Point a = ...;
ColoredPoint b = ...;
a.equals(b) // false, a says b is not a 'Point'
b.equals(a) // true, b says my 'color-ness' is irrelevant, I'm a Point -- represent!
The only way to ensure that a. equals(b) and b.equals(a) is always true is to reify the equality relation into its own first-class type or method.
class Point { public static boolean operator_equals(Point a, Point b); }
It's too bad that Java and other languages do not offer first class support for operators. a == b can be shorthand for Point.operator_equals(a, b). If there is any ambiguity at all (because b is a subclass and there exists a method ColoredPoint.operator_equals()) then raise an error and force the developer to be explicit about exactly which equality operator is intended. If such a method doesn't exist then raise an error and force the developer to say exactly what is intended by equality. (Don't fall back to reference equality!).
This would eliminate a whole lot of bugs and all the confusion around equality.
If `Point` is a subclass of `ColoredPoint`, and `p` and `cp` exist as instances respectively, there is ambiguity between `p == cp` and `cp == p`.
In Python there is first class support for operators: the `eq` dunder method:
def __eq__(self, other):
if not isinstance(other, type(self)):
return False
return self.point == other.point
if (getClass() != other.getClass())
return false;
The proposal is to capture equality (and all other operators) as static methods.
class Point2D {
public static boolean operator_equals(Point2D p1, Point2D p2) { ... }
}
class ColoredPoint {
public static boolean operator_equals(ColoredPoint cp, Point2D p2) { ... }
}
The point here is that equality is not something that can be decided by one object, it is an operator that establishes relations between types of objects. There's a very fundamental difference between sending a message to a single object and establishing a relation and this is the source of all the confusion around equality.
Dunno if you raise or just return false if they disagree.
1. Ask the LHS for its equality function.
2. Ask the RHS for its equality function.
3. If the two return different functions (non-identical), the objects are not equal.
4. Otherwise, return the result of invoking the function.
The first two steps are polymorphic, so objects can define interesting equality semantics with whatever policy makes sense for them. But step 3 ensures that the two objects must agree on that policy before you can compare them.
It sounds pretty reasonable, but I have no idea how "sounds reasonable" correlates with "is helpful in practice". (I think one of the commenters in the linked page might have raised that point too.)
Fulfilling axioms of equality definitely does sound useful for being able to write code, though -- having symmetry, not having to think about whether you need to write `a==b` or `b==a`, seems like it'd lighten the cognitive load.
I suppose also when the objects disagree about equality you also have some license to say "this may not do quite what you expect" and do your best to make the most of it.
> I was working on a hobby language a few years ago
Hah, you're famous enough that we've all probably heard of the language if it has seen the light of day ;-).
My own hobby language has no methods or dynamic dispatch of any kind, haha. It's a little stressful to have to come up with some equality rule that works for essentially every use-case, though -- I don't think it's sufficient to enumerate the data types in the language, I really have to go over all the ways I think they could be used :-/.
Oh well, it's fun at least.
Inheritance is just a scapegoat here. Changing the definition of the equality in the subclass is probably a design mistake (because it's confusing and error prone).
The core of the problem is that, contrary to trivial things like integers, with complex objects one may be interested in defining different equivalence relationships in different parts of the same application. If everyone insists to use the = sign to note "their" equality, inevitably there will be conflicts.
So in a way, not allowing to highjack the = operator (or == depending on how the language expresses assignment) and keep it for identity (i.e. address equality) could actually be the sane approach. In your example, renaming "equals" to "hasSameCoordinates" wouldn't be bad practice, I believe.
What is relevantly the same in one application may not be relevant in another. Equivalently, differences between objects may or may not matter, depending on the application.
One can go further to say that in many settings the correct output to an equality-query may appropriately depend on the identity of the caller.
eg. Even though Point may not have a color instance variable, there is no reason why it can't have a default color for all "plain" Points.
Of course, extending this to a smalltalk / ruby "Objects all the way down" hierarchy if Point inherits from Object then Object needs to have a default (x,y) position and colour.
It would seem mad to give place default values for every property of any object ever on the Object base class...
However one could provide default values for Point and ColoredPoint which the equality operator uses.
I can imagine someone using it eg as an identifier in a web form, and passing it back to the app to lookup in some keyed data structure where they have used id as the keyfn - and getting back the incorrect object because the id has been recycled. Then it's saved to the db and you get data corruption.
p = (id([]) == id([]))
: mklist 0 # alloc -> 0x1234
: call id # free(0x1234)
: mklist 0 # alloc -> 0x1234 (free list is a stack)
: call id # free(0x1234)
: cmp == # true