Existential Higher Kinded Method Parameter - scala

I have the following types defined:
trait Context
trait Attribute[C <: Context]
trait AttributeDefinition[A[_ <: Context] <: Attribute[C] forSome { type C <: Context }] {
def read[C <: Context]: A[C]
}
I want AttributeDefinition to return an Attribute parameterized by a context. Each definition applies to only one type of Attribute. Hypothetically:
class ConstantValueAttribute[C <: Context] extends Attribute[C]
object ConstantValueAttributeDefinition extends AttributeDefinition[ConstantValueAttribute] {
override def read[C <: Context]: ConstantValueAttribute[C] = ???
}
This totally compiles fine, but i have trouble crafting method signatures that accept an unbounded AttributeDefinition. As well as creating a collection of AttributeDefinitions. All the following fail:
def def1(attribute: AttributeDefinition): Unit = ???
def def2(attribute: AttributeDefinition[_]): Unit = ???
def def3(attribute: AttributeDefinition[_ <: Attribute[C] forSome { type C <: Context }]): Unit = ???
def def4(attribute: AttributeDefinition[A[_]] forSome { type A <: Attribute[C]; type C <: Context })
EDIT:
I am trying to find a method declaration like the above that will compile. I also am looking to figure out how to declare a collection of AttributeDefinitions.
val val1 = new mutable.ArrayBuffer[AttributeDefinition]
if that is not possible i would love to figure out how to simplify the traits above that can still capture the simple read method declaration.

Proposal with a type member
Essentially, what you want in both defN-declarations and Seq-collections of AttributeDeclaration is a higher kinded existential type for Attribute that is used as an argument for AttributeDeclaration. So, ideally, you would like to have:
def def1(attrDef: AttributeDeclaration[A] forSome {
type A[C <: Context] <: Attribute[C] }): Unit = ???
However, this does not work, and this is an unresolved issue since 2015, so chances are that it won't be fixed until dotty.
Instead of trying to force the compiler to work with higher kinded existentials so that you can throw away the unnecessary type parameter, I would propose that you don't add the annoying type parameter in the first place. Consider these definitions (compiles with 2.12.4):
trait Context
trait Attribute[C <: Context]
trait AttributeDefinition {
type A[C <: Context] <: Attribute[C]
def read[C <: Context]: A[C]
}
class ConstantValueAttribute[C <: Context] extends Attribute[C]
object ConstantValueAttributeDefinition extends AttributeDefinition {
type A[C <: Context] = ConstantValueAttribute[C]
def read[C <: Context]: ConstantValueAttribute[C] = ???
}
def def1(attrDef: AttributeDefinition): Unit = ???
val collDefs: Seq[AttributeDefinition] = List(ConstantValueAttributeDefinition)
These definitions have following properties:
Context and Attribute are left unchanged
A becomes a type member of AttributeDefinition, so it does not have to be forcefully erased by an existential later
read-signature is completely unchanged, it's literally the same as in your original code, character for character
declaration of the simplest and most intuitive def1 works immediately without changes (also essentially copied from your code 1:1)
declaration and definition of collections with AttributeDefinitions also works just as smoothly.
Recall that you don't even lose anything if you move something from type parameter to type member, because you can always refer to the type member by name (for example, when you want to impose an additional restriction on that type member). The following minimal example is supposed to demonstrate how to impose additional restrictions on type members (vaguely related to your code, uses Context):
trait Foo {
type Member
}
def restrictiveFoo(x: Foo { type Member <: Context }): Unit = ???
Here, you can force the argumen Foo to have type member that derives from Context. It would work with type Member = Context similarly. What I wanted to demonstrate by that: it's not like type members are forever hidden inside the trait, if you introduce them. You can do with them almost all the same things as with type parameter. To summarize:
Adding additional constraints on a (higher kinded) type member is easy
Erasing a superfluous type parameter with higher kinded existentials doesn't seem to work at all.
So, therefore, I would advise to use a type member.
Proposal with change of variance from A to +A
Another quick-fix to make it compile:
trait Context
trait Attribute[C <: Context]
trait AttributeDefinition[+A[X <: Context] <: Attribute[X]] {
def read[C <: Context]: A[C]
}
class ConstantValueAttribute[C <: Context] extends Attribute[C]
object ConstantValueAttributeDefinition
extends AttributeDefinition[ConstantValueAttribute] {
override def read[C <: Context]: ConstantValueAttribute[C] = ???
}
class FooValueAttribute[C <: Context] extends Attribute[C]
object FooValueAttributeDefinition
extends AttributeDefinition[FooValueAttribute] {
override def read[C <: Context]: FooValueAttribute[C] = ???
}
def def1(attrDef: AttributeDefinition[Attribute]): Unit = {}
def1(ConstantValueAttributeDefinition)
val listOfDefs: List[AttributeDefinition[Attribute]] = List(
ConstantValueAttributeDefinition,
FooValueAttributeDefinition
)
inspired by the answer to this question. Strangely enough, it's seems to be almost exactly the same constellation. It didn't solve the problem with higher kinded existentials though, instead the variance of A has been changed to +A, so that one could use Attribute as least upper bound of all concrete As.

