Postgres 9.5

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Help with an interesting Postgres question: Why isn't an Index Only Scan used on a partition accessed via the parent table?.

CREATE FUNCTION GetStringCount(strValue TEXT, strCount TEXT)
RETURNS INTEGER LANGUAGE SQL
AS '
  SELECT COALESCE((CHAR_LENGTH(strValue) - 
    CHAR_LENGTH(REPLACE(strValue, strCount, ''''))) / 
    CHAR_LENGTH(strCount), 0);
';

CREATE FUNCTION

CREATE TABLE example (
  col VARCHAR(4000)
);

INSERT INTO example VALUES
  ('Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua.'),
  ('At vero eos et accusam et justo duo dolores et ea rebum.'),
  ('Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit amet.'),
  (NULL);

INSERT 0 4

SELECT GetStringCount('Hello', 'l');
SELECT GetStringCount('This costs 5$.', '$');
SELECT GetStringCount('This costs 5€.', '€');

getstringcount

1

SELECT 1

SELECT *, GetStringCount(col, 'a') 
FROM example;

col
getstringcount

Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua.
11

At vero eos et accusam et justo duo dolores et ea rebum.
3

Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit amet.
8

null
0

SELECT 4

col	getstringcount
Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua.	11
At vero eos et accusam et justo duo dolores et ea rebum.	3
Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit amet.	8
null	0