00:00:09 You're welcome, S. H. A. C. H. Af. 00:06:16 Gracenotes: Do you understand the Eilbenberg-Moore category thing? 00:07:02 shachaf: I don't think I've seen those names in mah life 00:08:13 shachaf: read the Charity paper 00:08:15 it's interesting and stuff 00:08:16 kmc, shachaf, Gracenotes: what did you guys end up doing 00:08:20 there are commutative diagrams 00:08:40 nooodl: first we got hi by greeting each other for a while 00:08:45 and hugz all around 00:09:16 ghc joke 00:12:02 I really like the symmetry linear logic would give the getChar and putChar functions: getChar :: RealWorld -o (RealWorld * Char), putChar :: (RealWorld * Char) -o RealWorld 00:12:33 i hear realworld is satanic 00:12:43 i hear Bike is satanic 00:12:44 though those types are isomorphic to what Haskell has 00:12:45 In actual Haskell, yeah, I think so. 00:12:57 modulo optimization 00:13:09 i saw a sign on a church which i thought said satan worship 00:13:13 but it actually said sunday worship 00:13:18 Yeah, doesn't GHC have IO a = RealWorld -> (RealWorld, a) internally? 00:13:24 Or something like that? 00:13:35 "something like that", sure. 00:13:37 RealWorld is unboxed and so is the tuple 00:13:48 btw do people here use bessel functions. they seem cool. i like them 00:13:57 And also it's not RealWorld, it's State# RealWorld. 00:14:06 And it has nothing to do with the normal world-passing explanation of IO. 00:14:11 it's more like a low-level IO operation says "I will only give you back a real world when I'm done doing my thing, damnit" 00:14:12 It's just implementation trickery. 00:14:31 State# RealWorld fits in a zero-sized register. 00:14:35 let me show you my bessels 00:14:46 for example, putChar will only give you back a () when it gets an Int, namely the one that's returned from a write syscall 00:14:58 Bike: hm where was the place i heard about Bessel functions 00:15:25 So like "data IO a = IO (State# RealWorld -> (# State# RealWorld, a #))" or something? 00:15:49 imo ghci knows the exact definition (:i) 00:15:52 or 00:15:53 @src IO 00:15:53 Source not found. Are you on drugs? 00:15:56 help 00:16:14 I will halp 00:16:14 Anyway most things people say about this definition are false. 00:16:16 Looks like yeah, it's exactly what I just said. 00:17:16 shachaf: so does this mean that >>= for IO doesn't actually look like >>= for State, as one would think? 00:17:23 unIO :: IO a -> (State# RealWorld -> (# State# RealWorld, a #)) 00:17:23 unIO (IO a) = a 00:17:26 there's that 00:17:34 also: bindIO (IO m) k = IO $ \ s -> case m s of (# new_s, a #) -> unIO (k a) new_s 00:18:01 That looks just like >>= for State, doesn't it? 00:18:16 and GHC.Types, newtype IO a = IO (State# RealWorld -> (# State# RealWorld, a #)) 00:18:38 so, err, essentially what you said 00:18:39 The only point of it is to tell the compiler about certain data dependencies etc. that it's not allowed to do certain involving. 00:19:10 shachaf: btw: I don't know where the place you heard about bessels was?? 00:19:32 Bike: btw: ok?? 00:19:38 ok 00:23:24 scroll_count=0; 00:23:47 scroll_count+=4; 00:23:55 No. You have to put zero 00:24:19 scroll_count == scroll_count = scroll_count; 00:24:26 scroll_count*=1e518; 00:24:36 you don't tell me what i have to do! 00:24:43 I assume that associates as (scroll_count == scroll_count) = scroll_count, which is invalid. 00:25:08 if you assume it associates the other way, it is true 00:25:20 Not if scroll_count is NaN. 00:25:42 Don't you love values that aren't == to themselves... 00:26:11 I'm kind of disappointed that NaN isn't == to itself even in Haskell. 