This design is sometimes known as “Universal Equality”, it is the belief that whether two things are equal or not is a universal property.

What’s more, equality is a property of two objects, but in OO, you always call a method on one single object, and that object gets to solely decide how to handle that method call. So, in a design like Java’s, where equality is a property of one of the two objects being compared, it isn’t even possible to guarantee some basic properties of equality such as symmetry (a == b ⇔ b == a), because in the first case, the method is being called on a and in the second case it is being called on b and due to the basic principles of OO, it is solely a‘s decision (in the first case) or b‘s decision (in the second case) whether or not it considers itself equal to the other one. The only way to gain symmetry is to have the two objects cooperate, but if they don’t… tough luck.

One solution would be to make equality not a property of one object, but either a property of two objects, or a property of a third object. That latter option also solves the problem of universal equality, because if you make equality a property of a third “context” object, then you can imagine having different EqualityComparer objects for different contexts.

This is the design chosen for Haskell, for example, with the Eq typeclass. It is also the design chosen by some third-party Scala libraries (ScalaZ, for example), but not the Scala core or standard library, which uses universal equality for compatibility with the underlying host platform.

It is, interestingly, also the design chosen with Java’s Comparable/Comparator interfaces. The designers of Java clearly were aware of the problem, but for some reason only solved it for ordering, but not for equality (or hashing).

So, as to the question

why is there a Comparator interface but no Hasher and Equator?

the answer is “I don’t know”. Clearly, the designers of Java were aware of the problem, as evidenced by the existence of Comparator, but they obviously didn’t think it a problem for equality and hashing. Other languages and libraries make different choices.

The real answer to

why is there a Comparator interface but no Hasher and Equator?

is, quote courtesy of Josh Bloch:

The original Java APIs were done very quickly under a tight deadline to meet a closing market window. The original Java team did an incredible job, but not all of the APIs are perfect.

The problem lies solely in Java’s history, as with other similar matters, e.g. .clone() vs Cloneable.

tl;dr

it’s for historical reasons mainly; current behaviour/abstraction was introduced in JDK 1.0 and wasn’t fixed later on because it was virtually impossible to do so with maintaining backward code compatibility.

First, let’s sum up a couple of well-known Java facts:

1. Java, from the very beginning to the present day, was proudly backwards-compatible, requiring legacy APIs to be still supported in newer versions,
2. as such, almost each and every language construct introduced with JDK 1.0 lived to present day,
3. Hashtable, .hashCode() & .equals() were implemented in JDK 1.0, (Hashtable)
4. Comparable/Comparator was introduced in JDK 1.2 (Comparable),

Now, it follows:

5. it was virtually impossible & senseless to retrofit .hashCode() & .equals() to distinct interfaces while still maintaining backwards compatibility after the people realized there are better abstractions than putting them in superobject, because e.g. each and every one Java programmer by 1.2 knew that every Object has them, and they had to stay there physically to provide compiled code (JVM) compatibility also – and adding an explicit interface to every Object subclass that really implemented them would make this mess equal (sic!) to Clonable one (Bloch discusses why Cloneable sucks, also discussed in e.g. EJ 2nd and many other places, including SO),
6. they just left them there for the future generation to have a constant source of WTFs.

Now, you may ask “what does Hashtable have with all this”?

The answer is: hashCode() / equals() contract and not-so-good language design skills of core Java developers in 1995/1996.

Quote from Java 1.0 Language Spec, dated 1996 – 4.3.2 The Class Object, p.41:

The methods equals and hashCode are declared for the benefit of hashtables
such as java.util.Hashtable (§21.7). The method equals defines a notion
of object equality, which is based on value, not reference, comparison.

(note this exact statement has been changed in later versions, to say, quote: The method hashCode is very useful, together with the method equals, in hashtables such as java.util.HashMap., making it impossible to make the direct Hashtable–hashCode–equals connection without reading historical JLS!)

Java team decided they wanted a good dictionary-style collection, and they created Hashtable (good idea so far), but they wanted the programmer to be able to use it with as little code/learning curve as possible (oops! trouble incoming!) – and, since there was no generics yet [it’s JDK 1.0 after all], that would mean that either every Object put into Hashtable would have to explicitly implement some interface (and interfaces were still just in their inception back then… no Comparable yet even!), making this a deterrent to use it for many – or Object would have to implicitly implement some hashing method.

Obviously, they went with solution 2, for the reasons outlined above. Yup, now we know they were wrong. _{… it’s easy to be smart in hindsight. chuckle}

Now, hashCode() requires that every object having it has to have a distinct equals() method – so it was quite obvious that equals() had to be put in Object as well.

Since the default implementations of those methods on valid a&b Objects are essentially useless by being redundant (making a.equals(b) equal to a==b and a.hashCode() == b.hashCode() roughly equal to a==b also, unless hashCode and/or equals is overriden, or you GC hundreds of thousands of Objects during the lifecycle of your application¹), it’s safe to say they were provided mainly as a backup measure and for usage convenience. This is exactly how we get to the well-known fact that always override both .equals() & .hashCode() if you intend on actually comparing the objects or hash-storing them. Overriding only one of them without the other is a good way to screw your code (by wicked compare results or insanely high bucket collision values) – and getting your head around it is a source of constant confusion & errors for beginners (search SO to see it for yourself) and constant nuisance to more seasoned ones.

Also, note that although C# deals with equals & hashcode in a bit better way, Eric Lippert himself states that they did almost the same mistake with C# that Sun did with Java years before C#’s inception:

But why should it be the case that every object should be able to hash itself for insertion into a hash table? Seems like an odd thing to require every object to be able to do. I think if we were redesigning the type system from scratch today, hashing might be done differently, perhaps with an IHashable interface. But when the CLR type system was designed there were no generic types and therefore a general-purpose hash table needed to be able to store any object.

¹of course, Object#hashCode can still collide, but it takes a bit of effort to do that, see: http://bugs.java.com/bugdatabase/view_bug.do?bug_id=6809470 and linked bug reports for details; https://stackoverflow.com/questions/1381060/hashcode-uniqueness/1381114#1381114 covers this subject more in-depth.