[leshow]

I'm not sure if you can really express it in OO. Sum types are used to represent a closed set of variants. Inheritance like that isn't closed.

In languages that have both OO and ML/Haskell-style type systems like Scala, the fact that the set is closed is denoted by the keyword 'sealed'.

example

sealed trait Color

final case object Red extends Color

final case object Green extends Color

Color can only be Red OR Green. In your example you can have an Animal, a Dog, a Cat, and other things can inherit Animal and create more variants.

[vram22]

>Color can only be Red OR Green. In your example you can have an Animal, a Dog, a Cat, and other things can inherit Animal and create more variants.

True. I used traditional OO style inheritance in my example, and my question was about understanding the relationship between it and sum types, based on rbehrends' comment that I was replying to. Interesting, did not know this. So you are saying that sum types are sort of like inheritance with some limits - pre-defined types only. Sort of like an enum (though those do not have inheritance in them) but for classes or types.

[masklinn]

> So you are saying that sum types are sort of like inheritance with some limits

Traditionally sum types don't have inheritance, you have the sum type is a type and the variants (or constructors) are values of that type, but yes you could also model it as a "closed inheritance" hierarchy, in fact some languages do exactly that: Scala with sealed traits and case classes (the trait is the sum type, each class is a variant) and Kotlin with sealed classes.

The boundaries can also get fuzzy the other way around, OCaml has polymorphic variants and extensible variants which blur the line. Polymorphic variants are structural types where multiple sum types share the same value (polymorphic variant types are venn diagrams essentially), not entirely unlike integral types, and extensible variants (as their name denotes) can get cases added to them by users of the base package/type.

> Sort of like an enum

Sum types can be seen as an extension of enums yes, Rust and Swift call them that, in both languages they're enums where each "value" (variant) can carry different data sets (unlike e.g. Java enums where variants are instances of the enum class). Here's a "degenerate" C-style enum with Rust:

    enum Color { Blue, Red, Green }

and here's one with associated data:

    enum Color {
        RGB(u8, u8, u8),
        HSL(Hue, Saturation, Lightness),
        CMYK(u8, u8, u8, u8),
    }

[vram22]

Good info, thanks.

[vram22]

>final case object Red extends Color

On a side note, that syntax seems a little counter-intuitive - the extends word seems to indicate that Red is a subclass of Color, but from what you said seems more like Red and Green are values for Color. So it seems like an enum would be more appropriate here (for this use of Red, Green and Color)?

[dragonwriter]

A Scala “object” declaration declares a singleton; it's an object, but you can also define object-specific class features.

If the instances need behavior (which in practice they often do), this is useful. Presumably, in the example, they would in a substantive program, but the behavior is irrelevant to the illustration and thus omitted.

[vram22]

Interesting, thanks.