Appromiximate union types by intersections.

Appromiximate union types by intersections of their common base classes. Controlled by option -Xkeep-unions.
If option is set, no approximation is done.

Motivations for approximating: There are two. First, union types are departure from Scala 2. From time to
time they lead to failure of inference. One example experiences in Dotty was in a foldLeft, where the accumulator
type was inferred to be Tree before and was now a union of two tree specific kinds. Tree was the correct type, whereas
the union type was too specific. These failures are not common (in the Dotty codebase there were 3, I believe), but
they cause considerable difficulty to diagnose. So it seems safer to have a compatibility mode with Scala 2.
The second motivation is that union types can become large and unwieldy. A function like TreeCopier has a result
type consisting of ~ 40 alternatives, where the alternative type would be just Tree.

Once we gain more experience with union types, we might consider flipping the option, and making union types the
default. But for now it is safer this way, I believe.

Author: odersky

src/dotty/tools/dotc/core/TypeOps.scala

@@ -77,6 +77,37 @@ trait TypeOps { this: Context =>
     def apply(tp: Type) = simplify(tp, this)
   }
 
+  /** Approximate union type by intersection of its dominators.
+   *  See Type#approximateUnion for an explanation.
+   */
+  def approximateUnion(tp: Type): Type = {
+    /** a faster version of cs1 intersect cs2 */
+    def intersect(cs1: List[ClassSymbol], cs2: List[ClassSymbol]): List[ClassSymbol] = {
+      val cs2AsSet = new util.HashSet[ClassSymbol](100)
+      cs2.foreach(cs2AsSet.addEntry)
+      cs1.filter(cs2AsSet.contains)
+    }
+    /** The minimal set of classes in `cs` which derive all other classes in `cs` */
+    def dominators(cs: List[ClassSymbol], accu: List[ClassSymbol]): List[ClassSymbol] = (cs: @unchecked) match {
+      case c :: rest =>
+        val accu1 = if (accu exists (_ derivesFrom c)) accu else c :: accu
+        if (cs == c.baseClasses) accu1 else dominators(rest, accu1)
+    }
+    if (ctx.featureEnabled(defn.LanguageModuleClass, nme.keepUnions)) tp
+    else tp match {
+      case tp: OrType =>
+        val commonBaseClasses = tp.mapReduceOr(_.baseClasses)(intersect)
+        val doms = dominators(commonBaseClasses, Nil)
+        doms.map(tp.baseTypeWithArgs).reduceLeft(AndType.apply)
+      case tp @ AndType(tp1, tp2) =>
+        tp derived_& (approximateUnion(tp1), approximateUnion(tp2))
+      case tp: RefinedType =>
+        tp.derivedRefinedType(approximateUnion(tp.parent), tp.refinedName, tp.refinedInfo)
+      case _ =>
+        tp
+    }
+  }
+
   /** A type is volatile if its DNF contains an alternative of the form
    *  {P1, ..., Pn}, {N1, ..., Nk}, where the Pi are parent typerefs and the
    *  Nj are refinement names, and one the 4 following conditions is met:

src/dotty/tools/dotc/core/Types.scala

@@ -845,6 +845,19 @@ object Types {
      */
     def simplified(implicit ctx: Context) = ctx.simplify(this, null)
 
+    /** Approximations of union types: We replace a union type Tn | ... | Tn
+     *  by the smallest intersection type of baseclass instances of T1,...,Tn.
+     *  Example: Given
+     *
+     *      trait C[+T]
+     *      trait D
+     *      class A extends C[A] with D
+     *      class B extends C[B] with D with E
+     *
+     *  we approximate `A | B` by `C[A | B] with D`
+     */
+    def approximateUnion(implicit ctx: Context) = ctx.approximateUnion(this)
+
     /** customized hash code of this type.
      *  NotCached for uncached types. Cached types
      *  compute hash and use it as the type's hashCode.
@@ -1355,6 +1368,10 @@ object Types {
       if ((tp1 eq this.tp1) && (tp2 eq this.tp2)) this
       else AndType.make(tp1, tp2)
 
+    def derived_& (tp1: Type, tp2: Type)(implicit ctx: Context): Type =
+      if ((tp1 eq this.tp1) && (tp2 eq this.tp2)) this
+      else tp1 & tp2
+
     def derivedAndOrType(tp1: Type, tp2: Type)(implicit ctx: Context): Type =
       derivedAndType(tp1, tp2)
 
