User:Yayimhere/Cleverxia Collab

This is the collab between User:Cleverxia and User:Yayimhere.

Idk, do you have any ideas Cleverxia? Perhaps something based on N-Type?

isn't N-type just a variant of Haskell? also, I'm not familiar to functional languages.

Idk, I dont know Haskell lol. But is it really functional??

"Functional paradigm languages often include the syntactic traditions of combinatory logic and lambda calculus, and have a single syntax for all definitinos". Haskell satisfies all properties above

I mean N-Type.

(but if you really wants something in the functional paradigm, you can do eg. something on a tape of functions)

Sure.

Combinator	Definition	Bird name	Rank	Notes
B	S(KS)K	Bluebird	3	applicative, linear
B[1]	BBB	Blackbird		linear
B[2]	B(BBB)B	Bunting		linear
B[3]	B(BB)B	Becard		linear
C	S(BBS)(KK) or S(S(KS)(S(KK)S))(KK)	Cardinal	3	applicative, linear
D	BB	Dove		linear
D[1]	B(BB)	Dickcissel		linear
D[2]	BB(BB)	Dovekie		linear
E	B(BBB)	Eagle		linear
Ê	B(BBB)(B(BBB))	Bald eagle		linear
F	ETTET	Finch		linear
G	BBC	Goldfinch	4	applicative, linear
H	BW(BC)	Hummingbird
I	SKK	Identity bird	1	linear
J	B(BC)(W(BC(B(BBB))))	Jay bird	4	applicative, duplicative
K	K x y = x	Kestrel	2	cancellative
L	CBM or S(S(KS)K)(K(SII))	Lark	2	applicative, duplicative
M	OI or SII	Mockingbird	1	applicative, duplicative
M[2]	BM	Double mockingbird
O	SI	Owl	2	applicative, duplicative
Q	CB or S(K(S(S(KS)K)))K	Queer bird	3	applicative, linear
Q[1]	BCB	Quixotic bird		linear
Q[2]	C(BCB)	Quizzical bird		linear
Q[3]	BT	Quirky bird		linear
Q[4]	F*B	Quacky bird		linear
R	BBT or S(K(SS))(S(KK)K)	Robin	3	applicative, linear
S	S x y z = x z (y z)	Starling	3	applicative, duplicative
T	CI or S(K(SI))K	Thrush	2	applicative, linear
U	LO	Turing bird
V	BCT or S(S(KS)(S(KK)(S(KS)(S(K(SI))K))))(KK)	Vireo	3	applicative, linear
W	SS(SK) or SS(KI)	Warbler	2	applicative, duplicative
W[1]	CW	Converse warbler
Y	SLL or SSK(S(K(SS(S(SSK))))K)	Sage bird	1	duplicative
I*	S(SK)	Identity bird once removed
W*	BW	Warbler once removed
C*	BC	Cardinal once removed		linear
R*	C*C*	Robin once removed		linear
F*	BC*R*	Finch once removed		linear
V*	C*F*	Vireo once removed		linear
W**	B(BW)	Warbler twice removed
C**	BC*	Cardinal twice removed		linear
R**	BR*	Robin twice removed		linear
F**	BF*	Finch twice removed		linear
V**	BV*	Vireo twice removed		linear
θ	YO	Theta (Bird?) [unsourced]
ϕ	ϕ x y z w = x (y w) (z w);	Phoenix	4	applicative, duplicative
Ψ	Ψ x y z w = x (y z) (y w);	Psi bird	4	applicative, duplicative
ω	MM	Omega bird [unsourced]
ι	S(SI(KS))(KK)	Iota (not a bird)	1	linear

So for example we starts a infinite tape with the identity function and do something like each command applies something to it.

Wbu a brainfuck-y language, but where the only conditional is translating the numbers into functions. somehow

Maybe something like

• B try to beta-reduce cell
• [...] loops when cell is *exactly* the identity function

Hmmm, sure. Then I think we leave each cell starting as I, and then + and - could be designed specifically to be something where - is very beta reducible, and + *isn't*.

• something like -=some combinator, + wraps current cell in some very complex function and you need a specific function to apply on it to turn it into a simple form, maybe

+ could be - in Utral, and - could be ().

we may just use - for the very complex combinator, and use + for () (or just K or simply beta-reduction).

Using - as () makes more sense because it gets it "closer" to being the identity. + being beta reduction is boring IMO.

I think + should be duplicative. Maybe Ψ?

I personally think Ψ is not as good as ϕ in +'s.

Then we'll use ϕ!

anyway, anything for looping constructs or I/O?

Looping works with the idea you gave. I/O could use church numerals, printing the normal expression as is if it *isnt* a church numeral.

Caption text

command	meaning	Header text
+	apply the ϕ combinator to cell	Example
-	() in Utral	Example
>	same as in [[bf]	Example
<	same as in [[bf]	Example
[...]	Loop while current cell isn't exactly the identity function	Example
.	print current cell as church numeral, as an expression if not a church numeral	Example
,	read a character as a church numeral, unchange on EOF	Example
?	?	Example
β	Beta reduce current cell	Example
?	?	Example
?	?	Example

Though, two things:

• "A" is kinda boring because you can basically just try to do normal lambda calculus.
• maybe [] should loop when not the identity

Fixed.

Thanks. I think this is complete!

Perhaps for a name we could name it phifunc (from ϕ and function, as a parody of brainfuck)

Done. You can delete the page now

Cool. and cool name. I think im gonna keep this page around tho.