00:26:46 undefined ain't == to itself neither. 00:26:57 Yeah, but at least you don't get False. 00:27:25 scroll_count is an integer, duh 00:27:47 scroll_count="norway"; 00:28:00 "norway" can be cast to an integer, can't it? 00:28:06 all of your statements are in the shachaf namespace 00:28:19 tswett: in C, you can write char c = 'norway'; 00:29:12 or int c, if you like widening conversions 00:30:47 uint48_t c = 'norway'; 00:32:36 if you assume it associates the other way, it is true <-- i think it's undefined behavior hth 00:33:52 maybe a bit, maybe not as much in say C++0x (I don't recall if their new sequencing rules help here), but it's usually never unsafe to optimize 'x = x' to 'x' 00:34:25 Is there really a uint48_t... 00:34:38 no, but I think there could be 00:34:51 and multichar literals could have that type 00:34:57 (I think) 00:34:59 The other day, I was trying to write some C in front of some other guy, and neither of us could remember whether it was uint16 or uint_16. 00:35:05 (It is, of course, neither.) 00:35:13 Gracenotes: It might be unsafe if it is volatile, though, isn't it? 00:36:01 it will be undefined if it's not volatile and there's simultaneous modification/reading. 00:36:48 Maybe there should be a uint_t for all nonnegative integers . Who knows when you might need a 333-bit integer? 00:37:06 if it is volatile, then it might be false. 00:37:14 -!- Nisstyre has joined. 00:37:20 if only because there is a memory barrier automatically set up with read/write of a volatile. 00:37:24 Or a 0-bit integer? 00:37:29 void? 00:37:32 tswett: I think LLVM has such a thing! 00:37:47 zzo38: I'd be disappointed if it didn't. 00:37:48 up to (iirc) 8Mbit integers 00:39:23 Darn. I can think of a use for 38762521924-bit integers. 00:39:31 I wish C++ supported "void x;". 00:39:50 In GNU C you can create zero-length arrays. 00:39:54 void foo() { void x; x = bar(); return x; } 00:40:14 (Black-C, which is my own specification, inherits some of the features of GNU C, including zero-length arrays.) 00:40:49 tswett: http://llvm.org/docs/LangRef.html#integer-type 00:41:09 And I think zero-length arrays is a useful and reasonable and logical feature to have. 00:41:21 shachaf: does that make void unit? 00:41:35 So what's the significance of the number 196882, anyway? 00:41:39 Gracenotes: Yep. 00:41:50 It would mostly be used for if you make a structure with an array of varying length at the end, although it can be used for some other purposes too. 00:42:14 I expect it could be optimized away, though 00:43:17 one of the versions of a language I implemented with project partner for a compilers course had, initially, the unfortunate property that the grammar did not allow function calls as statements; only as expressions. 00:43:25 GNU C already supports void foo() { return bar(); } 00:43:32 (Where "void bar();".) 00:43:37 Does Black-C support that? 00:43:46 what's that useful for? 00:43:46 what's Black-C 00:43:50 so the only way you could call a void function was by declaring a void variable, which the grammar also forbade. 00:43:51 shachaf: can you cast something to void in GNU C? 00:43:54 zzo38-C? 00:43:58 kmc: yes 00:44:13 ISO 9899-38 00:44:25 tswett: "(void) foo();" is valid ISO C, isn't it? 00:44:34 izzo 3899? 00:44:35 I dunno. 00:44:51 kmc: "Black-C" is some document I wrote. It is: http://zzo38computer.org/textfile/miscellaneous/black_c.txt 00:45:04 shachaf: yes 00:45:30 Do you think some of these things is reasonable things? 00:47:09 happy Algerian Independence Day 00:47:20 oh heh i forgot. 