+- Signs in Generic Declaration in Scala
It's covariance and contravariance. https://en.wikipedia.org/wiki/Covariance_and_contravariance_(computer_science)
Basically it says for Generic types how inheritance will work.
Easy sample from Scala is - trait Seq[+A]
Because of the + , the code
val s: Seq[Person] = Seq[Student]()
will compile because Student extends Person. Without the + it won't work
A bit more complex sample -
class C[-A, +B] {
def foo(param: A): B = ???
}
class Person(val name: String)
class Student(name: String, val university: String) extends Person(name)
val sample: C[Student, Person] = new C[Person, Student]
"+" and "-" mean covariant and contravariant types respectively. In short, it means that:
PartialFunction[-A1, +B1]
<: PartialFunction[-A2, +B2]
only if A1 :> A2
and B1 <: B2
, where <:
is a subtyping relationship.
"-" usually applied for input parameters, "+" for output - in C# they even use respective keywords in
and out
. There is also some more primitive generic variance support in Java built up on existential types - actually you can do it using _ <: SomeType
(covariance) or abstract type members type T <: SomeType
in Scala as well.
Without modifiers PartialFunction[A1, B1]
would have no direct relationship to a PartialFunction[A2, B2]
(in other words, it would be invariant).
P.S. There are also some restrictions applied to such types, like covariant("+") type can't be in contravariant position (you can only return it from a method) and vice-versa. This is done in order to support Liskov Substitution Principle and naturally understandable by "in"/"out" interpretation.
Also, it worth noting that A => B
(syntax sugar for Function1
) itself is using co-/contra-variance:
trait Function1 [-T1, +R] extends AnyRef
As those functions can be extended through sub-typing which makes them theoretically partial as well (though it’s not how Scala treats these) - even technically “total” FunctionN in Scala could be extended, redefined, return null and so on.
To supplement the other answers, here is a link to the documentation for variances on the scala-lang site:
https://docs.scala-lang.org/tour/variances.html