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, 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 btw) said, 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):
do begin declare prods VARCHAR(4) ARRAY; declare currProd, initWord, currWord VARCHAR(300); declare runs, maxruns bigint = 0; declare currProdNo integer = 0; initWord :='11001'; maxruns := 100; runs := 0; prods = ARRAY ('010', '000', '1111'); currWord := :initWord; -- 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; currProd := :prods[:currProdNo]; if (left (:currWord, 1) = '1') then -- add current producer currWord := :currWord || :currProd; end if; -- remove leftmost character currWord := substring (:currWord, 2); -- 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; -- output the table var select * from :tmp; end;
Running this gives the following output:
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
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