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00:13:17 <salpynx> what is the BLC notation for this alpha / smaller iota?
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00:54:21 <salpynx> I'm not sure what to do with the Kz , (\_.z) at the end, I'm clearly doign at least one thing wrong to come up with length 29: 00 00 00 00 01 11110 01 110 01 1110 110
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02:11:13 <esolangs> [[User talk:PythonshellDebugwindow]] https://esolangs.org/w/index.php?diff=92027&oldid=84071 * Photon Niko * (+766) CIrcles?
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02:58:30 <salpynx> I think it is: 00 01 10 00 00 00 01 110 01 1110 110
03:00:57 <salpynx> λ.1(λλλ.2(3 2)) instead of λλλλ.4 2(3 2), which was what my first attempt was (barring notation errors)
03:01:31 <int-e> salpynx: alpha is 00 00 00 01 01 1110 10 01 110 00 110, alpha' is 00 00 00 01 01 110 10 01 1110 00 110
03:03:00 <int-e> \x\y\z. x z (y (\_. z)) and \x\y\z. y z (x (\_. z))
03:04:57 <salpynx> thanks, let me process that in terms of how I've been working to figure out where I went wrong...
03:08:22 <salpynx> so: λλλ. (2 1) (3 λ.2) in De Bruijn format?
03:20:39 <salpynx> I got the associativity direction wrong on the original lambda notion. I went wrong on the first step :(
03:35:33 <salpynx> why is (\_. z) = 00 110 and not 00 00 110 ? I can't see where in a description of BLC / De Bruijn / Lambda notation why a lambda taking one argument (00 x in BLC) can refer to the second argument
03:36:23 <int-e> \_. z is not a closed term by itself; z is free there
03:36:42 <int-e> but there's three more lambdas further out
03:37:24 <salpynx> so that's the significance of the underscore symbol?
03:37:58 <int-e> it just indicates that the variable is unused
03:38:10 <int-e> we could write \w.z instead
03:39:13 <salpynx> so 00 1110 would also be valid
03:39:36 <salpynx> but 00 11110 would be an error in that position?
03:39:55 <int-e> no that would still be fine
03:40:45 <int-e> 111110 would no longer refer to any of the lambdas
03:41:31 <salpynx> which lambda does 11110 refer to?
03:41:53 <int-e> that is, the first one
03:42:29 <int-e> i.e., with names: \x\y\z. x z (y (\_. x))
03:44:13 <int-e> the unnamed _ would have index 1, z has index 2, y has index 3, x has index 4; there's nothing beyond that
03:45:00 <int-e> maybe let's fully parenthesize the thing? alpha = \x\y\z. ((x z) (y (\_. z)))
03:46:42 <int-e> (the convention is that lambdas extend as far as possible to the right)
03:47:13 <salpynx> oh, I see, it's pretty straightforward; within \_, if z is 110, y is 1110 and x is 11110, and 111110 is undefined
03:49:31 <salpynx> Thanks, I think I've cleared up all my confusion on this. In the past I've always had to try and understand lambda calculus in terms of combinators, which made far more sense to me.
03:53:34 <salpynx> There's nothing like working on a problem and making a bunch of mistakes to cement understanding...
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04:22:30 <esolangs> [[Esolang:Introduce yourself]] https://esolangs.org/w/index.php?diff=92028&oldid=92004 * Dorcelessness * (+208)
04:25:24 <esolangs> [[User:Dorcelessness]] N https://esolangs.org/w/index.php?oldid=92029 * Dorcelessness * (+138) Created page with "I exist and do things. I'm currently making a sort of concept for an esolang that has no name, but it should be interesting. any pronouns"
04:26:39 <esolangs> [[User:Dorcelessness]] https://esolangs.org/w/index.php?diff=92030&oldid=92029 * Dorcelessness * (+100)
04:26:49 <esolangs> [[User:Dorcelessness]] https://esolangs.org/w/index.php?diff=92031&oldid=92030 * Dorcelessness * (+3)
04:59:33 <esolangs> [[Razetime]] N https://esolangs.org/w/index.php?oldid=92032 * Razetime * (+27) Redirected page to [[User:Razetime]]
05:25:14 <esolangs> [[Quiner]] https://esolangs.org/w/index.php?diff=92033&oldid=92017 * Razetime * (+135) Add hello world, bqn interpreter
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06:30:56 <salpynx> Is this correct?: \x\y\z\_. x z (y z) == \x\y\z. x z (y (\_. z))
06:31:13 <salpynx> If so, I got my first attempt half right by getting an equivalent De Bruijn form: λλλλ. (4 2)(3 2), but messed up the BLC slightly. It would still give 29 bits this way, so not as good as 26.
