How to implement the empty set - ∅? [closed]

Question

Assuming that you want to implement set theory concepts such as element, set, collection and relation in Java: How would you represent the empty set ∅?

Do I mislead myself, if I think of the NULL concept as it is used by the three-valued logic of databases?

Gnaw

I'm not sure there's a unique answer to this question; it depends on what you want to achieve. The obvious answer is "use an empty Set", but NULL might also be appropriate depending on what you're doing. – Dizzy

There are myriad ways to represent the empty set, depending on the intended application. Set<E> = new HashSet<E>() is one of the simplest. – Nosing

Collections.emptySet() comes to mind ... – Foretell

@OliCharlesworth: I'd say the absence of a set (you have zero sets), and an empty set (you have a set with zero elements) are not the same – Selah

A Set with no contents would work for me. I would not represent it in Java will a null. There could be some logic to this, but the code would be annoying since every time you referred to the collection you'd have to check for null. – Galligan

@LukasEder I have never seen a case in my programming career where that distinction made a difference or was even helpful. – Galligan

@TonyEnnis: Really? No set and an empty set are pretty different... – Dizzy

@TonyEnnis: One example is lazy initialisation. The absence of the set means that it hasn't been initialised yet – Selah

@oli Perhaps mathematically. While coding? Never. Now, if empty must be implemented as something distinct, I'd choose a method that didn't involve me scattering null checks all over my code. – Galligan

@TonyEnnis: Think about java.util.File.list(). It returns null if a file cannot provide its contained files (no set), or an empty array, if a file doesn't contain any files (empty set)... – Selah

@lukas I get it, but the practical difference is very slight. In your example, I can't show files no matter how it fails. In any event, I don't have a problem with a method returning a null versus an instance. However, the empty set IS a set (?right?) and assigning the null to some 'mySet' variable (which I believe is the use-case) would not be helpful at all. I'd sooner see an instance that behaves like a null-set than just using a Java null. In that regard, an empty Set would be more appropriate if mathematically imprecise. – Galligan

Thank you all for your efforts. Now, I definitely know how to approach this problem. – Gnaw

Answer 1

Use Collections.emptySet():

Returns the empty set (immutable). This set is serializable. Unlike the like-named field, this method is parameterized. This example illustrates the type-safe way to obtain an empty set:

 Set<String> s = Collections.emptySet();   

Implementation note: Implementations of this method need not create a separate Set object for each call. Using this method is likely to have comparable cost to using the like-named field. (Unlike this method, the field does not provide type safety.)

Doubleminded

Thank you for your suggestion. I will use your advice. – Gnaw

Answer 2

Using null to represent an empty set is a bad idea. A null doesn't behave like a Set because (obviously) all attempts to perform an operation on it will throw a NullPointerException. That means that if you use null to denote an empty set, you code will be littered with tests for null ... and if you miss one, you've got a bug.

The practical solution is to use Collections.emptySet() if you want an immutable empty set, or create an instance of the appropriate Set class (e.g. new HashSet<>()) if you want a mutable set that starts out empty.

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On rereading the question, I realize that you may have meant something different to my original understanding.

If you were trying to implement / model mathematical set theory concepts in Java from scratch, you would probably implement Set as an immutable class. (In mathematics, you don't mutate things!) The empty set is then just a Set instance with no elements in it. No special handling required.

The NULL concept is not required ... unless you are specifically trying to incorporate a "null", "undefined sets" or some similar concept in your mathematical model of sets. (If you are, I'm not sure we can advise you without understanding your model ... from a mathematical perspective.)

Retinitis

+1 for stating why the null is a bad idea. – Galligan