00:48:04 kmc: over in ##fiora we were discussing kmc hugz 00:49:11 what about them 00:49:19 shachaf: O no, I didn't mention "void foo() { return bar(); }" although I probably don't need to mention it, but maybe I should. 00:49:43 (If you read it, then you can see what things it does have) 00:50:27 `factor 38762521924 00:50:29 38762521924: 2 2 7 7 7 7 7 7 7 7 41 41 00:50:30 rainbow laser jesus 00:50:54 Oh look, it's a perfect square! I wonder what its square root is. 00:51:12 whence this number 00:51:31 I found its square root online, and then I found it by squaring its square root. 00:51:31 `factor 196882 00:51:32 196882: 2 7 7 7 7 41 00:51:40 shachaf: what about kmc hugz 00:54:41 tswett: ok but we still don't know its significance, right? 00:54:42 -!- nooodl has quit (Ping timeout: 264 seconds). 00:54:54 If that's the exclusive "we", then that's correct. 00:55:28 well if we exclude enough people... 00:55:47 There must be some set of people such that no person in the set is aware of the significance of that number! 00:56:19 Yes, the empty set, is one such set. There are probably others. 00:56:21 there might even be a way to prove that! 00:56:28 darn zzo38 ruining our joke 00:56:46 Oops sorry 00:56:54 it is the least set 00:57:01 hey oerjan 00:57:05 tell me a good fixed point theorem 00:57:12 but who are we to judge the relative worth of sets 00:57:20 i guess brouwer's is too obvious? 00:57:26 we, the measurers 00:57:33 banach's is where it's at come on 00:57:33 oh the last google hit mentions the monster group 00:58:32 although the variation in hits is rather impressive. 00:58:38 i guess most numbers do that. 00:58:40 I'm partial to the baby monster group tho 00:59:19 oh 196883 gave something monster-related as the first hit 00:59:39 `factor 196883 00:59:40 196883: 47 59 71 00:59:48 That number isn't much better. 01:00:24 "" 01:00:27 oops 01:00:36 "Robert A. Wilson has found explicitly (with the aid of a computer) two 196882 by 196882 matrices (with elements in the field of order 2) which together generate the monster group; this is one dimension lower than the 196883-dimensional representation in characteristic 0." 01:01:21 `factor 196884 01:01:22 196884: 2 2 3 3 3 1823 01:01:28 `factor 196881 01:01:29 196881: 3 29 31 73 01:01:43 196882 seems to be the best number so far. 01:02:28 i wonder if the large number of tiny prime factors for both 196882 and 196884 has some significance. 01:02:55 well i guess 1823 isn't very tiny. 01:03:50 shachaf: i am partial to the brouwer fixed-point theorem hth 01:04:24 i thought you were total :'( 01:04:48 `factor 488691 01:04:49 488691: 3 3 7 7757 01:04:55 just totalitarian, shachaf 01:05:04 `factor 288691 01:05:06 288691: 13 53 419 01:07:42 Hm. 3^10 * 109 + 2 = 23^5. 01:07:53 Pretty sure this is the most important theorem in the überverse. 01:08:25 (The überverse is the collection of everything, including at least one thing that is not in the überverse.) 01:08:38 shachaf: don't fix what ain't broke 01:09:27 tswett: O, so it also includes God (which, in turns, also includes the uberverse)? (or something like that; I don't know for sure) 01:09:29 Higgledy Piggledy / Oërjan Johansen / Likes Brouwer's Theorem / "hoping that helps"; // Secretly, though, he's a / Totalitarian / Undersea wizard king / Munching on kelps 01:12:50 It definitely contains God, yes. 01:14:12 `factor 7153 01:14:13 7153: 23 311 01:15:11 -!- dvorakbot has joined. 