Understanding of Upperbound and Lowerbound in Scala - scala

I have this scala code:
class Creature {
override def toString = "I exist"
}
class Person(val name: String) extends Creature {
override def toString = name
}
class Employee(override val name: String) extends Person(name) {
override def toString = name
}
class Test[T](val x: T = null) {
def upperBound[U <: T](v: U): Test[U] = {
new Test[U](v)
}
def lowerBound[U >: T](v: U): Test[U] = {
new Test[U](v)
}
}
We can see the hierarchy relationship between Creature, Person, and Employee:
Creature <- Person <- Employee
In the def main:
val test = new Test[Person]()
val ub = test.upperBound(new Employee("John Derp")) //#1 ok because Employee is subtype of Person
val lb = test.lowerBound(new Creature()) //#2 ok because Creature is supertype of Person
val ub2 = test.upperBound(new Creature()) //#3 error because Creature is not subtype of Person
val lb2 = test.lowerBound(new Employee("Scala Jo")) //#4 ok? how could? as Employee is not supertype of Person
What can I understand is:
A <: B define A must be subtype or equal to B (upper bound)
A >: B define A must be supertype or equal to B (lower bound)
But what happened to #4 ? Why there is no error? As the Employee is not supertype of Person, I expect it shouldn't conform to the bound type parameter [U >: T].
Anyone can explain?

This example may help
scala> test.lowerBound(new Employee("Scala Jo"))
res9: Test[Person] = Test#1ba319a7
scala> test.lowerBound[Employee](new Employee("Scala Jo"))
<console>:21: error: type arguments [Employee] do not conform to method lowerBound's type parameter bounds [U >: Person]
test.lowerBound[Employee](new Employee("Scala Jo"))
^
In general, it's connected to the Liskov Substitution Principle - you can use subtype anywhere instead of supertype (or "subtype can always be casted to its supertype"), so type inference trying to infer as nearest supertype as it can (like Person here).
So, for ub2 there is no such intersection between [Nothing..Person] and [Creature..Any], but for lb2 there is one between [Person..Any] and [Employee..Any] - and that's the Person. So, you should specify type explicitly (force Employee instead of [Employee..Any]) to avoid type inference here.
The example where lb2 expectedly failing even with type inference:
scala> def aaa[T, A >: T](a: A)(t: T, a2: A) = t
aaa: [T, A >: T](a: A)(t: T, a2: A)T
scala> aaa(new Employee(""))(new Person(""), new Employee(""))
<console>:19: error: type arguments [Person,Employee] do not conform to method aaa's type parameter bounds [T,A >: T]
aaa(new Employee(""))(new Person(""), new Employee(""))
^
Here type A is inferred inside first parameter list and fixated as Employee, so second parameter list (which throws an error) just have only choice - to use it as is.
Or most commonly used example with invariant O[T]:
scala> case class O[T](a: T)
defined class O
scala> def aaa[T, A >: T](t: T, a2: O[A]) = t
aaa: [T, A >: T](t: T, a2: O[A])T
scala> aaa(new Person(""), O(new Employee("")))
<console>:21: error: type mismatch;
found : O[Employee]
required: O[Person]
Note: Employee <: Person, but class O is invariant in type T.
You may wish to define T as +T instead. (SLS 4.5)
aaa(new Person(""), O(new Employee("")))
^
T is fixed to Employee here and it's not possible to cast O[Employee] to
O[Person] due to invariance by default.

I think it happens because you can pass any Person to your
Test[Person].lowerBound(Person)
and as Employee is a subclass of Person it is considered as Person which is legal here.

Related

aliasing proper type as existential type (why it compiles?)

