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 with ConstraintHandling with Skolemization {
  implicit val ctx: Context = initctx

  val state = ctx.typerState
  import state.constraint

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

  private var needsGc = false

  /** Is a subtype check in progress? 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 statistics: count how many isSubTypes are part of successful 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
  private var myNothingType: 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
  }
  def NothingType = {
    if (myNothingType == null) myNothingType = NothingClass.typeRef
    myNothingType
  }

  // Subtype testing `<:<`

  def topLevelSubType(tp1: Type, tp2: Type): Boolean = {
    if (tp2 eq NoType) return false
    if ((tp2 eq tp1) || (tp2 eq WildcardType)) return true
    try isSubType(tp1, tp2)
    finally
      if (Config.checkConstraintsSatisfiable)
        assert(isSatisfiable, constraint.show)
  }

  protected def isSubType(tp1: Type, tp2: Type): Boolean = ctx.traceIndented(s"isSubType ${traceInfo(tp1, tp2)}", subtyping) /*<|<*/ {
    if (tp2 eq NoType) false
    else if (tp1 eq tp2) true
    else {
      val saved = constraint
      val savedSuccessCount = successCount
      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()
          needsGc = false
        }
        if (Stats.monitored) recordStatistics(result, savedSuccessCount)
        result
      } catch {
        case NonFatal(ex) =>
          if (ex.isInstanceOf[AssertionError]) showGoal(tp1, tp2)
          recCount -= 1
          constraint = saved
          successCount = savedSuccessCount
          throw ex
      }
    }
  }

  private 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
      }
    }
  }

  private def firstTry(tp1: Type, tp2: Type): Boolean = tp2 match {
    case tp2: NamedType =>
      def compareAlias(info1: Type) = tp2.info match {
        case info2: TypeAlias => isSubType(tp1, info2.alias)
        case _ => info1 match {
          case info1: TypeAlias => isSubType(info1.alias, tp2)
          case NoType => secondTry(tp1, tp2)
          case _ => thirdTryNamed(tp1, tp2)
        }
      }
      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) &&
              (tp1.signature == tp2.signature) &&
              !tp1.isInstanceOf[WithFixedSym] &&
              !tp2.isInstanceOf[WithFixedSym]
            ) ||
            compareHK(tp1, tp2, inOrder = true) || 
            compareHK(tp2, tp1, inOrder = false) ||
            compareAlias(tp1.info)
          case _ =>
            compareHK(tp2, tp1, inOrder = false) || 
            compareAlias(NoType)
        }
      }
      compareNamed
    case tp2: ProtoType =>
      isMatchedByProto(tp2, tp1)
    case tp2: BoundType =>
      tp2 == tp1 || secondTry(tp1, tp2)
    case tp2: TypeVar =>
      isSubType(tp1, tp2.underlying)
    case tp2: WildcardType =>
      def compareWild = tp2.optBounds match {
        case TypeBounds(_, hi) => isSubType(tp1, hi)
        case NoType => true
      }
      compareWild
    case tp2: LazyRef =>
      isSubType(tp1, tp2.ref)
    case tp2: AnnotatedType =>
      isSubType(tp1, tp2.tpe) // todo: refine?
    case tp2: ThisType =>
      def compareThis = {
        val cls2 = tp2.cls
        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.
            val cls1 = tp1.cls
            cls1.classInfo.selfType.derivesFrom(cls2) &&
            cls2.classInfo.selfType.derivesFrom(cls1)
          case tp1: TermRef if tp2.cls eq tp1.symbol.moduleClass =>
            isSubType(tp1.prefix, cls2.owner.thisType)
          case _ =>
            secondTry(tp1, tp2)
        }
      }
      compareThis
    case tp2: SuperType =>
      def compareSuper = tp1 match {
        case tp1: SuperType =>
          isSubType(tp1.thistpe, tp2.thistpe) &&
          isSameType(tp1.supertpe, tp2.supertpe)
        case _ =>
          secondTry(tp1, tp2)
      }
      compareSuper
    case AndType(tp21, tp22) =>
      isSubType(tp1, tp21) && isSubType(tp1, tp22)
    case ErrorType =>
      true
    case _ =>
      secondTry(tp1, tp2)
  }

