Wentz: I was having a mathy discussion in ##programming
Gangloff: And it was, well, silly
Ishikawa: Because a spec is a spec, its defined by humans to be a certain thing
Silberman: And humans have defined anything to the power of 0 as 1, whether its the spec or infinity or whichever
Penner: Turing complete isn’t hard.
Demetree: The lambda calculus is turing complete.
Seargent: If you can implement the lambda calculus, you are turing complete.
Velez: You can implement the lambda calculus with just two Stacks.
Friddle: A JS array implements everything a Stack needs.
Brian: You can have multiple JS arrays at the same time.
Isla: Ergo, JS is turing complete.
Carotenuto: So, turing basically proves that a function hi,x where it is 1 if program ix halts, and 0 otherwise does not exist
Mellencamp: In terms of the halting problem, right?
Eidemiller: Er, he’s proving that h does not exist
Hengen: At least, according to the wikipedia explanation of his proof
Cadotte: Which is, well, wikipedia
Moake: What about ix = powerx,0
Kocian: How can you prove a general program converges onto a value if you cannot prove that it converges.
Senechal: What do you mean by not being able to prove that it halts/converges?
Broder: Have you solved the halting problem? 😛
Trevithick: Maybe i’m just insane
Scollard: What’s next? P != NP?
Glanden: Well i know what you mean, i guess the question is better phrased in what context
Sager: The halting problem states that it is impossible to know whether an arbitrary program halts converges or executes forever diverges.
Trobridge: Well it’d require a program that could read a program
Dustman: You’re asking now if it’s possible to know if that same arbitrary value halts converges onto a specific value.
Hirshberg: Same arbitrary function **
Firkey: Same arbitrary program **
Kypuros: Since we cannot even know if it’ll halt, how can we know it will halt on a specific value?
Golojuch: Well why can’t we know if it’ll halt? the power function by definition halts, it can be defined recursively
Demny: What it halts on is a bit subjective
Troise: Oh wait, you’re asking a different question.
Rojos: I’m focusing on h being the power function
Inacio: I was reading ix = powerx, 0 differently. 😛
Flenner: Yes, it’s possible to know about certain specific functions.
Enget: We always know that powerx, 0 halts given x : floating point number
Muro: Well, if a program was designed around that
Goudeau: If we know the structure of a program, we can generally know if it will halt or not.
Ramaswamy: I guess that’s like saying if there’s a program designed around a halting function, which still definitely halts
Straley: But it gets sorta recursive. a program that can read a program
Stotesberry: A program that can read a program that can read a program
Strycker: S/program/function/ ?
Pablo: Welcome to metaprogramming and tool authorship.
Mish: But that’s life right? it goes in a circle until an exception is defined
Romane: I’ve always enjoyed tool making and system design
Fack: Does system design fall under metaprogramming?
Barge: Programming about programming, yeah
Difilippo: But what is a design but a formula or a “program” for a program