Postgres analogue to CROSS APPLY in SQL Server

In Postgres 9.3 or later use a LATERAL join:

SELECT v.col_a, v.col_b, f.*  -- no parentheses, f is a table alias
FROM   v_citizenversions v
LEFT   JOIN LATERAL f_citizen_rec_modified(v.col1, v.col2) f ON true
WHERE  f.col_c = _col_c;

Why LEFT JOIN LATERAL ... ON true?

Record returned from function has columns concatenated

For older versions, there is a very simple way to accomplish what I think you are trying to with a set-returning function (RETURNS TABLE or RETURNS SETOF record OR RETURNS record):

SELECT *, (f_citizen_rec_modified(col1, col2)).*
FROM   v_citizenversions v

The function computes values once for every row of the outer query. If the function returns multiple rows, resulting rows are multiplied accordingly. All parentheses are syntactically required to decompose a row type. The table function could look something like this:

CREATE OR REPLACE FUNCTION f_citizen_rec_modified(_col1 int, _col2 text)
  RETURNS TABLE(col_c integer, col_d text)
  LANGUAGE sql AS
$func$
SELECT s.col_c, s.col_d
FROM   some_tbl s
WHERE  s.col_a = $1
AND    s.col_b = $2
$func$;

You need to wrap this in a subquery or CTE if you want to apply a WHERE clause because the columns are not visible on the same level. (And it's better for performance anyway, because you prevent repeated evaluation for every output column of the function):

SELECT col_a, col_b, (f_row).*
FROM  (
   SELECT col_a, col_b, f_citizen_rec_modified(col1, col2) AS f_row
   FROM   v_citizenversions v
   ) x
WHERE (f_row).col_c = _col_c;

There are several other ways to do this or something similar. It all depends on what you want exactly.

Necromancing:
New in PostgreSQL 9.3:

The LATERAL keyword

left | right | inner JOIN LATERAL

INNER JOIN LATERAL is the same as CROSS APPLY
and LEFT JOIN LATERAL is the same as OUTER APPLY

Example usage:

SELECT * FROM T_Contacts 

--LEFT JOIN T_MAP_Contacts_Ref_OrganisationalUnit ON MAP_CTCOU_CT_UID = T_Contacts.CT_UID AND MAP_CTCOU_SoftDeleteStatus = 1 
--WHERE T_MAP_Contacts_Ref_OrganisationalUnit.MAP_CTCOU_UID IS NULL -- 989


LEFT JOIN LATERAL 
(
    SELECT 
         --MAP_CTCOU_UID    
         MAP_CTCOU_CT_UID   
        ,MAP_CTCOU_COU_UID  
        ,MAP_CTCOU_DateFrom 
        ,MAP_CTCOU_DateTo   
   FROM T_MAP_Contacts_Ref_OrganisationalUnit 
   WHERE MAP_CTCOU_SoftDeleteStatus = 1 
   AND MAP_CTCOU_CT_UID = T_Contacts.CT_UID 

    /*  
    AND 
    ( 
        (__in_DateFrom <= T_MAP_Contacts_Ref_OrganisationalUnit.MAP_KTKOE_DateTo) 
        AND 
        (__in_DateTo >= T_MAP_Contacts_Ref_OrganisationalUnit.MAP_KTKOE_DateFrom) 
    ) 
    */
   ORDER BY MAP_CTCOU_DateFrom 
   LIMIT 1 
) AS FirstOE

Postgres analogue to CROSS APPLY in SQL Server

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