01:15:11 shachaf++ 01:17:19 Do you think a mobius strip is one sided, or do you think a mobius strip is two sided but that both sides are the same side? 01:17:21 So for a = 2^19, b = 7153, and c = 3^12, we have d = 2*3*7153, or... 01:17:26 $calc 2*3*7153 01:17:26 2*3*7153 = 42918 01:17:27 Note that .calc is deprecated, consider using .c 01:17:36 I think words don't actually mean things help. 01:18:01 Sure enough, c > d^(1+epsilon) for positive epsilon. 01:18:51 since when do we have a dvorakbot 01:19:03 Since 9:15 US EDT. 01:19:10 d.nl 01:19:12 ,day-o ircbi rb 01:19:21 it's old enough to have a deprecated command 01:19:24 $c log c / log d 01:19:25 Sorry, no result. 01:19:25 ekrpat 01:19:30 Uhhh. 01:19:34 -!- mnoqy has joined. 01:19:46 $c log (3^12) / log 42918 01:19:46 1.2358948 01:20:18 Bike: It doesn't? 01:20:28 it doesnt' 01:20:38 Are you sure? 01:20:43 no 01:20:46 So despite its musical importance, this ABC triple isn't good enough for this list: http://www.math.leidenuniv.nl/~desmit/abc/index.php?set=2 01:22:36 $c log 1024 / log 30 01:22:36 2.03795047 01:24:10 So wait. If a = 24 and b = 1000 and c = 1024, then we have d = 30, don't we? That'd make this an extremely high-quality triple. 01:24:29 shachaf: good poem tdh 01:24:40 Oh, duh, they have to be coprime. 01:24:58 So it's really a = 3, b = 125, c = 128. 01:25:02 $c log 128 / log 30 01:25:03 1.42656533 01:25:40 Apparently, the equality 3 + 125 = 128 was discovered by Benne de Weger in 1988. 01:25:59 It's very useful, we should thank them. 01:26:27 Yeah! 01:27:09 I know of three applications of this equality, two of them useful in music. 01:27:45 The first is that three major thirds are approximately an octave. The second is that 3 decibels are approximately a doubling. The third is that a kilo- is approximately a kibi-. 01:44:18 scrabble doesn't know "quine" :( 01:44:55 I need something to do for the next 17 minutes 01:45:00 Bike: it's a proper noun hth 01:45:02 porn 01:45:12 shachaf: like the kind of program. 01:45:21 no it's named after the person hth 01:45:26 it's not really a thing "sry" 01:45:51 Aren't there a lot of common nouns named after people? 01:46:20 yeah. 01:46:36 yeah, we call that kind of words sgeos 01:47:08 bikes, for instance, were clearly named after Bike. 01:47:21 yes] 01:52:45 hoovers are named after Phantom_Hoover 01:53:45 -!- Phantom_Hoover has quit (Quit: Leaving). 02:00:25 -!- Koen_ has quit (Quit: Koen_). 02:44:15 What's a nonlinear f such that f³ = id? 02:46:23 http://www.startrek.com/article/designing-the-romulan-dreadnought-warbirds https://encrypted.google.com/search?tbm=isch&q=babylon%205%20shadows 02:47:00 Bike: domain? 02:47:36 don't really care, just curious what it looks like. something easy like C would be nice i guess. 02:47:57 well, what does "linear" mean on an arbitrary set? 02:48:20 ok, the domain is a linear space. 02:48:40 Bike is a linear space 02:49:07 bikelinear 02:49:21 Bike's shed is the wrong colowr. 02:49:31 Therefore a linear space is a vehicle. 02:49:44 `smlist 408 02:49:46 smlist 408: shachaf monqy elliott mnoqy 02:49:48 `smlist (409) 02:49:50 smlist (409): shachaf monqy elliott mnoqy 02:49:51 Bikecurious 02:49:51 Bike: using the axiom of choice, divide the real numbers into three sets of cardinality c, putting 1, 2, and 3 in different sets 02:50:20 let f_1 : S_1 -> S_2, f_2 : S_2 -> S_3, f_3 : S_3 -> S_1 be bijections 02:50:46 erm, wait 02:50:48 no f_# 02:50:51 *no f_3 02:51:00 f_3 was my favorite :( 02:51:10 then take f_1 \cup f_2 \cup (f_2 \circ f_1)^{-1} 02:51:27 1 \cup 02:51:44 clearly nonlinear since 1 |-> 2, 2 |-> 3, 3 |-> 1 02:52:06 and should be pretty easy to see that its cube is the identity 02:52:34 ok, well. points for answering. 