Language Design: Equality & Identity

Part 3: Solution

Published on 2017-10-31. Last updated on 2022-06-08

Let’s take a step back and think about what these equality operations do:

Reference equality acts as a built-in, hard-coded comparison of the references themselves, while value equality compares equality according to a user-defined implementation.

Is it possible to come up with a re-interpretation of reference equality that retains the existing behavior of reference types, but adds reasonable behavior for value types, so that the complexity of having multiple, different comparison operations can be reduced?

Yes! There is a very useful reinterpretation of reference equality that addresses the mentioned issues and solves a few other problems along the way.

The core insight is that there are two useful, fundamental ways to compare things: By identity and by equality.

Defining Equality and Identity

  • Equality checks whether two things are equal, based on some library-defined definition of equality.
  • Identity checks whether two things are identical, based on a built-in definition of identity.

What is an identity comparison?

The definition extends the concept of reference comparisons to value types, by comparing the bits (and the type) of the value at hand:

  • reference types compare the bits of the reference itself.
  • value types compare the bits of themselves, e. g. the bits of an Int, a Float, or a Complex value.

This means that an instance of a reference type is only identical to another instance if they are the same reference, and an instance of a value types is only identical to another instance if their values match up exactly.

Having one operation, which is well-defined on both value types and reference types, considerably simplify things in generic contexts.

How do equality and identity comparisons work?

Compared to the rather complicated, indirect approaches shown earlier, introducing the concept of identity and equality works out beautifully: It reduces complexity and avoids unnecessary boxing.

The following table shows how this definition of identity and equality could work in practice:

  type ∘ is == ∘ is ===
true ∘ true value true true
1 ∘ 1 value true true
1.0 ∘ 1.0 value true true
Float.NaN ∘ Float.NaN value false true
+0.0 ∘ -0.0 value true false
BigInt(1) ∘ BigInt(1) reference true false1
“abc” ∘ “abc” reference true false1


  • Languages should provide two, distinct operations that provide equality comparisons and identity comparisons.
  • Ideally, these operations do not exist on the languages’ top type, but are only available when the type is constrained appropriately (e. g. fun same[E : Identity](a: E, b: E) = a === b).
  1. assuming a reference-based type  2