Prevent recursive trigger in PostgreSQL

This is what I do in PostgreSQL 9.2, although I must admit I did not find this approach documented. There is a function pg_trigger_depth() documented here, which I use to differentiate between original and nested calls in the trigger.

CREATE TRIGGER trg_taxonomic_positions
AFTER INSERT OR UPDATE OF taxonomic_position
ON taxon_concepts
FOR EACH ROW
WHEN (pg_trigger_depth() = 0)
EXECUTE PROCEDURE trg_taxonomic_positions()

At the beggining of the definition of the trigger you can disable triggers on that particular table, and reenable them at the end (and make sure an exception doesn't terminate the execution before expected!). This has many deep holes, but may work for some light implementations. Notice that for this implementation, you will also need priviliges to disable triggers.

To avoid unbounded recursion, see my answer here. As others have commented, if your data structure is a true tree (the root(s) will have no parent(s)) and the recursion will always stop at the root(s). For nodes with only one parent pointer, the only way for unbounded recursion would be if there were loops present. (the method in my link will visit any node at most once)

In pg, it's up to you to track trigger recursion.

If a trigger function executes SQL commands then these commands might fire triggers again. This is known as cascading triggers. There is no direct limitation on the number of cascade levels. It is possible for cascades to cause a recursive invocation of the same trigger; for example, an INSERT trigger might execute a command that inserts an additional row into the same table, causing the INSERT trigger to be fired again. It is the trigger programmer's responsibility to avoid infinite recursion in such scenarios.

https://www.postgresql.org/docs/13/trigger-definition.html