path: root/src/dotty/tools/dotc/core/TypeComparer.scala

package dotty.tools
package dotc
package core

import Types._, Contexts._, Symbols._, Flags._, Names._, NameOps._, Denotations._
import typer.Mode
import Decorators._
import StdNames.{nme, tpnme}
import collection.mutable
import printing.Disambiguation.disambiguated
import util.{Stats, DotClass, SimpleMap}
import config.Config
import config.Printers._
import TypeErasure.{erasedLub, erasedGlb}
import scala.util.control.NonFatal

/** Provides methods to compare types.
 */
class TypeComparer(initctx: Context) extends DotClass {
  implicit val ctx: Context = initctx

  val state = ctx.typerState
  import state.constraint

  private var pendingSubTypes: mutable.Set[(Type, Type)] = null
  private var recCount = 0

  /** If the constraint is frozen we cannot add new bounds to the constraint. */
  protected var frozenConstraint = false

  /** If the constraint is ignored, subtype checks only take into account
   *  declared bounds of PolyParams. Used when forming unions and intersectons
   *  of constraint bounds
   */
  protected var ignoreConstraint = false

  /** Compare a solution of the constraint instead of the constrained parameters.
   *  The solution maps every parameter to its lower bound.
   */
  protected var solvedConstraint = false

  private var needsGc = false
  
  /** Bounds for constrained parameters yet to be added to the constraint */
  private var pendingBoundss: SimpleMap[PolyParam, TypeBounds] = SimpleMap.Empty

  /** If `param` is in `needsSatCheck` then the constraint should be checked
   *  for satisfiability after `param`'s bound are updated.
   */
  private var needsSatCheck: Set[PolyParam] = Set()

  /** Is a subtype check in course? In that case we may not
   *  permanently instantiate type variables, because the corresponding
   *  constraint might still be retracted and the instantiation should
   *  then be reversed.
   */
  def subtypeCheckInProgress: Boolean = {
    val result = recCount > 0
    if (result) {
      constr.println("*** needsGC ***")
      needsGc = true
    }
    result
  }

  /** For stastics: count how many isSubTypes are part of succesful comparisons */
  private var successCount = 0
  private var totalCount = 0

  private var myAnyClass: ClassSymbol = null
  private var myNothingClass: ClassSymbol = null
  private var myNullClass: ClassSymbol = null
  private var myObjectClass: ClassSymbol = null
  private var myAnyType: TypeRef = null

  def AnyClass = {
    if (myAnyClass == null) myAnyClass = defn.AnyClass
    myAnyClass
  }
  def NothingClass = {
    if (myNothingClass == null) myNothingClass = defn.NothingClass
    myNothingClass
  }
  def NullClass = {
    if (myNullClass == null) myNullClass = defn.NullClass
    myNullClass
  }
  def ObjectClass = {
    if (myObjectClass == null) myObjectClass = defn.ObjectClass
    myObjectClass
  }
  def AnyType = {
    if (myAnyType == null) myAnyType = AnyClass.typeRef
    myAnyType
  }

  /* Constraint handling:
   *
   * Constraints are required to be in normalized form. This means
   * (1) if P <: Q in C then also Q >: P in C
   * (2) if P r Q in C and Q r R in C then also P r R in C, where r is <: or :>
   * 
   * "P <: Q in C" means here: There is a constraint P <: H[Q], 
   *     where H is the multi-hole context given by:
   *    
   *      H = []
   *          H & T
   *          T & H
   *          H | H
   *          
   *  (the idea is that a parameter Q in a H context is guaranteed to be a supertype of P).
   *          
   * "P >: Q in C" means: There is a constraint P >: L[Q], 
   *     where L is the multi-hole context given by:
   * 
   *      L = []
   *          L | T
   *          T | L
   *          L & L
   */

  /** Map that approximates each param in constraint by its lower bound.
   *  Currently only used for diagnostics.
   */
  val approxParams = new TypeMap {
    def apply(tp: Type): Type = tp.stripTypeVar match {
      case tp: PolyParam if constraint contains tp =>
        this(constraint.bounds(tp).lo)
      case tp =>
        mapOver(tp)
    }
  }

  /** Test whether the lower bounds of all parameters in this
   *  constraint are a solution to the constraint.
   */
  def isSatisfiable: Boolean = {
    val saved = solvedConstraint
    solvedConstraint = true
    try
      constraint.forallParams { param =>
        val TypeBounds(lo, hi) = constraint.at(param)
        isSubType(lo, hi) || {
          ctx.log(i"sub fail $lo <:< $hi")
          ctx.log(i"approximated = ${approxParams(lo)} <:< ${approxParams(hi)}")
          false
        }
      }
    finally solvedConstraint = saved
  }

  /** Make p2 = p1, transfer all bounds of p2 to p1 */
  private def unify(p1: PolyParam, p2: PolyParam): Boolean = {
    constr.println(s"unifying $p1 $p2")
    val constraint1 = constraint.unify(p1, p2)
    val bounds = constraint1.bounds(p1)
    isSubType(bounds.lo, bounds.hi) && { constraint = constraint1; true }
  }
  
  /** If current constraint set is not frozen, add the constraint
   *
   *      param >: bound   if fromBelow is true
   *      param <: bound   otherwise
   *
   *  to the bounds of `param`. If `bound` is itself a constrained parameter, also
   *  add the dual constraint to `bound`.
   *  @pre `param` is in the constraint's domain
   *  @return Whether the augmented constraint is still satisfiable.
   */
  def addConstraint(param: PolyParam, bound0: Type, fromBelow: Boolean): Boolean = {
    
    /** Add bidirectional constraint. If new constraint implies 'A <: B' we also
     *  make sure 'B >: A' gets added and vice versa. Furthermore, if the constraint
     *  implies 'A <: B <: A', A and B get unified. 
     */
    def addBi(param: PolyParam, bound: Type, fromBelow: Boolean): Boolean = 
      constraint.bounds(param) match {
        case TypeBounds(plo: PolyParam, phi) if (plo eq phi) && constraint.contains(plo) => 
          addBi(plo, bound, fromBelow)
        case _ =>
          bound match {
            case bound: PolyParam if constraint contains bound =>
              val TypeBounds(lo, hi) = constraint.bounds(bound)
              if (lo eq hi)
                addBi(param, lo, fromBelow)
              else if (param == bound)
                true
              else if (fromBelow && param.occursIn(lo, fromBelow = true))
                unify(param, bound)
              else if (!fromBelow && param.occursIn(hi, fromBelow = false))
                unify(bound, param)
              else
                addUni(param, bound, fromBelow) &&
                  addUni(bound, param, !fromBelow)
            case bound: AndOrType if fromBelow != bound.isAnd =>
              addBi(param, bound.tp1, fromBelow) &&
                addBi(param, bound.tp2, fromBelow)
            case bound: WildcardType =>
              true
            case bound => // !!! remove to keep the originals
              addUni(param, bound, fromBelow)
          }
      }
    
