,7 @@ object Preconditions extends LazyLogging {
def findOracle(f: Formula) = {
f.collect {
case f: Fun if (f.isOracle()) => List(f.name)
case f: Fun if f.isOracle => List(f.name)
}
}
val oracles = findOracle(stmt.guard)
......@@ -68,10 +75,10 @@ object Preconditions extends LazyLogging {
def fixguard(f: Formula, choice:Fun) = {
val nooracles = f.everywhere {
case f: Fun if f.isOracle() => True
case f: Fun if f.isOracle => True
}
val decl = spec.declass.getOrElse(b.pred.get, (List(), False))._2
val decl = spec.declass.getOrElse(name, (List(), False))._2
// FIXME: substitutions?
// FIXME: decl in T2?
And(nooracles, Or(And(decl.in(T1), choice.in(T1)), And(Neg(decl.in(T1)), choice)))
......@@ -86,7 +93,7 @@ object Preconditions extends LazyLogging {
} else b
}
def subst(f: Formula, updates: List[(String, (List[FOLTL.Var], FOLTL.Formula))], b: SimpleBlock) = {
def subst(f: Formula, updates: List[(String, (List[FOLTL.Var], FOLTL.Formula))], b: SimpleBlock): Formula = {
updates.foldRight(f)((update, f) => {
val (repname, (vars, form)) = update
......@@ -105,7 +112,7 @@ object Preconditions extends LazyLogging {
})
}
def getUpdate(s:Statement, choice:Option[Fun], spec:NISpec, properties:InvProperties) = {
def getUpdate(s:Statement, spec:NISpec, properties:InvProperties): Formula = {
val frees = s.guard.freeVars -- s.tuple.toSet -- spec.constants
......@@ -120,12 +127,12 @@ object Preconditions extends LazyLogging {
form
}
def elaborate(block: SimpleBlock, spec:NISpec, properties:InvProperties) = {
val stepOne = if (!properties.stubborn) elaborateSteps(block, spec, properties) else List(block)
def elaborate(block: SimpleBlock, spec:NISpec, properties:InvProperties): List[SimpleBlock] = {
val stepOne = elaborateSteps(block, spec, properties)
stepOne map { b => elaborateOraclyBlock(b, spec) }
}
def weakestPrecondition(post: Formula, outerb: SimpleBlock, spec: NISpec, properties: InvProperties) = {
def weakestPrecondition(post: Formula, outerb: SimpleBlock, spec: NISpec, properties: InvProperties): Formula = {
// TODO: Make 2-trace elaboration optional
......@@ -138,11 +145,11 @@ object Preconditions extends LazyLogging {
precond
}
private def weakestPreconditionSingle(f: Formula, b: SimpleBlock, spec: NISpec, properties: InvProperties) = {
private def weakestPreconditionSingle(f: Formula, b:SimpleBlock, spec: NISpec, properties: InvProperties) = {
val updates = for (s <- b.steps) yield {
s.fun -> (s.tuple, {
getUpdate(s, b, spec, properties)
getUpdate(s, spec, properties)
})
}
......@@ -152,18 +159,20 @@ object Preconditions extends LazyLogging {
// TODO: have we proven this correct?
val removed = FOTransformers.eliminateDoubleQuantifiers(replaced)
if (Utils.DEBUG_MODE) {
if (FormulaFunctions.collectQuantifiers(removed) != FormulaFunctions.collectQuantifiers(replaced)) {
logger.warn(s"Removed a quantifier:\nBefore: ${replaced}\nAfter:$removed")
val neg1 = replaced.toNegNf
val neg2 = removed.toNegNf
if (FormulaFunctions.collectQuantifiers(neg1) != FormulaFunctions.collectQuantifiers(neg2)) {
logger.warn(s"Would have removed a quantifier:\nBefore: ${neg1}\nAfter: $neg2")
}
}
removed
replaced
}
def abstractedPrecondition(f: Formula, b: SimpleBlock, spec: NISpec, properties: InvProperties, untouched: Set[String]) = {
def abstractedPrecondition(f: Formula, b: SimpleBlock, spec: NISpec, properties: InvProperties, untouched: Set[String]): Formula = {
val precond = weakestPrecondition(f, b, spec, properties)
// Assume untoucheds empty
// Assume untouched predicates empty
val untouchedprecond = precond.assumeEmpty(untouched.toList)
val z3simpednewinv = Z3BSFO.simplifyBS(untouchedprecond)
......@@ -179,7 +188,7 @@ object Preconditions extends LazyLogging {
// Abstract away inner existentials
val universalinv = if (removedannotations.toNegNf.hasSubFormula {
case e:Exists => true
case _:Exists => true
}) {
FOTransformers.abstractExistentials(removedannotations)
} else {
......
