Talk:FROSTWIRE-666

complete basis?

I have tried to find a complete basis in these commands, but can't see a way to construct K from the available combinators. User:Yayimhere, did you construct these to be Turing complete?

I believe S can be made from ʎ̥ɯ̽ɯ̽, so including "S from SKI" doesn't seem necessary. Swapping S with "K from SKI" should make this Turing complete. Also, ꞎ seems to recurse indefinitely regardless of the arguments, is it meant to be usable? (it's fine if not) Salpynx (talk) 02:42, 30 October 2024 (UTC)

yes,thx,k,no/yes |Yayimhere (talk) 06:04, 30 October 2024 (UTC)|

Ok, I have made a Python module (Gist) that lets you import the FROSTWIRE-666 combinators to use with other Python functions. There's also a test file that checks that Church numerals work as expected. I don't know if this will help you get ideas for implementing your languages, it's not very normal Python at all (don't use globals like that!). It'd be nicer in a properly functional language (maybe you should try converting it!). With the change to add K, I believe this is Turing complete with the subset: K, ʎ̥, and ɯ̽. For the other combinators, ᶑ̊ is useful (swap), but ɤ̞ and ꞎ seem a bit wild with recursion (if I have interpreted them correctly). Salpynx (talk) 08:46, 30 October 2024 (UTC)

COOOOOLLLL! also ɤ̞ and ꞎdont recurse if im correct Yayimhere (talk) 13:00, 30 October 2024 (UTC)

I quite like this language. The name is appealing. I'm still playing around with it. The Theta combinator used in ꞎ is the Turing wikipedia:Fixed-point_combinator, which can be used to implement recursive functions. It's made from the Y-combinator, which is explained in a Python context in this blog post. Python hitting recursion limits seems to be expected. I might try implementing something in a different language that can handle this style of functional programming better. (note to self: implementing division using ꞎ... might be a thing to try) Anyway, this has been entertaining 🤪 Salpynx (talk) 08:18, 1 November 2024 (UTC)

Further note: ꞎ x y z simplifies to θ x y (zx) but please don't change the 'official' definition, it may as well be verbose for the lulz Salpynx (talk) 08:30, 1 November 2024 (UTC)

How did you get so much into this lul. also if the ꞎ thing is true then KKKꞎ should be θ? Yayimhere (talk) 12:48, 1 November 2024 (UTC)

also i wonder if its possible to get k out of ʎ̥