    /** Add constraint without propagating in the other direction or unifying */
    def addUni(param: PolyParam, bound: Type, fromBelow: Boolean): Boolean = {
      val oldBounds = constraint.bounds(param)
      def narrowedBounds(bounds: TypeBounds): TypeBounds = {
        val savedIgnore = ignoreConstraint
        val savedFrozen = frozenConstraint
        ignoreConstraint = true
        frozenConstraint = true
        try
          if (fromBelow) bounds.derivedTypeBounds(bounds.lo | bound, bounds.hi)
          else bounds.derivedTypeBounds(bounds.lo, bounds.hi & bound)
        finally {
          ignoreConstraint = savedIgnore
          frozenConstraint = savedFrozen
        }
      }
      val newBounds = narrowedBounds(oldBounds)
      (param == bound) || 
      (oldBounds eq newBounds) || 
      { val pendingBounds = pendingBoundss(param)
        if (pendingBounds == null)
          // Why the pendingBoundss tests? It is possible that recursive subtype invocations
          // come back with another constraint for `param`. An example came up when compiling 
          // ElimRepeated where we got the constraint
          //
          //      Coll <: IterableLike[Tree, Coll]
          //
          // and added 
          //
          //      List[Tree] <: Coll
          //
          // The recursive bounds test is then
          //
          //      List[Tree] <: IterableLike[Tree, Coll]
          //
          // and because of the F-bounded polymorphism in the supertype of List, 
          // i.e. List[T] <: IterableLike[T, List[T]], this leads again to
          //
          //      List[Tree] <: Coll
          try {
            pendingBoundss = pendingBoundss.updated(param, newBounds)
            isSubType(newBounds.lo, newBounds.hi) && {
              constraint = constraint.updated(param, pendingBoundss(param))
              if (needsSatCheck(param)) {
                assert(isSatisfiable)
                needsSatCheck -= param
              }
              true
            }
          }
          finally pendingBoundss = pendingBoundss.remove(param)
        else {
          // TODO: investigate - if the last line in this comment is uncommented, we get a cyclic
          //       constraint error in tools/io. For now, we do without even though this
          //       risks allowing unsatisfiable constraints to get through.
          //       Unsatisfiable constraints are caught by an assertion that is executed later
          //       in case we got here.
          //pendingBoundss = pendingBoundss.updated(param, narrowedBounds(pendingBounds))

          needsSatCheck += param
          true
        }
      }
    }
 
    val bound = (if (false) ctx.deSkolemize(bound0, toSuper = fromBelow) else bound0)
      .dealias.stripTypeVar
    def description = s"${param.show} ${if (fromBelow) ">:>" else "<:<"} ${bound.show} to ${constraint.show}"
    constr.println(s"adding $description")
    val res = addBi(param, bound, fromBelow)
    constr.println(s"added $description")
    if (Config.checkConstraintsNonCyclicTrans) constraint.checkNonCyclicTrans()
    if (needsSatCheck(param)) assert(isSatisfiable)
    res
  }

  def isConstrained(param: PolyParam): Boolean =
    !frozenConstraint && !solvedConstraint && (constraint contains param)

  /** Solve constraint set for given type parameter `param`.
   *  If `fromBelow` is true the parameter is approximated by its lower bound,
   *  otherwise it is approximated by its upper bound. However, any occurrences
   *  of the parameter in a refinement somewhere in the bound are removed.
   *  (Such occurrences can arise for F-bounded types).
   *  The constraint is left unchanged.
   *  @return the instantiating type
   *  @pre `param` is in the constraint's domain.
   */
  def approximation(param: PolyParam, fromBelow: Boolean): Type = {
    val avoidParam = new TypeMap {
      override def stopAtStatic = true
      def apply(tp: Type) = mapOver {
        tp match {
          case tp: RefinedType if param occursIn tp.refinedInfo => tp.parent
          case _ => tp
        }
      }
    }
    val bounds = constraint.bounds(param)
    val bound = if (fromBelow) bounds.lo else bounds.hi
    val inst = avoidParam(bound)
    typr.println(s"approx ${param.show}, from below = $fromBelow, bound = ${bound.show}, inst = ${inst.show}")
    inst
  }

  // Subtype testing `<:<`

  def topLevelSubType(tp1: Type, tp2: Type): Boolean = {
    if (tp2 eq NoType) return false
    if ((tp2 eq tp1) ||
        (tp2 eq WildcardType) ||
        (tp2 eq AnyType) && tp1.isValueType) return true
    isSubType(tp1, tp2)
  }

  protected def isSubTypeWhenFrozen(tp1: Type, tp2: Type): Boolean = {
    val saved = frozenConstraint
    frozenConstraint = true
    try isSubType(tp1, tp2)
    finally frozenConstraint = saved
  }

  private def traceInfo(tp1: Type, tp2: Type) =
    s"${tp1.show} <:< ${tp2.show}" +
    (if (ctx.settings.verbose.value) s" ${tp1.getClass} ${tp2.getClass}${if (frozenConstraint) " frozen" else ""}" else "")

  def isSubType(orig1: Type, orig2: Type): Boolean = {

    def ctdSubType(tp1: Type, tp2: Type): Boolean = /*>|>*/ ctx.traceIndented(s"isSubType ${traceInfo(tp1, tp2)}, class1 = ${tp1.getClass}, class2 = ${tp2.getClass}", subtyping) /*<|<*/ {
      if (tp2 eq NoType) false
      else if (tp1 eq tp2) true
      else {
        val saved = constraint
        val savedSuccessCount = successCount
        val savedRLC = Types.reverseLevelCheck // !!! TODO: remove
        Types.reverseLevelCheck = false
        try {
          recCount = recCount + 1
          val result =
            if (recCount < LogPendingSubTypesThreshold) firstTry(tp1, tp2)
            else monitoredIsSubType(tp1, tp2)
          recCount = recCount - 1
          if (!result) constraint = saved
          else if (recCount == 0 && needsGc) state.gc()

          def recordStatistics = {
            // Stats.record(s"isSubType ${tp1.show} <:< ${tp2.show}")
            totalCount += 1
            if (result) successCount += 1 else successCount = savedSuccessCount
            if (recCount == 0) {
              Stats.record("successful subType", successCount)
              Stats.record("total subType", totalCount)
              successCount = 0
              totalCount = 0
            }
          }
          if (Stats.monitored) recordStatistics

          result
        } catch {
          case NonFatal(ex) =>
            def showState = {
              println(disambiguated(implicit ctx => s"assertion failure for ${tp1.show} <:< ${tp2.show}, frozen = $frozenConstraint"))
              def explainPoly(tp: Type) = tp match {
                case tp: PolyParam => println(s"polyparam ${tp.show} found in ${tp.binder.show}")
                case tp: TypeRef if tp.symbol.exists => println(s"typeref ${tp.show} found in ${tp.symbol.owner.show}")
                case tp: TypeVar => println(s"typevar ${tp.show}, origin = ${tp.origin}")
                case _ => println(s"${tp.show} is a ${tp.getClass}")
              }
              explainPoly(tp1)
              explainPoly(tp2)
            }
            if (ex.isInstanceOf[AssertionError]) showState
            recCount -= 1
            constraint = saved
            successCount = savedSuccessCount
            throw ex
        } finally {
          Types.reverseLevelCheck = savedRLC
        }
      }
    }
      
    def narrowRefined(tp: Type): Type = tp match {
      case tp: RefinedType => RefinedThis(tp, 0) // !!! TODO check that we can drop narrowRefined entirely
      case _ => tp
    }