The correct signature would be
def `def`[A[_ <: Context] <: Attribute[C] forSome { type C <: Context }](attribute: AttributeDefinition[A]) = ???
You need to use a type parameter for your function, which should have (at least) the same constraints as the one in your type.
Note: in my opinion this is a reason why you should avoid putting type constraints on the type arguments for your type, they should only be put on functions/operations instead.

trait Context
trait Attribute[+Context]
trait AttributeDefinition[Attribute] {
def read[Context]: Attribute
}
class ConstantValueAttribute extends Attribute[Context]
object ConstantValueAttributeDefinition extends AttributeDefinition[ConstantValueAttribute] {
def read[Context]: ConstantValueAttribute = ???
}
def def1[C](attribute: AttributeDefinition[C]) : Unit = ???
As a hint for simplification too.

Related

Type bounds constraints restrictions in Higher Kinds when extending a trait

Let's set up issue conditions
trait Bound
trait Bound2 extends Bound
trait T1[B <: Bound]
trait T2[B <: Bound2] extends T1[B]
trait WrapperT1[Tz[B2 <: Bound] <: T1[B2]]
This code compile without problem, issue comes when trying to extend WrapperT1
trait WrapperT2[Tz[B2 <: Bound2] <: T2[B2]] extends WrapperT1[T2]
// Compilator error
kinds of the type arguments (T2) do not conform to the expected kinds of the type parameters (type Tz) in trait WrapperT1.
[error] ex.T2's type parameters do not match type Tz's expected parameters:
[error] type B's bounds <: Bound2 are stricter than type B2's declared bounds <: ex.Bound
[error] trait WrapperT2[Tz[B2 <: Bound2] <: T2[B2]] extends WrapperT1[T2]
Yes B2 <: Bound2 is stricter than B2 <: Bound but i'm not understanding why the compilator complains for this reason and i would be grateful to know more about it.
Potential solution but does it has some drawbacks ?
trait Bound
trait Bound2 extends Bound
trait T1[B] {
implicit val ev: B <:< Bound
}
trait T2[B] extends T1[B] {
// this is possible thank's to covariance of class `<:<[-From, +To]` if i'm not wrong
implicit val ev: B <:< Bound2
}
trait WrapperT1[Tz[B2] <: T1[B2]]
// Compiles
trait WrapperT2[Tz[B2] <: T2[B2]] extends WrapperT1[Tz]
This looks nice and we keep the compilation checks about B2 generic type but is there any inconveniant using it ?
To understand why the compiler complains, let's look at this piece of code (which is the same as your code, but with different names)
trait Show[A <: AnyRef] {
def show(a: A): Unit
}
trait ShowString[S <: CharSequence] extends Show[S] {
def show(s: S): Unit = println(s)
}
trait Wrapper1[S[A <: AnyRef] <: Show[A]] {
def show[A <: AnyRef](a: A)(implicit show: S[A]): Unit = show.show(a)
}
trait Wrapper2[S[C <: CharSequence] <: ShowString[C]] extends Wrapper1[S]
Here, too, the compiler emits the error type C's bounds <: CharSequence are stricter than type A's declared bounds <: AnyRef, but let's pretend you somehow get it to compile here. That would mean if someone wanted to use your wrapper class to print, say, a list, they wouldn't be able to do that, meaning that your wrapper class would be basically useless.
val w2: Wrapper[ShowString] = ???
w2.show(List(1, 2))
//Error: could not find implicit value for parameter show: ShowString[List[Int]]
In this case, it's just that the implicit isn't found. However, if you have a method in wrapper that accepts a S[_] (or Tz[_], from your example) and you try to shoehorn an object of the wrong type into your show method, you could get a runtime exception.
It fails for the same reason you can't do this
trait T1[A] {
def process(a: A): Unit
}
trait T2 extends T1[Int] {
def process(i: Int): Unit = ???
}
val t2: T2 = ???
t2.process("not an int")
T2 is just not equipped to handle anything that is not an Int, and the same applies here.

