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So you look up other tables in a CHECK constraint.

CHECK constraints are supposed to run IMMUTABLE checks. What passes OK for a row at one time should pass OK at any time (at the end of a transaction if "deferred"). That's how CHECK constraints are defined in the SQL standard. That's also reason for this restriction (per documentation):

Currently, CHECK expressions cannot contain subqueries nor refer to variables other than columns of the current row.

Now, expressions in CHECK constraints are allowed to use functions, even user-defined functions. Those should be restricted to IMMUTABLE functions, but Postgres does not currently enforce this. According to this related discussion on pgsql-hackers, one reason is to allow references to the current time, which is not IMMUTABLE by nature.

But you are looking up rows of another table, which is completely in violation of how CHECK constraints are supposed to work. I am not surprised that pg_dump fails to provide for this.

Move your check in another table to a trigger (which is the right tool), and it should work with modern versions of Postgres.

##PostgreSQL 9.2 or later

While the above is true for any version of Postgres, several tools have been introduced with Postgres 9.2 to help with your situation:

###pgdpump option --exclude-table-data

A simple solution would be to dump the db without data for the violating table with:

--exclude-table-data=my_schema.my_tbl 

Then append just the data for this table at the end of the dump with:

--data-only --table=my_schema.my_tbl 

But complications with other constraints on the same table might ensue. There is an even better solution: ###NOT VALID

There is the NOT VALID modifier for constraints. Only available for FK constraint in v9.1, but this was extended to CHECK constraints in 9.2. Per documentation:

If the constraint is marked NOT VALID, the potentially-lengthy initial check to verify that all rows in the table satisfy the constraint is skipped. The constraint will still be enforced against subsequent inserts or updates [...]

A plain postgres dump file consists of three "sections":

• pre_data
• data
• post-data

^{Postgres 9.2 also introduced an option to dump sections separately with -- section=sectionname, but that's not helping with the problem at hand.}

Here is where it gets interesting. Per documentation:

Post-data items include definitions of indexes, triggers, rules, and constraints other than validated check constraints. Pre-data items include all other data definition items.

Bold emphasis mine.
You can change the offending CHECK constraint to NOT VALID, which moves the the constraint to the post-data section. Drop and recreate:

ALTER TABLE a DROP CONSTRAINT a_constr_1; ALTER TABLE a ADD CONSTRAINT a_constr_1 CHECK (fail_if_b_empty()) NOT VALID; 

This should solve your problem. You can even leave the constraint in that state, since that better reflects what it actually does: check new rows, but give no guarantees for existing data. There is nothing wrong with a NOT VALID check constraint. If you prefer, you can validate it later:

ALTER TABLE a VALIDATE CONSTRAINT a_constr_1; 

But then you are back to the status quo ante.