    def firstTry(tp1: Type, tp2: Type): Boolean = {
      tp2 match {
        case tp2: NamedType =>
          def isHKSubType = tp2.name == tpnme.Apply && {
            val lambda2 = tp2.prefix.LambdaClass(forcing = true)
            lambda2.exists && !tp1.isLambda &&
              tp1.testLifted(lambda2.typeParams, isSubType(_, tp2.prefix))
          }
          def compareNamed = {
            implicit val ctx: Context = this.ctx // Dotty deviation: implicits need explicit type
            tp1 match {
              case tp1: NamedType =>
                val sym1 = tp1.symbol
                (if ((sym1 ne NoSymbol) && (sym1 eq tp2.symbol)) (
                  ctx.erasedTypes
                  || sym1.isStaticOwner
                  || { // Implements: A # X  <:  B # X
                       // if either A =:= B (i.e. A <: B and B <: A), or the following three conditions hold:
                       //  1. X is a class type,
                       //  2. B is a class type without abstract type members.
                       //  3. A <: B.
                       // Dealiasing is taken care of elsewhere.
                       val pre1 = tp1.prefix
                       val pre2 = tp2.prefix
                       (  isSameType(pre1, pre2)
                       ||    sym1.isClass
                          && pre2.classSymbol.exists
                          && pre2.abstractTypeMembers.isEmpty
                          && isSubType(pre1, pre2)
                       )
                     }
                  )
                else (tp1.name eq tp2.name) && isSameType(tp1.prefix, tp2.prefix)
                ) || isHKSubType || secondTryNamed(tp1, tp2)
              case tp1: ThisType if tp1.cls eq tp2.symbol.moduleClass =>
                isSubType(tp1.cls.owner.thisType, tp2.prefix)
              case _ =>
                isHKSubType || secondTry(tp1, tp2)
            }
          }
          compareNamed
        case tp2: ProtoType =>
          isMatchedByProto(tp2, tp1)
        case tp2: PolyParam =>
          def comparePolyParam =
            tp2 == tp1 || {
              if (solvedConstraint && (constraint contains tp2)) ctdSubType(tp1, bounds(tp2).lo)
              else
                ctdSubTypeWhenFrozen(tp1, bounds(tp2).lo) || {
                  if (isConstrained(tp2)) addConstraint(tp2, tp1.widenExpr, fromBelow = true)
                  else (ctx.mode is Mode.TypevarsMissContext) || secondTry(tp1, tp2)
                }
            }
          comparePolyParam
        case tp2: BoundType =>
          tp2 == tp1 || secondTry(tp1, tp2)
        case tp2: TypeVar =>
          ctdSubType(tp1, tp2.underlying)
        case tp2: WildcardType =>
          def compareWild = tp2.optBounds match {
            case TypeBounds(_, hi) => ctdSubType(tp1, hi)
            case NoType => true
          }
          compareWild
        case tp2: LazyRef =>
          ctdSubType(tp1, tp2.ref)
        case tp2: AnnotatedType =>
          ctdSubType(tp1, tp2.tpe) // todo: refine?
        case tp2: ThisType =>
          tp1 match {
            case tp1: ThisType =>
              // We treat two prefixes A.this, B.this as equivalent if
              // A's selftype derives from B and B's selftype derives from A.
              tp1.cls.classInfo.selfType.derivesFrom(tp2.cls) &&
                tp2.cls.classInfo.selfType.derivesFrom(tp1.cls)
            case _ =>
              secondTry(tp1, tp2)
          }
        case tp2: SuperType =>
          tp1 match {
            case tp1: SuperType =>
              ctdSubType(tp1.thistpe, tp2.thistpe) &&
                isSameType(tp1.supertpe, tp2.supertpe)
            case _ =>
              secondTry(tp1, tp2)
          }
        case AndType(tp21, tp22) =>
          ctdSubType(tp1, tp21) && ctdSubType(tp1, tp22)
        case ErrorType =>
          true
        case _ =>
          secondTry(tp1, tp2)
      }
    }

    def secondTry(tp1: Type, tp2: Type): Boolean = tp1 match {
      case tp1: NamedType =>
        tp2 match {
          case tp2: ThisType if tp2.cls eq tp1.symbol.moduleClass =>
            isSubType(tp1.prefix, tp2.cls.owner.thisType)
          case _ =>
            secondTryNamed(tp1, tp2)
        }
      case OrType(tp11, tp12) =>
        isSubType(tp11, tp2) && isSubType(tp12, tp2)
      case tp1: PolyParam =>
        def comparePolyParam =
          tp1 == tp2 || {
            if (solvedConstraint && (constraint contains tp1)) isSubType(bounds(tp1).lo, tp2)
            else
              isSubTypeWhenFrozen(bounds(tp1).hi, tp2) || {
                if (isConstrained(tp1))
                  addConstraint(tp1, tp2, fromBelow = false) && {
                    if ((!frozenConstraint) &&
                      (tp2 isRef defn.NothingClass) &&
                      state.isGlobalCommittable) {
                      def msg = s"!!! instantiated to Nothing: $tp1, constraint = ${constraint.show}"
                      if (Config.flagInstantiationToNothing) assert(false, msg)
                      else ctx.log(msg)
                    }
                    true
                  }
                else (ctx.mode is Mode.TypevarsMissContext) || thirdTry(tp1, tp2)
              }
          }
        comparePolyParam
      case tp1: RefinedThis =>
        tp2 match {
          case tp2: RefinedThis if tp1.level == tp2.level => true
          case _ => thirdTry(tp1, tp2)
        }
      case tp1: BoundType =>
        tp1 == tp2 || thirdTry(tp1, tp2)
      case tp1: TypeVar =>
        (tp1 eq tp2) || isSubType(tp1.underlying, tp2)
      case tp1: WildcardType =>
        def compareWild = tp1.optBounds match {
          case TypeBounds(lo, _) => isSubType(lo, tp2)
          case _ => true
        }
        compareWild
      case tp1: LazyRef =>
        isSubType(tp1.ref, tp2)
      case tp1: AnnotatedType =>
        isSubType(tp1.tpe, tp2)
      case ErrorType =>
        true
      case _ =>
        thirdTry(tp1, tp2)
    }

    def secondTryNamed(tp1: NamedType, tp2: Type): Boolean = {
      tp1.info match {
        // There was the following code, which was meant to implement this logic:
        //    If x has type A | B, then x.type <: C if
        //    x.type <: C assuming x has type A, and
        //    x.type <: C assuming x has type B.
        // But it did not work, because derivedRef would always give back the same
        // type and cache the denotation. So it ended up copmparing just one branch.
        // The code seems to be unncessary for the tests and does not seems to help performance.
        // So it is commented out. If we ever need to come back to this, we would have
        // to create unchached TermRefs in order to avoid cross talk between the branches.
        /*
      case OrType(tp11, tp12) =>
        val sd = tp1.denot.asSingleDenotation
        def derivedRef(tp: Type) =
          NamedType(tp1.prefix, tp1.name, sd.derivedSingleDenotation(sd.symbol, tp))
        secondTry(OrType.make(derivedRef(tp11), derivedRef(tp12)), tp2)
      */
        case TypeBounds(lo1, hi1) =>
          val gbounds1 = ctx.gadt.bounds(tp1.symbol)
          if (gbounds1 != null)
            ctdSubTypeWhenFrozen(gbounds1.hi, tp2) ||
            narrowGADTBounds(tp1, tp2, fromBelow = false) ||
            thirdTry(tp1, tp2)
          else if (lo1 eq hi1) ctdSubType(hi1, tp2)
        else thirdTry(tp1, tp2)
        case _ =>
        thirdTry(tp1, tp2)
      }
    }

