#hereyougo

[staiiiircasewiiiit]

were getting ready to use that money instead of money that I put in the snapple machine that wasn't money and we getting ready to drop Edwin off to nurse Eunice in Andrew Irvings house is Marlenes house. We going to get caught I'm not in the mood for it. I gave my brothers dripped paint white and red Jordan to Andrew Irving. Hes doing jail time for us at all times.

[dacuala]

i like this motivating example for this:

fn print(x: Option<&str>) {

let x = match x {

Some(x) => x,

None => panic!("expected Some"),

};

println!("{x}");

}

which is similar to the implementation of unwrap. i dont think lifetimes are involved here? like in haskell you have e.g. error :: String -> a (which prints an error and aborts the program, which you can use as a value of any type a).

you can also implement a pseudo-never at the user level with an uninhabited enum {} - if you match a value of this type, you can coerce it to a value of any other type.

this and never let you express things that dont happen at the type level, like a Result<T, !> is a type-level guarantee that there is no Err variant (and thus it is always Ok), which is particularly useful for implementing traits where there is no possible error

Rust’s never type is wild to me.

So, if you’re not familiar with type theory, the empty type, which we’ll denote ∅ here (which Rust calls never, but more on that later) is the type with no elements.

But…how do you actually say that the type “has no elements” within the type theory?

You can’t say something like ¬∃x, x : ∅, in part because inside most type theories, this statement doesn’t even make sense: we need to know the type of x when bound, and more importantly, typing judgments like x : ∅ are not statements you can make within the theory itself.

Actually, you often don’t even want to use ¬ at all: we want to define ¬P in terms of ∅ as P → ∅ ! This is because having an element of the empty type would (if all goes well) be a contradiction, so if you can construct such a contradiction out of P (i.e. ->), then P must be false. ∅ is near the foundations, so we don’t have much to work with when setting up its meaning.

What we can do is encode the principle of explosion, i.e. that given an element of the empty type (a contradiction!) we can derive anything.

That is, we have an axiom explode : ∀(A : Type), ∅ → A. For any type A, give me an element x of ∅, and I will hand you an element of that type (namely explode A x : A).

(If you’re familiar, ignore universe polymorphism/Type vs. Prop and the fact that A isn’t a type family.)

This is what makes the empty type the empty type. If we didn’t include this axiom, the empty type would have no real emptiness behavior besides “gee, I can’t quite figure out how to make an element of this type”. You wouldn’t know it’s empty, since there would be no consequences to finding out that something has type ∅.

(Aside: this axiom fits into a very general pattern of what it means to define a type inductively, and lets us do “induction on the empty type”. It’s not ad-hoc!)

———

So it should be clear that if you ever do find an element of ∅, your theory is inconsistent, as you can prove anything you want.

Which is why Rust’s empty type, called never, is pretty neat. To me, someone who does not know Rust, and who literally opened the docs as soon as I installed them, scrolled down, and said “ooh, what’s never?”

See, Rust expressions can have type never. (I’m calling them expressions; I don’t know if this is what rustaceans call them)

But, how?! Surely that breaks everything! Well…yes. Which is why the only way to maintain consistency is to have these expressions break everything.

Let me explain: the things with type never never return a value (hence the name). They diverge: they’re things like exit or break or infinite loops.

And thanks to the explode axiom, these expressions can be coerced to any type. For example, you can say x: u32 = { exit() }, and Rust will say “makes sense to me”. (Apologies for any bad Rust syntax.)

This is—surprisingly!—fine.

exit() : never, just like any element of the empty type, really is a contradiction in the type system, but being able to write it in Rust code doesn’t actually make the type system inconsistent—since we leave the type system as soon as it’s encountered. (Or, in the case of an infinite loop, we never manage to actually finish constructing a value of never.)

So, while the syntax of Rust can contain “contradictions”, they never get the chance to behave as contradictions in the model of Rust’s type system formed by the values it constructs at runtime. I.e. running a real program never invalidates the type system. We’re saved from the runtime nonsense that would be created by explode A x by having the system actually explode instead.

There’s something to be said for this, but it is weird. Saying “x : u32” in Rust is apparently scoped in a certain way: it says “as long as the value we call x exists, it has type u32.” It doesn’t guarantee the existence of something with type u32.

This means that you don’t actually have to break the whole type system to use never; you just have to break the context in which x exists. E.g., if you’re inside a function, then let x: bool { return 500 }, where the return returns to the outer function, is fine. x never finishes being constructed, so the guarantee provided by its type annotation is (vacuously) satisfied.

I wonder if this is linked to the notion of lifetimes in Rust, and how that’s reflected in the theory behind the type system. And I’m not a type theorist (or someone who knows Rust), but I am also curious how type theorists talk about diverging terms; in Lean, for example, a top-level term of type Empty is verboten. You create diverging terms by using the partial keyword, and then you’re prohibited from proving anything about their behavior (but they still have types as usual).