02:54:58 f(1) = 2, f(2) = 3, f(3) = 1, f(x) = x for anything else also works >:) 02:55:09 let me amend my question 02:55:16 answers that aren't boring + suck 02:55:19 plz 02:55:41 "a continuous one" would probably be what you want 02:55:48 assuming that exists 02:56:14 which it might not, on R, i don't quite recall 02:56:47 also do you actually need AC for coppro's answer. it doesn't seem ACy. 02:57:00 hm no you don't. 02:57:09 well you don't *have* to use it 02:57:17 just throw it in there for the hell of it 02:57:20 but it is coppro's axiom of choice, after all 02:57:27 but i mean, (-inf,1] (1,3) [3,inf) 02:57:36 coppro chose to use it 02:58:24 i vaguely think i've seen a reddit post asking this question. though it might just have been similar. 02:58:35 twist: Bike is a reddit post 02:58:42 !!!!! 02:59:09 gasp 02:59:20 wow that rainbow was p. bad 02:59:29 also inappropriate for the occasion 02:59:31 Bike: yes 02:59:37 of course a continuous one on R would have to be monotonous 02:59:40 why would you need AC 02:59:47 Bike: prove to me that you can break R into three sets with size c without it 02:59:54 i just gave you an example. 03:00:19 >_> 03:00:26 look, a penis! 03:00:27 * coppro hides 03:00:29 at least i don't /think/ you need AC for that 03:00:33 spoiler i'm shit at zfc 03:00:51 Bike: i heard HoTT was better 03:01:01 i'm even shittier at hott, hth. 03:01:24 you don't need any more AC than you need to construct the reals in the first place, anyway. by which i mean you can actually write "reasonably" simple explicit bijections. 03:01:49 oerjan: but that's so boring 03:03:07 hey oerjan do you know about T-algebras 03:03:15 oh hm 03:04:05 oh maybe that's the same as a T-module 03:04:09 do you know about T-modules 03:04:17 Bike: another boring, yet continuous option is to modify f(x)=-x by just stretching the parts before and after 0 in such a way that it's not linear but cancels out 03:04:24 i think 03:04:41 oerjan: that doesn't work for ^3 03:05:00 coppro: it doesn't? you don't have to stretch the same amount on each side... 03:05:22 oerjan: f^3 is not even close to id because it inverts sign 03:05:25 oops 03:05:37 can't just use a third root of unity instead of -1? 03:05:44 oh hm in that case f must actually be monotonic 03:06:14 Bike: fine if you use complexes it's just to do a distorded rotation around 0 03:06:23 *distorted 03:06:48 *monotonic _increasing_ 03:07:14 oerjan: just say functor imo 03:07:20 shachaf: cannot say i recall the word T-algebra, no 03:09:20 now, being increasing means that if f(x)>x, then f(f(f(x))) > x still, and vice versa for <. nope, continuous on R won't work. 03:10:07 so uh, why does it have to be monotonic, i misssed that. 03:10:07 * f(f(f(x))) > f(f(x)) > f(x) > x 03:10:34 Bike: every continuous bijection from R to R is strictly increasing or decreasing 03:10:49 oh. well then. 03:11:15 er... what about identity 03:11:18 decreasing will give a decreasing third power, so won't work. 03:11:44 Bike: except identity of course, which slips by because f(x) is neither > nor < x 03:12:47 i should become one of those loons who collect pdfs on their hard drive 03:12:50 like Bike 03:13:01 gimme a good paper manager first 03:13:12 http://www.youtube.com/watch?v=mFFGW8DLBrw 03:13:22 Bike: imo you give me one 03:13:23 checkmate 03:13:30 :( 03:13:51 Bike: also strictly increasing means that x < y => f(x) < f(y) in case you were confused by that f(x) > x thing which was something else following from it. 03:14:09 nah i knew that much 03:14:14 or contradicting it, rather 03:14:22 oerjan: what kind of functor is that 03:14:31 well, fuck orderings, complexes are where it's at imo. 03:14:45 shachaf: from the partial order category of R to itself hth 03:14:55 wait so what's non-strictly increasing 03:15:25 shachaf: you're allowed to have f(x) = f(y) 03:15:45 that sounds more like a functor to me 03:15:54 so what kind of functor does it have to be to be strictly increasing 03:16:04 faithful or something? 