    def thirdTry(tp1: Type, tp2: Type): Boolean = tp2 match {
      case tp2: NamedType =>
        def compareNamed: Boolean = tp2.info match {
          case TypeBounds(lo2, hi2) =>
            val gbounds2 = ctx.gadt.bounds(tp2.symbol)
            if (gbounds2 != null)
              ctdSubTypeWhenFrozen(tp1, gbounds2.lo) ||
              narrowGADTBounds(tp2, tp1, fromBelow = true) ||
              fourthTry(tp1, tp2)
            else
              ((frozenConstraint || !isCappable(tp1)) && ctdSubType(tp1, lo2)
                || fourthTry(tp1, tp2))

          case _ =>
            val cls2 = tp2.symbol
            if (cls2.isClass) {
              val base = tp1.baseTypeRef(cls2)
              if (base.exists && (base ne tp1)) return ctdSubType(base, tp2)
              if (cls2 == defn.SingletonClass && tp1.isStable) return true
            }
          fourthTry(tp1, tp2)
        }
        compareNamed
      case tp2 @ RefinedType(parent2, name2) =>
        def compareRefined: Boolean = {
          val normalPath =
            ctdSubType(tp1, parent2) && (
              name2 == nme.WILDCARD
              || hasMatchingMember(name2, tp1, tp2)
              || fourthTry(tp1, tp2))
          normalPath ||
            needsEtaLift(tp1, tp2) && tp1.testLifted(tp2.typeParams, isSubType(_, tp2))
        }
        compareRefined
      case OrType(tp21, tp22) =>
        eitherIsSubType(tp1, tp21, tp1, tp22) || fourthTry(tp1, tp2)
      case tp2 @ MethodType(_, formals2) =>
        def compareMethod = tp1 match {
          case tp1 @ MethodType(_, formals1) =>
            (tp1.signature sameParams tp2.signature) &&
              (if (Config.newMatch) subsumeParams(formals1, formals2, tp1.isJava, tp2.isJava)
              else matchingParams(formals1, formals2, tp1.isJava, tp2.isJava)) &&
              tp1.isImplicit == tp2.isImplicit && // needed?
              isSubType(tp1.resultType, tp2.resultType.subst(tp2, tp1))
          case _ =>
            false
        }
        compareMethod
      case tp2: PolyType =>
        def comparePoly = tp1 match {
          case tp1: PolyType =>
            (tp1.signature sameParams tp2.signature) &&
              matchingTypeParams(tp1, tp2) &&
              isSubType(tp1.resultType, tp2.resultType.subst(tp2, tp1))
          case _ =>
            false
        }
        comparePoly
      case tp2 @ ExprType(restpe2) =>
        def compareExpr = tp1 match {
          // We allow ()T to be a subtype of => T.
          // We need some subtype relationship between them so that e.g.
          // def toString   and   def toString()   don't clash when seen
          // as members of the same type. And it seems most logical to take
          // ()T <:< => T, since everything one can do with a => T one can
          // also do with a ()T by automatic () insertion.
          case tp1 @ MethodType(Nil, _) => ctdSubType(tp1.resultType, restpe2)
          case _ => ctdSubType(tp1.widenExpr, restpe2)
        }
        compareExpr
      case tp2 @ TypeBounds(lo2, hi2) =>
        def compareTypeBounds = tp1 match {
          case tp1 @ TypeBounds(lo1, hi1) =>
            (tp2.variance > 0 && tp1.variance >= 0 || isSubType(lo2, lo1)) &&
              (tp2.variance < 0 && tp1.variance <= 0 || ctdSubType(hi1, hi2))
          case tp1: ClassInfo =>
            val tt = tp1.typeRef
            ctdSubType(lo2, tt) && isSubType(tt, hi2)
          case _ =>
            false
        }
        compareTypeBounds
      case ClassInfo(pre2, cls2, _, _, _) =>
        def compareClassInfo = tp1 match {
          case ClassInfo(pre1, cls1, _, _, _) =>
            (cls1 eq cls2) && isSubType(pre2, pre1)
          case _ =>
            false
        }
        compareClassInfo
      case JavaArrayType(elem2) =>
        def compareJavaArray = tp1 match {
          case JavaArrayType(elem1) => isSubType(elem1, elem2)
          case _ => fourthTry(tp1, tp2)
        }
        compareJavaArray
      case _ =>
        fourthTry(tp1, tp2)
    }

    def fourthTry(tp1: Type, tp2: Type): Boolean = tp1 match {
      case tp1: TypeRef =>
        tp1.info match {
          case TypeBounds(lo1, hi1) =>
            ctdSubType(hi1, tp2)
          case _ =>
            def isNullable(tp: Type): Boolean = tp.dealias match {
              case tp: TypeRef => tp.symbol.isNullableClass
              case RefinedType(parent, _) => isNullable(parent)
              case AndType(tp1, tp2) => isNullable(tp1) && isNullable(tp2)
              case OrType(tp1, tp2) => isNullable(tp1) || isNullable(tp2)
              case _ => false
            }
            (tp1.symbol eq NothingClass) && tp2.isInstanceOf[ValueType] ||
              (tp1.symbol eq NullClass) && isNullable(tp2)
        }
      case tp1: SingletonType =>
        isNewSubType(tp1.underlying.widenExpr, tp2) || {
          // if tp2 == p.type  and p: q.type then try   tp1 <:< q.type as a last effort.
          tp2 match {
            case tp2: TermRef =>
              tp2.info match {
                case tp2i: TermRef =>
                  ctdSubType(tp1, tp2i)
                case ExprType(tp2i: TermRef) if (ctx.phase.id > ctx.gettersPhase.id) =>
                  ctdSubType(tp1, tp2i)
                case _ =>
                  false
              }
            case _ =>
              false
          }
        }
      case tp1: RefinedType =>
         isNewSubType(tp1.parent, tp2) || 
           needsEtaLift(tp2, tp1) && tp2.testLifted(tp1.typeParams, ctdSubType(tp1, _))
      case AndType(tp11, tp12) =>
        eitherIsSubType(tp11, tp2, tp12, tp2)
      case JavaArrayType(elem1) =>
        tp2 isRef ObjectClass
      case _ =>
        false
    }

    /** Returns true iff either `tp11 <:< tp21` or `tp12 <:< tp22`, trying at the same time
     *  to keep the constraint as wide as possible. Specifically, if
     *
     *    tp11 <:< tp12 = true   with post-constraint c1
     *    tp12 <:< tp22 = true   with post-constraint c2
     *
     *  and c1 subsumes c2, then c2 is kept as the post-constraint of the result,
     *  otherwise c1 is kept.
     *
     *  This method is used to approximate a solution in one of the following cases
     *
     *     T1 & T2 <:< T3
     *     T1 <:< T2 | T3
     *
     *  In the first case (the second one is analogous), we have a choice whether we
     *  want to establish the subtyping judgement using
     *
     *     T1 <:< T3   or    T2 <:< T3
     *
     *  as a precondition. Either precondition might constrain type variables.
     *  The purpose of this method is to pick the precondition that constrains less.
     *  The method is not complete, because sometimes there is no best solution. Example:
     *
     *     A? & B?  <:  T
     *
     *  Here, each precondition leads to a different constraint, and neither of
     *  the two post-constraints subsumes the other.
     */
    def eitherIsSubType(tp11: Type, tp21: Type, tp12: Type, tp22: Type) = {
      val preConstraint = constraint
      ctdSubType(tp11, tp21) && {
        val leftConstraint = constraint
        constraint = preConstraint
        if (ctdSubType(tp12, tp22) && !subsumes(leftConstraint, constraint, preConstraint))
          constraint = leftConstraint
        true
      } || ctdSubType(tp12, tp22)
    }