General way of ensuring implicit definition always has higher/lower priority

I have a somewhat complex typeclass situation in the following format:
sealed trait TypeClass[S <: MyType] {
type Out <: MyType
}
sealed trait LowPriorityTypeClass {
// Case: OtherTypeClass is NOT defined for the input type S.
// The output type is the same as the input type.
implicit def default[S <: MyType]: TypeClass.Aux[S, S] = ???
}
object TypeClass extends LowPriorityTypeClass {
type Aux[S <: MyType, O <: MyType] = TypeClass[S] { type Out = O }
// Case: OtherTypeClass is defined for the input type S.
// The output type is the same as in the OtherTypeClass definition.
implicit def hasOtherTC[S <: MyType, O <: MyType](
implicit otherTC: OtherTypeClass.Aux[S, O],
): TypeClass.Aux[S, O] = ???
}
The default definition was put in the LowPriorityTypeClass trait with the intention of having a lower priority. However, an ambiguity with hasOtherTC still happens for some type S, apparently because the declaration of default is more specific than the declaration of hasOtherTC for that type S.
Is there a general way to ensure that an implicit definition will always have a higher/lower priority than other definition? (My question is not for the specific code above.)
Let me know if posting a more complete sample code would help.
Please see Why is this implicit ambiguity behaviour happening? including comments.
There is no sense in introducing trait LowPriorityTypeClass in this case because anyway implicit default is more specific than hasOtherTC.
There is no general way. You can use type classes Not (shapeless.Refute, implicitbox.Not) or shapeless.LowPriority, implicitbox.Priority or library https://github.com/milessabin/export-hook.
object TypeClass {
type Aux[S <: MyType, O <: MyType] = TypeClass[S] {type Out = O}
implicit def hasOtherTC[S <: MyType, O <: MyType](implicit
otherTC: OtherTypeClass.Aux[S, O]
): TypeClass.Aux[S, O] = ???
implicit def default[S <: MyType](implicit
noOtherTC: Refute[OtherTypeClass[S]]
): TypeClass.Aux[S, S] = ???
}

