Huh. Just realized that the S combinator from the SKI calculus is a J-like hook. That's mildly compelling.

@B.Wilson ⍛

@Adám SKI left-associates, so S is more like monadic f∘g⍨, no? Sxyz ←→ xz(yz), which looks like z x(y z) ←→ x∘y⍨z in infix.

Well, I don't think you can strictly preserve a left-to-rightedess when it comes to translating combinators to APL's right-to-leftedness, but yes.

Conor say's the mirror of S is Σ (and the mirror of K is π), but of course, an SKI calculus is equivalent to a ΣπI calculus.

isn't κ the mirror of K?

@RubenVerg Sounds like it should be, but not what it says here.

interesting, always seen it called κ Kite

Uiua and BQN both call it Kite but don't give it a symbol, just KI

in the Greek letters are mirrored system, π would be mirror P so (at least with my set) it'd be mirror mirror!

I'm sure I've seen κ somewhere but maybe I just extrapolated from the pattern

@RubenVerg Maybe write to Conor and ask. Although, iiuc, there's really little rhyme or reason to the combinator letters.

(I wrote to him once and got no reply, maybe I had the wrong email though)

@Adám the original ones have some history probably

@RubenVerg X DM's have high success rate :-)

@RubenVerg A German named Moses parted the North Sea and found the S, K, and I combinators guarded by three giant clams. I stands for "identisch", K for "konstant", and S comes from "verschmelzung", which appropriately means "to merge or fuse", since it fuses "ver" which means "united" and "schmelzung" which means to "melt". S smelts, solders, or stitches its first two arguments together.

Wolfram smiled upon Moses that day.

@Adám just made an account, apparently i have to pay to DM them?

uh, that's new if so. I can forward a msg

maybe ask to follow me instead? i have lots of combinator things to ask diluted in time(:

(if they follow me i don't have to pay, it says)

this one

i guess he follows me

@RubenVerg maybe you should just ask him on Tacit Talk?

if you want a 5 hour long episode, sure

i don't really mind chatting through another medium but he didn't answer my email(:

maybe i should try mastodon

wanted to do that first before twitter but i don't know which server to choose(:

dms are also probably a better place to organize for TT itself

@RubenVerg i'll ask

thanks

done

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