Toes♀

@ Toes @ani.social

Posts

84
Comments

1289
Joined

2 yr. ago

🦋⃟💙 This city makes me feel so small A million people in this town But I could scream without a sound So I get high to pass the time Talk to someone I met online To make myself feel less alone

1mo ago

Galaxy S26 Ultra leak gives glimpse at new Privacy Display feature in action
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4

Toes♀ @ani.social 1mo ago
Been wanting this feature for the better part of a decade.

1mo ago

What's a video game you were bummed about finishing, wishing the experience lasted longer?

Baldur's Gate III, takes a long time to get started.

Its towards the very end of act 2 when the game feels like you've finally finished the "tutorial" section and are ready to play for real.

They needed another 6 to 9 acts easy.

1mo ago

Whats the worst baby name?

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Toes♀ @ani.social 1mo ago

Any of the biblical names, let's try to be more original and not get bullied

1mo ago

What's some small, completely meaningless detail in life that you can never unsee?

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Toes♀ @ani.social 1mo ago

Turns out there's a difference between a pepper and salt shaker. The diameter of the holes are wider for pepper, but you'll see many places put salt in them.

1mo ago

Do Costcos usually have an ATM machine?

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Toes♀ @ani.social 1mo ago

You can call your local one and ask.

It probably varies from store to store.

Your bank will also be able to tell you about any in network ones to save on fees.

1mo ago

What should I do with 2 old machines (Mac Mini and HP Pavilion g7)?

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Toes♀ @ani.social 1mo ago

Replace the Mac mini drive with a cheap ssd.

If you have one of the early Mac minis, try the 32bit version of alpine Linux.

My pending project is to set it up as a old game server.

1mo ago

Thats enough internet for today

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Toes♀ @ani.social 1mo ago

🤤

2mo ago

Is there a secure video chat that does not require a phone number?

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Toes♀ @ani.social 2mo ago

You can use element for that, just don't use a matrix.org account.

2mo ago

Why Japan’s internet looks weird — unless you live here

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Toes♀ @ani.social 2mo ago

I remember reading somewhere that japan and Korea still need to worry about internet explorer 6 support.

2mo ago

What are social status games? Are we hardwired to want social status?

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Toes♀ @ani.social 2mo ago

Ah I think I understand now.

Yeah, I would agree that people are hardwired to feel pressure to fit in socially. There's a balance too, if you don't stand out at all your chances of fulfilling those needs could be harmed. But if you're too odd, you'll be shunned. The internet did wonders connecting odd ducks to each other.

2mo ago

What are social status games? Are we hardwired to want social status?

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Toes♀ @ani.social 2mo ago

Are you talking about social pressures like when your coworkers all have better cars than you?

2mo ago

Quentin Tarantino probably got into movie making after misunderstanding what "film footage" meant.

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Toes♀ @ani.social 2mo ago

That's the kind of dedication we need in the cinema industry!

2mo ago

What is the cheapest console to get and collect for that still holds up?

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Toes♀ @ani.social 2mo ago

The SNES was my favourite console. Huge game library, still looks great on a oled or crt screen.

However, a modded handheld could play all those games and more such as a vita.

Could also put a pi in a portable case.

2mo ago

There are no odd numbers divisible by 2

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Toes♀ @ani.social 2mo ago

By god they are right, this might change the future of mathematics!

    

// 2024‑edition Rust
use std::rc::Rc;

/// Church numeral: given a successor `s: fn(u32) -> u32`,
/// returns a function that applies `s` n times.
type Church = Rc<dyn Fn(fn(u32) -> u32) -> Rc<dyn Fn(u32) -> u32>>;

/// 0 ≡ λs.λx.x
fn zero() -> Church {
    println!("Define 0");
    Rc::new(|_s| Rc::new(|x| {
        println!("  0 applied to {}", x);
        x
    }))
}

/// succ ≡ λn.λs.λx. s (n s x)
fn succ(n: Church) -> Church {
    // `label` is printed *before* the closure is created, so the closure
    // does not capture any non‑'static reference.
    println!("Build successor");
    Rc::new(move |s| {
        // `inner` is the predecessor numeral applied to the same successor
        let inner = n(s);
        Rc::new(move |x| {
            // first run the predecessor
            let y = inner(x);
            println!("  predecessor applied to {} → {}", x, y);
            // then apply the extra successor step
            let z = s(y);
            println!("  +1 applied to {} → {}", y, z);
            z
        })
    })
}

/// Convert a Church numeral to a Rust integer, printing each step.
fn to_int(n: &Church) -> u32 {
    let inc: fn(u32) -> u32 = |k| {
        println!("    inc({})", k);
        k + 1
    };
    let f = n(inc);               // f: Rc<dyn Fn(u32) -> u32>
    println!("  evaluate numeral starting at 0");
    f(0)
}

/// Even ⇔ divisible by 2
fn is_even(n: &Church) -> bool { to_int(n) % 2 == 0 }
fn is_odd(n: &Church) -> bool  { !is_even(n) }

fn main() {
    // ---- build the numerals step‑by‑step ----
    let zero = zero();                     // 0
    let one  = succ(zero.clone());         // 1 = succ 0
    let two  = succ(one.clone());          // 2 = succ 1

    // ---- show the numeric values (trace) ----
    println!("\n--- evaluating 0 ---");
    println!("0 as integer → {}", to_int(&zero));

    println!("\n--- evaluating 1 ---");
    println!("1 as integer → {}", to_int(&one));

    println!("\n--- evaluating 2 ---");
    println!("2 as integer → {}", to_int(&two));

    // ---- parity of 2 (the proof) ----
    println!("\n--- parity of 2 ---");
    println!("Is 2 even? {}", is_even(&two)); // true
    println!("Is 2 odd?  {}", is_odd(&two));  // false

    // Proof: “divisible by 2” ⇔ “even”.
    // Since `is_odd(&two)` is false, no odd number can satisfy the
    // divisibility‑by‑2 condition.
    assert!(!is_odd(&two));
    println!("\nTherefore, no odd number is divisible by 2.");
}