Generic bounds, most of them are unclear

It's kind of complicated to learn Scala's generic bounds. I know that:
T : Tr - T has type of Tr, meaning it implements a trait Tr
T <: SuperClass - T is subclass of SuperClass
T :> ChildClass - T is superclass of ChildClass
However, there are also many more operators:
<% and %>
=:=
<:< and >:>
<% and %>
<%< and >%>
I read about them, but as I said, there was was not comprehensible explanations. Could you make it clearer?
I've used a few type constraints:
The easiest are <: and >:. These are simple bounds on the type hierarchy.
trait A
trait B extends A
trait C extends B
then for a method
def doSomething[T >:C <:B](data:T)
either B or C can be substituted instead of T
Then type constraints that involves an addition of implicit parameter to the method.
def doSmth1[T: MyTypeInfo] (data:T)
is rewritten during compilation as
def doSmth1[T] (data:T)(implicit ev: MyTypeInfo[T])
whereas
def doSmth2[T <% SomeArbitratyType] (data:T)
is rewritten as
def doSmth2[T] (data:T)(implicit ev: T => SomeArbitratyType)
Both of the methods can be called if in the scope there is an instance that fits the implicit parameter. If there is no appropriate instance then compiler issues an error.
The view bound (<%) requires an implicit conversion that converts T to an instance of the other type (SomeArbitratyType).
More powerful is using "type classes". Inside the type class instance one may put many useful methods that can deal with the type T. In particular, one may put a conversion method and achieve similar result as view bounds.
Examples:
trait MyTypeInfo[T] {
def convertToString(data:T):String
}
def printlnAdv[T : MyTypeInfo](data:T) {
val ev = implicitly[MyTypeInfo[T]]
println(ev.convertToString(data))
}
somewhere in the scope there should be implicit value of type MyTypeInfo[T]:
implicit val doubleInfo = new MyTypeInfo[Double] {
def convertToString(data:Double):String = data.toString
}
or
implicit def convertToString(data:T):String
def printlnAdv[T <% String](data:T) {
val conversionResult = data : String
println(conversionResult)
}
somewhere in the scope there should be implicit function:
implicit def convertDoubleToString(data:Double):String = data.toString
The next weird symbols are =:= and <:<. These are used in methods that wish to ensure that a type has some property. Of course, if you declare a generic parameter then it is enough to have <: and >: to specify the type. However, what to do with types that are not generic parameters? For instance, the generic parameter of an enclosing class, or some type that is defined within another type. The symbols help here.
trait MyAlmostUniversalTrait[T] {
def mySpecialMethodJustForInts(data:T)(implicit ev:T =:= Int)
}
The trait can be used for any type T. But the method can be called only if the trait is instantiated for Int.
Similar use case exists for <:<. But here we have not "equals" constraint, but "less than" (like T<: T2).
trait MyAlmostUniversalTrait[T] {
def mySpecialMethod(data:T)(implicit ev:T <:< MyParentWithInterestingMethods)
}
Again the method can only can called for types that are descendants of MyParentWithInterestingMethods.
Then <%< is very similar to <%, however it is used the same way as <:< — as an implicit parameter when the type is not a generic parameter. It gives a conversion to T2:
trait MyAlmostUniversalTrait[T] {
def mySpecialMethod(data:T)(implicit ev:T <%< String) {
val s = data:String
...
}
}
IMHO <%< can safely be ignored. And one may simply declare the required conversion function:
trait MyAlmostUniversalTrait[T] {
def mySpecialMethod(data:T)(implicit ev:T => String) {
val s = data:String
...
}
}

