this post was submitted on 11 Apr 2024
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Programming Languages
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@onlinepersona @armchair_progamer
A type has a number of 'inhabitants'. 'Sum' indeed corresponds to adding the possible inhabitants together.
A Boolean has two inhabitants - true and false. A byte has 256 inhabitants. A BoolOrByte type has 258 inhabitants.
If you have BoolByte pair, that's a product type - 512 possible inhabitants.
It may make no fucking sense depending on your exposure to Java, where Void (literally 'empty') has an inhabitant, and Boolean has 5.
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?Anti Commercial-AI license
@onlinepersona
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.
Car = String X String x u8
.An enum is a series of "or"s.
can also be thought of as
Animal = Dog | Cat | Giraffe | Chimpanzee
. WhereDog
is a type that only has single value in its set akaAnimal = {1} | {2} | {3} | {4}
, but it could also be strings, or other objects. Rust however allows more complex objects:In this case is
Something(u32)
the equivalent of any "tagged"u32
, meaning in memory it's something like aTag + 32 bits
whereTag
is a constant string of bits, maybe itself au32
? Wouldn't that make it a product type?But then
LotsOfThings
is itself a product typeLotsOfThings = bool x String
.So to put it all together
ComplexEnum = Nothing | TaggedU32 | (bool x String)
? Is that correct?Anti Commercial-AI license
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 as1 x u32
because tags are constants.OK, so finally I get it. It's pity none of the blogs I've read or wikipedia articles in existence spell it out this way. Instead it's a bunch of math mumbo jumbo.
Thanks for helping me reach understanding 🙏 And thanks to @[email protected] too.
Anti Commercial-AI license