@@ -1735,10 +1752,38 @@ object Types {
         case OrType(tp1, tp2) => isSingleton(tp1) & isSingleton(tp2)
         case _ => false
       }
+      def isFullyDefined(tp: Type): Boolean = tp match {
+        case tp: TypeVar => tp.isInstantiated && isFullyDefined(tp.instanceOpt)
+        case tp: TypeProxy => isFullyDefined(tp.underlying)
+        case tp: AndOrType => isFullyDefined(tp.tp1) && isFullyDefined(tp.tp2)
+        case _ => true
+      }
+      def isOrType(tp: Type): Boolean = tp.stripTypeVar.dealias match {
+        case tp: OrType => true
+        case AndType(tp1, tp2) => isOrType(tp1) | isOrType(tp2)
+        case RefinedType(parent, _) => isOrType(parent)
+        case WildcardType(bounds: TypeBounds) => isOrType(bounds.hi)
+        case _ => false
+      }
+
+      // First, solve the constraint.
       var inst = ctx.typeComparer.approximation(origin, fromBelow)
+
+      // Then, approximate by (1.) and (2.) and simplify as follows.
+      // 1. If instance is from below and is a singleton type, yet
+      // upper bound is not a singleton type, widen the instance.
       if (fromBelow && isSingleton(inst) && !isSingleton(upperBound))
         inst = inst.widen
-      instantiateWith(inst.simplified)
+        
+      inst = inst.simplified
+
+      // 2. If instance is from below and is a fully-defined union type, yet upper bound
+      // is not a union type, approximate the union type from above by an intersection
+      // of all common base types.
+      if (fromBelow && isOrType(inst) && isFullyDefined(inst) && !isOrType(upperBound))
+        inst = inst.approximateUnion
+        
+      instantiateWith(inst)
     }
 
     /** Unwrap to instance (if instantiated) or origin (if not), until result

src/dotty/tools/dotc/typer/Namer.scala

@@ -576,7 +576,7 @@ class Namer { typer: Typer =>
         // println(s"final inherited for $sym: ${inherited.toString}") !!!
         // println(s"owner = ${sym.owner}, decls = ${sym.owner.info.decls.show}")
         val rhsCtx = ctx.fresh addMode Mode.InferringReturnType
-        def rhsType = typedAheadExpr(mdef.rhs, rhsProto)(rhsCtx).tpe.widen
+        def rhsType = typedAheadExpr(mdef.rhs, rhsProto)(rhsCtx).tpe.widen.approximateUnion
         def lhsType = fullyDefinedType(rhsType, "right-hand side", mdef.pos)
         inherited orElse lhsType
       }

test/dotc/tests.scala

@@ -43,6 +43,7 @@ class tests extends CompilerTest {
   @Test def pos_structural() = compileFile(posDir, "structural", twice)
   @Test def pos_i39 = compileFile(posDir, "i39", twice)
   @Test def pos_overloadedAccess = compileFile(posDir, "overloadedAccess", twice)
+  @Test def pos_approximateUnion = compileFile(posDir, "approximateUnion", twice)
 */
   @Test def pos_all = compileFiles(posDir, twice)
 

tests/pos/approximateUnion.scala

@@ -0,0 +1,96 @@
+object approximateUnion {
+
+  trait C[+T]
+  trait D
+  trait E
+  trait X[-T]
+
+  {
+    trait A extends C[A] with D
+    trait B extends C[B] with D
+
+    val coin = true
+    val x = if (coin) new A else new B
+    val y = Some(if (coin) new A else new B)
+
+    val xtest: C[A | B] & D = x
+    val ytest: Some[C[A | B] & D] = y
+  }
+
+  {
+    trait A extends C[X[A]] with D
+    trait B extends C[X[B]] with D with E
+
+    val coin = true
+    val x = if (coin) new A else new B
+    val y = Some(if (coin) new A else new B)
+
+    val xtest: C[X[A & B]] & D = x
+    val ytest: Some[C[X[A & B]] & D] = y
+  }
+}
+
+object approximateUnion2 {
+
+  trait C[T]
+  trait D
+  trait E
+  trait X[-T]
+
+  {
+    trait A extends C[A] with D
+    trait B extends C[B] with D
+
+    val coin = true
+    val x = if (coin) new A else new B
+    val y = Some(if (coin) new A else new B)
+
+    val xtest: C[_ >: A & B <: A | B] & D = x
+    val ytest: Some[C[_ >: A & B <: A | B] & D] = y
+  }
+
+  {
+    trait A extends C[X[A]] with D
+    trait B extends C[X[B]] with D with E
+
+    val coin = true
+    val x = if (coin) new A else new B
+    val y = Some(if (coin) new A else new B)
+
+    val xtest: C[_ >: X[A | B] <: X[A & B]] & D = x
+    val ytest: Some[C[_ >: X[A | B] <: X[A & B]]] = y
+  }
+}
+
+object approximateUnion3 {
+
+  trait C[-T]
+  trait D
+  trait E
+  trait X[-T]
+
+  {
+    trait A extends C[A] with D
+    trait B extends C[B] with D
+
+    val coin = true
+    val x = if (coin) new A else new B
+    val y = Some(if (coin) new A else new B)
+
+    val xtest: C[A & B] & D = x
+    val ytest: Some[C[A & B] & D] = y
+  }
+
+  {
+    trait A extends C[X[A]] with D
+    trait B extends C[X[B]] with D with E
+
+    val coin = true
+    val x = if (coin) new A else new B
+    val y = Some(if (coin) new A else new B)
+
+    val xtest: C[X[A | B]] & D = x
+    val ytest2: Some[C[X[A | B]] & D] = y
+  }
+}
+