    /** Like tp1 <:< tp2, but returns false immediately if we know that
     *  the case was covered previously during subtyping.
     */
    def isNewSubType(tp1: Type, tp2: Type): Boolean =
      if (isCovered(tp1) && isCovered(tp2)) {
        //println(s"useless subtype: $tp1 <:< $tp2")
        false
      } else ctdSubType(tp1, tp2)

    def ctdSubTypeWhenFrozen(tp1: Type, tp2: Type): Boolean = {
      val saved = frozenConstraint
      frozenConstraint = true
      try ctdSubType(tp1, tp2)
      finally frozenConstraint = saved
    } 

    def monitoredIsSubType(tp1: Type, tp2: Type) = {
      if (pendingSubTypes == null) {
        pendingSubTypes = new mutable.HashSet[(Type, Type)]
        ctx.log(s"!!! deep subtype recursion involving ${tp1.show} <:< ${tp2.show}, constraint = ${state.constraint.show}")
        ctx.log(s"!!! constraint = ${constraint.show}")
        assert(!ctx.settings.YnoDeepSubtypes.value)
        if (Config.traceDeepSubTypeRecursions && !this.isInstanceOf[ExplainingTypeComparer])
          ctx.log(TypeComparer.explained(implicit ctx => ctx.typeComparer.isSubType(tp1, tp2)))
      }
      val p = (tp1, tp2)
      !pendingSubTypes(p) && {
        try {
          pendingSubTypes += p
          firstTry(tp1, tp2)
        } finally {
          pendingSubTypes -= p
        }
      }
    }

    ctdSubType(orig1, orig2)
  }

  def hasMatchingMember(name: Name, orig1: Type, tp2: RefinedType): Boolean = /*>|>*/ ctx.traceIndented(s"hasMatchingMember($orig1 . $name, ${tp2.refinedInfo}) ${orig1.member(name).info.show}", subtyping) /*<|<*/ {
    val base = orig1.ensureSingleton
    var rinfo2 = tp2.refinedInfo.substRefinedThis(0, base)
    def qualifies(m: SingleDenotation) = isSubType(m.info, rinfo2)
    def memberMatches(mbr: Denotation): Boolean = mbr match { // inlined hasAltWith for performance
      case mbr: SingleDenotation => qualifies(mbr)
      case _ => mbr hasAltWith qualifies
    }
    memberMatches(base member name) ||
      orig1.isInstanceOf[SingletonType] &&
      { // special case for situations like:
        //    foo <: C { type T = foo.T }
        rinfo2 match {
          case rinfo2: TypeAlias =>
            !ctx.phase.erasedTypes && (base select name) =:= rinfo2.alias
          case _ => false
        }
      }
  }

  /** A type has been covered previously in subtype checking if it
   *  is some combination of TypeRefs that point to classes, where the
   *  combiners are RefinedTypes, AndTypes or AnnotatedTypes.
   */
  private def isCovered(tp: Type): Boolean = tp.dealias.stripTypeVar match {
    case tp: TypeRef => tp.symbol.isClass && tp.symbol != NothingClass && tp.symbol != NullClass
    case tp: ProtoType => false
    case tp: RefinedType => isCovered(tp.parent)
    case tp: AnnotatedType => isCovered(tp.underlying)
    case AndType(tp1, tp2) => isCovered(tp1) && isCovered(tp2)
    case _ => false
  }

  /** The current bounds of type parameter `param` */
  def bounds(param: PolyParam): TypeBounds = constraint at param match {
    case bounds: TypeBounds if !ignoreConstraint => bounds
    case _ => param.binder.paramBounds(param.paramNum)
  }

  /** Defer constraining type variables when compared against prototypes */
  def isMatchedByProto(proto: ProtoType, tp: Type) = tp.stripTypeVar match {
    case tp: PolyParam if !solvedConstraint && (constraint contains tp) => true
    case _ => proto.isMatchedBy(tp)
  }

  /** Can type `tp` be constrained from above by adding a constraint to
   *  a typevar that it refers to? In that case we have to be careful not
   *  to approximate with the lower bound of a type in `thirdTry`. Instead,
   *  we should first unroll `tp1` until we hit the type variable and bind the
   *  type variable with (the corresponding type in) `tp2` instead.
   */
  def isCappable(tp: Type): Boolean = tp match {
    case tp: PolyParam => !solvedConstraint && (constraint contains tp)
    case tp: TypeProxy => isCappable(tp.underlying)
    case tp: AndOrType => isCappable(tp.tp1) || isCappable(tp.tp2)
    case _ => false
  }

  /** Does `tp` need to be eta lifted to be comparable to `target`? */
  def needsEtaLift(tp: Type, target: RefinedType): Boolean = {
    //default.echo(i"needs eta $tp $target?", {
    val name = target.refinedName
    (name.isLambdaArgName || (name eq tpnme.Apply)) && target.isLambda &&
    tp.exists && !tp.isLambda
    //})
  }

  def narrowGADTBounds(tr: NamedType, bound: Type, fromBelow: Boolean): Boolean = 
    ctx.mode.is(Mode.GADTflexible) && {
    val tparam = tr.symbol
    val bound1 = bound // ctx.deSkolemize(bound, toSuper = fromBelow)
    println(s"narrow gadt bound of $tparam: ${tparam.info} from ${if (fromBelow) "below" else "above"} to $bound1 ${bound1.isRef(tparam)}")
    !bound1.isRef(tparam) && { 
      val oldBounds = ctx.gadt.bounds(tparam)
      val newBounds = 
        if (fromBelow) TypeBounds(oldBounds.lo | bound1, oldBounds.hi)
        else TypeBounds(oldBounds.lo, oldBounds.hi & bound1)
      isSubType(newBounds.lo, newBounds.hi) &&
      { ctx.gadt.setBounds(tparam, newBounds); true }
    }
  }

  // Tests around `matches`

  /** A function implementing `tp1` matches `tp2`. */
  final def matchesType(tp1: Type, tp2: Type, alwaysMatchSimple: Boolean): Boolean = tp1 match {
    case tp1: MethodType =>
      tp2 match {
        case tp2: MethodType =>
          tp1.isImplicit == tp2.isImplicit &&
            matchingParams(tp1.paramTypes, tp2.paramTypes, tp1.isJava, tp2.isJava) &&
            matchesType(tp1.resultType, tp2.resultType.subst(tp2, tp1), alwaysMatchSimple)
        case tp2: ExprType =>
          tp1.paramNames.isEmpty &&
            matchesType(tp1.resultType, tp2.resultType, alwaysMatchSimple)
        case _ =>
          false
      }
    case tp1: ExprType =>
      tp2 match {
        case tp2: MethodType =>
          tp2.paramNames.isEmpty &&
            matchesType(tp1.resultType, tp2.resultType, alwaysMatchSimple)
        case tp2: ExprType =>
          matchesType(tp1.resultType, tp2.resultType, alwaysMatchSimple)
        case _ =>
          false // was: matchesType(tp1.resultType, tp2, alwaysMatchSimple)
      }
    case tp1: PolyType =>
      tp2 match {
        case tp2: PolyType =>
          sameLength(tp1.paramNames, tp2.paramNames) &&
            matchesType(tp1.resultType, tp2.resultType.subst(tp2, tp1), alwaysMatchSimple)
        case _ =>
          false
      }
    case _ =>
      tp2 match {
        case _: MethodType | _: PolyType =>
          false
        case tp2: ExprType =>
          false // was: matchesType(tp1, tp2.resultType, alwaysMatchSimple)
        case _ =>
          alwaysMatchSimple || isSameType(tp1, tp2)
      }
  }

