There was an interesting (aka nerdy) question in the SAP Community Q&A the other day:
“Are SQLScript and HANA SQL Turing complete?”
I took a swing at it and the following is my result (a slightly edited version of my original answer).
Alright, let’s do this! (even though I don’t have an idea why it would matter at all…)
So, I’m not a computer scientist, and only a third through “The Annotated Turing” (which seems to be a great book, btw). This means what follows is the layman’s approach on this.
First off, I had to understand, what is meant by “Turing complete” and how to show that a language has that characteristic.
For that, there are a couple of Wikipedia entries and SO discussions available and I leave that for everyone to read (e.g. here and here).
One of those discussions linked to a presentation that claimed to prove that PostgreSQL-SQL with recursive common table expressions (CTS) is Turing complete. In order to prove this, the author of the presentation (here) said, that it’s enough to prove that a language can emulate another language that has already been shown to be Turing complete.
Fair call.
The author’s choice was a cyclic tag system with a specific rule set (rule 110) which apparently has been shown to be Turing complete.
Then the author goes on and implements this cyclic tag system with a recursive common table expression and thereby proves the claim.
Yippie.
So, what does that mean for SAP HANA SQL?
SAP HANA SQL/SQLScript does not support recursive common table expressions (much to the distaste of everyone who tries to handle hierarchies and does not know about SAP HANA’s special hierarchy views and functions (look there) and it also does not support recursive procedure calls.
Bummer, one might think.
Fortunately, every recursion can be expressed as an iteration (compare here), so I thought, let’s try this cyclic tag system in SQLScript.
This is the result (HANA 1, rev.122.15, on my NUC system). The SQL code is also available in my 
GitHub repo.
do begin
declare prods VARCHAR(4) ARRAY;
declare currProd, initWord, currWord VARC<span data-mce-type="bookmark" style="display: inline-block; width: 0px; overflow: hidden; line-height: 0;" class="mce_SELRES_start"></span>HAR(300); -- 300 is arbitrary and would be exceeded for more runs
declare currProdNo integer = 0;
declare runs, maxruns bigint = 0;
initWord :='11001'; -- the starting/initial 'word'
maxruns := 100; -- a limit to the number of iterations
-- rule 110 is suspected to run indefinitively
prods = ARRAY ('010', '000', '1111'); -- the three 'producer rules' stored in a string array
currWord := :initWord;
runs := 0;
-- dummy table var to monitor output
tmp = select :runs as RUNS, :currProd as CURRPROD, :currWord as CURRWORD
from dummy;
while (:runs < :maxruns) DO
runs := :runs+1;
currProdNo := mod(:runs,3)+1; -- pick rule no. 1,2 or 3 but never 0
-- as SQLScript arrays are 1 based
currProd := :prods[:currProdNo];
if (left (:currWord, 1)='1') then -- add current producer to the 'word'
currWord := :currWord || :currProd;
end if;
currWord := substring (:currWord, 2); -- remove leftmost character
-- save current state into temp table var
tmp = select RUNS, CURRPROD, CURRWORD from :tmp
union all
select :runs as RUNS, :currProd as CURRPROD, :currWord as CURRWORD
from dummy;
end while;
select * from :tmp; -- output the table var
end;
Running this gives the following output:
/*
Statement 'do begin declare prods VARCHAR(4) ARRAY; declare currProd, initWord, currWord VARCHAR(300); declare ...'
successfully executed in 7<span data-mce-type="bookmark" style="display: inline-block; width: 0px; overflow: hidden; line-height: 0;" class="mce_SELRES_start"></span>17 ms 39 µs (server processing time: 715 ms 590 µs)
Fetched 101 row(s) in 2 ms 517 µs (server processing time: 0 ms 424 µs)
RUNS CURRPROD CURRWORD
0 ? 11001
1 000 1001000
2 1111 0010001111
3 010 010001111
4 000 10001111
5 1111 00011111111
6 010 0011111111
7 000 011111111
8 1111 11111111
9 010 1111111010
10 000 111111010000
11 1111 111110100001111
12 010 11110100001111010
13 000 1110100001111010000
14 1111 1101000011110100001111
15 010 101000011110100001111010
16 000 01000011110100001111010000
17 1111 1000011110100001111010000
18 010 000011110100001111010000010
19 000 00011110100001111010000010
20 1111 0011110100001111010000010
21 010 011110100001111010000010
22 000 11110100001111010000010
23 1111 11101000011110100000101111
24 010 1101000011110100000101111010
25 000 101000011110100000101111010000
[...]
*/
That looks suspiciously like the output from the Wikipedia link (above) and does not seem to stop (except for the super-clever maxruns variable ).
With that, I’d say, it’s possible to create a cyclic tag system rule 110 with SQLScript.
The tag system is Turing complete, therefore SQLScript must be Turing complete.
Still, I have no idea why this would matter at all and that’s really all I can say/write about this.
Cheers,
Lars