This isn’t the first time people have talked about this, by far, I’m sure; happy to hear any takes (or corrections). Much to learn! :)

[chelshiart]

Is it weird to say that I'm lowkey delighted by the MB casting? Because seeing that actor reminds me that back when my siblings and I were kids, one time we were refueling the car and WHAM started playing on the radio, so we started miming the entirety of the gas station scene from Zoolander. I got to be Brint and blow everyone up in slow motion, and it was GREAT. 

Also it gave me the idea to draw this, so hereyougo :D 

Anyway, I'm happily in the 'wait-and-see' camp, and looking forward to see how they adapt the story to the visual medium! 

(Also bonus Ratthi speaking truth bombs: )

[imheresorry]

When Ford saw Fiddleford's dead body hereyougo

[grumblrs-confessional-booth]

can we see sun god..

Hereyougo keepinmind thisisjust mydrawingof Himsinceinformation andpicturesare notwidelyavailable howeverImsure

ifyouwent lookingyoudeventually findmorein booksorsomewhere PSimnot thebestat drawingsokeep thatinmind!!!

[42-forty-two-42]

FLOWERS FROM A

*reads tag*

friend... This handwriting sucks, anyways hereyougo BYYEEEEE

💐

4͈̬͑̒ͅ2̰̈́͘ ͚̑̒4͍͌̾̌2̨̡̛̰͋ ̫̺̣̇4͚̈2̢̭̗͒̀̄ ̭̯͕́͗̚4̢̲́ͅ2̧̹̀̈̚.͓̪̂͂͑.̤̫́̑͝.͖̠͍́̐4̠̝͑2̗̋̈́̾.̲͙̲͋.͖̖̃͠ͅ.͕̞͇̒́̉4̬̼͊̓͂2̢̬͕̃̊ ̛̼̎̐4͓̐2̱̭͚̏ ̖̠̈́̌̿4̦̜̽̀͠2͍̇̿̍͜ ͓̦̓̅͜4̱̠͗̋̑2̈̈͘ͅ ̲̳͔͆͂4̠̏̕2̨̓͂ ̠͒̒͜4͂͜2̗͖̗͗ ̖̟̂̓͌4̗̕̕2̭̤̦̐͊.͓̩̓̈́͝.̞̀͘.̺̊̎̈́

( Again with the flowers...Why...Although this one is even more anonymous... )

[sadfruittheatre]

UHH UHHHHH HEREYOUGO *drops this at your doorstep and runs*

HELLO PLEASE COME BACK THANK YOU FOR DRAWING SUCH A BEAUTIFUL BABY BOY!!!!!

[fnvbennygecko]

im sorry but i think zelda should’ve stayed a dragon. i think if anything her possibly turning back into a hylian should’ve been like. dlc. or something i just think her sacrifice and then immediately going uhhh teehee she’s actually normal again. NO!!!! she sacrificed herself. she’s a dragon now. like i wouldnt mind her turning back it’s just how they do it feels so like. um well. hereyougo BYE. just so rushed. idk. sigh.

[dutifullyloudmilkshake]

[bangastrology]

What's your opinion on Scorpio venus + Libra mars? Thank you!.

https://bangastrology.tumblr.com/post/190554191495/what-is-your-opinion-on-someone-with-a-scorpio

[rattledazzlebones]

Last day. This ones for Alternate Universe. Had fun.

@ironstrangehaven

[fitness-trending-content]

40 min. LOW IMPACT AEROBICS, Fun workout for seniors and beginners 👴 🕺 https://newsinfitness.com/40-min-low-impact-aerobics-fun-workout-for-seniors-and-beginners/

[bagelbucket]

yeah hereyougo

can someone post that gif of jack and enniskissing

[adamboden]

Massive #goodluck #welldone and #itsgoingtobeokay to all our young people collecting #gcseresults today! #freshstart #hereyougo #theworldisyouroyster #dontworrybehappy Get in touch for places or to see how Bodens helps children to achieve their potential #performingarts #dramaschool #act #sing #dance #actortraining #dancetraining #singingtraining #acting #singing #dancing #training #afterschool #childrensclasses #kidsclasses #theatreschool #performing #performingartsschool #performingartsclasses #musicaltheatre https://www.instagram.com/p/ChrF03uImVA/?igshid=NGJjMDIxMWI=

[rsastudios]

Howdy 👋🏽 @madelenelisella Sytled: @cammacky . . . . . #postmypicsticks #fashionphotographer #cheadsmagazine #bauthentique #bohochic #laphotographer #behangover #wearethepeoplemag #acidmirroragency #yumemag #igworldclub_women #inpmag #yafloves #lamodels #coyculture#stickandstonesagency #rektmag #nextdoormodel #portraitpage #portraitsociety #fashion #lfmag #visualsoflife #editorial #liveauthentique #arsenic #naturalight #lastdaze #hereyougo (at Cabazon Dinosaurs)

[iassignpeoplehomestucktrolls]

Blubblub blub glub glubblub (hereyougo)

Blub blub blub glub glub blub

- @iassignpeoplehomestucktrolls

glublublub glublub blub gluh