#lambda calculus

[pig-lota]

So I want to write a story but mostly all I can come up with is a really in depth magic system so I am tempted to just write a story about Kaisa and Johanna from Hilda but with my magic system. I need to relearn some lambda calculus to finish up the magic system.

If a webserial about Kaisa and Johanna falling in love with probably bad writing but a very nerdy magic system added in sounds appealing to anyone please let me know lol. (Basically I'm thinking something along the lines of Johanna wants to learn some magic to make sure she can protect herself and Hilda, and Hilda/Frida introduced her to Kaisa, chemistry ensues. I'm planning on basically adding a written notation to the witchcraft in Hilda which is based on geometric logic and operations. So like writing the navier Stokes equation in a custom visual lambda calculus notation could be involved in controlling wind.

[hexiflexi]

just found out about lambda calculus!

(beta reduction my love, please I must learn more...)

[pretzelbea]

just learned about lambda calculus. why tf did I not learn about this shit it’s cool as fuck.

[paracanisbrunnea]

everything i'm about to say is based on this video up to and including the section on boolean arithmetic, so you should watch this before continuing

i believe i know how to write not only OR (^) as the video challenges, but also NAND (!&), NOR (!^), and XOR.

I'll recap AND (&) first, because in order to reach ^, i had to understand &. & is written as follows:

\xy.(x(y FALSE))

but reasoning this was necessary to understand how to write OR. 2swap mentions using x as a selector, but on first watch, i didn't know what they meant. It took me two or three viewings to understand that x is being used as a stand-in for the first boolean, and this is used to encode the answer. If x is FALSE(F), the output is FALSE, because FALSE is simply a function that picks the second of two values. If x is TRUE(T), x is whatever y is. This is explained in the video.

Now we arrive at OR. The way OR works is that ^ is TRUE if any of its arguments are TRUE. we can encode this as follows:

\xy(x(T_))

If x is FALSE, x will select whatever the second input is, since the statement can still be TRUE is the first statement is FALSE. This is written as:

\xy(x(T y))

This is the OR function.

I also promised NAND, NOR, and XOR, so i will cover !& and !^ next.

I reached !& and !^ with the same reasoning as OR. where x is a function that determines trueness or falseness.

Let's start with NAND. NAND TAKES 2 inputs, and is false if both arguments are true.

\xy(x(__))

Alternatively, we can think of NAND as a function where if ANY input is false, the argument is TRUE. we can write this by encoding TRUE in the second slot, because the argument would automatically pass if the first argument were FALSE.

\xy(x(_T))

if the first argument of NAND is TRUE, !& is whatever the second argument isn't. If x is TRUE, but y is FALSE, !& is TRUE. If x is TRUE and y is TRUE, !& is FALSE. This can be written as:

\xy(x(!y T))

This means if x is TRUE, x is not y, and y will be passed through the NOT function \w(w(F T)).

NOR is simpler. !^ is FALSE if any argument is TRUE.

\xy(x(F !y))

which brings us to XOR. i believe XOR is \xy(x(!y y)). I will explain my though process.

XOR is a function of two inputs that can only be true if ONE of the arguments is TRUE.

\xy(x(__))

If x is FALSE, x is whatever y is. if x is TRUE however, x is whatever y ISN'T.

\xy(x(!y y))

\xy(x((\w.w(f t))y y))

\xy(x((\w.w(\ab.b)(\ab.a) y) y)

[michaelrotonal]

(λx.x x)(λx.x x)

[piratesexmachine420]

Whoa lambda calculus is so cool

[retrocompmx]

Efemérides computacional: 14 de junio de 1903 nace Alonzo Church, fundador de la informática teórica

Conoce a Alonzo Church, el padre de la informática teórica. Su cálculo lambda sentó las bases de la computación moderna mucho antes de las PCs. #alonzochurch #informáticateórica #retrocomputingmx #cálculolambda

[suchpostsveryblogwow]

I've been meditating on the Lambda Calculus lately and today I was scrolling Tumblr and heard some quote about how if all you're ever doing is thinking then eventually all you ever have to think about is thinking itself and I was like damn called out

[monado-stew]

[rainbowtiredoftheworld]

I keep seeing software developers with my same degree, who get payed (presumably) the same as me, bragging that they copy-paste code from chatgpt, and like... Do you not have dignity? Aren't you ashamed of yourselves? The average quality of code is already abysmal, what is there to be proud in making it worse?

[gayarograce]

yknow, lambda calculus is something that, since i've found out about it, i wish i could actually wrap my head around, but try as i might i just can't quite fully understand using it

[notarealwelder]

Suppose you have 2 paths p : x ↝ y and q : y ↝ z. What's a better symbol for their concatenation, the path (p ? q) : x ↝ z?

(That is to say, we have 2 continuous functions p,q : [0;1] → X, with endpoints p 0 = x, p 1 = q 0 = y, q 1 = z. )

[fragonards-fav-fatal-femme]

We all know too horny to function, but have we considered too function to horny?

[jamierthanyou]

wow i absolutely do NOT understand sequential lambda-calculus

[wakuseicloset]

Why did umineko turn into a logic/semantics class

[yuritypology]

'god i wish i had smart in stem autism instead of blorbo autism' is such weak mentality because if you have stem autism your special interests wouldn't be something like curing cancer or fusion reaction but about lambda calculus and katydid morphology