Why avoid subtyping?

Question

I have seen many people in the Scala community advise on avoiding subtyping "like a plague". What are the various reasons against the use of subtyping? What are the alternatives?

Answer 1

Types determine the granularity of composition, i.e. of extensibility.

For example, an interface, e.g. Comparable, that combines (thus conflates) equality and relational operators. Thus it is impossible to compose on just one of the equality or relational interface.

In general, the substitution principle of inheritance is undecidable. Russell's paradox implies that any set that is extensible (i.e. does not enumerate the type of every possible member or subtype), can include itself, i.e. is a subtype of itself. But in order to identify (decide) what is a subtype and not itself, the invariants of itself must be completely enumerated, thus it is no longer extensible. This is the paradox that subtyped extensibility makes inheritance undecidable. This paradox must exist, else knowledge would be static and thus knowledge formation wouldn't exist.

Function composition is the surjective substitution of subtyping, because the input of a function can be substituted for its output, i.e. any where the output type is expected, the input type can be substituted, by wrapping it in the function call. But composition does not make the bijective contract of subtyping-- accessing the interface of the output of a function, does not access the input instance of the function.

Thus composition does not have to maintain the future (i.e. unbounded) invariants and thus can be both extensible and decidable. Subtyping can be MUCH more powerful where it is provably decidable, because it maintains this bijective contract, e.g. a function that sorts a immutable list of the supertype, can operate on the immutable list of the subtype.

So the conclusion is to enumerate all the invariants of each type (i.e. of its interfaces), make these types orthogonal (maximize granularity of composition), and then use function composition to accomplish extension where those invariants would not be orthogonal. Thus a subtype is appropriate only where it provably models the invariants of the supertype interface, and the additional interface(s) of the subtype are provably orthogonal to the invariants of the supertype interface. Thus the invariants of interfaces should be orthogonal.

Category theory provides rules for the model of the invariants of each subtype, i.e. of Functor, Applicative, and Monad, which preserve function composition on lifted types, i.e. see the aforementioned example of the power of subtyping for lists.

Answer 2

One reason is that equals() is very hard to get right when sub-typing is involved. See How to Write an Equality Method in Java. Specifically "Pitfall #4: Failing to define equals as an equivalence relation". In essence: to get equality right under sub-typing, you need a double dispatch.

Answer 3

I think the general context is for the lanaguage to be as "pure" as possible (ie using as much as possible pure functions), and comes from the comparison with Haskell.
From "Ruminations of a Programmer"

Scala, being a hybrid OO-FP language has to take care of issues like subtyping (which Haskell does not have).

As mentioned in this PSE answer:

no way to restrict a subtype so that it can't do more than the type it inherits from.
For example, if the base class is immutable and defines a pure method foo(...), derived classes must not be mutable or override foo() with a function that is not pure

But the actual recommendation would be to use the best solution adapted to the program you are currently developing.

Answer 4

Focusing on subtyping, ignoring the issues related to classes, inheritance, OOP, etc.. We have the idea subtyping represents a isa relation between types. For example, types A and B have different operations but if A isa B we then can use any of B's operations on an A.

OTOH, using another traditional relation, if C hasa B then we can reuse any of B's operations on a C. Usually languages let you write one with a nicer syntax, a.opOnB instead of a.super.opOnB as it would be in the case of composition, c.b.opOnB

The problem is that in many cases there's more than one way to relate two types. For example Real can be embedded in Complex assuming 0 on the imaginary part, but Complex can be embedded in Real by ignoring the imaginary part, so both can be seen as subtypes of the other and subtyping forces one relation to be viewed as preferred. Also, there are more possible relations (e.g. view Complex as a Real using theta component of polar representation).

In formal terminology we usually say morphism to such relations between types and there are special kinds of morphisms for relations with different properties (e.g. isomorphism, homomorphism).

In a language with subtyping usually there's much more sugar on isa relations and given many possible embeddings we tend to see unnecessary friction whenever we're using the unpreferred relation. If we bring inheritance, classes and OOP to the mix the problem becomes much more visible and messy.

Answer 5

My answer does not answer why it is avoided but tries to give another hint at why it can be avoided.

Using "type classes" you can add an abstraction over existing types/classes without modifying them. Inheritance is used to express that some classes are specializations of a more abstract class. But with type classes you can take any existing classes and express that they all share a common property, for example they are Comparable. And as long as you are not concerned with them being Comparable you don't even notice it. The classes don't inherit any methods from some abstract Comparable type as long as you don't use them. It's a bit like programming in dynamic languages.

Further reads:

http://blog.tmorris.net/the-power-of-type-classes-with-scala-implicit-defs/

http://debasishg.blogspot.com/2010/07/refactoring-into-scala-type-classes.html

Answer 6

I don't know Scala, but I think the mantra 'prefer composition over inheritance' applies for Scala exactly the way it does for every other OO programming language (and subtyping is often used with the same meaning as 'inheritance'). Here

Prefer composition over inheritance?

you will find some more information.

Answer 7

I think lots of Scala programmers are former Java programmers. They are used to think in term of Object Oriented subtyping and they should be able to easily find OO-like solution for most problems. But Functional Programing is a new paradigm to discover, so people ask for a different kind of solutions.

Answer 8

This is the best paper I have found on the subject. A motivating quote from the paper –

We argue that while some of the simpler aspects of object-oriented languages are compatible with ML, adding a full-fledged class-based object system to ML leads to an excessively complex type system and relatively little expressive gain