IntoLoad

IntoLoad was an attempt to make Underload into a group(similarly to Burro), though this has not been proven. instead of using concatenation, it uses "ordered interleaving"(will be explained later), to construct programs, when using this operator, every program is reversible. Equality is "computing the same function", in which erroring is considered a function, but errors are unique to each program.

Description

Every command is written (n,c), where c is a single underload command other than ~((S) is considered a single command, where S must be IntoLoad code), or e(which is a NOP and does nothing), and n is a signed integer. Any single command is a program. A string of these pairs S is a program if an only if there exists some strings X and Y, where O(x,y) = S, where O does the following process on X and Y:

• Find every pair of pair of pairs within X and Y, (n1,c1) and (n2,c2), that have an equal index.
• Concatenate them together, as either (n1,c1)(n2,c2) or (n2,c2)(n1,c1):

• n1 > n2 -> (n1,c1)(n2,c2)
• n2 > n1 -> (n2,c2)(n1,c1)
• n1 = n2 = n -> (n,e)

• Concatenate the results together, ordering from least to highest index. If they are of different lengths, then the "leftovers" in the longer is appended to the end.

Now, the following is a process to find the inverse of P is for every command in P, you replace it in P' with the following translations:

(n,^) <-> (n-1,())
(n,(S)) <-> (n+1,!) (S) ≠ ()
(n,:) <-> (n+1,1)
(n,*) <-> (n-1,())
(n,a) <-> (n+1,^)
(n,S) <-> (n-1,())