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¿Cómo saber si existe una función en PostgreSQL?

Sí, no puede encontrar funciones en pg_class porque las funciones se almacenan en la tabla del sistema pg_proc

postgres-# \df
                               List of functions
 Schema |        Name        | Result data type | Argument data types  |  Type  
--------+--------------------+------------------+----------------------+--------
 public | foo                | integer          | a integer, b integer | normal
 public | function_arguments | text             | oid                  | normal
(2 rows)

Consulta de lista de funciones personalizadas basadas en pg_proc es simplemente

postgres=# select p.oid::regprocedure
              from pg_proc p 
                   join pg_namespace n 
                   on p.pronamespace = n.oid 
             where n.nspname not in ('pg_catalog', 'information_schema');
           oid           
-------------------------
 foo(integer,integer)
 function_arguments(oid)
(2 rows)

Las pruebas más sencillas y rápidas sobre la existencia de funciones son la conversión (sin parámetros) a regproc o regprocedure (con parámetros):

postgres=# select 'foo'::regproc;
 regproc 
---------
 foo
(1 row)

postgres=# select 'foox'::regproc;
ERROR:  function "foox" does not exist
LINE 1: select 'foox'::regproc;
               ^
postgres=# select 'foo(int, int)'::regprocedure;
     regprocedure     
----------------------
 foo(integer,integer)
(1 row)

postgres=# select 'foo(int, text)'::regprocedure;
ERROR:  function "foo(int, text)" does not exist
LINE 1: select 'foo(int, text)'::regprocedure;
               ^

o puede hacer algo similar con la prueba contra pg_proc

postgres=# select exists(select * from pg_proc where proname = 'foo');
 exists 
--------
 t
(1 row)

postgres=# select exists(select * 
                            from pg_proc 
                           where proname = 'foo' 
                             and function_arguments(oid) = 'integer, integer');
 exists 
--------
 t
(1 row)

donde:

CREATE OR REPLACE FUNCTION public.function_arguments(oid)
RETURNS text LANGUAGE sql AS $function$
    select string_agg(par, ', ') 
       from (select format_type(unnest(proargtypes), null) par 
                from pg_proc where oid = $1) x
$function$

o puede usar funciones de compilación:pg_get_function_arguments

PD. truco para simplemente orientarse en el catálogo del sistema. Usa un psql opción -E :

[[email protected] ~]$ psql -E postgres
psql (9.2.8, server 9.5devel)
Type "help" for help.

postgres=# \df
********* QUERY **********
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;
**************************

                               List of functions
 Schema |        Name        | Result data type | Argument data types  |  Type  
--------+--------------------+------------------+----------------------+--------
 public | foo                | integer          | a integer, b integer | normal
 public | function_arguments | text             | oid                  | normal
(2 rows)