  /** Are `syms1` and `syms2` parameter lists with pairwise equivalent types? */
  private def matchingParams(formals1: List[Type], formals2: List[Type], isJava1: Boolean, isJava2: Boolean): Boolean = formals1 match {
    case formal1 :: rest1 =>
      formals2 match {
        case formal2 :: rest2 =>
          (isSameType(formal1, formal2)
            || isJava1 && (formal2 isRef ObjectClass) && (formal1 isRef AnyClass)
            || isJava2 && (formal1 isRef ObjectClass) && (formal2 isRef AnyClass)) &&
          matchingParams(rest1, rest2, isJava1, isJava2)
        case nil =>
          false
      }
    case nil =>
      formals2.isEmpty
  }

  private def subsumeParams(formals1: List[Type], formals2: List[Type], isJava1: Boolean, isJava2: Boolean): Boolean = formals1 match {
    case formal1 :: rest1 =>
      formals2 match {
        case formal2 :: rest2 =>
          (isSubType(formal2, formal1)
            || isJava1 && (formal2 isRef ObjectClass) && (formal1 isRef AnyClass)
            || isJava2 && (formal1 isRef ObjectClass) && (formal2 isRef AnyClass)) &&
          subsumeParams(rest1, rest2, isJava1, isJava2)
        case nil =>
          false
      }
    case nil =>
      formals2.isEmpty
  }

  /** Do poly types `poly1` and `poly2` have type parameters that
   *  have the same bounds (after renaming one set to the other)?
   */
  private def matchingTypeParams(poly1: PolyType, poly2: PolyType): Boolean =
    (poly1.paramBounds corresponds poly2.paramBounds)((b1, b2) =>
      isSameType(b1, b2.subst(poly2, poly1)))

  // Type equality =:=

  /** Two types are the same if are mutual subtypes of each other */
  def isSameType(tp1: Type, tp2: Type): Boolean =
    if (tp1 eq NoType) false
    else if (tp1 eq tp2) true
    else isSubType(tp1, tp2) && isSubType(tp2, tp1)

  /** Same as `isSameType` but also can be applied to overloaded TermRefs, where
   *  two overloaded refs are the same if they have pairwise equal alternatives
   */
  def isSameRef(tp1: Type, tp2: Type): Boolean = ctx.traceIndented(s"isSameRef($tp1, $tp2") {
    def isSubRef(tp1: Type, tp2: Type): Boolean = tp1 match {
      case tp1: TermRef if tp1.isOverloaded =>
        tp1.alternatives forall (isSubRef(_, tp2))
      case _ =>
        tp2 match {
          case tp2: TermRef if tp2.isOverloaded =>
            tp2.alternatives exists (isSubRef(tp1, _))
          case _ =>
            isSubType(tp1, tp2)
        }
    }
    isSubRef(tp1, tp2) && isSubRef(tp2, tp1)
  }

  /** The greatest lower bound of two types */
  def glb(tp1: Type, tp2: Type): Type = /*>|>*/ ctx.traceIndented(s"glb(${tp1.show}, ${tp2.show})", subtyping, show = true) /*<|<*/ {
    if (tp1 eq tp2) tp1
    else if (!tp1.exists) tp2
    else if (!tp2.exists) tp1
    else if ((tp1 isRef AnyClass) || (tp2 isRef NothingClass)) tp2
    else if ((tp2 isRef AnyClass) || (tp1 isRef NothingClass)) tp1
    else tp2 match {  // normalize to disjunctive normal form if possible.
      case OrType(tp21, tp22) =>
        tp1 & tp21 | tp1 & tp22
      case _ =>
        tp1 match {
          case OrType(tp11, tp12) =>
            tp11 & tp2 | tp12 & tp2
          case _ =>
            val t1 = mergeIfSub(tp1, tp2)
            if (t1.exists) t1
            else {
              val t2 = mergeIfSub(tp2, tp1)
              if (t2.exists) t2
              else andType(tp1, tp2)
            }
        }
    }
  }

  /** The greatest lower bound of a list types */
  final def glb(tps: List[Type]): Type =
    (defn.AnyType /: tps)(glb)

  /** The least upper bound of two types
   *  @note  We do not admit singleton types in or-types as lubs.
   */
  def lub(tp1: Type, tp2: Type): Type = /*>|>*/ ctx.traceIndented(s"lub(${tp1.show}, ${tp2.show})", subtyping, show = true) /*<|<*/ {
    if (tp1 eq tp2) tp1
    else if (!tp1.exists) tp1
    else if (!tp2.exists) tp2
    else if ((tp1 isRef AnyClass) || (tp2 isRef NothingClass)) tp1
    else if ((tp2 isRef AnyClass) || (tp1 isRef NothingClass)) tp2
    else {
      val t1 = mergeIfSuper(tp1, tp2)
      if (t1.exists) t1
      else {
        val t2 = mergeIfSuper(tp2, tp1)
        if (t2.exists) t2
        else {
          val tp1w = tp1.widen
          val tp2w = tp2.widen
          if ((tp1 ne tp1w) || (tp2 ne tp2w)) lub(tp1w, tp2w)
          else orType(tp1w, tp2w) // no need to check subtypes again
        }
      }
    }
  }

  /** The least upper bound of a list of types */
  final def lub(tps: List[Type]): Type =
    (defn.NothingType /: tps)(lub)

  /** Merge `t1` into `tp2` if t1 is a subtype of some &-summand of tp2.
   */
  private def mergeIfSub(tp1: Type, tp2: Type): Type =
    if (isSubTypeWhenFrozen(tp1, tp2))
      if (isSubTypeWhenFrozen(tp2, tp1)) tp2 else tp1 // keep existing type if possible
    else tp2 match {
      case tp2 @ AndType(tp21, tp22) =>
        val lower1 = mergeIfSub(tp1, tp21)
        if (lower1 eq tp21) tp2
        else if (lower1.exists) lower1 & tp22
        else {
          val lower2 = mergeIfSub(tp1, tp22)
          if (lower2 eq tp22) tp2
          else if (lower2.exists) tp21 & lower2
          else NoType
        }
      case _ =>
        NoType
    }

  /** Merge `tp1` into `tp2` if tp1 is a supertype of some |-summand of tp2.
   */
  private def mergeIfSuper(tp1: Type, tp2: Type): Type =
    if (isSubTypeWhenFrozen(tp2, tp1))
      if (isSubTypeWhenFrozen(tp1, tp2)) tp2 else tp1 // keep existing type if possible
    else tp2 match {
      case tp2 @ OrType(tp21, tp22) =>
        val higher1 = mergeIfSuper(tp1, tp21)
        if (higher1 eq tp21) tp2
        else if (higher1.exists) higher1 | tp22
        else {
          val higher2 = mergeIfSuper(tp1, tp22)
          if (higher2 eq tp22) tp2
          else if (higher2.exists) tp21 | higher2
          else NoType
        }
      case _ =>
        NoType
    }

