.TH "Stdlib.Hashtbl" 3 2024-02-29 OCamldoc "OCaml library"
.SH NAME
Stdlib.Hashtbl \- no description
.SH Module
Module   Stdlib.Hashtbl
.SH Documentation
.sp
Module
.BI "Hashtbl"
 : 
.B (module Stdlib__Hashtbl)

.sp

.sp

.sp
.sp

.PP
Unsynchronized accesses
.PP

.PP
Unsynchronized accesses to a hash table may lead to an invalid hash table
state\&. Thus, concurrent accesses to a hash tables must be synchronized
(for instance with a 
.ft B
Mutex\&.t
.ft R
)\&.
.PP

.PP
.SS Generic interface

.PP
.I type 
.B (!'a, !'b)
.I t 

.sp
The type of hash tables from type 
.ft B
\&'a
.ft R
to type 
.ft B
\&'b
.ft R
\&.

.sp

.I val create 
: 
.B ?random:bool -> int -> ('a, 'b) t
.sp

.ft B
Hashtbl\&.create n
.ft R
creates a new, empty hash table, with
initial size 
.ft B
n
.ft R
\&.  For best results, 
.ft B
n
.ft R
should be on the
order of the expected number of elements that will be in
the table\&.  The table grows as needed, so 
.ft B
n
.ft R
is just an
initial guess\&.
.sp
The optional 
.ft B
~random
.ft R
parameter (a boolean) controls whether
the internal organization of the hash table is randomized at each
execution of 
.ft B
Hashtbl\&.create
.ft R
or deterministic over all executions\&.
.sp
A hash table that is created with 
.ft B
~random
.ft R
set to 
.ft B
false
.ft R
uses a
fixed hash function (
.ft B
Hashtbl\&.hash
.ft R
) to distribute keys among
buckets\&.  As a consequence, collisions between keys happen
deterministically\&.  In Web\-facing applications or other
security\-sensitive applications, the deterministic collision
patterns can be exploited by a malicious user to create a
denial\-of\-service attack: the attacker sends input crafted to
create many collisions in the table, slowing the application down\&.
.sp
A hash table that is created with 
.ft B
~random
.ft R
set to 
.ft B
true
.ft R
uses the seeded
hash function 
.ft B
Hashtbl\&.seeded_hash
.ft R
with a seed that is randomly chosen at hash
table creation time\&.  In effect, the hash function used is randomly
selected among 
.ft B
2^{30}
.ft R
different hash functions\&.  All these hash
functions have different collision patterns, rendering ineffective the
denial\-of\-service attack described above\&.  However, because of
randomization, enumerating all elements of the hash table using 
.ft B
Hashtbl\&.fold
.ft R
or 
.ft B
Hashtbl\&.iter
.ft R
is no longer deterministic: elements are enumerated in
different orders at different runs of the program\&.
.sp
If no 
.ft B
~random
.ft R
parameter is given, hash tables are created
in non\-random mode by default\&.  This default can be changed
either programmatically by calling 
.ft B
Hashtbl\&.randomize
.ft R
or by
setting the 
.ft B
R
.ft R
flag in the 
.ft B
OCAMLRUNPARAM
.ft R
environment variable\&.

.sp
.B "Before4.00"
the 
.ft B
~random
.ft R
parameter was not present and all
hash tables were created in non\-randomized mode\&.


.sp

.I val clear 
: 
.B ('a, 'b) t -> unit
.sp
Empty a hash table\&. Use 
.ft B
reset
.ft R
instead of 
.ft B
clear
.ft R
to shrink the
size of the bucket table to its initial size\&.

.sp

.I val reset 
: 
.B ('a, 'b) t -> unit
.sp
Empty a hash table and shrink the size of the bucket table
to its initial size\&.

.sp
.B "Since"
4.00

.sp

.I val copy 
: 
.B ('a, 'b) t -> ('a, 'b) t
.sp
Return a copy of the given hashtable\&.

.sp

.I val add 
: 
.B ('a, 'b) t -> 'a -> 'b -> unit
.sp

.ft B
Hashtbl\&.add tbl key data
.ft R
adds a binding of 
.ft B
key
.ft R
to 
.ft B
data
.ft R
in table 
.ft B
tbl
.ft R
\&.
.sp
Warning: Previous bindings for 
.ft B
key
.ft R
are not removed, but simply
hidden\&. That is, after performing 
.ft B
Hashtbl\&.remove
.ft R
.ft B
tbl key
.ft R
,
the previous binding for 
.ft B
key
.ft R
, if any, is restored\&.
(Same behavior as with association lists\&.)
.sp
If you desire the classic behavior of replacing elements,
see 
.ft B
Hashtbl\&.replace
.ft R
\&.

.sp

.I val find 
: 
.B ('a, 'b) t -> 'a -> 'b
.sp

.ft B
Hashtbl\&.find tbl x
.ft R
returns the current binding of 
.ft B
x
.ft R
in 
.ft B
tbl
.ft R
,
or raises 
.ft B
Not_found
.ft R
if no such binding exists\&.

