postgres=# \h create index
Command:   CREATE INDEX
Description: define a new index
Syntax:
CREATE [ UNIQUE ] INDEX [ CONCURRENTLY ] [ [ IF NOT EXISTS ] name ] ON table_name [ USING method ]
  ( { column_name | ( expression ) } [ COLLATE collation ] [ opclass ] [ ASC | DESC ] [ NULLS { FIRST | LAST } ] [, ...] )
  [ WITH ( storage_parameter = value [, ... ] ) ]
  [ TABLESPACE tablespace_name ]
  [ WHERE predicate ]

postgres=# drop table tmp_t0;
DROP TABLE
postgres=# create table tmp_t0(c0 varchar(100),c1 varchar(100));
CREATE TABLE
postgres=# insert into tmp_t0(c0,c1) select md5(id::varchar),md5((id+id)::varchar) from generate_series(1,100000) as id;
INSERT 0 100000
postgres=# create index idx_tmp_t0_1 on tmp_t0 using hash(c0);
CREATE INDEX
postgres=# \d+ tmp_t0
                     Table "public.tmp_t0"
 Column |     Type     | Collation | Nullable | Default | Storage | Stats target | Description 
--------+------------------------+-----------+----------+---------+----------+--------------+-------------
 c0   | character varying(100) |      |     |     | extended |       | 
 c1   | character varying(100) |      |     |     | extended |       | 
Indexes:
  "idx_tmp_t0_1" hash (c0)

postgres=# explain select * from tmp_t0 where c0 = 'd3d9446802a44259755d38e6d163e820';
                 QUERY PLAN                 
----------------------------------------------------------------------------
 Index Scan using idx_tmp_t0_1 on tmp_t0 (cost=0.00..8.02 rows=1 width=66)
  Index Cond: ((c0)::text = 'd3d9446802a44259755d38e6d163e820'::text)
(2 rows)

demo=# create index on flights using hash(flight_no);
demo=# explain (costs off) select * from flights where flight_no = 'PG0001';
           QUERY PLAN           
----------------------------------------------------
 Bitmap Heap Scan on flights
  Recheck Cond: (flight_no = 'PG0001'::bpchar)
  -> Bitmap Index Scan on flights_flight_no_idx
     Index Cond: (flight_no = 'PG0001'::bpchar)
(4 rows)

demo=# select  opf.opfname as opfamily_name,
     amproc.amproc::regproc AS opfamily_procedure
from   pg_am am,
     pg_opfamily opf,
     pg_amproc amproc
where  opf.opfmethod = am.oid
and   amproc.amprocfamily = opf.oid
and   am.amname = 'hash'
order by opfamily_name,
     opfamily_procedure;
  
   opfamily_name  |  opfamily_procedure  
--------------------+-------------------------
 abstime_ops    | hashint4extended
 abstime_ops    | hashint4
 aclitem_ops    | hash_aclitem
 aclitem_ops    | hash_aclitem_extended
 array_ops     | hash_array
 array_ops     | hash_array_extended
 bool_ops      | hashcharextended
 bool_ops      | hashchar
 bpchar_ops     | hashbpcharextended
 bpchar_ops     | hashbpchar
 bpchar_pattern_ops | hashbpcharextended
 bpchar_pattern_ops | hashbpchar
 bytea_ops     | hashvarlena
 bytea_ops     | hashvarlenaextended
 char_ops      | hashcharextended
 char_ops      | hashchar
 cid_ops      | hashint4extended
 cid_ops      | hashint4
 date_ops      | hashint4extended
 date_ops      | hashint4
 enum_ops      | hashenumextended
 enum_ops      | hashenum
 float_ops     | hashfloat4extended
 float_ops     | hashfloat8extended
 float_ops     | hashfloat4
 float_ops     | hashfloat8
 ...

hank=# select hashtext('zhang');
 hashtext  
-------------
 -1172392837
(1 row)
hank=# select hashint4(10);
 hashint4  
-------------
 -1547814713
(1 row)