  private def secondTry(tp1: Type, tp2: Type): Boolean = tp1 match {
    case tp1: NamedType =>
      tp1.info match {
        case info1: TypeAlias => isSubType(info1.alias, tp2)
        case _ => compareHK(tp1, tp2, inOrder = true) || thirdTry(tp1, tp2)
          // Note: If we change the order here, doing compareHK first and following aliases second,
          // we get a -Ycheck error when compiling dotc/transform. Need to investigate.
      }
    case tp1: PolyParam =>
      def flagNothingBound = {
        if (!frozenConstraint && tp2.isRef(defn.NothingClass) && state.isGlobalCommittable) {
          def msg = s"!!! instantiated to Nothing: $tp1, constraint = ${constraint.show}"
          if (Config.failOnInstantiationToNothing) assert(false, msg)
          else ctx.log(msg)
        }
        true
      }
      def comparePolyParam =
        ctx.mode.is(Mode.TypevarsMissContext) ||
        isSubTypeWhenFrozen(bounds(tp1).hi, tp2) || {
          if (canConstrain(tp1)) addConstraint(tp1, tp2, fromBelow = false) && flagNothingBound
          else thirdTry(tp1, tp2)
        }
      comparePolyParam
    case tp1: ThisType =>
      tp2 match {
        case tp2: TermRef if tp1.cls eq tp2.symbol.moduleClass =>
          isSubType(tp1.cls.owner.thisType, tp2.prefix)
        case _ =>
          thirdTry(tp1, tp2)
      }
    case tp1: SkolemType =>
      tp2 match {
        case tp2: SkolemType if tp1 == tp2 => true
        case _ => thirdTry(tp1, tp2)
      }
    case tp1: TypeVar =>
      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 OrType(tp11, tp12) =>
      isSubType(tp11, tp2) && isSubType(tp12, tp2)
    case ErrorType =>
      true
    case _ =>
      thirdTry(tp1, tp2)
  }

  private def thirdTryNamed(tp1: Type, tp2: NamedType): Boolean = tp2.info match {
    case TypeBounds(lo2, _) =>
      def compareGADT: Boolean = {
        val gbounds2 = ctx.gadt.bounds(tp2.symbol)
        (gbounds2 != null) &&
          (isSubTypeWhenFrozen(tp1, gbounds2.lo) ||
            narrowGADTBounds(tp2, tp1, isUpper = false))
      }
      ((frozenConstraint || !isCappable(tp1)) && isSubType(tp1, lo2) ||
        compareGADT ||
        fourthTry(tp1, tp2))

    case _ =>
      val cls2 = tp2.symbol
      if (cls2.isClass) {
        val base = tp1.baseTypeRef(cls2)
        if (base.exists && (base ne tp1)) return isSubType(base, tp2)
        if (cls2 == defn.SingletonClass && tp1.isStable) return true
      }
      fourthTry(tp1, tp2)
  }
  
