BUT

BUT is a esolang created by User:Yayimhere with 2 unbounded decimal counters(u and r. also if decremented to negative will be set to 0) and 4 functions(i, t ,f and k) and these functions can be changed. it was inspired by Emmental and most of ais523's works

commands

heres the functions(when i reference y i mean counter y and the same with u):

$f(x)=x+{\frac {y}{10^{\left\lfloor \log _{10}(y)\right\rfloor }+1}}$

$k(x)=\log _{u}(x)^{y}-x$

$t(x)=x-5$

$i(x)=x+2$

syntax

command	description
p/b	apply function p to counter b
[p;q]	redefine function p to the BUT code q(recursive functions are not allowed). y is a placeholder for the register the function is used on
(q;b)	loop code q(only checking at the brackets) until counter b is 0
:	halt
#	escape loop without question
|n	goto line n
{b.}	set counter b to user input
{b,}	print counter b as a ascii char

tips

• running the function t on counter b, and then running I twice, that becomes minus 1!
• similarly, running i three times, and then t once, becomes PLUS 1!

examples

Cat:

{r.}({r,}{r.};r)

translation to Minsky machine

notes:

• this translation uses Extended Short Minsky Machine Notation
• the two registers are u and r

this is the translation:

℘xy <-> t/y i/y i/y(|x#;)
℘y <-> i/y i/y i/y t/y
℘x <-> |x
℘ <-> :

this proves that BUT is Turing-complete. the functions can be redefined:

[t;t/y i/y i/y]
[i;i/y i/y i/y t/y]

and now the translation becomes:

℘xy <-> t/y(|x+2#;)
℘y <-> i/y
℘x <-> |x+2
℘ <-> :