src/main/scala/de/tum/workflows/Utils.scala
View file @ 14b736c7
......@@ -5,8 +5,7 @@ import de.tum.workflows.foltl.FOLTL._
import java.io.File
import java.io.PrintWriter
import de.tum.workflows.toz3.InvariantChecker
import de.tum.workflows.toz3.InvProperties
import de.tum.workflows.toz3.{InvProperties, InvariantChecker, Z3BSFO}
import com.typesafe.scalalogging.LazyLogging
import de.tum.workflows.MainInvariantsInference.logger
......@@ -74,13 +73,18 @@ object Utils extends LazyLogging {
val basename = name.split("/").last
val filenames = s"${basename}_$model${if (desc.isEmpty()) "" else s"_$desc"}"
// do not blow up the formula with auxilliary elimination
val (res, graph, labelling, provens, dot, time) =
InvariantChecker.checkInvariantFPLabelling(spec, inv, properties)
logger.info(s"Invariant was ${inv}")
logger.info(s"Invariant was ${if (res) "" else "not "}proven (took $time ms)\n")
if (!res) {
val headinv = labelling.last(graph.nodes.head)
val satq = And(spec.always, Neg(headinv))
logger.info(s"Initial state violating the invariant: ${Z3BSFO.debugmodelBS(satq)}")
}
for ((s, i) <- dot.zipWithIndex) {
Utils.write(name,s"${filenames}_$i.dot", s)
}
......
src/main/scala/de/tum/workflows/WorkflowParser.scala
View file @ 14b736c7
......@@ -76,15 +76,16 @@ object WorkflowParser extends RegexParsers with PackratParsers with LazyLogging
val preds = allpredicates(list)
// Filter to just the first
val filtered = preds groupBy (_.name) map (_._2.head) toSet
val oracles = filtered.filter(_.isOracle())
val bs = filtered.filter(_.isB())
val rels = filtered -- oracles -- bs
Signature(oracles, bs, rels)
val filtered = preds.groupBy(_.name).map(_._2.head).toSet
val oracles = filtered.filter(_.isOracle)
val constinputs = filtered.filter(_.isConstInput)
val bs = filtered.filter(_.isB)
val rels = filtered -- oracles -- constinputs -- bs
Signature(oracles, constinputs, bs, rels)
}
def typeMap(typedvars: List[Var]) = {
typedvars.map(v => v.name -> v.typ) toMap
typedvars.map(v => v.name -> v.typ).toMap
}
def inferType(typemap: Map[String, String], v:Var) = {
......@@ -136,13 +137,15 @@ object WorkflowParser extends RegexParsers with PackratParsers with LazyLogging
def TUPLE = "(" ~> repsep(TYPEDVAR, ",") <~ ")"
def FUN = VAR ~ TUPLE ^^ { case f ~ tup => Fun(f.name, tup) }
def EQ = (VAR <~ "=") ~ VAR ^^ { case v1 ~ v2 => Equal(v1, v2) } | (VAR <~ "≠") ~ VAR ^^ { case v1 ~ v2 => Neg(Equal(v1, v2)) }
def EQUIV = "(" ~> (SIMPLETERM <~ "<->") ~ (TERM <~ ")") ^^ { case t1 ~ t2 => Equiv(t1, t2) }
def EXISTS = "∃" ~> (repsep(TYPEDVAR, ",") <~ ("."?)) ~ TERM ^^ { case vs ~ t => Exists(vs, t) }
def FORALL = "∀" ~> (repsep(TYPEDVAR, ",") <~ ("."?)) ~ TERM ^^ { case vs ~ t => Forall(vs, t) }
def QUANTIFIER = EXISTS | FORALL
def QUANTIFIER:PackratParser[Formula] = EXISTS | FORALL
