All unique keys have at least one optional column

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Goal Find base tables where all unique keys (sets of columns covered by a unique constraint, or a unique index) have at least one optional column. In this case there can be rows in the table where the values that should identify the row are missing. Because NULL is not a value and is not duplicate of another NULL the, follwing is possible: CREATE TABLE Uniq(a INTEGER NOT NULL,
b INTEGER,
CONSTRAINT ak_uniq UNIQUE (a, b));

INSERT INTO Uniq(a, b) VALUES (1, NULL);
INSERT INTO Uniq(a, b) VALUES (1, NULL);
Type Problem detection (Each row in the result could represent a flaw in the design)
Reliability High (Few or no false-positive results)
License MIT License
Data Source INFORMATION_SCHEMA+system catalog
SQL Query 
WITH unique_columns AS (SELECT 
  n.nspname AS table_schema,
  c2.relname AS table_name,
  a.attname AS column_name,
  c.relname AS index_name
FROM 
  pg_catalog.pg_class AS c INNER JOIN pg_catalog.pg_index AS i ON i.indexrelid = c.oid
  INNER JOIN pg_catalog.pg_class AS c2  ON i.indrelid = c2.oid
  INNER JOIN pg_catalog.pg_namespace AS n ON c.relnamespace = n.oid
  INNER JOIN pg_catalog.pg_authid AS u ON  n.nspowner = u.oid
  INNER JOIN pg_catalog.pg_attribute AS a ON a.attrelid = c.oid    
WHERE c.relkind = 'i'
AND i.indisunique=TRUE
AND i.indisprimary=FALSE
AND a.attnum>=1
AND a.attisdropped = FALSE
AND (n.nspname = 'public'
	 OR u.rolname <> 'postgres'))

SELECT A.table_schema, A.table_name, Count(DISTINCT index_name) AS nr_of_nullable_keys
FROM unique_columns AS U INNER JOIN information_schema.columns A USING (table_schema, table_name, column_name)
INNER JOIN information_schema.tables T USING (table_schema, table_name)
INNER JOIN information_schema.schemata S ON A.table_schema=S.schema_name
WHERE T.table_type='BASE TABLE'
AND (A.table_schema = 'public'
OR S.schema_owner<>'postgres')
AND A.is_nullable='YES'
GROUP BY  A.table_schema, A.table_name
HAVING Count(DISTINCT index_name)=(SELECT Count(DISTINCT index_name) AS cnt FROM unique_columns AS u WHERE u.table_schema=A.table_schema AND u.table_name=A.table_name)
ORDER BY table_schema, table_name;
Collections

This query belongs to the following collections:

NameDescription
Find problems about integrity constraintsA selection of queries that return information about the state of integrity constraints in the datadabase. Contains all the types of queries - problem detection, software measure, and general overview
Find problems automaticallyQueries, that results point to problems in the database. Each query in the collection produces an initial assessment. However, a human reviewer has the final say as to whether there is a problem or not .
Categories

This query is classified under the following categories:

NameDescription
Missing dataQueries of this category provide information about missing data (NULLs) in a database.
UniquenessQueries of this category provide information about uniqueness constraints (PRIMARY KEY, UNIQUE, EXCLUDE) as well as unique indexes.
Validity and completenessQueries of this category provide information about whether database design represents the world (domain) correctly (validity) and whether database design captures all the information about the world (domain) that is correct and relevant (completeness).