Covariance and contravariance - simple explanation

This is a very concise tutorial on covariance and contravariance. In 10 minutes you should understand what these concepts are and how to use them. The examples are in Scala, but apply to Java or C# as well.


Assuming Apple is a subclass of Fruit, covariance lets you treat say List[Apple] as List[Fruit].

val apples = List(new Apple(), new Apple())

def processList(list:List[Fruit]) = {
  // read the list

This seems obvious - indeed, a list of apples is a list of fruit, right?

The surprise comes when we find out this does not work for arrays. Why is that so? Because you could do the following:

val a = Array(new Apple(), new Apple())

def processArray(array:Array[Fruit]) = {
  array(1) = new Orange() // putting an Orange into array of Apples!

The main difference between List and Array here is that the List is immutable (you cannot change its contents) while the Array is mutable. As long as we are dealing with immutable types, everything is OK (as in the first example).

So how does the compiler know that List is immutable? Here is the declaration of List:

sealed abstract class List[+A]

The +A type parameter says "List is covariant in A". That means the compiler checks that there is no way to change contents of the List, which eliminates the problem we had with arrays.

Simply put, a covariant class is a class from which you can read stuff out, but you can't put stuff in.


Now when you already understand covariance, contravariance will be easier - it is exactly the opposite in every sense.

You can put stuff in a contravariant class, but you can never get it out (imagine a Logger[-A] - you put stuff in to be logged). That doesn't sound too useful, but there is one particularly useful application: functions. Say you've got a function taking Fruit:

// isGoodFruit is a func of type Fruit=>Boolean
def isGoodFruit(f:Fruit) = f.ageDays < 3

and filter a list of Apples using this function:

val list:List[Apple] = List(new Apple(), new Apple())
list.filter(isGoodFruit) // filter takes a func Apple=>Boolean

So a function on Fruits is a function on Apples - the filter will throw Apples in and isGoodFruit will know how to handle them.

The type of isGoodFruit is actually Function[Fruit, Boolean] - yes, in Scala even functions are traits, declared as:

trait Function[-A,+B]

So functions are contravariant in their parameter types and covariant in their return types.

OK, that's it; this is the minimal explanation I wanted to cover.

Posted by Martin Konicek on 11:39 PM 8 comments

Software engineering radio - best episodes

Software engineering radio is an excellent podcast full of in-depth information for developers; contains high quality content different from what you usually find online.


NoSQL and MongoDB with Dwight Merriman
Top 10 Architecture Mistakes with Eoin Woods
Being a consultant - honest, informal and funny
Software Craftsmanship with Bob Martin - concentrated motivation
Stefan Tilkov on REST - quite practical
Singularity research OS - microkernels, safety, static code analysis


Martin Odersky on Scala - great interview with the author of Scala
Scala Update with Martin Odersky - second half provides insights into possible future of programming


Btw, Markus Völter (the guy behind se-radio) also does a podcast on technology and science. Software engineer talking to a Nuclear fusion expert - what could we want more? ;) I really enjoyed the following episodes:

Astrobiology at the NASA Astrobiology Institute
Quantum computing - kudos for mentioning the "next technical revolution"
Nuclear Fusion at MPI für Plasmaphysik

Please help me find great episodes - if you know about an episode that you really enjoyed, post it into comments. Thanks!

Posted by Martin Konicek on 2:00 PM 7 comments