def SIMPLETERM = (tt | ff | FUN)
lazy val TERM:PackratParser[Formula] = (AND | OR | IMPLIES | NEG | SIMPLETERM | GLOBALLY | FINALLY | QUANTIFIER)
def SIMPLETERM = tt | ff | FUN | EQ
lazy val TERM:PackratParser[Formula] = AND | OR | IMPLIES | NEG | SIMPLETERM | GLOBALLY | FINALLY | QUANTIFIER | EQUIV
def ADD = TERM ~ ("→" | "->") ~ VAR ~ "+=" ~ TUPLE ^^ { case guard ~ _ ~ fun ~ _ ~ tup => Add(guard, fun.name, tup) }
def REM = TERM ~ ("→" | "->") ~ VAR ~ "-=" ~ TUPLE ^^ { case guard ~ _ ~ fun ~ _ ~ tup => Remove(guard, fun.name, tup) }
......@@ -154,7 +157,8 @@ object WorkflowParser extends RegexParsers with PackratParsers with LazyLogging
def BLOCK = "forall" ~> ("may"?) ~ repsep(TYPEDVAR, ",") ~ (STMT+) ^? ({
// all free variables contained
case may ~ vars ~ stmts if validblock(vars, stmts) => {
val typemap = typeMap(vars)
// add quantified variables to typemap
val typemap = typeMap(vars ++ stmts.flatMap(_.guard.boundVars))
val typedstmts = stmts map (inferTypes(typemap, _))
if (may.isEmpty) {
ForallBlock(vars, typedstmts)
......@@ -186,7 +190,7 @@ object WorkflowParser extends RegexParsers with PackratParsers with LazyLogging
(("Declassify" ~> DECLASS)?) ~
("Target" ~> FUN) ~
(("Causality" ~> repsep(TYPEDVAR, ","))?) ^^ {
case _ ~ w ~ decl ~ tar ~ causals => NISpec(w, toMap(decl.toList), tar, causals.getOrElse(List()))
case _ ~ w ~ decl ~ tar ~ causals => NISpec(w, toMap(decl.toList), True, tar, causals.getOrElse(List()))
}
def toMap(list:List[(Fun, Formula)]):Map[String, (List[Var], Formula)] = {
......
src/main/scala/de/tum/workflows/blocks/Workflow.scala
View file @ 14b736c7
......@@ -11,8 +11,8 @@ object Signature {
}
case class Workflow(sig: Signature, steps: List[Block]) {
override def toString() = steps.mkString("\n")
lazy val isomitting = {
override def toString(): String = steps.mkString("\n")
lazy val isomitting: Boolean = {
steps.exists(_.isomitting)
}
}
......@@ -24,18 +24,8 @@ trait Spec {
def w: Workflow
}
case class InvSpec(w: Workflow, always: Formula, invariant: Formula) extends Spec {
override def toString = {
s"Spec\nWorkflow:\n$w\nAlways:$always\nInvariant:$invariant"
}
def toNISpec() = {
NISpec(w, Map(), Fun("NOTHING", List()), List())
}
}
case class NISpec(w: Workflow, declass: Map[String, (List[Var], Formula)], target: Fun, causals:List[Var]) extends Spec with LazyLogging {
override def toString = {
case class NISpec(w: Workflow, declass: Map[String, (List[Var], Formula)], always: Formula, target: Fun, causals:List[Var]) extends Spec with LazyLogging {
override def toString: String = {
s"NISpec\nWorkflow:\n$w\nDeclass:$declass\nTarget:$target"
}
......@@ -47,7 +37,7 @@ case class NISpec(w: Workflow, declass: Map[String, (List[Var], Formula)], targe
// TODO: How to check for more constants?
