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The name for them feels a bit unfortunate, to me. The vast majority of programmers know of algebra from grade school, at best. And there you think of algebra

by taeric 1y ago

The name for them feels a bit unfortunate, to me. The vast majority of programmers know of algebra from grade school, at best. And there you think of algebra as being able to do symbolic operations on equations. Not so much as "algebra over a field." I think it is fair to say that that is the more unfortunate naming, maybe? I still contend that that is what people think of when they hear the term, though.

bananaflag 1y ago
I always thought "algebraic" sounds unscary because in high school / undergraduate, algebra feels easier than analysis. Now, "analytic data types", that would be something.
- thechao 1y ago
  Right. So, there's a unit type: the type that the sum of returns the other type, i.e., a + () = a So that means there's an identity type for the product type operator: a * 1 = a I.e., the type that you can "multiply" by that doesn't give you a two-field tuple, but just returns the single-field tuple. If "1" is a type, then we can build a sum-type with it: a + 1 = (a, 1) Ok. Cool. But! If we can "add 1", then we should be able to remove "1", right? That kinda implies that "-1" exists: (a, 1) -1 = (a,) # don't shoot the messenger, I'm just riffing But, that also implies that we can allow a product type whose result is the "-1" type? (i, i) = -1 OH NOES!
- adastra22 1y ago
  Why not just “struct” or “record” and “enum” or “variant”?
- taeric 1y ago
  Apologies, I missed this yesterday. It isn't that it is scary. It is that it connotes something about equations and such. It is literally the name of the class people learn how to symbolically solve quadratic equations and such. I was saying in another thread that I think this would be a lot more obvious if people actually did algebra on the types. But we don't. At least, I can't recall ever seeing it done. Closest I've seen is in places where people have to do so to justify the naming here. And I want to be clear, I specifically mean using + and * with types. And not that it can be done. Is it done?
dfabulich 1y ago
I strongly agree. Algebraic types aren't "scary," but "algebraic types" is a bad term for what they are. In all popular languages that support "sum types" we just call them "unions." Your favorite programming language probably already supports unions, including Python, TypeScript, Kotlin, Swift, PHP, Rust, C, and C++. C# is getting unions next year. The article never mentions the word "union," which is overwhelmingly more likely to be the term the reader is acquainted with. It mentions "sets" only at the start, preferring the more obscure terms "sum types" and "product types." A union of type sets kinda like a sum, but calling it a "sum" obscures what you're doing with it, rather than revealing. The "sum" is the sum of possible values in the union, but all of the most important types (numbers, arrays, strings) already have an absurdly large number of possible values, so computing the actual number of possible values is a pointless exercise, and a distraction from the union set. Stop trying to make "algebraic" happen. It's not going to happen.
- chrisnight 1y ago
  > In all popular languages that support "sum types" we just call them "unions." When I was doing research on type theory in PL, there was an important distinction made between sum types and unions, so it’s important not to conflate them. Union types have the property that Union(A, A) = A, but the same doesn’t hold for sum types. Sum types differentiate between each member, even if they encapsulate the same type inside of it. A more appropriate comparison is tagged unions.
  - wasabi991011 1y ago
    So, disjoint union in set theory terms? If I understand correctly .
  - adastra22 1y ago
    What you are calling Union type is not what GP is talking about.
- dkarl 1y ago
  > Stop trying to make "algebraic" happen. It's not going to happen It's been used for decades, there's no competitor, and ultimately it expresses a truth that is helpful to understand. I agree that the random mixture of terminology is unhelpful for beginners, and it would be better to teach the concepts as set theory, sticking to set theoretic terminology. In the end, though, they'll have to be comfortable understanding the operations as algebra as well.
dkarl 1y ago
I think the term "algebra" is nice and neutral, common ground from grade school through college mathematics and higher, and I think it's a good clue for someone who doesn't have much math background. "You know how you learned to do math operations on numbers, and then in algebra class you learned to do them on other things like variables and equations? You can do operations on types as well." It's inevitable that someone starting from zero like this needs some time to get used to the ideas. Nobody learns this stuff instantly. Even if they can read an explanation in ten minutes and understand every word of it, it still takes time for the ideas to sink in and become natural. That's why an undergraduate math course might only cover a couple hundred pages in a semester. For someone not used to the process of absorbing ideas like these, the time it takes can be confusing and disappointing, but it's normal. I think one point of confusion that could be avoided is that areas of math that are initially taught as separate topics often get freely mixed in introductory explanations of type theory. For example, someone who is exposed to a little bit of set theory in one class, and a little bit of logic in another, probably thinks of these things as separate from each other and both separate from algebra. But then an explanation like this confuses them by freely interchanging "union" and "sum" and the operator "|" which programmers learn as logical "or." Ideally, I think an introduction should stick to a single set of terminology from one area (I would pick set theory) at first, and after the student is comfortable with the concepts and operations, only then show how the other terminology maps to the ideas the student has learned.
- taeric 1y ago
  Oddly, that is precisely my problem with it as a name. I can't do any "basic algebra" operations on these things. I say this as someone that is having to help my grade schoolers learn algebra this week, actually. :D I can squint to see where things are going and how they intersect. But it takes a lot of squinting.
  - adastra22 1y ago
    Where are grade schoolers learning algebra?
    - 1y ago

by taeric 1y ago

bananaflag 1y ago

I always thought "algebraic" sounds unscary because in high school / undergraduate, algebra feels easier than analysis. Now, "analytic data types", that would be something.

