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Multiversal Equality

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Previously, Scala had universal equality: Two values of any types could be compared with each other with == and !=. This came from the fact that == and != are implemented in terms of Java's equals method, which can also compare values of any two reference types.

Universal equality is convenient. But it is also dangerous since it undermines type safety. For instance, let's assume one is left after some refactoring with an erroneous program where a value y has type S instead of the correct type T.

val x = ... // of type T
val y = ... // of type S, but should be T
x == y      // typechecks, will always yield false

If y gets compared to other values of type T, the program will still typecheck, since values of all types can be compared with each other. But it will probably give unexpected results and fail at runtime.

Multiversal equality is an opt-in way to make universal equality safer. It uses a binary typeclass Eql to indicate that values of two given types can be compared with each other. The example above would not typecheck if S or T was a class that derives Eql, e.g.

class T derives Eql

Alternatively, one can also provide an Eql given instance directly, like this:

given as Eql[T, T] = Eql.derived

This definition effectively says that values of type T can (only) be compared to other values of type T when using == or !=. The definition affects type checking but it has no significance for runtime behavior, since == always maps to equals and != always maps to the negation of equals. The right hand side Eql.derived of the definition is a value that has any Eql instance as its type. Here is the definition of class Eql and its companion object:

package scala
import annotation.implicitNotFound

@implicitNotFound("Values of types ${L} and ${R} cannot be compared with == or !=")
sealed trait Eql[-L, -R]

object Eql {
  object derived extends Eql[Any, Any]
}

One can have several Eql givens for a type. For example, the four definitions below make values of type A and type B comparable with each other, but not comparable to anything else:

given as Eql[A, A] = Eql.derived
given as Eql[B, B] = Eql.derived
given as Eql[A, B] = Eql.derived
given as Eql[B, A] = Eql.derived

The scala.Eql object defines a number of Eql givens that together define a rule book for what standard types can be compared (more details below).

There's also a "fallback" instance named eqlAny that allows comparisons over all types that do not themselves have an Eql given. eqlAny is defined as follows:

def eqlAny[L, R]: Eql[L, R] = Eql.derived

Even though eqlAny is not declared a given instance, the compiler will still construct an eqlAny instance as answer to an implicit search for the type Eql[L, R], unless L or R have Eql given instances defined on them, or the language feature strictEquality is enabled

The primary motivation for having eqlAny is backwards compatibility, if this is of no concern, one can disable eqlAny by enabling the language feature strictEquality. As for all language features this can be either done with an import

import scala.language.strictEquality

or with a command line option -language:strictEquality.

Deriving Eql Instances

Instead of defining Eql instances directly, it is often more convenient to derive them. Example:

class Box[T](x: T) derives Eql

By the usual rules if typeclass derivation, this generates the following Eql instance in the companion object of Box:

given [T, U] as Eql[Box[T], Box[U]] given Eql[T, U] = Eql.derived

That is, two boxes are comparable with == or != if their elements are. Examples:

new Box(1) == new Box(1L)   // ok since there is an instance for `Eql[Int, Long]`
new Box(1) == new Box("a")  // error: can't compare
new Box(1) == 1             // error: can't compare

Precise Rules for Equality Checking

The precise rules for equality checking are as follows.

If the strictEquality feature is enabled then a comparison using x == y or x != y between values x: T and y: U is legal if

  1. there is a given instance for Eql[T, U], or
  2. one of T, U is Null.

In the default case where the strictEquality feature is not enabled the comparison is also legal if

  1. T and U the same, or
  2. one of T and Uis a subtype of the lifted version of the other type, or
  3. neither T nor U have a _reflexive Eql given.

Explanations:

  • lifting a type S means replacing all references to abstract types in covariant positions of S by their upper bound, and to replacing all refinement types in covariant positions of S by their parent.
  • a type T has a _reflexive Eql given if the implicit search for Eql[T, T] succeeds.

Predefined Eql Instances

The Eql object defines givens for comparing - the primitive types Byte, Short, Char, Int, Long, Float, Double, Boolean, and Unit, - java.lang.Number, java.lang.Boolean, and java.lang.Character, - scala.collection.Seq, and scala.collection.Set.