}
def checkSanity() = {
def checkSanity(): Boolean = {
var sane = true
// TODO: check all types
......@@ -65,18 +55,18 @@ case class NISpec(w: Workflow, declass: Map[String, (List[Var], Formula)], targe
// Oracle only positive
val f = stmt.guard.toNegNf
val noneg = !f.hasSubFormula {
case Neg(f:Fun) if f.isOracle() => true
case Neg(f:Fun) if f.isOracle => true
}
if (!noneg) {
logger.error(s"Found negated oracle in guard for statement $stmt")
}
val allvars = !(f hasSubFormula {
case f:Fun if f.isOracle && f.params != frees => true
})
if (!allvars) {
logger.error(s"Found oracle with wrong parameters in statement $stmt")
}
noneg && allvars
// val allvars = !(f hasSubFormula {
// case f:Fun if f.isOracle && f.params != frees => true
// })
// if (!allvars) {
// logger.error(s"Found oracle with wrong parameters in statement $stmt")
// }
noneg // && allvars
}
// check same relation only updated once per block
......@@ -103,9 +93,13 @@ case class NISpec(w: Workflow, declass: Map[String, (List[Var], Formula)], targe
sane &&= isSane(w.steps)
sane
}
def addKnowledge(k:Formula) = {
NISpec(w, declass, And.make(always, k), target, causals)
}
}
object NISpec {
val EMPTY = NISpec(Workflow.EMPTY, Map(), Fun("NOTHING", List()), List())
val EMPTY = NISpec(Workflow.EMPTY, Map(), True, Fun("NOTHING", List()), List())
}
abstract sealed class Block {
......@@ -113,13 +107,15 @@ abstract sealed class Block {
}
abstract sealed class SimpleBlock extends Block {
type This >: this.type <: SimpleBlock
def agents: List[Var]
def steps: List[Statement]
def may: Boolean
def pred: Option[String]
def updateSteps(s:List[Statement])
def updateSteps(s:List[Statement]):This
override def isomitting = {
override def isomitting: Boolean = {
// a simple block is omitting, if there exists a statement where not all agents appear in the tuple
steps.exists(s => agents.exists(a => !s.tuple.contains(a)))
}
......@@ -128,11 +124,11 @@ abstract sealed class SimpleBlock extends Block {
// before transformation
val before = steps.exists(s => {
s.guard.hasSubFormula {
case f:Fun => f.isOracle()
case f:Fun => f.isOracle
}
})
// after transformation
val after = pred.exists(name => Fun(name, agents).isOracle())
val after = pred.exists(name => Fun(name, agents).isOracle)
before || after
}
......@@ -150,50 +146,56 @@ abstract sealed class SimpleBlock extends Block {
}
abstract class Statement {
type This >: this.type <: Statement
def guard: Formula
def fun: String
def tuple: List[Var]
def updateGuard(newguard: Formula)
def updateGuard(newguard: Formula): This
lazy val freeVars = guard.freeVars ++ tuple
lazy val freeVars: Set[Var] = guard.freeVars ++ tuple
}
case class Add(guard: Formula, fun: String, tuple: List[Var]) extends Statement {
override def toString() = guard + " → " + fun + " += " + tuple.mkString("(", ",", ")") + ";"
type This = Add
override def toString(): String = guard + " → " + fun + " += " + tuple.mkString("(", ",", ")") + ";"
override def updateGuard(newguard: Formula) = Add(newguard, fun, tuple)
}
case class Remove(guard: Formula, fun: String, tuple: List[Var]) extends Statement {
override def toString() = guard + " → " + fun + " -= " + tuple.mkString("(", ",", ")") + ";"
type This = Remove
override def toString(): String = guard + " → " + fun + " -= " + tuple.mkString("(", ",", ")") + ";"