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09:40:33 <tromp> salpynx: no, that's not correct
09:41:14 <tromp> this alpha is not a regular combinator, you cannot push the last \_ to the front
09:42:35 <tromp> so it doesn't correspond to a single rewrite rule like the regular combinator S x y z = x z (y z) that only has variables on the right
09:43:06 <tromp> the best you can do is alpha x y z = x z (y (K z))
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11:58:15 <esolangs> [[Quiner]] https://esolangs.org/w/index.php?diff=92035&oldid=92034 * Umnikos * (+199) Order the example code snippets better
12:02:23 <esolangs> [[Quiner]] https://esolangs.org/w/index.php?diff=92036&oldid=92035 * Umnikos * (+50) Further clarify "a/?"
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12:31:53 <esolangs> [[Quiner]] https://esolangs.org/w/index.php?diff=92039&oldid=92038 * Umnikos * (+22) Add an example of a quine
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13:12:00 <fizzie> `js [1,2,3] + [4,5,6] // TIL, via Twitterers
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13:35:41 <esolangs> [[Init]] M https://esolangs.org/w/index.php?diff=92041&oldid=92026 * WhyNot? * (+38)
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13:47:18 <esolangs> [[Quiner]] https://esolangs.org/w/index.php?diff=92043&oldid=92040 * Umnikos * (+471) Add a section on multi-line programs
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14:41:24 <esolangs> [[Init]] https://esolangs.org/w/index.php?diff=92044&oldid=92042 * WhyNot? * (+59)
14:44:43 <esolangs> [[User talk:SunnyMoon]] https://esolangs.org/w/index.php?diff=92045&oldid=91997 * SunnyMoon * (+216) Secret message: I am dumb
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15:12:42 <esolangs> [[Impossible.]] N https://esolangs.org/w/index.php?oldid=92047 * WhyNot? * (+78) Created page with "(Made by [[WhyNot?]]) This language is impossible. Therefore, there is no use."
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15:15:51 <esolangs> [[User:WhyNot?]] M https://esolangs.org/w/index.php?diff=92050&oldid=92046 * WhyNot? * (+18)
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16:14:32 <int-e> tromp: eww that means there's still a challenge to find a "proper" complete combinator?
16:15:16 <int-e> (obviously iota isn't proper in that sense either)
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16:16:23 <tromp> we can say alpha is the least irregular of all single point combinators. i'm sure a regular one is impossible
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16:16:53 <tromp> alpha only has one lambda inside an application
16:18:59 <tromp> if a regular combinator erases one of its variable, then it has an application of K not to a variable but to some term, which I think prevents deriving K from it
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16:46:17 <esolangs> [[Init]] M https://esolangs.org/w/index.php?diff=92051&oldid=92044 * PythonshellDebugwindow * (-57) /* Language */ remove outdated categories
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17:36:07 <esolangs> [[QWOP]] https://esolangs.org/w/index.php?diff=92052&oldid=86650 * Kaveh Yousefi * (+160) Added a hyperlink to my implementation of the QWOP programming language on GitHub.
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20:26:03 <salpynx> tromp: Right, the internal Kz can potentially be used _multiple_ times to swallow variables, depending on y. Putting it at the front, like I did, only swallows one. I tried with super simple examples (x=I, y=I. z=I) and (x=I, y=K, z=I) and got identical results. Using (x=I, y=S, z=I) shows the difference though.
