I am looking to define the following algebraic data type in scala:
sealed trait Beat
case object Rest extends Beat
case object Hit extends Beat
Is there any difference, if I were to define this instead as:
abstract sealed class Beat
case object Rest extends Beat
case object Hit extends Beat
i.e. using an abstract sealed class instead of a trait? The definitions appear to be equivalent.
There is no difference in the meaning of sealed whether you put it on an (abstract) class or a trait. So in your case, the two examples are indeed (almost) equivalent.
A difference between an abstract class and a trait comes apparent when a subclass wants to inherit from another class: A class/trait can always only extend a single class, but multiple traits. For example:
class SomeClass
sealed trait Beat1
abstract sealed class Beat2
case object Rest1 extends SomeClass with Beat1 // ok
case object Rest2 extends SomeClass with Beat2 // compile error
Otherwise, an abstract class and a trait are pretty much equivalent. The biggest differences in practice probably only appear once you are concerned about binary compatibility (kind of out of scope for this answer).
To add to gzm0's answer, a further difference between an abstract sealed class and a trait is that an abstract sealed class, like any other class but unlike a trait, can have constructor parameters:
abstract sealed class Duck(sound: String)
case object RealDuck extends Duck("quack")
case object RubberDuck extends Duck("squeak")