Why can I do the following:
class A
type M[_] = A
I would expect I can only alias type that expects one type parameter, for example a List[_], but it works also with plain classes.
If I create a method:
def foo(m: M[_]) = m
and call it with wrong parameter:
scala> foo("a")
<console>:15: error: type mismatch;
found : String("a")
required: M[_]
(which expands to) A[]
foo("a")
I get such error. What is the meaning of A[]?
Going further, how to explain this:
scala> type M[_, _] = A
<console>:12: error: _ is already defined as type _
type M[_, _] = A
Is there a way to assure that what I put on the right hand side of my alias will be a parametrized type?
type M[_] = A is the same as type M[X] = A: a constant function on types. M[X] is A whatever X is: M[Int] is A, M[String] is A, M[Any] is A, etc. _ in this case is just an identifier (which explains the error for type M[_, _] as well).
Of course, in def foo(m: M[_]) = m, M[_] is an existential type: M[T] forSome { type T }. I don't know why Scala says it expands to A[] in the error message, though; this may be a bug. You can check it's the same type as A by calling
scala> implicitly[M[_] =:= A]
res0: =:=[A[],A] = <function1>
Is there a way to assure that what I put on the right hand side of my alias will be a parametrized type?
You can declare an abstract member type with higher-kind
trait Foo { type M[_] }
and it can only be implemented by parametrized types:
class Bar1 extends Foo { type M = Int } // fails
class Bar2 extends Foo { type M[X] = List[X] } // works
Of course, as mentioned in the first paragraph, M in type M[X] = Int is parametrized, and I don't think there is a way to rule it out.

Scala covariance and lower bound i dont get it

I am currently learning scala and i am confused about the variance annotations especially the covariance and contravariance.
So i did some research an came upon following example
class Box[+T] {
def put[U >: T](x: U): List[U] = {
List(x)
}
}
class Animal {
}
class Cat extends Animal {
}
class Dog extends Animal {
}
var sb: Box[Animal] = new Box[Cat];
So this says class Box is covariant in T whiche means Box[Cat] is a subclass of Box[Animal] since Cat is a subclass of Animal. Sofar i understand this. But when it comes to method parameters my understanding ends. The spec says methods parameters can not be covariant so we have to use this lower bound annotation.
Lets look at the method definiton
def put[U >: T](x: U): List[U] = {
List(x)
}
So [U >: T] says that U must be a superclass of T
Trying following code
var sb: Box[Animal] = new Box[Cat];
sb.put(new Cat);
Works as expected but this drives me nuts
var sb: Box[Animal] = new Box[Cat];
sb.put(1);
It logically makes no sense to me to put an INT into a Box of Animals alltough its correct since INT will be resolved to Any which is a superclass of Animal.
So my question is
How do i have to adapt the code that the put method accepts only subtypes of
animal? I can not use the upper bound annotation
class Box[+T] {
def put[U <: T](x: U): List[U] = {
List(x)
}
}
since i get this well known error
covariant type T occurs in contravariant position in type
You can add both a lower and an upper bound:
class Box[+T] { def put[U >: T <: Animal](x: U): List[U] = List(x) }
But this is not what you want, since you wire the definition of Box to Animal and logically there is no reason to add such an upper bound.
You say:
It logically makes no sense to me to put an INT into a Box of Animals alltough its correct since INT will be resolved to Any which is a superclass of Animal.
You don't put an Int into a Box[Animal], the existing box is immutable (and it is not possible to make it mutable, since the definition of covariance doesn't allow it). Instead you get a box (or in case of your put method) of a new type. If your goal is to get only a List[Anmial], then you just have to specify that:
scala> class Box[+T] { def put[U >: T](x: U): List[U] = List(x) }
defined class Box
scala> var b: Box[Animal] = new Box[Cat]
b: Box[Animal] = Box#23041911
scala> val xs: List[Animal] = b put new Dog
xs: List[Animal] = List(Dog#f8d6ec4)
scala> val xs: List[Animal] = b put 1
<console>:14: error: type mismatch;
found : Int(1)
required: Animal
val xs: List[Animal] = b put 1
^
scala> val xs = b put 1 // this will result in a List[Any]
xs: List[Any] = List(1)
There is no need to complicate the definition of the put method.
For a more in depth explanation about why co- and contravariance is needed see this question.

