Recursive Fibonacci sequence up to nth number in SQL

fib.sql

WITH RECURSIVE fib (a, b, n) AS (
    SELECT 0, 1, 1
  UNION ALL
    SELECT b, a+b, n+1 FROM fib
)
SELECT a FROM fib WHERE n<=8;

Fair enough, all functions drill down to some clever JMP instructions. What boggles my mind is that the "body" of the recursive CTE where the UNION ALL is iterating the result does not care about it's outer scope wanting to have just n<=8 results. I feel like the base case is missing. There is no returning of a value, it is iterating till infinity.

Don't get me wrong I'm convinced this is a recursive pattern and I enjoyed reading your comment!

Here is another implementation I made today in plpgsql, tail recursion:

CREATE OR REPLACE FUNCTION fibTailRecursive(n INTEGER, prevFib INTEGER DEFAULT 0, fib INTEGER DEFAULT 1)
RETURNS INTEGER AS $$
BEGIN
  IF (n = 0) THEN
    RETURN prevFib;
  END IF;
  RETURN fibTailRecursive(n - 1, fib, prevFib + fib);
END;
$$ LANGUAGE plpgsql;

When I was coding my solution in TablePlus it DID notice that it's outer scope only cares about n=8. That's why it ran forever for you but not for me. TablePlus is smart about that stuff. But I see what you mean, haha.

Recursion has sort of come under the dominion of functional programming, and this is a clearly non-functional approach to recursion. Do you have Hangouts? I'd love to chat more. It warms my heart to see people pursuing curiosity and intellectual gratification.