Postgresql: Conditionally unique constraint

PostgreSQL doesn't define a partial (i.e. conditional) UNIQUE constraint - however, you can create a partial unique index.

PostgreSQL uses unique indexes to implement unique constraints, so the effect is the same, with an important caveat: you can't perform upserts (ON CONFLICT DO UPDATE) against a unique index like you would against a unique constraint.

Also, you won't see the constraint listed in information_schema.

CREATE UNIQUE INDEX stop_myc ON stop (col_a) WHERE (col_b is NOT null);

See partial indexes.

it has already been said that PG doesn't define a partial (ie conditional) UNIQUE constraint. Also documentation says that the preferred way to add a unique constraint to a table is ADD CONSTRAINT Unique Indexes

The preferred way to add a unique constraint to a table is ALTER TABLE ... ADD CONSTRAINT. The use of indexes to enforce unique constraints could be considered an implementation detail that should not be accessed directly. One should, however, be aware that there's no need to manually create indexes on unique columns; doing so would just duplicate the automatically-created index.

There is a way to implement it using Exclusion Constraints, (thank @dukelion for this solution)

In your case it will look like

ALTER TABLE stop ADD CONSTRAINT myc EXCLUDE (col_a WITH =) WHERE (col_b IS null);