How can i convert an array (or jsonb_array) to a nested json object?

I have a set of data, lets say an array of json objects. like so:

[
  { "id": 1, "name": "level 1"},
  { "id": 3, "name": "level 2"},
  { "id": 8, "name": "level 3"}
]

and i wanne nest those items based on their order in the array

{ 
  "id": 1,
  "name": "level 1",
  "child": { 
    "id": 3,
    "name": "level 2",
    "child": { 
      "id": 8,
      "name": "level 3"
    } 
  }
}

So far the only way i can think of is building a custom aggregate, but that's not only a lot of work, but also hard in terms of deployment (it's not my database)

Are there ways of doing this in a query?

So far I'm thinking in the line of using unnest to create different rows for each item in the array. Then adding a rownumber to the rows to maintain order and then somehow add the item from row 2 into the item of row 1.. but so far i've not been able to do that.. Also it has to be recursive which i don't know if it's gonne work

In other words.. I need help..

Solution using a custom aggregate

CREATE FUNCTION nested_jsonb (a jsonb, b jsonb) RETURNS jsonb LANGUAGE sql IMMUTABLE AS 
$$   
SELECT CASE
         WHEN a IS null THEN b
         ELSE b || jsonb_build_object('child', a)
       END ;
$$ ;

CREATE AGGREGATE nested_jsonb(c jsonb)
( sfunc = nested_jsonb 
, stype = jsonb 
) ;

Then run the following query with your array of json objects :

SELECT nested_jsonb (a.content ORDER BY a.id DESC)
  FROM jsonb_array_elements
            ('[ { "id": 1, "name": "level 1"}
              , { "id": 3, "name": "level 2"}
              , { "id": 8, "name": "level 3"}
              ]' :: jsonb
            ) WITH ORDINALITY AS a(content,id)

and you get the expected result

{"id": 1, "name": "level 1", "child": {"id": 3, "name": "level 2", "child": {"id": 8, "name": "level 3"}}}

Solution using a recursive query

CREATE FUNCTION nested_object_jsonb (input jsonb) RETURNS jsonb LANGUAGE sql IMMUTABLE AS 
$$
WITH RECURSIVE t (content, id) AS
( SELECT input[-1] AS content
       , jsonb_array_length(input) - 2 AS id
  UNION ALL
  SELECT input[t.id] || jsonb_build_object('child', t.content)
       , id - 1
    FROM t
   WHERE id >= 0
)
SELECT t.content
  FROM t
 WHERE t.id < 0 ;
$$ ;

Then run the following query :

SELECT nested_object_jsonb
            ('[ { "id": 1, "name": "level 1"}
              , { "id": 3, "name": "level 2"}
              , { "id": 8, "name": "level 3"}
              ]' :: jsonb
            )

and you get the expected result

{"id": 1, "name": "level 1", "child": {"id": 3, "name": "level 2", "child": {"id": 8, "name": "level 3"}}}

see dbfiddle