/sci/ - Science & Math

S and K combinators only do computable functions.
Also please fuck off back to /g/.

>>15031127
>S and K combinators only do computable functions.
Can set theory make things which are not computable?

I am working on a /g/ thread now. I have Maid Phone code to share. It is a very basic text chat. I am also trying to figure out if I have anything to post in /x/, since I was invited to /x/.

>>15031144
No, but it pretends to make them using theological power of the completed infinity. Heres an example:
Let f(n) be 1 if n codes a program which halts in a finite number of steps, and 0 otherwise. To actually calculate the output of the function you would be required to perform an infinife amount of work in general, but if youre only pretending to be able to calculate it, this makes it a legitimate function just as real as f(n)=n+1.
This is one of the main qualms of the finitist community - that mathematicians pretend to be able to do things they cannot do and blur the line between the ideal and the actual.

>>15031160
If set theory can pretend to do something why can't combinators?

>>15031105
Hello and welcome back dragon maid anon, i know what combinatorics is but unfortunately i don't know what combinators are, what's their definition and where are they introduced?

>>15031328
Good to see you vampire maid from touhou. Somebody named Schonfinkel made it up in the 1920s. He was trying to remove stuff from symbolic logic because he thought it was interesting that everything can be expressed as NAND.

So he made 's' and 'k'.
[s[x_][y_][z_] -> x[z][y[z]]]
[k[x_][y_] -> x]

I don't know exactly how to use them because I haven't finished the book or the show. 's' and 'k' happen a lot of times and then you have a tree somehow.

>combinators show
https://youtu.be/PG2G5xSz0NQ

I would link the book but tiktok killed zlibrary. I have a paper one.

Have you heard of the https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence ?
Basically it relates proofs to programs and the propositions they prove to the types of those programs.
For example a proof of "A and B" is an ordered pair where the first item is a proof of A and the second a proof of B, and a proof of "A implies B" is a function that takes a proof of A as input and delivers a proof of B as output.

The combinators have a nice relation to Hilbert's axioms for logic:
https://en.wikipedia.org/wiki/Hilbert_system#Logical_axioms
>P1. [math]\phi \to \phi [/math]
>P2. [math]\phi \to \left( \psi \to \phi \right) [/math]
>P3. [math]\left( \phi \to \left( \psi \rightarrow \xi \right) \right) \to \left( \left( \phi \to \psi \right) \to \left( \phi \to \xi \right) \right)[/math]
>P4. [math]\left ( \lnot \phi \to \lnot \psi \right) \to \left( \psi \to \phi \right) [/math]
P1 is I
P2 is K
P3 is S

>>15031171
You could do that. For example, you could make up a halting oracle combinator that would tell you whether programs would halt, but if you wrote a program that invoked that combinator, you wouldn't be able to run it.

I like to use type theory as a floor (basically the proofs as programs idea), and in type theory we do similar stuff when we want to play pretend. For example, the axiom of excluded middle can be expressed as a pretend function that takes an arbitrary statement and tells you whether it is true or false.

>>15031105
Remember that anon that was going to foil all of your faggot globohomo plans? I'm currently learning optics and solid-state physics. Keep making your faggot waste-of-time threads while I'm absorbing knowledge that'll lead me into fucking over any hardware your maids carry, for the day the UN decides to send their animated army of non-deterministic automata.

>>15031105
>Wolfy
>in her book
it's an old autistic man you delusional faggot

>>15031899
He doesn't care and will never acknowledge it. I've tried asking him why he refers to everyone as a woman but he never replies.