<:< operator in scala

Can anybody provide some details on <:< operator in scala. I think:

if(apple <:< fruit)  //checks if apple is a subcl开发者_如何学Pythonass of fruit.

Are there any other explanations? I see many definitions in the scala source file.

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The <:< type is defined in Predef.scala along with the related types =:= and <%< as follows:

// used, for example, in the encoding of generalized constraints
// we need a new type constructor `<:<` and evidence `conforms`, as 
// reusing `Function2` and `identity` leads to ambiguities (any2stringadd is inferred)
// to constrain any abstract type T that's in scope in a method's argument list (not just the method's own type parameters)
// simply add an implicit argument of type `T <:< U`, where U is the required upper bound (for lower-bounds, use: `U <: T`)
// in part contributed by Jason Zaugg
sealed abstract class <:<[-From, +To] extends (From => To)
implicit def conforms[A]: A <:< A = new (A <:< A) {def apply(x: A) = x} // not in the <:< companion object because it is also intended to subsume identity (which is no longer implicit)

This uses the Scala feature that a generic type op[T1, T2] can be written T1 op T2. This can be used, as noted by aioobe, to provide an evidence parameter for methods that only apply to some instances of a generic type (the example given is the toMap method that can only be used on a Traversable of Tuple2). As noted in the comment, this generalizes a normal generic type constraint to allow it to refer to any in-scope abstract type/type parameter. Using this (implicit ev : T1 <:< T2) has the advantage over simply using an evidence parameter like (implicit ev: T1 => T2) in that the latter can lead to unintended in-scope implicit values being used for the conversion.

I'm sure I'd seen some discussion on this on one of the Scala mailing lists, but can't find it at the moment.

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<:< is not an operator - it is an identifier and is therefore one of:

• the name of a type (class, trait, type alias etc)
• the name of a method/val or var

In this case, <:< appears twice in the library, once in Predef as a class and once as a method on Manifest.

For the method on Manifest, it checks whether the type represented by this manifest is a subtype of that represented by the manifest argument.

For the type in Predef, this is relatively new and I am also slightly confused about it because it seems to be part of a triumvirate of identical declarations!

class <%<[-From, +To] extends (From) ⇒ To
class <:<[-From, +To] extends (From) ⇒ To
class =:=[From, To] extends (From) ⇒ To

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I asked around, and this is the explanation I got:

<:< is typically used as an evidence parameter. For example in TraversableOnce, toMap is declared as def toMap[T, U](implicit ev: A <:< (T, U)): immutable.Map[T, U]. This expresses the constraint that the toMap method only works if the traversable contains 2-tuples. flatten is another example. <:< is used to express the constraint that you can only flatten a traversable of traversables.

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Actually, it checks if the class represented by the Manifest apple is a subclass of the class represented by the manifest fruit.

For instance:

manifest[java.util.List[String]] <:< manifest[java.util.ArrayList[String]] == false
manifest[java.util.ArrayList[String]] <:< manifest[java.util.List[String]] == true

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Copy from scala.Predef.scala:

// Type Constraints --------------------------------------------------------------

  // used, for example, in the encoding of generalized constraints
  // we need a new type constructor `<:<` and evidence `conforms`, as 
  // reusing `Function2` and `identity` leads to ambiguities (any2stringadd is inferred)
  // to constrain any abstract type T that's in scope in a method's argument list (not just the method's own type parameters)
  // simply add an implicit argument of type `T <:< U`, where U is the required upper bound (for lower-bounds, use: `U <: T`)
  // in part contributed by Jason Zaugg
  sealed abstract class <:<[-From, +To] extends (From => To)
  implicit def conforms[A]: A <:< A = new (A <:< A) {def apply(x: A) = x}

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To better understand the implementation.

sealed abstract class <:<[-From, +To] extends (From => To)
implicit def conforms[A]: A <:< A = new (A <:< A) {def apply(x: A) = x}

I tried to devise a simpler implementation. The following did not work.

sealed class <:<[-From <: To, +To]
implicit def conforms[A <: B, B]: A <:< B = new (A <:< B)

At least because it won't type check in all valid use cases.

case class L[+A]( elem: A )
{
   def contains[B](x: B)(implicit ev: A <:< B) = elem == x
}

error: type arguments [A,B] do not conform to class <:<'s
       type parameter bounds [-From <: To,+To]
def contains[B](x: B)(implicit ev: A <:< B) = elem == x
                                     ^

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Hmm... I can't seem to find "<:<" anywhere as well, but "<:" denotes subtyping. From http://jim-mcbeath.blogspot.com/2008/09/scala-syntax-primer.html#types :

List[T] forSome { type T <: Component }

In the above example, we are saying T is some type which is a subtype of Component.

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From the sources we have the following explanation:

  /**
   * An instance of `A <:< B` witnesses that `A` is a subtype of `B`.
   * Requiring an implicit argument of the type `A <:< B` encodes
   * the generalized constraint `A <: B`.
   *
   * @note we need a new type constructor `<:<` and evidence `conforms`,
   * as reusing `Function1` and `identity` leads to ambiguities in
   * case of type errors (`any2stringadd` is inferred)
   *
   * To constrain any abstract type T that's in scope in a method's
   * argument list (not just the method's own type parameters) simply
   * add an implicit argument of type `T <:< U`, where `U` is the required
   * upper bound; or for lower-bounds, use: `L <:< T`, where `L` is the
   * required lower bound.
   *
   * In part contributed by Jason Zaugg.
   */
  @implicitNotFound(msg = "Cannot prove that ${From} <:< ${To}.")
  sealed abstract class <:<[-From, +To] extends (From => To) with Serializable
  private[this] final val singleton_<:< = new <:<[Any,Any] { def apply(x: Any): Any = x }
  // The dollar prefix is to dodge accidental shadowing of this method
  // by a user-defined method of the same name (SI-7788).
  // The collections rely on this method.
  implicit def $conforms[A]: A <:< A = singleton_<:<.asInstanceOf[A <:< A]

  @deprecated("Use `implicitly[T <:< U]` or `identity` instead.", "2.11.0")
  def conforms[A]: A <:< A = $conforms[A]

  /** An instance of `A =:= B` witnesses that the types `A` and `B` are equal.
   *
   * @see `<:<` for expressing subtyping constraints
   */
  @implicitNotFound(msg = "Cannot prove that ${From} =:= ${To}.")
  sealed abstract class =:=[From, To] extends (From => To) with Serializable
  private[this] final val singleton_=:= = new =:=[Any,Any] { def apply(x: Any): Any = x }
  object =:= {
     implicit def tpEquals[A]: A =:= A = singleton_=:=.asInstanceOf[A =:= A]
  }