override def updateGuard(newguard: Formula) = Remove(newguard, fun, tuple)
}
case class ForallBlock(agents: List[Var], steps: List[Statement]) extends SimpleBlock {
type This = ForallBlock
val may = false
override def toString() = "forall " + agents.map(_.withType).mkString(",") + steps.mkString("\n ", "\n ", "")
override def pred() = None
override def toString(): String = "forall " + agents.map(_.withType).mkString(",") + steps.mkString("\n ", "\n ", "")
override def updateSteps(newsteps: List[Statement]) = ForallBlock(agents, newsteps)
}
case class ForallMayBlock(agents: List[Var], choice: String, steps: List[Statement]) extends SimpleBlock {
type This = ForallMayBlock
val may = true
override def toString() = "forall " + agents.map(_.withType).mkString(",") + " may (" + pred + ")" + steps.mkString("\n ", "\n ", "")
override def pred() = Some(choice)
override def toString(): String = "forall " + agents.map(_.withType).mkString(",") + " may (" + pred + ")" + steps.mkString("\n ", "\n ", "")
override def updateSteps(newsteps: List[Statement]) = ForallMayBlock(agents, choice, newsteps)
}
case class Loop(steps: List[Block]) extends Block {
override def toString() = {
override def toString(): String = {
// indentation
"loop(*)\n" + Utils.indentLines(steps.mkString("\n"))
}
override def isomitting = {
override def isomitting: Boolean = {
steps.exists(_.isomitting)
}
}
case class NondetChoice(left: List[Block], right: List[Block]) extends Block {
override def toString() = {
override def toString(): String = {
"choose {\n" + Utils.indentLines(left.mkString("\n")) + "\n} {\n" + Utils.indentLines(right.mkString("\n")) + "\n}\n"
}
override def isomitting = {
override def isomitting: Boolean = {
left.exists(_.isomitting) || right.exists(_.isomitting)
}
}
src/main/scala/de/tum/workflows/foltl/FOLTL.scala
View file @ 14b736c7
package de.tum.workflows.foltl
import de.tum.workflows.Utils
import de.tum.workflows.foltl.FOLTL.FunFromVar
import de.tum.workflows.foltl.FOLTL.FunFromVar.getVars
import scala.annotation.tailrec
import scala.util.matching.Regex
//import de.tum.workflows.foltl.TermFunctions._
......@@ -37,7 +35,7 @@ object FOLTL {
lazy val bracketed: String = this match {
case _: BinOp => "(" + this + ")"
case _ => this.toString()
case _ => this.toString
}
// single arrow is for maps
......@@ -80,15 +78,15 @@ object FOLTL {
val DEFAULT_TYPE = "T"
}
case class Var(name: String, typ: String = Var.DEFAULT_TYPE) extends Formula {
override def toString() = s"$name"
def withType() = s"$name:$typ"
override def toString = s"$name"
def withType = s"$name:$typ"
}
object Fun {
def apply(name: String, params: List[Var]): Fun = Fun(name, None, params)
}
object FunNameFromVar {
val PredicateNoParam = "([a-zA-Z0-9]+)(#([a-zA-Z0-9]+))?".r
val PredicateNoParam: Regex = "([a-zA-Z0-9]+)(#([a-zA-Z0-9]+))?".r
def unapply(s: String): Option[(String, Option[String])] = {
s match {
......@@ -99,15 +97,15 @@ object FOLTL {
}
}
object FunFromVar {
val Predicate = "([a-zA-Z0-9]+)(#([a-zA-Z0-9]+))?((_[a-zA-Z0-9]+#[a-zA-Z0-9]+)*)".r
val Predicate: Regex = "([a-zA-Z0-9]+)(#([a-zA-Z0-9]+))?((_[a-zA-Z0-9]+#[a-zA-Z0-9]+)*)".r
def getVars(s: String) = {
val split = s split ("_")
def getVars(s: String): List[Var] = {
val split = s split "_"
if (split.length > 1) {
split.drop(1).map(str => {
val Array(name, typ) = str.split("#")
Var(name, typ)
}) toList
}).toList
