create or replace function logging_msfunc_strict(text,anyelement)
returns text as
$$
select $1 || '+' || quote_nullable($2)
$$
LANGUAGE sql strict IMMUTABLE;
create or replace function logging_minvfunc_strict(text, anyelement)
returns text as
$$
select $1 || '-' || quote_nullable($2)
$$
LANGUAGE sql strict IMMUTABLE;
create aggregate logging_agg_strict(text)
(    stype = text,    sfunc = logging_sfunc_strict,    mstype =  text,    msfunc = logging_msfunc_strict,    minvfunc = logging_minvfunc_strict
);
create aggregate logging_agg_strict_initcond(anyelement)
(    stype = text,    sfunc = logging_sfunc_strict,    mstype = text,     msfunc = logging_msfunc_strict,    minvfunc = logging_minvfunc_strict,    initcond = 'I',    minitcond = 'MI'
);
execute following query: 
SELECT    p::text || ',' || i::text || ':' || COALESCE(v::text, 'NULL') AS _row,    logging_agg_strict (v) OVER w AS nstrict,    logging_agg_strict_initcond (v) OVER w AS nstrict
FROM (    VALUES (1, 1, NULL),        (1, 2, 'a'),        (1, 3, 'b'),        (1, 4, NULL),        (1, 5, NULL),        (1, 6, 'c'),        (2, 1, NULL),        (2, 2, 'x'),        (3, 1, 'z')) AS t (p, i, v)    WINDOW w AS (PARTITION BY p ORDER BY i ROWS BETWEEN 1 PRECEDING AND CURRENT ROW);
return following result: 
_row   |  nstrict  |    nstrict
----------+-----------+---------------- 1,1:NULL | [[null]]  | MI 1,2:a    | a         | MI+'a' 1,3:b    | a+'b'     | MI+'a'+'b' 1,4:NULL | a+'b'-'a' | MI+'a'+'b'-'a' 1,5:NULL | [[null]]  | MI 1,6:c    | c         | MI+'c' 2,1:NULL | [[null]]  | MI 2,2:x    | x         | MI+'x' 3,1:z    | z         | MI+'z'
(9 rows)For now I don't understand row  1,4:NULL | a+'b'-'a' | MI+'a'+'b'-'a'. I am not sure why the 1st time you encounter NULL then it will call inverse transition function Overall, not sure about the idea of inverse transition function.