03:16:17 invertible, of course 03:16:21 or wait 03:16:34 it doesn't have to be onto 03:16:47 right 03:16:59 also continuity is also a stronger requirement. 03:17:03 sure 03:17:21 x such that f(x) < x is like an f-algebra 03:17:36 or is that ≤ 03:17:42 it's ≤ :'( 03:17:47 < is the devi 03:17:49 l 03:17:53 If it is a (thin) ordering category, then you need to have less or equal, as the morphisms, I think. 03:18:19 zzo38: greater or equal would also work hth 03:18:26 Yes, that would also work 03:18:49 Although I have generally seen less or equal; of course then the opposite category becomes greater or equal 03:19:14 what's a monad in a partial order called again 03:19:30 oh a closure operator 03:20:08 f such that x ≤ f(y) iff f(x) ≤ f(y) 03:22:16 (f x -> f y) -> (x -> f y) is just =<< :) 03:22:27 right 03:22:37 but you get the rest for free 03:22:55 wait 03:23:23 (x -> f y) -> (f * x -> f y) is just =<< :) 03:23:29 help 03:23:37 what does a-star have to do with it 03:24:08 my network connection broke down as i was typing 03:24:18 what's a-star but a secondhand search algorithm 03:24:31 * (x -> f y) -> (f x -> f y) is just =<< :) 03:24:57 yes 03:25:09 don't worry i ignored what you wrote and just assumed you wrote that 03:25:12 i think what happened is that it got so slow irssi thought the was being pasted instead of going to beginning of line 03:25:30 i think we've gotten pretty far from the original topic of things that aren't sucky 03:26:07 i'm with Bike computers suck 03:26:24 I think a monad would be x less or equal to f(x) and f(f(x)) less or equal to f(x), for example, a bitwise OR by a constant, I suppose, would be it. Is that it? 03:26:44 yeah fuck computers. 03:26:49 s/slow/jammed up/ 03:27:26 zzo38: And also monotonically increasing. 03:27:30 Because a monad is a functor. 03:28:21 Yes, and a monad is a functor. I forgot that. I still think bitwise OR by a constant, works 03:29:00 zzo38: that's pretty much the direct definition of closure operation 03:29:21 yep 03:29:35 well in particular x ≤ f(x) and f(f(x)) ≤ f(x) means that f(f(x)) = f(x) 03:29:46 since f(x) ≤ f(f(x)) 03:29:51 So yes you do need x less or equal to y, then it must also mean f(x) less or equal f(y) which still bitwise OR has. 03:30:14 shachaf: Yes, it must, I did see that too 03:31:47 A partial ordering is the same as a thin category. I suppose other mathematics things might also be considered as some kinds of categories, such as monoids as a category with one object, the paths of directed graphs as a category, etc 03:32:57 zzo38: No, a preorder is the same as a thin (small) category. 03:33:30 No antisymmetry required. 03:33:32 a skeletal thin category, then 03:34:39 It is skeletal if no different objects are equal, I suppose. 03:34:45 * oerjan just realized that is a pun 03:35:17 zzo38: which is part of the definition of partial order 03:35:37 O, I didn't know that. Now I know thank you 03:38:13 you're welcome 03:39:02 oerjan: i demand wisdom entries 03:39:04 http://www.youtube.com/watch?v=Sp9llVV0aS4 03:39:55 `run echo 'A partial order is just a thin skeletal category.' >wisdom/'partial order' 03:39:59 No output. 03:40:29 wait doesn't it have to be small 03:40:39 `run echo 'A preorder is just a thin category.' >wisdom/'preorder' 03:40:43 No output. 03:40:46