} else {
List()
}
......@@ -123,20 +121,21 @@ object FOLTL {
}
case class Fun(name: String, ind: Option[String], params: List[Var]) extends Formula {
override def toString() = name + Utils.mkString(ind, "(", "", ")") + params.map(_.name).mkString("(", ",", ")")
override def toString: String = name + Utils.mkString(ind, "(", "", ")") + params.map(_.name).mkString("(", ",", ")")
def updatedParams(index: Int, p: Var) = Fun(name, ind, params.updated(index, p))
def updatedParams(list: List[Var]) = Fun(name, ind, list)
def isOracle() = name.startsWith("O")
def isAux() = name.startsWith("choice")
def isB() = name.startsWith("B")
def isOracle: Boolean = name.startsWith("O")
def isConstInput: Boolean = name.startsWith("I")
def isAux: Boolean = name.startsWith("choice")
def isB: Boolean = name.startsWith("B")
def encodeToVar() = {
def encodeToVar(): Var = {
val pi = if (ind.isDefined) "#" + ind.get else ""
val tup = params.map(p => p.name + "#" + p.typ)
Var(name + pi + Utils.mkString(tup, "_", "_", ""))
}
def encodeName() = {
def encodeName(): String = {
val pi = if (ind.isDefined) "#" + ind.get else ""
name + pi
}
......@@ -148,26 +147,26 @@ object FOLTL {
def vars: List[Var]
def t: Formula
override def toString() = {
override def toString: String = {
// show types only in quantifiers
qname + " " + vars.map(_.withType()).mkString(",") + ". " + t.bracketed
qname + " " + vars.map(_.withType).mkString(",") + ". " + t.bracketed
}
}
object Quantifier {
def unapply(q: Quantifier) = Some((q.make, q.vars, q.t))
def make(m: (List[Var], Formula) => Quantifier, l:List[Var], f:Formula) = {
def make(m: (List[Var], Formula) => Quantifier, l:List[Var], f:Formula): Formula = {
if (l.isEmpty) f else m(l, f)
}
}
object Exists {
def make = Quantifier.make(Exists.apply, _:List[Var], _:Formula)
def make: (List[Var], Formula) => Formula = Quantifier.make(Exists.apply, _:List[Var], _:Formula)
}
object Forall {
def make = Quantifier.make(Forall.apply, _:List[Var], _:Formula)
def make: (List[Var], Formula) => Formula = Quantifier.make(Forall.apply, _:List[Var], _:Formula)
}
object ForallOtherThan {
def make(l:List[Var], otherthan:List[Var], f:Formula) = {
def make(l:List[Var], otherthan:List[Var], f:Formula): Formula = {
if (otherthan.isEmpty || l.isEmpty) { Forall.make(l, f) } else {
ForallOtherThan(l, otherthan, f)
}
......@@ -175,17 +174,17 @@ object FOLTL {
}
case class Exists(vars: List[Var], t: Formula) extends Quantifier {
val qname = "∃"
val make = Quantifier.make(Exists.apply, _, _)
val make: (List[Var], Formula) => Formula = Quantifier.make(Exists.apply, _, _)
}
case class Forall(vars: List[Var], t: Formula) extends Quantifier {
val qname = "∀"
val make = Quantifier.make(Forall.apply, _, _)
val make: (List[Var], Formula) => Formula = Quantifier.make(Forall.apply, _, _)
}
case class ForallOtherThan(vars: List[Var], otherthan: List[Var], t: Formula) extends Quantifier {
val qname = "∀"
val make = ForallOtherThan.apply(_: List[Var], otherthan, _: Formula)
override def toString() = {
s"$qname ${vars.map(_.withType()).mkString(",")} ∉ {${otherthan.map(_.withType()).mkString(",")}}. ${t.bracketed}"
override def toString: String = {
s"$qname ${vars.map(_.withType).mkString(",")} ∉ {${otherthan.map(_.withType).mkString(",")}}. ${t.bracketed}"
}
}
......@@ -219,11 +218,11 @@ object FOLTL {
def opname: String
def t: Formula