This essay says that inheritance is harmful and if possible you should “ban inheritance completely”. You see these arguments a lot, as well as things like “prefer composition to inheritance”. A lot of these arguments argue that in practice inheritance has problems. But they don’t preclude inheritance working in another context, maybe with a better language syntax. And it doesn’t explain why inheritance became so popular in the first place. I want to explore what’s fundamentally challenging about inheritance and why we all use it anyway.
OK, that explains bool | byte, but how is an enum a sum type? And what’s a product type? A product of sets is a cartesian product. How does that work with types?
An enum is a sum type because the number of inhabitants of the enum is the sum of the inhabitants of its parts.
A product type’s number of inhabitants is the product of its parts’ inhabitants. So a struct would fit that definition, or a pair, or a tuple.
Looking at the pic on your Cartesian product link:
if A is an enum {x,y,z} and B is an enum {1,2,3}, then a struct AxB has 9 possible inhabitants.
OK, I think I’m getting it.
A product is a set that this is the result of an ordered cartesian products.
struct Car {
make: String,
model: String,
seats: u8,
}
Car = String X String x u8.
An enum is a series of "or"s.
enum Animal {
Dog,
Cat,
Giraffe,
Chimpanzee,
}
can also be thought of as Animal = Dog | Cat | Giraffe | Chimpanzee. Where Dog is a type that only has single value in its set aka Animal = {1} | {2} | {3} | {4}, but it could also be strings, or other objects. Rust however allows more complex objects:
enum ComplexEnum {
Nothing,
Something(u32),
LotsOfThings {
usual_struct_stuff: bool,
blah: String,
}
}
In this case is Something(u32) the equivalent of any “tagged” u32, meaning in memory it’s something like a Tag + 32 bits where Tag is a constant string of bits, maybe itself a u32? Wouldn’t that make it a product type?
But then LotsOfThings is itself a product type LotsOfThings = bool x String.
So to put it all together ComplexEnum = Nothing | TaggedU32 | (bool x String)? Is that correct?
So to put it all together
ComplexEnum = Nothing | TaggedU32 | (bool x String)? Is that correct?
Pretty much, yeah. But just be aware the tags are effectively unique constants, so each has only one value. For consistency I would write it as:
ComplexEnum = Nothing | Something(u32) | LotsOfThings(bool x String)
In this notation,Something(u32) could also be written as 1 x u32 because tags are constants.