This is a simple example:
object CoerciveCovariance {
trait Cov[+T]
def cast[A, B](v: Cov[A])(
implicit
ev: A <:< B
) = {
v: Cov[B]
}
}
It doesn't compile:
CoerciveCovariance.scala:11:5: Found: (v : xxx.CoerciveCovariance.Cov[A])
Required: xxx.CoerciveCovariance.Cov[B]
one error found
Is it very hard to make to compiler to figure out the missing coercive upcasting from Cov[A] to Cov[B]? Why is it not the default behaviour?
Because type inference and implicit resolution are different. <: and + belong to type inference, <:< belongs to implicit resolution.
They make impact to each other. Indeed, type inference makes impact to implicit resolution
trait TC[A]
implicit val int: TC[Int] = null
def foo[A](a: A)(implicit tc: TC[A]) = null
foo(1) // compiles
foo("a") // doesn't compile
Here firstly type A is inferred to be Int (or String) and then it's checked that there is an implicit for Int (and no implicit for String).
Similarly, implicit resolution makes impact to type inference
trait TC[A, B]
implicit val int: TC[Int, String] = null
def foo[A, B](a: A)(implicit tc: TC[A, B]): B = ???
val x = foo(1)
// checking the type
x: String // compiles
Here the type String was inferred from the type class having the only instance.
So type inference and implicit resolution make impact to each other but are different.
If A <: B then A <:< B
def test[A <: B, B] = implicitly[A <:< B] // compiles
but if A <:< B then not necessarily A <: B
def checkSubtype[A <: B, B] = null
def test[A, B](implicit ev: A <:< B) = checkSubtype[A, B] // doesn't compile
<: is checked by the compiler according to the spec https://scala-lang.org/files/archive/spec/2.13/03-types.html#conformance
<:< is just a type class
sealed abstract class <:<[-From, +To] extends (From => To) with Serializable
with the only instance
object <:< {
implicit def refl[A]: A =:= A = singleton.asInstanceOf[A =:= A] // the instance
}
sealed abstract class =:=[From, To] extends (From <:< To) with Serializable
So <:< doesn't have many properties of an order. By default there is no transitivity
def test[A, B, C](implicit ev: A <:< B, ev1: B <:< C) = implicitly[A <:< C] // doesn't compile
no antisymmetry
def test[A, B](implicit ev: A <:< B, ev1: B <:< A) = implicitly[A =:= B] // doesn't compile
no monotonicity
def test[A, B, F[+_]](implicit ev: A <:< B) = implicitly[F[A] <:< F[B]] // doesn't compile
Although starting from Scala 2.13 the following methods are defined in the standard library
sealed abstract class <:<[-From, +To] extends (From => To) with Serializable {
def andThen[C](r: To <:< C): From <:< C = {
type G[-T] = T <:< C
substituteContra[G](r)
}
def liftCo[F[+_]]: F[From] <:< F[To] = {
type G[+T] = F[From] <:< F[T]
substituteCo[G](implicitly[G[From]])
}
}
object <:< {
def antisymm[A, B](implicit l: A <:< B, r: B <:< A): A =:= B = singleton.asInstanceOf[A =:= B]
}
but they do not define implicits. So if you need these properties you can define transitivity
implicit def trans[A, B, C](implicit ev: A <:< B, ev1: B <:< C): A <:< C = ev.andThen(ev1)
def test[A, B, C](implicit ev: A <:< B, ev1: B <:< C) = implicitly[A <:< C] // compiles
Antisymmetry is trickier
implicit def antisym[A, B](implicit ev: A <:< B, ev1: B <:< A): (A =:= B) = <:<.antisymm[A, B]
def test[A, B](implicit ev2: A <:< B, ev3: B <:< A) = implicitly[A =:= B] // doesn't compile
If you resolve implicits manually ... = implicitly[A =:= B](antisym[A, B]), you'll see the reason (although implicitly[A =:= B](antisym[A, B](ev2, ev3)) works)
ambiguous implicit values:
both method antisym in object App of type [A, B](implicit ev: A <:< B, ev1: B <:< A): A =:= B
and value ev2 of type A <:< B
match expected type A <:< B
So you have to resolve this ambiguity prioritizing implicits. You can't decrease the priority of implicit parameter ev2. So you have to decrease the priority of antisym, which is your implicit in the current scope, you can't put it to the implicit scope (companion object etc.). The only way I found is with shapeless.LowPriority
implicit def antisym[A, B](implicit ev: A <:< B, ev1: B <:< A, lp: LowPriority): (A =:= B) = <:<.antisymm[A, B]
def test[A, B](implicit ev2: A <:< B, ev3: B <:< A) = implicitly[A =:= B] // compiles
Similarly you can define monotonicity
implicit def liftCo[A, B, F[+_]](implicit ev: A <:< B): F[A] <:< F[B] = ev.liftCo[F]
def test[A, B, F[+_]](implicit ev: A <:< B) = implicitly[F[A] <:< F[B]] // compiles
def test1[A, B](implicit ev: A <:< B) = implicitly[Cov[A] <:< Cov[B]] // compiles
But if you put all instances into the scope you'll have compile-time Stackoverflow
implicit def liftCo[A, B, F[+_]](implicit ev: A <:< B): F[A] <:< F[B] = ev.liftCo[F]
implicit def trans[A, B, C](implicit ev: A <:< B, ev1: B <:< C): A <:< C = ev.andThen(ev1)
implicit def antisym[A, B](implicit ev: A <:< B, ev1: B <:< A, lp: LowPriority): (A =:= B) = <:<.antisymm[A, B]
def test[A, B, F[+_]](implicit ev: A <:< B) = implicitly[F[A] <:< F[B]] // doesn't compile, Stackoverflow
So I guess you see why those methods are not defined as implicits by default. This would pollute the implicit scope.
More about the difference <: vs. <:< https://blog.bruchez.name/posts/generalized-type-constraints-in-scala/
Besides (compile-time) type class <:< there is also (runtime) method <:< from scala-reflect
import scala.language.experimental.macros
import scala.reflect.macros.blackbox
def checkSubtype[A, B]: Unit = macro checkSubtypeImpl[A, B]
def checkSubtypeImpl[A: c.WeakTypeTag, B: c.WeakTypeTag](c: blackbox.Context): c.Tree = {
import c.universe._
println(weakTypeOf[A] <:< weakTypeOf[B])
q"()"
}
type A <: B
type B
checkSubtype[A, B] // scalac: true // scalacOptions += "-Ymacro-debug-lite"
type A
type B
checkSubtype[A, B] // scalac: false
Scala 2.13.10.
Ensure arguments to generic method have same type in trait method
What is the implicit resolution chain of `<:<`
Type parameter under self-type doesn't conform to upper bound despite evidence