One of those rare comments that I can't intuit the meaning of even though I know the definitions of all the words. In so far as this is math, this is completely, perfectly, thoroughly, abstract.
So in reality did you mean to say reified ie made concrete? Or did you mean to say obviated ie made irrelevant? And you think computer science did this? The thing where the point of the game is to build more and more abstract representations of things?
Like what do you think the word "abstracted" actually means?
The comment is praise for maintaining compatibility. To me, the sentence "It’s a testament to computer science that this has been so thoroughly abstracted over the years" means: "It’s a testament to computer science that the original notation has been successfully applied to many things without drastic changes". I don't know whether that is one of the standard definitions of the past tense verb "abstracted", but it's a common usage in software engineering.
> has been successfully applied to many things without drastic changes. but it's a common usage in software engineering.
give me an example sentence. let me try one: "<protobufs> have been abstracted over the years because they have been applied to many things without drastic changes". doesn't work
the only way in which "abstracted" is used in SWE is "abstracted away" or "abstracted out", which means ~the details aren't important or ~it's being handled by someone/something else for you. having written out this response i am now 100% sure it's the former in this case.
no one seems to get that what i'm making fun of here is this person reveling in the fact that they don't have to understand type theory "like our forefathers did" but then stating that fact using theory speak. it's like which is it: do you care about abstractions and abstracting things out (and thus should be fine with type theory) or are you a blue collar dev that just copy-pastes. you can't have it both ways (certainly you might try but this leads to the cognitive dissonance on display here).
It seems clear enough to me what the GP might have meant, at least clear enough that it need not be responded to with remarks like "Like what do you think the word "abstracted" actually means?" that reads to me as saying that, whatever the GP thinks, it is wrong.
Type notation presumably started off as a very concrete thing—probably just about anyone can read something like BOOL = TRUE | FALSE. But then—I'm speaking here from a general perspective of computer-theoretic notation, so it's entirely possible that these are not actual notations that occur in type theory—things were added like syntactic sugar, say, for character classes, about whose abstract-ness we can argue but which definitely adds a decoding layer for people not used to it; and things like parametrized types/higher types that very definitely do add abstraction. It's very likely that, almost any time a definition benefits from an extra side remark, "For example, …", it is illustrating an additional abstraction.
> let me give you an example sentence and you tell me if the word "abstracted" makes sense, in context:
> "the accounting spreadsheet abstracts away all of the calculus because all the numbers are written down exhaustively"
I'm not even sure what the meaning is supposed to be, because I would not expect to use a spreadsheet to do calculus. (Of course there are ways of forcing calculus into a spreadsheet, but I wonder if you just meant 'calculation'.) Here I would say that it is absolutely relevant to speak of a spreadsheet abstracting away the details of a computation: the logic of the spreadsheet will probably refer often to the contents of cells, without worrying about what the contents are, and that is very definitely a kind of abstraction.
I would certainly not call the process of entering numbers into a spreadsheet an abstraction; but it seems to be the opposite of what type theory does. For example, type theory allows general reasoning about families of types, without reasoning case by case for each individual one. This seems to be the very essence of abstraction (in which capacity it is, conceptually, not completely distinct from the formulas in a spreadsheet).
If you see no abstraction, only concreteness, in type-theory notation, I suspect that is more an indication that you have learned to see through the abstraction than that it isn't there.
how does it make sense to utter the sentence "this has been abstracted [away]" when the `this` is itself the essence of abstraction.
i'm not really sure how people aren't getting what i'm putting down here: type theory can't be abstracted away because type theory itself is the thing that does the abstracting.
> > It’s a testament to computer science that this has been so thoroughly abstracted over the years
As your brackets indicate, you are reading a word "[away]" that is not explicitly present in the text. It seems to me to make more sense to read it without adding "away". (Wiktionary, for example, does not require that, or any, preposition in sense 6 of https://en.wiktionary.org/wiki/abstract#Verb, which is the one that seems to me to fit here.)
For example, I am a mathematician, and I could say that mathematics has been abstracted over the years (millennia!). I do not mean that the mathematics has been abstracted away, which I agree with you would be in some sense meaningless, but rather that the mathematics itself has literally been abstracted: from only being able to count and do arithmetic with specific real-world objects, to being able to do count and do arithmetic with numerals that did not refer to a specific thing, to being able to use letter to refer to numerals of unknown or variable value, to … well, there's not such a clear linear progression after that, but there's definitely a tower of abstraction. I hope that this sense of "mathematics has been thoroughly abstracted over the years" is an intelligible one (even if phrased differently from the way I assume you, or perhaps even I, might phrase it ourselves). It is in that sense that I take the sentence "It’s a testament to computer science that this [meaning, I think, notation in type theory] has been so thoroughly abstracted over the years".
1. Separated or disconnected; withdrawn; removed; apart. [First attested in the mid 16th century.]
2. (now rare) Separated from matter; abstract; ideal, not concrete.
3. (now rare) Abstract; abstruse; difficult.
4. Inattentive to surrounding objects; absent in mind; meditative.
three of these four connote the same thing as "away".
i mean what's the point of fighting so hard to make up an interpretation of this word that doesn't exist when the obvious interpretation clearly fits: this person is happy that the type theory isn't relevant anymore.
> i mean what's the point of fighting so hard to make up an interpretation of this word that doesn't exist when the obvious interpretation clearly fits: this person is happy that the type theory isn't relevant anymore.
I agree that it's probably not worth two or more people, none of whom is ljm, fighting over what ljm might have meant, but neither I nor hathawsh (https://news.ycombinator.com/item?id=37149803) reads the comment the way that you do, so I am not so sure that this is the obvious interpretation, and I am fairly sure that it is not the most charitable interpretation.
The interpretation I reference in https://news.ycombinator.com/item?id=37152933does exist, and is supported by a dictionary definition just as yours is; so, without addressing whether it is obvious or whether it fits—surely subjective matters—it is certainly a possible interpretation, just as yours is.
anything is possible, including that none of these words are actually the words we think they are and we're actually communicating across an interdimensional gateway that's doing the translation for us. it is certainly possible, but just like with which interpretation of abstracted to take, it's certainly not probable.
Type theory started being developed before CS and computers were a thing. It was developed as a foundation for logic and math when the naive set theory was shown to be self-contradictory. Its notation developed with the general development of math notation as logic and model theory evolved over time.
Lambda calculus is an abstraction of computation - but it needs to be defined, somehow, and you can use prose ("a term is a character representing a parameter or value, an application of a term to another term is expressed by writing the two terms with a space between them") or rules ("term := x | y | z ; app := x x") where the rules are an abstraction of the ideas in the prose.
Similarly you can describe substitution with words or a formal syntax. The latter is usually more concise and less ambiguous.
Lambda calculus is arguably far more abstract because often type theories imply a lot of implrmentation constraints, which makes sense since that's kind of the piount.