  /** Form a normalized conjunction of two types.
   *  Note: For certain types, `&` is distributed inside the type. This holds for
   *  all types which are not value types (e.g. TypeBounds, ClassInfo,
   *  ExprType, MethodType, PolyType). Also, when forming an `&`,
   *  instantiated TypeVars are dereferenced and annotations are stripped.
   *  Finally, refined types with the same refined name are
   *  opportunistically merged.
   *
   *  Sometimes, the conjunction of two types cannot be formed because
   *  the types are in conflict of each other. In particular:
   *
   *    1. Two different class types are conflicting.
   *    2. A class type conflicts with a type bounds that does not include the class reference.
   *    3. Two method or poly types with different (type) parameters but the same
   *       signature are conflicting
   *
   *  In these cases, one of the types is picked (@see andConflict).
   *  This is arbitrary, but I believe it is analogous to forming
   *  infeasible TypeBounds (where low bound is not a subtype of high bound).
   *  Such TypeBounds can also be arbitrarily instantiated. In both cases we need to
   *  make sure that such types do not actually arise in source programs.
   */
  final def andType(tp1: Type, tp2: Type, erased: Boolean = ctx.erasedTypes) = ctx.traceIndented(s"glb(${tp1.show}, ${tp2.show})", subtyping, show = true) {
    val t1 = distributeAnd(tp1, tp2)
    if (t1.exists) t1
    else {
      val t2 = distributeAnd(tp2, tp1)
      if (t2.exists) t2
      else if (erased) erasedGlb(tp1, tp2, isJava = false)
      else {
        //if (isHKRef(tp1)) tp2
        //else if (isHKRef(tp2)) tp1
        //else
        AndType(tp1, tp2)
      }
    }
  }

  /** Form a normalized conjunction of two types.
   *  Note: For certain types, `|` is distributed inside the type. This holds for
   *  all types which are not value types (e.g. TypeBounds, ClassInfo,
   *  ExprType, MethodType, PolyType). Also, when forming an `|`,
   *  instantiated TypeVars are dereferenced and annotations are stripped.
   *
   *  Sometimes, the disjunction of two types cannot be formed because
   *  the types are in conflict of each other. (@see `andType` for an enumeration
   *  of these cases). In cases of conflict a `MergeError` is raised.
   *
   *  @param erased   Apply erasure semantics. If erased is true, instead of creating
   *                  an OrType, the lub will be computed using TypeCreator#erasedLub.
   */
  final def orType(tp1: Type, tp2: Type, erased: Boolean = ctx.erasedTypes) = {
    val t1 = distributeOr(tp1, tp2)
    if (t1.exists) t1
    else {
      val t2 = distributeOr(tp2, tp1)
      if (t2.exists) t2
      else if (erased) erasedLub(tp1, tp2)
      else
        //if (isHKRef(tp1)) tp1
        //else if (isHKRef(tp2)) tp2
        //else
        OrType(tp1, tp2)
    }
  }

  /** Try to distribute `&` inside type, detect and handle conflicts */
  private def distributeAnd(tp1: Type, tp2: Type): Type = tp1 match {
    // opportunistically merge same-named refinements
    // this does not change anything semantically (i.e. merging or not merging
    // gives =:= types), but it keeps the type smaller.
    case tp1: RefinedType =>
      tp2 match {
        case tp2: RefinedType if tp1.refinedName == tp2.refinedName =>
          tp1.derivedRefinedType(
              tp1.parent & tp2.parent,
              tp1.refinedName,
              tp1.refinedInfo & tp2.refinedInfo)
        case _ =>
          NoType
      }
    case tp1: TypeBounds =>
      tp2 match {
        case tp2: TypeBounds => tp1 & tp2
        case _ => andConflict(tp1, tp2)
      }
    case tp1: ClassInfo =>
      tp2 match {
        case tp2: ClassInfo if tp1.cls eq tp2.cls =>
          tp1.derivedClassInfo(tp1.prefix & tp2.prefix)
        case _ =>
          andConflict(tp1, tp2)
      }
    case tp1 @ MethodType(names1, formals1) =>
      tp2 match {
        case tp2 @ MethodType(names2, formals2)
        if Config.newMatch && (tp1.isImplicit == tp2.isImplicit) && formals1.hasSameLengthAs(formals2) =>
          tp1.derivedMethodType(
              mergeNames(names1, names2, nme.syntheticParamName),
              (formals1 zipWithConserve formals2)(_ | _),
              tp1.resultType & tp2.resultType.subst(tp2, tp1))
        case tp2 @ MethodType(names2, formals2)
        if matchingParams(formals1, formals2, tp1.isJava, tp2.isJava) &&
           tp1.isImplicit == tp2.isImplicit =>
          tp1.derivedMethodType(
              mergeNames(names1, names2, nme.syntheticParamName),
              formals1, tp1.resultType & tp2.resultType.subst(tp2, tp1))
        case _ =>
          andConflict(tp1, tp2)
      }
    case tp1: PolyType =>
      tp2 match {
        case tp2: PolyType if matchingTypeParams(tp1, tp2) =>
          tp1.derivedPolyType(
              mergeNames(tp1.paramNames, tp2.paramNames, tpnme.syntheticTypeParamName),
              tp1.paramBounds, tp1.resultType & tp2.resultType.subst(tp2, tp1))
        case _ =>
          andConflict(tp1, tp2)
      }
    case ExprType(rt1) =>
      tp2 match {
        case ExprType(rt2) =>
          ExprType(rt1 & rt2)
        case _ =>
          rt1 & tp2
      }
    case tp1: TypeVar if tp1.isInstantiated =>
      tp1.underlying & tp2
    case tp1: AnnotatedType =>
      tp1.underlying & tp2
    case _ =>
      NoType
  }

  /** Try to distribute `|` inside type, detect and handle conflicts */
  private def distributeOr(tp1: Type, tp2: Type): Type = tp1 match {
    case tp1: RefinedType =>
      tp2 match {
        case tp2: RefinedType if tp1.refinedName == tp2.refinedName =>
          tp1.derivedRefinedType(
              tp1.parent | tp2.parent,
              tp1.refinedName,
              tp1.refinedInfo | tp2.refinedInfo)
        case _ =>
          NoType
      }
    case tp1: TypeBounds =>
      tp2 match {
        case tp2: TypeBounds => tp1 | tp2
        case _ => orConflict(tp1, tp2)
      }
    case tp1: ClassInfo =>
      tp2 match {
        case tp2: ClassInfo if tp1.cls eq tp2.cls =>
          tp1.derivedClassInfo(tp1.prefix | tp2.prefix)
        case _ =>
          orConflict(tp1, tp2)
      }
    case tp1 @ MethodType(names1, formals1) =>
      tp2 match {
        case tp2 @ MethodType(names2, formals2)
        if Config.newMatch && (tp1.isImplicit == tp2.isImplicit) && formals1.hasSameLengthAs(formals2) =>
          tp1.derivedMethodType(
              mergeNames(names1, names2, nme.syntheticParamName),
              (formals1 zipWithConserve formals2)(_ & _),
              tp1.resultType | tp2.resultType.subst(tp2, tp1))
        case tp2 @ MethodType(names2, formals2)
        if matchingParams(formals1, formals2, tp1.isJava, tp2.isJava) &&
           tp1.isImplicit == tp2.isImplicit =>
          tp1.derivedMethodType(
              mergeNames(names1, names2, nme.syntheticParamName),
              formals1, tp1.resultType | tp2.resultType.subst(tp2, tp1))
        case _ =>
          orConflict(tp1, tp2)
      }
    case tp1: PolyType =>
      tp2 match {
        case tp2: PolyType if matchingTypeParams(tp1, tp2) =>
          tp1.derivedPolyType(
              mergeNames(tp1.paramNames, tp2.paramNames, tpnme.syntheticTypeParamName),
              tp1.paramBounds, tp1.resultType | tp2.resultType.subst(tp2, tp1))
        case _ =>
          orConflict(tp1, tp2)
      }
    case ExprType(rt1) =>
      ExprType(rt1 | tp2.widenExpr)
    case tp1: TypeVar if tp1.isInstantiated =>
      tp1.underlying | tp2
    case tp1: AnnotatedType =>
      tp1.underlying | tp2
    case _ =>
      NoType
  }