thechao 1y ago
Right. So, there's a unit type: the type that the sum of returns the other type, i.e., a + () = a So that means there's an identity type for the product type operator: a * 1 = a I.e., the type that you can "multiply" by that doesn't give you a two-field tuple, but just returns the single-field tuple. If "1" is a type, then we can build a sum-type with it: a + 1 = (a, 1) Ok. Cool. But! If we can "add 1", then we should be able to remove "1", right? That kinda implies that "-1" exists: (a, 1) -1 = (a,) # don't shoot the messenger, I'm just riffing But, that also implies that we can allow a product type whose result is the "-1" type? (i, i) = -1 OH NOES!
adastra22 1y ago
Why not just “struct” or “record” and “enum” or “variant”?
taeric 1y ago
Apologies, I missed this yesterday. It isn't that it is scary. It is that it connotes something about equations and such. It is literally the name of the class people learn how to symbolically solve quadratic equations and such. I was saying in another thread that I think this would be a lot more obvious if people actually did algebra on the types. But we don't. At least, I can't recall ever seeing it done. Closest I've seen is in places where people have to do so to justify the naming here. And I want to be clear, I specifically mean using + and * with types. And not that it can be done. Is it done?

dfabulich 1y ago

I strongly agree. Algebraic types aren't "scary," but "algebraic types" is a bad term for what they are. In all popular languages that support "sum types" we just call them "unions." Your favorite programming language probably already supports unions, including Python, TypeScript, Kotlin, Swift, PHP, Rust, C, and C++. C# is getting unions next year. The article never mentions the word "union," which is overwhelmingly more likely to be the term the reader is acquainted with. It mentions "sets" only at the start, preferring the more obscure terms "sum types" and "product types." A union of type sets kinda like a sum, but calling it a "sum" obscures what you're doing with it, rather than revealing. The "sum" is the sum of possible values in the union, but all of the most important types (numbers, arrays, strings) already have an absurdly large number of possible values, so computing the actual number of possible values is a pointless exercise, and a distraction from the union set. Stop trying to make "algebraic" happen. It's not going to happen.

chrisnight 1y ago
> In all popular languages that support "sum types" we just call them "unions." When I was doing research on type theory in PL, there was an important distinction made between sum types and unions, so it’s important not to conflate them. Union types have the property that Union(A, A) = A, but the same doesn’t hold for sum types. Sum types differentiate between each member, even if they encapsulate the same type inside of it. A more appropriate comparison is tagged unions.
- wasabi991011 1y ago
  So, disjoint union in set theory terms? If I understand correctly .
- adastra22 1y ago
  What you are calling Union type is not what GP is talking about.
dkarl 1y ago
> Stop trying to make "algebraic" happen. It's not going to happen It's been used for decades, there's no competitor, and ultimately it expresses a truth that is helpful to understand. I agree that the random mixture of terminology is unhelpful for beginners, and it would be better to teach the concepts as set theory, sticking to set theoretic terminology. In the end, though, they'll have to be comfortable understanding the operations as algebra as well.

dkarl 1y ago

I think the term "algebra" is nice and neutral, common ground from grade school through college mathematics and higher, and I think it's a good clue for someone who doesn't have much math background. "You know how you learned to do math operations on numbers, and then in algebra class you learned to do them on other things like variables and equations? You can do operations on types as well." It's inevitable that someone starting from zero like this needs some time to get used to the ideas. Nobody learns this stuff instantly. Even if they can read an explanation in ten minutes and understand every word of it, it still takes time for the ideas to sink in and become natural. That's why an undergraduate math course might only cover a couple hundred pages in a semester. For someone not used to the process of absorbing ideas like these, the time it takes can be confusing and disappointing, but it's normal. I think one point of confusion that could be avoided is that areas of math that are initially taught as separate topics often get freely mixed in introductory explanations of type theory. For example, someone who is exposed to a little bit of set theory in one class, and a little bit of logic in another, probably thinks of these things as separate from each other and both separate from algebra. But then an explanation like this confuses them by freely interchanging "union" and "sum" and the operator "|" which programmers learn as logical "or." Ideally, I think an introduction should stick to a single set of terminology from one area (I would pick set theory) at first, and after the student is comfortable with the concepts and operations, only then show how the other terminology maps to the ideas the student has learned.

taeric 1y ago
Oddly, that is precisely my problem with it as a name. I can't do any "basic algebra" operations on these things. I say this as someone that is having to help my grade schoolers learn algebra this week, actually. :D I can squint to see where things are going and how they intersect. But it takes a lot of squinting.
- adastra22 1y ago
  Where are grade schoolers learning algebra?
  - 1y ago