what's different between <:< and <: in scala

I already know that:
<: is the Scala syntax type constraint
while <:< is the type that leverage the Scala implicit to reach the type constrait
for example:
object Test {
// the function foo and bar can have the same effect
def foo[A](i:A)(implicit ev : A <:< java.io.Serializable) = i
foo(1) // compile error
foo("hi")
def bar[A <: java.io.Serializable](i:A) = i
bar(1) // compile error
bar("hi")
}
but I want to know when we need to use <: and <:< ?
and if we already have <:, why we need <:< ?
thanks!
The main difference between the two is, that the <: is a constraint on the type, while the <:< is a type for which the compiler has to find evidence, when used as an implicit parameter. What that means for our program is, that in the <: case, the type inferencer will try to find a type that satisfies this constraint. E.g.
def foo[A, B <: A](a: A, b: B) = (a,b)
scala> foo(1, List(1,2,3))
res1: (Any, List[Int]) = (1,List(1, 2, 3))
Here the inferencer finds that Int and List[Int] have the common super type Any, so it infers that for A to satisfy B <: A.
<:< is more restrictive, because the type inferencer runs before the implicit resolution. So the types are already fixed when the compiler tries to find the evidence. E.g.
def bar[A,B](a: A, b: B)(implicit ev: B <:< A) = (a,b)
scala> bar(1,1)
res2: (Int, Int) = (1,1)
scala> bar(1,List(1,2,3))
<console>:9: error: Cannot prove that List[Int] <:< Int.
bar(1,List(1,2,3))
^
1. def bar[A <: java.io.Serializable](i:A) = i
<: - guarantees that instance of i of type parameter A will be subtype of Serializable
2. def foo[A](i:A)(implicit ev : A <:< java.io.Serializable) = i
<:< - guarantees that execution context will contains implicit value (for ev paramenter) of type A what is subtype of Serializable.
This implicit defined in Predef.scala and for foo method and it is prove if instance of type parameter A is subtype of Serializable:
implicit def conforms[A]: A <:< A = singleton_<:<.asInstanceOf[A <:< A]
fictional case of using <:< operator:
class Boo[A](x: A) {
def get: A = x
def div(implicit ev : A <:< Double) = x / 2
def inc(implicit ev : A <:< Int) = x + 1
}
val a = new Boo("hi")
a.get // - OK
a.div // - compile time error String not subtype of Double
a.inc // - compile tile error String not subtype of Int
val b = new Boo(10.0)
b.get // - OK
b.div // - OK
b.inc // - compile time error Double not subtype of Int
val c = new Boo(10)
c.get // - OK
c.div // - compile time error Int not subtype of Double
c.inc // - OK
if we not call methods what not conform <:< condition than all compile and execute.
There are definitely differences between <: and <:<; here is my attempt at explaining which one you should pick.
Let's take two classes:
trait U
class V extends U
The type constraint <: is always used because it drives type inference. That's the only thing it can do: constrain the type on its left-hand side.
The constrained type has to be referenced somewhere, usually in the parameter list (or return type), as in:
def whatever[A <: U](p: A): List[A] = ???
That way, the compiler will throw an error if the input is not a subclass of U, and at the same time allow you to refer to the input's type by name for later use (for example in the return type). Note that if you don't have that second requirement, all this isn't necessary (with exceptions...), as in:
def whatever(p: U): String = ??? // this will obviously only accept T <: U
The Generalized Type Constraint <:< on the other hand, has two uses:
You can use it as an after-the-fact proof that some type was inferred. As in:
class List[+A] {
def sum(implicit ev: A =:= Int) = ???
}
You can create such a list of any type, but sum can only be called when you have the proof that A is actually Int.
You can use the above 'proof' as a way to infer even more types. This allows you to infer types in two steps instead of one.
For example, in the above List class, you could add a flatten method:
def flatten[B](implicit ev: A <:< List[B]): List[B]
This isn't just a proof, this is a way to grab that inner type B with A now fixed.
This can be used within the same method as well: imagine you want to write a utility sort function, and you want both the element type T and the collection type Coll. You could be tempted to write the following:
def sort[T, Coll <: Seq[T]](l: Coll): Coll
But T isn't constrained to be anything in there: it doesn't appear in the arguments nor output type. So T will end up as Nothing, or Any, or whatever the compiler wants, really (usually Nothing). But with this version:
def sort[T, Coll](l: Coll)(implicit ev: Coll <:< Seq[T]): Coll
Now T appears in the parameter's types. There will be two inference runs (one per parameter list): Coll will be inferred to whatever was given, and then, later on, an implicit will be looked for, and if found, T will be inferred with Coll now fixed. This essentially extracts the type parameter T from the previously-inferred Coll.
So essentially, <:< checks (and potentially infers) types as a side-effect of implicit resolution, so it can be used in different places / at different times than type parameter inference. When they happen to do the same thing, stick to <:.
After some thinking, I think it has some different.
for example:
object TestAgain {
class Test[A](a: A) {
def foo[A <: AnyRef] = a
def bar(implicit ev: A <:< AnyRef) = a
}
val test = new Test(1)
test.foo // return 1
test.bar // error: Cannot prove that Int <:< AnyRef.
}
this menas:
the scope of <: is just in the method param generic tpye scope foo[A <: AnyRef]. In the example, the method foo have it's generic tpye A, but not the A in class Test[A]
the scope of <:< , will first find the method's generic type, but the method bar have no param generic type, so it will find the Test[A]'s generic type.
so, I think it's the main difference.