  private def thirdTry(tp1: Type, tp2: Type): Boolean = tp2 match {
    case tp2: NamedType =>
      thirdTryNamed(tp1, tp2)
    case tp2: PolyParam =>
      def comparePolyParam =
        (ctx.mode is Mode.TypevarsMissContext) ||
        isSubTypeWhenFrozen(tp1, bounds(tp2).lo) || {
          if (canConstrain(tp2)) addConstraint(tp2, tp1.widenExpr, fromBelow = true)
          else fourthTry(tp1, tp2)
        }
      comparePolyParam
    case tp2: RefinedType =>
      def compareRefined: Boolean = {
        val tp1w = tp1.widen
        val skipped2 = skipMatching(tp1w, tp2)
        if ((skipped2 eq tp2) || !Config.fastPathForRefinedSubtype) {
          val name2 = tp2.refinedName
          val normalPath =
            isSubType(tp1, tp2.parent) &&
              (  name2 == nme.WILDCARD
              || hasMatchingMember(name2, tp1, tp2)
              || fourthTry(tp1, tp2)
              )
          normalPath ||
            needsEtaLift(tp1, tp2) && tp1.testLifted(tp2.typeParams, isSubType(_, tp2))
        }
        else // fast path, in particular for refinements resulting from parameterization.
          isSubType(tp1, skipped2) &&
          isSubRefinements(tp1w.asInstanceOf[RefinedType], tp2, skipped2)
      }
      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, _) => isSubType(tp1.resultType, restpe2)
        case _ => isSubType(tp1.widenExpr, restpe2)
      }
      compareExpr
    case tp2 @ TypeBounds(lo2, hi2) =>
      def compareTypeBounds = tp1 match {
        case tp1 @ TypeBounds(lo1, hi1) =>
          (tp2.variance > 0 && tp1.variance >= 0 || (lo2 eq NothingType) || isSubType(lo2, lo1)) &&
          (tp2.variance < 0 && tp1.variance <= 0 || (hi2 eq AnyType) || isSubType(hi1, hi2))
        case tp1: ClassInfo =>
          val tt = tp1.typeRef
          isSubType(lo2, tt) && isSubType(tt, hi2)
        case _ =>
          false
      }
      compareTypeBounds
    case ClassInfo(pre2, cls2, _, _, _) =>
      def compareClassInfo = tp1 match {
        case ClassInfo(pre1, cls1, _, _, _) =>
          (cls1 eq cls2) && isSubType(pre1, pre2)
        case _ =>
          false
      }
      compareClassInfo
    case _ =>
      fourthTry(tp1, tp2)
  }

  private def fourthTry(tp1: Type, tp2: Type): Boolean = tp1 match {
    case tp1: TypeRef =>
      tp1.info match {
        case TypeBounds(_, hi1) =>
          def compareGADT = {
            val gbounds1 = ctx.gadt.bounds(tp1.symbol)
            (gbounds1 != null) &&
              (isSubTypeWhenFrozen(gbounds1.hi, tp2) ||
               narrowGADTBounds(tp1, tp2, isUpper = true))
          }
          isSubType(hi1, tp2) || compareGADT
        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 =>
      /** if `tp2 == p.type` and `p: q.type` then try `tp1 <:< q.type` as a last effort.*/
      def comparePaths = tp2 match {
        case tp2: TermRef =>
          tp2.info match {
            case tp2i: TermRef =>
              isSubType(tp1, tp2i)
            case ExprType(tp2i: TermRef) if (ctx.phase.id > ctx.gettersPhase.id) =>
              // After getters, val x: T becomes def x: T
              isSubType(tp1, tp2i)
            case _ =>
              false
          }
        case _ =>
          false
      }
      isNewSubType(tp1.underlying.widenExpr, tp2) || comparePaths
    case tp1: RefinedType =>
       isNewSubType(tp1.parent, tp2) ||
         needsEtaLift(tp2, tp1) && tp2.testLifted(tp1.typeParams, isSubType(tp1, _))
    case AndType(tp11, tp12) =>
      eitherIsSubType(tp11, tp2, tp12, tp2)
    case JavaArrayType(elem1) =>
      def compareJavaArray = tp2 match {
        case JavaArrayType(elem2) => isSubType(elem1, elem2)
        case _ => tp2 isRef ObjectClass
      }
      compareJavaArray 
    case _ =>
      false
  }

