DROP FUNCTION without knowing the number/type of parameters?

Basic query

This query creates all necessary DDL statements:

SELECT 'DROP FUNCTION ' || oid::regprocedure
FROM   pg_proc
WHERE  proname = 'my_function_name'  -- name without schema-qualification
AND    pg_function_is_visible(oid);  -- restrict to current search_path

Output:

DROP FUNCTION my_function_name(string text, form text, maxlen integer);
DROP FUNCTION my_function_name(string text, form text);
DROP FUNCTION my_function_name(string text);

Execute the commands after checking plausibility.

Pass the function name case-sensitive and with no added double-quotes to match against pg_proc.proname.

The cast to the object identifier type regprocedure (oid::regprocedure), and then to text implicitly, produces function names with argument types, automatically double-quoted and schema-qualified according to the current search_path where needed. No SQL injection possible.

pg_function_is_visible(oid) restricts the selection to functions in the current search_path ("visible"). You may or may not want this.

If you have multiple functions of the same name in multiple schemas, or overloaded functions with various function arguments, all of those will be listed separately. You may want to restrict to specific schema(s) or specific function parameter(s).

Related:

• When / how are default value expression functions bound with regard to search_path?

Function

You can build a plpgsql function around this to execute the statements immediately with EXECUTE. For Postgres 9.1 or later: Careful! It drops your functions!

CREATE OR REPLACE FUNCTION f_delfunc(_name text, OUT functions_dropped int)
   LANGUAGE plpgsql AS
$func$
-- drop all functions with given _name in the current search_path, regardless of function parameters
DECLARE
   _sql text;
BEGIN
   SELECT count(*)::int
        , 'DROP FUNCTION ' || string_agg(oid::regprocedure::text, '; DROP FUNCTION ')
   FROM   pg_catalog.pg_proc
   WHERE  proname = _name
   AND    pg_function_is_visible(oid)  -- restrict to current search_path
   INTO   functions_dropped, _sql;     -- count only returned if subsequent DROPs succeed

   IF functions_dropped > 0 THEN       -- only if function(s) found
     EXECUTE _sql;
   END IF;
END
$func$;

Call:

SELECT f_delfunc('my_function_name');

The function returns the number of functions found and dropped if no exceptions are raised. 0 if none were found.

Further reading:

• How does the search_path influence identifier resolution and the "current schema"
• Truncating all tables in a Postgres database
• PostgreSQL parameterized Order By / Limit in table function

For Postgres versions older than 9.1 or older variants of the function using regproc and pg_get_function_identity_arguments(oid) check the edit history of this answer.

You would need to write a function that took the function name, and looked up each overload with its parameter types from information_schema, then built and executed a DROP for each one.

EDIT: This turned out to be a lot harder than I thought. It looks like information_schema doesn't keep the necessary parameter information in its routines catalog. So you need to use PostgreSQL's supplementary tables pg_proc and pg_type:

CREATE OR REPLACE FUNCTION udf_dropfunction(functionname text)
  RETURNS text AS
$BODY$
DECLARE
    funcrow RECORD;
    numfunctions smallint := 0;
    numparameters int;
    i int;
    paramtext text;
BEGIN
FOR funcrow IN SELECT proargtypes FROM pg_proc WHERE proname = functionname LOOP

    --for some reason array_upper is off by one for the oidvector type, hence the +1
    numparameters = array_upper(funcrow.proargtypes, 1) + 1;

    i = 0;
    paramtext = '';

    LOOP
        IF i < numparameters THEN
            IF i > 0 THEN
                paramtext = paramtext || ', ';
            END IF;
            paramtext = paramtext || (SELECT typname FROM pg_type WHERE oid = funcrow.proargtypes[i]);
            i = i + 1;
        ELSE
            EXIT;
        END IF;
    END LOOP;

    EXECUTE 'DROP FUNCTION ' || functionname || '(' || paramtext || ');';
    numfunctions = numfunctions + 1;

END LOOP;

RETURN 'Dropped ' || numfunctions || ' functions';
END;
$BODY$
  LANGUAGE plpgsql VOLATILE
  COST 100;

I successfully tested this on an overloaded function. It was thrown together pretty fast, but works fine as a utility function. I would recommend testing more before using it in practice, in case I overlooked something.

Improving original answer in order to take schema into account, ie. schema.my_function_name,

select
    format('DROP FUNCTION %s(%s);',
      p.oid::regproc, pg_get_function_identity_arguments(p.oid))
FROM pg_catalog.pg_proc p
LEFT JOIN pg_catalog.pg_namespace n ON n.oid = p.pronamespace
WHERE
    p.oid::regproc::text = 'schema.my_function_name';