  /** Handle `&`-conflict. If `tp2` is strictly better than `tp1` as determined
   *  by @see `isAsGood`, pick `tp2` as the winner otherwise pick `tp1`.
   *  Issue a warning and return the winner.
   */
  private def andConflict(tp1: Type, tp2: Type): Type = {
    // println(disambiguated(implicit ctx => TypeComparer.explained(_.typeComparer.isSubType(tp1, tp2)))) !!!DEBUG
    val winner = if (isAsGood(tp2, tp1) && !isAsGood(tp1, tp2)) tp2 else tp1
    def msg = disambiguated { implicit ctx =>
      s"${mergeErrorMsg(tp1, tp2)} as members of one type; keeping only ${showType(winner)}"
    }
    /* !!! DEBUG
    println("right not a subtype of left because:")
    println(TypeComparer.explained { implicit ctx => tp2 <:< tp1})
    println("left not a subtype of right because:")
    println(TypeComparer.explained { implicit ctx => tp1 <:< tp2})
    assert(false, s"andConflict ${tp1.show} and ${tp2.show}")
    */
    ctx.warning(msg, ctx.tree.pos)
    winner
  }

  /** Handle `|`-conflict by raising a `MergeError` exception */
  private def orConflict(tp1: Type, tp2: Type): Type =
    throw new MergeError(mergeErrorMsg(tp1, tp2))

  /** Merge two lists of names. If names in corresponding positions match, keep them,
   *  otherwise generate new synthetic names.
   */
  private def mergeNames[N <: Name](names1: List[N], names2: List[N], syntheticName: Int => N): List[N] = {
    for ((name1, name2, idx) <- (names1, names2, 0 until names1.length).zipped)
    yield if (name1 == name2) name1 else syntheticName(idx)
  }.toList

  /** Show type, handling type types better than the default */
  private def showType(tp: Type)(implicit ctx: Context) = tp match {
    case ClassInfo(_, cls, _, _, _) => cls.showLocated
    case bounds: TypeBounds => "type bounds" + bounds.show
    case _ => tp.show
  }

  /** The error message kernel for a merge conflict */
  private def mergeErrorMsg(tp1: Type, tp2: Type)(implicit ctx: Context) =
    s"cannot merge ${showType(tp1)} with ${showType(tp2)}"

  /** A comparison function to pick a winner in case of a merge conflict */
  private def isAsGood(tp1: Type, tp2: Type): Boolean = tp1 match {
    case tp1: ClassInfo =>
      tp2 match {
        case tp2: ClassInfo =>
          isSubType(tp1.prefix, tp2.prefix) || (tp1.cls.owner derivesFrom tp2.cls.owner)
        case _ =>
          false
      }
    case tp1: PolyType =>
      tp2 match {
        case tp2: PolyType =>
          tp1.typeParams.length == tp2.typeParams.length &&
          isAsGood(tp1.resultType, tp2.resultType.subst(tp2, tp1))
        case _ =>
          false
      }
    case tp1: MethodType =>
      tp2 match {
        case tp2: MethodType =>
          def asGoodParams(formals1: List[Type], formals2: List[Type]) =
            (formals2 corresponds formals1)(isSubType)
          asGoodParams(tp1.paramTypes, tp2.paramTypes) &&
          (!asGoodParams(tp2.paramTypes, tp1.paramTypes) ||
           isAsGood(tp1.resultType, tp2.resultType))
        case _ =>
          false
      }
    case _ =>
      false
  }

  /** Constraint `c1` subsumes constraint `c2`, if under `c2` as constraint we have
   *  for all poly params `p` defined in `c2` as `p >: L2 <: U2`:
   *
   *     c1 defines p with bounds p >: L1 <: U1, and
   *     L2 <: L1, and
   *     U1 <: U2
   *
   *  Both `c1` and `c2` are required to derive from constraint `pre`, possibly
   *  narrowing it with further bounds.
   */
  def subsumes(c1: Constraint, c2: Constraint, pre: Constraint): Boolean =
    if (c2 eq pre) true
    else if (c1 eq pre) false
    else {
      val saved = constraint
      try
        c2.forallParams(p => c1.contains(p) && isSubType(c1.bounds(p), c2.bounds(p)))
      finally constraint = saved
    }

  /** A new type comparer of the same type as this one, using the given context. */
  def copyIn(ctx: Context) = new TypeComparer(ctx)

  /** A hook for showing subtype traces. Overridden in ExplainingTypeComparer */
  def traceIndented[T](str: String)(op: => T): T = op
}

object TypeComparer {

  /** Show trace of comparison operations when performing `op` as result string */
  def explained[T](op: Context => T)(implicit ctx: Context): String = {
    val nestedCtx = ctx.fresh.setTypeComparerFn(new ExplainingTypeComparer(_))
    op(nestedCtx)
    nestedCtx.typeComparer.toString
  }
}

/** A type comparer that can record traces of subtype operations */
class ExplainingTypeComparer(initctx: Context) extends TypeComparer(initctx) {
  private var indent = 0
  private val b = new StringBuilder

  private var skipped = false

  override def traceIndented[T](str: String)(op: => T): T =
    if (skipped) op
    else {
      indent += 2
      b append "\n" append (" " * indent) append "==> " append str
      val res = op
      b append "\n" append (" " * indent) append "<== " append str append " = " append show(res)
      indent -= 2
      res
    }

  private def show(res: Any) = res match {
    case res: printing.Showable if !ctx.settings.Yexplainlowlevel.value => res.show
    case _ => String.valueOf(res)
  }

  override def isSubType(tp1: Type, tp2: Type) =
    traceIndented(s"${show(tp1)} <:< ${show(tp2)}${if (Config.verboseExplainSubtype) s" ${tp1.getClass} ${tp2.getClass}" else ""}${if (frozenConstraint) " frozen" else ""}") {
      super.isSubType(tp1, tp2)
    }

  override def hasMatchingMember(name: Name, orig1: Type, tp2: RefinedType): Boolean = 
    traceIndented(s"hasMatchingMember(${show(orig1)} . $name, ${show(tp2.refinedInfo)}), member = ${show(orig1.member(name).info)}") {
      super.hasMatchingMember(name, orig1, tp2)
    }

  override def lub(tp1: Type, tp2: Type) =
    traceIndented(s"lub(${show(tp1)}, ${show(tp2)})") {
      super.lub(tp1, tp2)
    }

  override def glb(tp1: Type, tp2: Type) =
    traceIndented(s"glb(${show(tp1)}, ${show(tp2)})") {
      super.glb(tp1, tp2)
    }

  override def addConstraint(param: PolyParam, bound: Type, fromBelow: Boolean): Boolean =
    traceIndented(s"add constraint $param ${if (fromBelow) ">:" else "<:"} $bound $frozenConstraint") {
      super.addConstraint(param, bound, fromBelow)
    }

  override def copyIn(ctx: Context) = new ExplainingTypeComparer(ctx)

  override def toString = "Subtype trace:" + { try b.toString finally b.clear() }
}