20:28:07 * oerjan doesn't understand tromp's argument that no single proper combinator can be a basis, but assumes it must be true since none seems to be known
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20:28:34 <salpynx> alpha looks very like the S combinator, but with that internal K, which can be utilised to do K-like things depending on the values of x, y, z
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20:29:11 <sprout_> oerjan: there's a single combinator basis. I think a guy named Fokking wrote a paper on it
20:29:46 <sprout_> https://link.springer.com/article/10.1007/BF03180572
20:30:41 <int-e> alpha fits that description
20:30:55 <int-e> namely, it's "a single closed lambda-expression"
20:31:44 <oerjan> sprout_: _proper_ here means it must be of the form \v1 ... vn. P(v1, ..., vn) where P only does applications of the variables to each other
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20:38:41 <salpynx> so that's what I was just seeing, that alpha is basically S, (S = x z (y z)), but with that second z replaced with a K z -- so y is operating on something other than one of the variables, therefore breaks the defn of 'proper'
20:49:01 <salpynx> hmm.. so my mistake above was proper, but I'm guessing is extremely unlikely to be a complete basis :)
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20:57:33 <oerjan> oh tromp called it "regular" rather than "proper".
20:58:06 <oerjan> i think the other term was used in some wikipedia discussion or article i looked at
21:03:26 <tromp> that's from footnote 1 on page 12 of https://lmcs.episciences.org/6522/pdf but i recall seeing it elsewhere too
21:04:25 <oerjan> hm i think i understand ...
21:05:05 <esolangs> [[MacroBeep]] https://esolangs.org/w/index.php?diff=92053&oldid=91914 * PixelatedStarfish * (+1) /* Proof of Turing Completeness */
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21:11:56 <esolangs> [[MacroBeep]] https://esolangs.org/w/index.php?diff=92054&oldid=92053 * PixelatedStarfish * (+17) /* Interpreter Specifications */
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21:13:26 <tromp> int-e: I tried adding a reader to your code, but keep getting no parse errors. : https://pastebin.com/1061in22
21:16:04 <esolangs> [[MacroBeep]] https://esolangs.org/w/index.php?diff=92055&oldid=92054 * PixelatedStarfish * (+5007) /* Test Cases */
21:17:18 <tromp> some code he pasted earlier
21:17:36 <tromp> for finding terms over some combinatory basis
21:18:42 <esolangs> [[MacroBeep]] https://esolangs.org/w/index.php?diff=92056&oldid=92055 * PixelatedStarfish * (+5680) /* Test Cases */
21:20:50 <shachaf> I'm not sure what the type L is exactly, but that Read instance looks reasonable to me, except that it seems to be reading an integer, which will take all the digits it can.
21:21:12 <shachaf> So `11 will be read as applying 11 to nothing, rather than 1 to 1.
21:21:19 <esolangs> [[MacroBeep]] https://esolangs.org/w/index.php?diff=92057&oldid=92056 * PixelatedStarfish * (-400) /* Test Cases */
21:21:24 <shachaf> But e.g. `1^1 should be parsed correctly.
21:22:45 <tromp> ah, thx. now i see how to fix it
21:23:02 <tromp> needed to use schar c = do skipSpaces; _ <- char c; return ()
21:23:18 <tromp> which let's me separate ints by spaces
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22:11:09 <salpynx> "1 A regular combinator is a combinator in which no lambda abstraction occurs inside function application." footnote 1, p.12, On properties of B-terms. / Ikebuchi, Mirai; Nakano, Keisuke. In: Logical Methods in Computer Science, Vol. 16, No. 2, 8, 2020, p. 1-23.
22:23:37 <oerjan> https://olydis.medium.com/one-point-bases-for-%CE%BB-calculus-4163b1b326ad seems relevant. alpha is missing but there are some similar in spirit.
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22:49:33 <int-e> . o O ( ^`00 is a bit hard to read :) )
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