  /** If `projection` is of the form T # Apply where `T` is an instance of a Lambda class,
   *  and `other` is not a type lambda projection, then convert `other` to a type lambda `U`, and
   *  continue with `T <:< U` if `inOrder` is true and `U <:< T` otherwise.
   */
  def compareHK(projection: NamedType, other: Type, inOrder: Boolean) =
    projection.name == tpnme.Apply && {
      val lambda = projection.prefix.LambdaClass(forcing = true)
      lambda.exists && !other.isLambda &&
        other.testLifted(lambda.typeParams,
          if (inOrder) isSubType(projection.prefix, _) else isSubType(_, projection.prefix))
    }

  /** 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.
   */
  private def eitherIsSubType(tp11: Type, tp21: Type, tp12: Type, tp22: Type) = {
    val preConstraint = constraint
    isSubType(tp11, tp21) && {
      val leftConstraint = constraint
      constraint = preConstraint
      if (isSubType(tp12, tp22) && !subsumes(leftConstraint, constraint, preConstraint))
        constraint = leftConstraint
      true
    } || isSubType(tp12, tp22)
  }

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

  /** Does type `tp1` have a member with name `name` whose normalized type is a subtype of 
   *  the normalized type of the refinement `tp2`?
   *  Normalization is as follows: If `tp2` contains a skolem to its refinement type,
   *  rebase both itself and the member info of `tp` on a freshly created skolem type.
   */
  protected def hasMatchingMember(name: Name, tp1: Type, tp2: RefinedType): Boolean = {
    val saved = skolemsOutstanding
    try {
      val rebindNeeded = tp2.refinementRefersToThis
      val base = if (rebindNeeded) ensureStableSingleton(tp1) else tp1
      val rinfo2 = if (rebindNeeded) tp2.refinedInfo.substSkolem(tp2, base) else tp2.refinedInfo
      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
      }
      /*>|>*/ ctx.traceIndented(i"hasMatchingMember($base . $name :? ${tp2.refinedInfo}) ${base.member(name).info.show} $rinfo2", subtyping) /*<|<*/ {
        memberMatches(base member name) ||
        tp1.isInstanceOf[SingletonType] &&
        { // special case for situations like:
          //    class C { type T }
          //    val foo: C
          //    foo.type <: C { type T = foo.T }
          rinfo2 match {
            case rinfo2: TypeAlias => (base select name) =:= rinfo2.alias
            case _ => false
          }
        }
      }
    }
    finally skolemsOutstanding = saved
  }

  /** Skip refinements in `tp2` which match corresponding refinements in `tp1`.
   *  "Match" means: 
   *   - they appear in the same order, 
   *   - they refine the same names, 
   *   - the refinement in `tp1` is an alias type, and 
   *   - neither refinement refers back to the refined type via a refined this.
   *  @return  The parent type of `tp2` after skipping the matching refinements.
   */
  private def skipMatching(tp1: Type, tp2: RefinedType): Type = tp1 match {
    case tp1 @ RefinedType(parent1, name1)
    if name1 == tp2.refinedName && 
       tp1.refinedInfo.isInstanceOf[TypeAlias] &&
       !tp2.refinementRefersToThis &&
       !tp1.refinementRefersToThis =>
      tp2.parent match {
        case parent2: RefinedType => skipMatching(parent1, parent2)
        case parent2 => parent2
      }
    case _ => tp2
  }

  /** Are refinements in `tp1` pairwise subtypes of the refinements of `tp2`
   *  up to parent type `limit`?
   *  @pre `tp1` has the necessary number of refinements, they are type aliases,
   *       and their names match the corresponding refinements in `tp2`.
   *       Further, no refinement refers back to the refined type via a refined this.
   *  The precondition is established by `skipMatching`.
   */
  private def isSubRefinements(tp1: RefinedType, tp2: RefinedType, limit: Type): Boolean =
    isSubType(tp1.refinedInfo, tp2.refinedInfo) && (
      (tp2.parent eq limit) ||
      isSubRefinements(
        tp1.parent.asInstanceOf[RefinedType], tp2.parent.asInstanceOf[RefinedType], limit))

