How can I get a list of all functions stored in the database of a particular schema in PostgreSQL?

Question

\df <schema>.*

in psql gives the necessary information.

To see the query that's used internally connect to a database with psql and supply an extra "-E" (or "--echo-hidden") option and then execute the above command.

After some searching, I was able to find the information_schema.routines table and the information_schema.parameters tables. Using those, one can construct a query for this purpose. LEFT JOIN, instead of JOIN, is necessary to retrieve functions without parameters.

SELECT routines.routine_name, parameters.data_type, parameters.ordinal_position
FROM information_schema.routines
    LEFT JOIN information_schema.parameters ON routines.specific_name=parameters.specific_name
WHERE routines.specific_schema='my_specified_schema_name'
ORDER BY routines.routine_name, parameters.ordinal_position;

If any one is interested here is what query is executed by psql on postgres 9.1:

SELECT n.nspname as "Schema",
  p.proname as "Name",
  pg_catalog.pg_get_function_result(p.oid) as "Result data type",
  pg_catalog.pg_get_function_arguments(p.oid) as "Argument data types",
 CASE
  WHEN p.proisagg THEN 'agg'
  WHEN p.proiswindow THEN 'window'
  WHEN p.prorettype = 'pg_catalog.trigger'::pg_catalog.regtype THEN 'trigger'
  ELSE 'normal'
 END as "Type"
FROM pg_catalog.pg_proc p
     LEFT JOIN pg_catalog.pg_namespace n ON n.oid = p.pronamespace
WHERE pg_catalog.pg_function_is_visible(p.oid)
      AND n.nspname <> 'pg_catalog'
      AND n.nspname <> 'information_schema'
ORDER BY 1, 2, 4;

You can get what psql runs for a backslash command by running psql with the -E flag.

There's a handy function, oidvectortypes, that makes this a lot easier.

SELECT format('%I.%I(%s)', ns.nspname, p.proname, oidvectortypes(p.proargtypes)) 
FROM pg_proc p INNER JOIN pg_namespace ns ON (p.pronamespace = ns.oid)
WHERE ns.nspname = 'my_namespace';

Credit to Leo Hsu and Regina Obe at Postgres Online for pointing out oidvectortypes. I wrote similar functions before, but used complex nested expressions that this function gets rid of the need for.

See related answer.

---

(edit in 2016)

Summarizing typical report options:

-- Compact:
SELECT format('%I.%I(%s)', ns.nspname, p.proname, oidvectortypes(p.proargtypes))

-- With result data type: 
SELECT format(
       '%I.%I(%s)=%s', 
       ns.nspname, p.proname, oidvectortypes(p.proargtypes),
       pg_get_function_result(p.oid)
)

-- With complete argument description: 
SELECT format('%I.%I(%s)', ns.nspname, p.proname, pg_get_function_arguments(p.oid))

-- ... and mixing it.

-- All with the same FROM clause:
FROM pg_proc p INNER JOIN pg_namespace ns ON (p.pronamespace = ns.oid)
WHERE ns.nspname = 'my_namespace';

NOTICE: use p.proname||'_'||p.oid AS specific_name to obtain unique names, or to JOIN with information_schema tables — see routines and parameters at @RuddZwolinski's answer.

---

The function's OID (see pg_catalog.pg_proc) and the function's specific_name (see information_schema.routines) are the main reference options to functions. Below, some useful functions in reporting and other contexts.

--- --- --- --- ---
--- Useful overloads: 

CREATE FUNCTION oidvectortypes(p_oid int) RETURNS text AS $$
    SELECT oidvectortypes(proargtypes) FROM pg_proc WHERE oid=$1;
$$ LANGUAGE SQL IMMUTABLE;

CREATE FUNCTION oidvectortypes(p_specific_name text) RETURNS text AS $$
    -- Extract OID from specific_name and use it in oidvectortypes(oid).
    SELECT oidvectortypes(proargtypes) 
    FROM pg_proc WHERE oid=regexp_replace($1, '^.+?([^_]+)$', '\1')::int;
$$ LANGUAGE SQL IMMUTABLE;

CREATE FUNCTION pg_get_function_arguments(p_specific_name text) RETURNS text AS $$
    -- Extract OID from specific_name and use it in pg_get_function_arguments.
    SELECT pg_get_function_arguments(regexp_replace($1, '^.+?([^_]+)$', '\1')::int)
$$ LANGUAGE SQL IMMUTABLE;

--- --- --- --- ---
--- User customization: 

CREATE FUNCTION pg_get_function_arguments2(p_specific_name text) RETURNS text AS $$
    -- Example of "special layout" version.
    SELECT trim(array_agg( op||'-'||dt )::text,'{}') 
    FROM (
        SELECT data_type::text as dt, ordinal_position as op
        FROM information_schema.parameters 
        WHERE specific_name = p_specific_name 
        ORDER BY ordinal_position
    ) t
$$ LANGUAGE SQL IMMUTABLE;