Types in Scala - lower bounds

on code below.
My expectation is that T must be a of type B or A, so call to lowerBound(new D) should probably not compile (?). Similar experiments with upperbound give me expected typecheck errors.
Thanks for giving the hint.
object varianceCheck {
class A {
override def toString = this.getClass.getCanonicalName
}
class B extends A
class C extends B
class D extends C
def lowerBound[T >: B](param: T) = { param }
println(lowerBound(new D)) //> varianceCheck.D
}
With your implementation you can write:
scala> def lowerBound[T >: B](param: T) = { param }
lowerBound: [T >: B](param: T)T
scala> lowerBound(new AnyRef {})
res0: AnyRef = $anon$1#2eef224
where AnyRef is a super type of all object/reference types (actually it is an alias for Java Object class). And this is right, T >: B expresses that the type parameter T or the abstract type T refer to a supertype of type B.
You just have a bad example with toString, cause this method has all object types, but if you change it to, let's say on someMethod, your lowerBound won't compile:
<console>:18: error: value someMethod is not a member of type parameter T
def lowerBound[T >: B](param: T) = { param.someMethod }
If you change this to T <: B, which means that parameter of type T is a subclass of B, than everything is good, cause this param has someMethod method:
def lowerBound[T <: B](param: T) = { param.someMethod }
Faced same question as well. Seems compiler doing great job to help us shoot our feets. If you extract result of the lowerBound you may notice that it is of type B
val b: B = lowerBound(new D)
println(b) //> varianceCheck.D
And then if you try though to request type D explicitly
lowerBound[D](new D)
you will see the compiler error that you expected:
Error:(12, 21) type arguments [D] do not conform to method lowerBound's type parameter bounds [T >: B]
lowerBound[D](new D)

How to infer the right type parameter from a projection type?

I have some troubles having Scala to infer the right type from a type projection.
Consider the following:
trait Foo {
type X
}
trait Bar extends Foo {
type X = String
}
def baz[F <: Foo](x: F#X): Unit = ???
Then the following compiles fine:
val x: Foo#X = ???
baz(x)
But the following won't compile:
val x: Bar#X = ???
baz(x)
Scala sees the "underlying type String" for x, but has lost the information that x is a Bar#X. It works fine if I annotate the type:
baz[Bar](x)
Is there a way to make Scala infer the right type parameter for baz?
If not, what is the general answer that makes it impossible?
The program compiles by adding this implicit conversion in the context:
implicit def f(x: Bar#X): Foo#X = x
As this implicit conversion is correct for any F <: Foo, I wonder why the compiler does not do that by itself.
You can also:
trait Foo {
type X
}
trait Bar extends Foo {
type X = String
}
class BarImpl extends Bar{
def getX:X="hi"
}
def baz[F <: Foo, T <: F#X](clz:F, x: T): Unit = { println("baz worked!")}
val bi = new BarImpl
val x: Bar#X = bi.getX
baz(bi,x)
but:
def baz2[F <: Foo, T <: F#X](x: T): Unit = { println("baz2 failed!")}
baz2(x)
fails with:
test.scala:22: error: inferred type arguments [Nothing,java.lang.String] do not conform to method baz2's type parameter bounds [F <: this.Foo,T <: F#X]
baz2(x)
^
one error found
I think basically, F <: Foo tells the compiler that F has to be a subtype of Foo, but when it gets an X it doesn't know what class your particular X comes from. Your X is just a string, and doesn't maintain information pointing back to Bar.
Note that:
def baz3[F<: Foo](x : F#X) = {println("baz3 worked!")}
baz3[Bar]("hi")
Also works. The fact that you defined a val x:Bar#X=??? just means that ??? is restricted to whatever Bar#X might happen to be at compile time... the compiler knows Bar#X is String, so the type of x is just a String no different from any other String.