  /** 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
  }

  /** Defer constraining type variables when compared against prototypes */
  def isMatchedByProto(proto: ProtoType, tp: Type) = tp.stripTypeVar match {
    case tp: PolyParam if 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.
   */
  private def isCappable(tp: Type): Boolean = tp match {
    case tp: PolyParam => 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`? */
  private 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
    //})
  }

  /** Narrow gadt.bounds for the type parameter referenced by `tr` to include
   *  `bound` as an upper or lower bound (which depends on `isUpper`).
   *  Test that the resulting bounds are still satisfiable.
   */
  private def narrowGADTBounds(tr: NamedType, bound: Type, isUpper: Boolean): Boolean =
    ctx.mode.is(Mode.GADTflexible) && {
    val tparam = tr.symbol
    val bound1 = deSkolemize(bound, toSuper = !isUpper)
    typr.println(s"narrow gadt bound of $tparam: ${tparam.info} from ${if (isUpper) "above" else "below"} to $bound1 ${bound1.isRef(tparam)}")
    !bound1.isRef(tparam) && {
      val oldBounds = ctx.gadt.bounds(tparam)
      val newBounds =
        if (isUpper) TypeBounds(oldBounds.lo, oldBounds.hi & bound1)
        else TypeBounds(oldBounds.lo | bound1, oldBounds.hi)
      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 tp2: ClassInfo if tp1 contains tp2.typeRef => 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 tp2: TypeBounds if tp2 contains tp1.typeRef => tp1
        case _ => andConflict(tp1, tp2)
      }
    case tp1 @ MethodType(names1, formals1) =>
      tp2 match {
        case tp2 @ MethodType(names2, formals2)
        if Config.newMatch && tp1.signature.sameParams(tp2.signature) &&
           tp1.isImplicit == tp2.isImplicit =>
          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 tp2: ClassInfo if tp1 contains tp2.typeRef => tp1
        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 tp2: TypeBounds if tp2 contains tp1.typeRef => tp2
        case _ => orConflict(tp1, tp2)
      }
    case tp1 @ MethodType(names1, formals1) =>
      tp2 match {
        case tp2 @ MethodType(names2, formals2)
        if Config.newMatch && tp1.signature.sameParams(tp2.signature) &&
           tp1.isImplicit == tp2.isImplicit =>
          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
  }

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

  // ----------- Diagnostics --------------------------------------------------
  
  /** A hook for showing subtype traces. Overridden in ExplainingTypeComparer */
  def traceIndented[T](str: String)(op: => T): T = op
    
  private def traceInfo(tp1: Type, tp2: Type) =
    s"${tp1.show} <:< ${tp2.show}" + {
      if (ctx.settings.verbose.value || Config.verboseExplainSubtype) {
        s" ${tp1.getClass}, ${tp2.getClass}" + 
        (if (frozenConstraint) " frozen" else "") + 
        (if (ctx.mode is Mode.TypevarsMissContext) " tvars-miss-ctx" else "")
      }
      else ""
    }

  /** Show subtype goal that led to an assertion failure */
  def showGoal(tp1: Type, tp2: Type) = {
    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)
  }

  /** Record statistics about the total number of subtype checks
   *  and the number of "successful" subtype checks, i.e. checks
   *  that form part of a subtype derivation tree that's ultimately successful.
   */
  def recordStatistics(result: Boolean, prevSuccessCount: Int) = {
    // Stats.record(s"isSubType ${tp1.show} <:< ${tp2.show}")
    totalCount += 1
    if (result) successCount += 1 else successCount = prevSuccessCount
    if (recCount == 0) {
      Stats.record("successful subType", successCount)
      Stats.record("total subType", totalCount)
      successCount = 0
      totalCount = 0
    }
  }
}

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, tp1: Type, tp2: RefinedType): Boolean =
    traceIndented(s"hasMatchingMember(${show(tp1)} . $name, ${show(tp2.refinedInfo)}), member = ${show(tp1.member(name).info)}") {
      super.hasMatchingMember(name, tp1, 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() }
}