this post was submitted on 11 Apr 2024
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Programming Languages

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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.

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[โ€“] onlinepersona 10 points 7 months ago* (last edited 7 months ago) (19 children)

๐Ÿ™„ people who blindly say "inheritance is bad" or "composition over inheritance" and mean "no inheritance" are just like followers of religion. Always repeating the same stuff without thinking and being completely convinced they are right. Nigh everything has a place and a valid usecase and just because you don't see it doesn't mean nobody else does.

Edit: Also "sum types" and "algebraic data types" are horrible names. Pretty much the equivalent of "imaginary numbers". What the fuck is a "sum type"? How do you "add" types together? Adding numbers makes sense, it has a real world equivalent. Two balls in a cup, add one ball and you have three balls in a cup. Add color to water and you have colored water. Simple. But types? The fuck?

str | int is a sum type --> does that mean sum types are adding two spaces of possibilities together aka a union of two sets? The wikipedia article is so friggin bad at explaining it to people who aren't in the know.

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[โ€“] oessessnex 5 points 7 months ago (2 children)

The sum and product types follow pretty much the same algebraic laws as natural numbers if you take isomorphism as equality.

Also class inheritance allows adding behaviour to existing classes, so it's essentially a solution to the expression problem.

[โ€“] onlinepersona 1 points 7 months ago (1 children)

Yes, I know some of those words. Could you repeat that for those that aren't mathematicians or in the know?

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[โ€“] oessessnex 1 points 7 months ago* (last edited 7 months ago)

As you already figured out the types are sets with a certain number of elements.

Two types are isomorphic if you can write a function that converts all elements of the first one into the elements of the second one and a function which does the reverse. You can then use this as the equality.

The types with the same number of elements are isomorphic, i.e True | False = Left | Right. For example, you can write a function that converts True to Left, False to Right, and a function that does the reverse.

Therefore you essentially only need types 0, 1, 2, 3, ..., where type 0 has 0 elements, type 1 has 1 element, etc. and all others are isomorphic to one of these.

Let's use (*) for the product and (+) for the sum, and letters for generic types. Then you can essentially manipulate types as natural numbers (the same laws hold, associativity, commutativity, identity elements, distributivity).

For example:

2 = 1 + 1 can be interpreted as Bool = True | False

2 * 1 = 2 can be interpreted as (Bool, Unit) = Bool

2 * x = x + x can be interpreted as (Bool, x) = This of x | That of x

o(x) = x + 1 can be interpreted as Option x = Some of x | None

l(x) = o(x * l(x)) = x * l(x) + 1 can be interpreted as List x = Option (x, List x)

l(x) = x * l(x) + 1 = x * (x * l(x) + 1) + 1 = x * x * l(x) + x + 1 = x * x * (l(x) + 1) + x + 1 = x * x * l(x) + x * x + x + 1 so a list is either empty, has 1 element or 2 elements, ... (if you keep substituting)

For the expression problem, read this paper: doi:10.1007/BFb0019443

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