hank=# select a.amname, p.name, pg_indexam_has_property(a.oid,p.name)
hank-# from pg_am a,
hank-#   unnest(array['can_order','can_unique','can_multi_col','can_exclude']) p(name)
hank-# where a.amname = 'hash'
hank-# order by a.amname;
 amname |   name   | pg_indexam_has_property 
--------+---------------+-------------------------
 hash  | can_order   | f
 hash  | can_unique  | f
 hash  | can_multi_col | f
 hash  | can_exclude  | t
(4 rows)
hank=# select p.name, pg_index_has_property('hank.idx_test_name'::regclass,p.name)
hank-# from unnest(array[
hank(#    'clusterable','index_scan','bitmap_scan','backward_scan'
hank(#   ]) p(name);
   name   | pg_index_has_property 
---------------+-----------------------
 clusterable  | f
 index_scan  | t
 bitmap_scan  | t
 backward_scan | t
(4 rows)
hank=# select p.name,
hank-#   pg_index_column_has_property('hank.idx_test_name'::regclass,1,p.name)
hank-# from unnest(array[
hank(#    'asc','desc','nulls_first','nulls_last','orderable','distance_orderable',
hank(#    'returnable','search_array','search_nulls'
hank(#   ]) p(name);
    name    | pg_index_column_has_property 
--------------------+------------------------------
 asc        | f
 desc        | f
 nulls_first    | f
 nulls_last     | f
 orderable     | f
 distance_orderable | f
 returnable     | f
 search_array    | f
 search_nulls    | f
(9 rows)

hank=# select  opf.opfname AS opfamily_name,
hank-#     amop.amopopr::regoperator AS opfamily_operator
hank-# from   pg_am am,
hank-#     pg_opfamily opf,
hank-#     pg_amop amop
hank-# where  opf.opfmethod = am.oid
hank-# and   amop.amopfamily = opf.oid
hank-# and   am.amname = 'hash'
hank-# order by opfamily_name,
hank-#     opfamily_operator;
  opfamily_name  |           opfamily_operator           
--------------------+------------------------------------------------------------
 abstime_ops    | =(abstime,abstime)
 aclitem_ops    | =(aclitem,aclitem)
 array_ops     | =(anyarray,anyarray)
 bool_ops      | =(boolean,boolean)
 bpchar_ops     | =(character,character)
 bpchar_pattern_ops | =(character,character)
 bytea_ops     | =(bytea,bytea)
 char_ops      | =("char","char")
 cid_ops      | =(cid,cid)
 date_ops      | =(date,date)
 enum_ops      | =(anyenum,anyenum)
 float_ops     | =(real,real)
 float_ops     | =(double precision,double precision)
 float_ops     | =(real,double precision)
 float_ops     | =(double precision,real)
 hash_hstore_ops  | =(hstore,hstore)
 integer_ops    | =(integer,bigint)
 integer_ops    | =(smallint,smallint)
 integer_ops    | =(integer,integer)
 integer_ops    | =(bigint,bigint)
 integer_ops    | =(bigint,integer)
 integer_ops    | =(smallint,integer)
 integer_ops    | =(integer,smallint)
 integer_ops    | =(smallint,bigint)
 integer_ops    | =(bigint,smallint)
 interval_ops    | =(interval,interval)
 jsonb_ops     | =(jsonb,jsonb)
 macaddr8_ops    | =(macaddr8,macaddr8)
 macaddr_ops    | =(macaddr,macaddr)
 name_ops      | =(name,name)
 network_ops    | =(inet,inet)
 numeric_ops    | =(numeric,numeric)
 oid_ops      | =(oid,oid)
 oidvector_ops   | =(oidvector,oidvector)
 pg_lsn_ops     | =(pg_lsn,pg_lsn)
 range_ops     | =(anyrange,anyrange)
 reltime_ops    | =(reltime,reltime)
 text_ops      | =(text,text)
 text_pattern_ops  | =(text,text)
 time_ops      | =(time without time zone,time without time zone)
 timestamp_ops   | =(timestamp without time zone,timestamp without time zone)
 timestamptz_ops  | =(timestamp with time zone,timestamp with time zone)
 timetz_ops     | =(time with time zone,time with time zone)
 uuid_ops      | =(uuid,uuid)
 xid_ops      | =(xid,xid)

create extension pageinspect;

hank=# select hash_page_type(get_raw_page('hank.idx_test_name',0));
 hash_page_type 
----------------
 metapage
(1 row)

hank=# select ntuples, maxbucket
hank-# from hash_metapage_info(get_raw_page('hank.idx_test_name',0));  
 ntuples | maxbucket 
---------+-----------
  1000 |     3
(1 row)

hank=# select hash_page_type(get_raw_page('hank.idx_test_name',1));
 hash_page_type 
----------------
 bucket
(1 row)
hank=# select live_items, dead_items
hank-# from hash_page_stats(get_raw_page('hank.idx_test_name',1));  
 live_items | dead_items 
------------+------------
    407 |     0
(1 row)