What does “abstract over” mean?

Question

Often in the Scala literature, I encounter the phrase \"abstract over\", but I don\'t understand the intent. For example, Martin Odersky writes

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Answer 1

To a first approximation, being able to "abstract over" something means that instead of using that something directly, you can make a parameter of it, or otherwise use it "anonymously".

Scala allows you to abstract over types, by allowing classes, methods, and values to have type parameters, and values to have abstract (or anonymous) types.

Scala allows you to abstract over actions, by allowing methods to have function parameters.

Scala allows you to abstract over features, by allowing types to be defined structurally.

Scala allows you to abstract over type parameters, by allowing higher-order type parameters.

Scala allows you to abstract over data access patterns, by allowing you to create extractors.

Scala allows you to abstract over "things that can be used as something else", by allowing implicit conversions as parameters. Haskell does similarly with type classes.

Scala doesn't (yet) allow you to abstract over classes. You can't pass a class to something, and then use that class to create new objects. Other languages do allow abstraction over classes.

("Monads abstract over type constructors" is only true in a very restrictive way. Don't get hung up on it until you have your "Aha! I understand monads!!" moment.)

The ability to abstract over some aspect of computation is basically what allows code reuse, and enables the creation of libraries of functionality. Scala allows many more sorts of things to be abstracted over than more mainstream languages, and libraries in Scala can be correspondingly more powerful.