Given instances are defined so that every one of these types has a reflexive Eql given, and the following holds:

  • Primitive numeric types can be compared with each other.
  • Primitive numeric types can be compared with subtypes of java.lang.Number (and vice versa).
  • Boolean can be compared with java.lang.Boolean (and vice versa).
  • Char can be compared with java.lang.Character (and vice versa).
  • Two sequences (of arbitrary subtypes of scala.collection.Seq) can be compared with each other if their element types can be compared. The two sequence types need not be the same.
  • Two sets (of arbitrary subtypes of scala.collection.Set) can be compared with each other if their element types can be compared. The two set types need not be the same.
  • Any subtype of AnyRef can be compared with Null (and vice versa).

Why Two Type Parameters?

One particular feature of the Eql type is that it takes two type parameters, representing the types of the two items to be compared. By contrast, conventional implementations of an equality type class take only a single type parameter which represents the common type of both operands. One type parameter is simpler than two, so why go through the additional complication? The reason has to do with the fact that, rather than coming up with a type class where no operation existed before, we are dealing with a refinement of pre-existing, universal equality. It's best illustrated through an example.

Say you want to come up with a safe version of the contains method on List[T]. The original definition of contains in the standard library was:

class List[+T] {
  ...
  def contains(x: Any): Boolean
}

That uses universal equality in an unsafe way since it permits arguments of any type to be compared with the list's elements. The "obvious" alternative definition

  def contains(x: T): Boolean

does not work, since it refers to the covariant parameter T in a nonvariant context. The only variance-correct way to use the type parameter T in contains is as a lower bound:

  def contains[U >: T](x: U): Boolean

This generic version of contains is the one used in the current (Scala 2.12) version of List. It looks different but it admits exactly the same applications as the contains(x: Any) definition we started with. However, we can make it more useful (i.e. restrictive) by adding an Eql parameter:

  def contains[U >: T](x: U) given Eql[T, U]: Boolean // (1)

This version of contains is equality-safe! More precisely, given x: T, xs: List[T] and y: U, then xs.contains(y) is type-correct if and only if x == y is type-correct.

Unfortunately, the crucial ability to "lift" equality type checking from simple equality and pattern matching to arbitrary user-defined operations gets lost if we restrict ourselves to an equality class with a single type parameter. Consider the following signature of contains with a hypothetical Eql1[T] type class:

  def contains[U >: T](x: U) given Eql1[U]: Boolean   // (2)

This version could be applied just as widely as the original contains(x: Any) method, since the Eql1[Any] fallback is always available! So we have gained nothing. What got lost in the transition to a single parameter type class was the original rule that Eql[A, B] is available only if neither A nor B have a reflexive Eql given. That rule simply cannot be expressed if there is a single type parameter for Eql.

The situation is different under -language:strictEquality. In that case, the Eql[Any, Any] or Eql1[Any] instances would never be available, and the single and two-parameter versions would indeed coincide for most practical purposes.

But assuming -language:strictEquality immediately and everywhere poses migration problems which might well be unsurmountable. Consider again contains, which is in the standard library. Parameterizing it with the Eql type class as in (1) is an immediate win since it rules out non-sensical applications while still allowing all sensible ones. So it can be done almost at any time, modulo binary compatibility concerns. On the other hand, parameterizing contains with Eql1 as in (2) would make contains unusable for all types that have not yet declared an Eql1 given, including all types coming from Java. This is clearly unacceptable. It would lead to a situation where, rather than migrating existing libraries to use safe equality, the only upgrade path is to have parallel libraries, with the new version only catering to types deriving Eql1 and the old version dealing with everything else. Such a split of the ecosystem would be very problematic, which means the cure is likely to be worse than the disease.

For these reasons, it looks like a two-parameter type class is the only way forward because it can take the existing ecosystem where it is and migrate it towards a future where more and more code uses safe equality.

In applications where -language:strictEquality is the default one could also introduce a one-parameter type alias such as

type Eq[-T] = Eql[T, T]

Operations needing safe equality could then use this alias instead of the two-parameter Eql class. But it would only work under -language:strictEquality, since otherwise the universal Eq[Any] instance would be available everywhere.

More on multiversal equality is found in a blog post and a Github issue.