Kinds not conforming with type lambda

Having trouble with type "kinds":
trait Sys[ S <: Sys[S]]
trait Expr[S <: Sys[S], A]
trait Attr[S <: Sys[S], A[_]]
def test[ S <: Sys[S]]: Attr[S, ({type l[x<:Sys[x]]=Expr[x,Int]})#l] = ???
This fails with
error: kinds of the type arguments (S,[x <: Sys[x]]Expr[x,Int]) do not conform
to the expected kinds of the type parameters (type S,type A) in trait Attr.
[x <: Sys[x]]Expr[x,Int]'s type parameters do not match type A's expected parameters:
type x's bounds <: Sys[x] are stricter than type _'s declared bounds >: Nothing <: Any
def test[S <: Sys[S]]: Attr[S, ({type l[x<:Sys[x]]=Expr[x,Int]})#l] = ???
^
What's the problem with the declared bounds? Do I need to carry that cr*ppy partially applied type into the type constructor of trait Attr? And why? Can I fix this without touching the definition of Attr?
I do need the bounds in function test in order for the implementation to work, but I do not want to proliferate those bounds to the public interface Attr.
Note: If I use a type member (what I don't want), it works:
trait Attr[S <: Sys[S]] { type A[_]}
def test[ S <: Sys[S]]: Attr[S] { type A[S <: Sys[S]] = Expr[S, Int]} = ???
As you observed, you can't always mismatch bounds when providing a higher-kinded type argument. Interestingly, it is actually a variance issue:
class A
class B extends A
trait NeedsNeedsA[T[S <: A]]
trait NeedsNeedsB[T[S <: B]]
trait NeedsA[S <: A]
trait NeedsB[S <: B]
def x: NeedsNeedsA[NeedsB] // fails
def y: NeedsNeedsB[NeedsA] // works
which makes sense if you think of a higher-kinded type as a function on types, contravariant in its argument's bound.
Interestingly, in a structural type, which is on the surface a lot like subtyping, Scala does not give the same error:
def t: MemberNeedsA { type T[S <: B] }
def u: MemberNeedsB { type T[S <: A] }
the reason being that a structural type is sort of like an intersection:
def s: MemberNeedsA with MemberNeedsB
and it may be that that intersection cannot actually exist in nature, but Scala doesn't check that.
OK, but that's not so relevant to your question. Back to your question: I think you have a variance issue. You want test to give the caller back an Attr, and an Attr posseses a type function (A[_]), and you want to say, this Attr has a type function that requires a more specific argument. I think you can see why you shouldn't be allowed to do that -- it's the same reason you can't substitute a function requiring a more specific argument in place of one that would require a more general argument.
At this point I'm afraid the solution will have to depend on what you want Attr to be able to accomplish. You need to figure out why you need to restrict the type argument in some cases more than others. If it makes conceptual sense in your program that "some Attrs are more restrictive than others", you could define:
trait Attr[S <: Sys[S], B[Y <: B[Y]], A[X <: B[X]]]
def test[S <: Sys[S]]: Attr[S, Sys, L] = ...
But the solution will depend on what the restriction on A[_]'s argument is intended to mean.

Exchanging a type parameter's upper bound for an evidence parameter

I want to relax the constraints on a trait's type parameter and instead impose them on a method in the form of an evidence parameter. Given some skeletal setup:
trait State[Repr]
object Observer {
def apply[Repr <: State[Repr]](reader: Reader[Repr]): Observer[Repr] =
new Observer[Repr] {}
}
trait Observer[A]
trait Reader [A]
This works:
trait StateX[Repr <: StateX[Repr]] extends State[Repr] {
protected def reader: Reader[Repr]
def observe: Observer[Repr] = Observer(reader)
}
And this doesn't:
trait StateY[Repr] extends State[Repr] {
protected def reader: Reader[Repr]
def observe(implicit ev: Repr <:< State[Repr]): Observer[Repr] = Observer(reader)
}
With message "inferred type arguments [Repr] do not conform to method apply's type parameter bounds [Repr <: State[Repr]]". Since the evidence ev suggests this conformation, I wonder how StateY can be fixed.
Your problem is that even though evidence of the form A <:< B implies that a value of type A can be converted to a value of type B it doesn't imply A <: B ... indeed, the main reason for using a type constraint or a view bound rather than an ordinary type bound is precisely because such a subtype relationship doesn't hold.
Consequently the constraint in StateY, Repr <:< State[Repr], isn't sufficient to satisfy the bound Repr <: State[Repr] on Observer's apply method. Given that you want to relax the constraint on StateX's type parameter your only option is to weaken the constraint on the apply method's type parameter correspondingly. That gets you something like the following using a view bound instead of an ordinary type bound,
object Observer {
def apply[Repr <% State[Repr]](reader : Reader[Repr]) : Observer[Repr] =
new Observer[Repr] {}
}
or alternatively,
object Observer {
def apply[Repr](reader : Reader[Repr])
(implicit ev : Repr <:< State[Repr]) : Observer[Repr] =
new Observer[Repr] {}
}
if you'd rather use constraints throughout.
The evidence suggests that a Repr can be converted to State[Repr]. It says nothing about what can be done with a Reader[Repr].
There is no general method (independant of T) to convert T[A] to T[B] given an A => B. That might be possible for a covariant T, but there is no such thing in the language.