.sp

.I val find_opt 
: 
.B ('a, 'b) t -> 'a -> 'b option
.sp

.ft B
Hashtbl\&.find_opt tbl x
.ft R
returns the current binding of 
.ft B
x
.ft R
in 
.ft B
tbl
.ft R
,
or 
.ft B
None
.ft R
if no such binding exists\&.

.sp
.B "Since"
4.05

.sp

.I val find_all 
: 
.B ('a, 'b) t -> 'a -> 'b list
.sp

.ft B
Hashtbl\&.find_all tbl x
.ft R
returns the list of all data
associated with 
.ft B
x
.ft R
in 
.ft B
tbl
.ft R
\&.
The current binding is returned first, then the previous
bindings, in reverse order of introduction in the table\&.

.sp

.I val mem 
: 
.B ('a, 'b) t -> 'a -> bool
.sp

.ft B
Hashtbl\&.mem tbl x
.ft R
checks if 
.ft B
x
.ft R
is bound in 
.ft B
tbl
.ft R
\&.

.sp

.I val remove 
: 
.B ('a, 'b) t -> 'a -> unit
.sp

.ft B
Hashtbl\&.remove tbl x
.ft R
removes the current binding of 
.ft B
x
.ft R
in 
.ft B
tbl
.ft R
,
restoring the previous binding if it exists\&.
It does nothing if 
.ft B
x
.ft R
is not bound in 
.ft B
tbl
.ft R
\&.

.sp

.I val replace 
: 
.B ('a, 'b) t -> 'a -> 'b -> unit
.sp

.ft B
Hashtbl\&.replace tbl key data
.ft R
replaces the current binding of 
.ft B
key
.ft R
in 
.ft B
tbl
.ft R
by a binding of 
.ft B
key
.ft R
to 
.ft B
data
.ft R
\&.  If 
.ft B
key
.ft R
is unbound in 
.ft B
tbl
.ft R
,
a binding of 
.ft B
key
.ft R
to 
.ft B
data
.ft R
is added to 
.ft B
tbl
.ft R
\&.
This is functionally equivalent to 
.ft B
Hashtbl\&.remove
.ft R
.ft B
tbl key
.ft R
followed by 
.ft B
Hashtbl\&.add
.ft R
.ft B
tbl key data
.ft R
\&.

.sp

.I val iter 
: 
.B ('a -> 'b -> unit) -> ('a, 'b) t -> unit
.sp

.ft B
Hashtbl\&.iter f tbl
.ft R
applies 
.ft B
f
.ft R
to all bindings in table 
.ft B
tbl
.ft R
\&.
.ft B
f
.ft R
receives the key as first argument, and the associated value
as second argument\&. Each binding is presented exactly once to 
.ft B
f
.ft R
\&.
.sp
The order in which the bindings are passed to 
.ft B
f
.ft R
is unspecified\&.
However, if the table contains several bindings for the same key,
they are passed to 
.ft B
f
.ft R
in reverse order of introduction, that is,
the most recent binding is passed first\&.
.sp
If the hash table was created in non\-randomized mode, the order
in which the bindings are enumerated is reproducible between
successive runs of the program, and even between minor versions
of OCaml\&.  For randomized hash tables, the order of enumeration
is entirely random\&.
.sp
The behavior is not specified if the hash table is modified
by 
.ft B
f
.ft R
during the iteration\&.

.sp

.I val filter_map_inplace 
: 
.B ('a -> 'b -> 'b option) -> ('a, 'b) t -> unit
.sp

.ft B
Hashtbl\&.filter_map_inplace f tbl
.ft R
applies 
.ft B
f
.ft R
to all bindings in
table 
.ft B
tbl
.ft R
and update each binding depending on the result of
.ft B
f
.ft R
\&.  If 
.ft B
f
.ft R
returns 
.ft B
None
.ft R
, the binding is discarded\&.  If it
returns 
.ft B
Some new_val
.ft R
, the binding is update to associate the key
to 
.ft B
new_val
.ft R
\&.
.sp
Other comments for 
.ft B
Hashtbl\&.iter
.ft R
apply as well\&.

.sp
.B "Since"
4.03

.sp

.I val fold 
: 
.B ('a -> 'b -> 'acc -> 'acc) -> ('a, 'b) t -> 'acc -> 'acc
.sp

.ft B
Hashtbl\&.fold f tbl init
.ft R
computes
.ft B
(f kN dN \&.\&.\&. (f k1 d1 init)\&.\&.\&.)
.ft R
,
where 
.ft B
k1 \&.\&.\&. kN
.ft R
are the keys of all bindings in 
.ft B
tbl
.ft R
,
and 
.ft B
d1 \&.\&.\&. dN
.ft R
are the associated values\&.
Each binding is presented exactly once to 
.ft B
f
.ft R
\&.
.sp
The order in which the bindings are passed to 
.ft B
f
.ft R
is unspecified\&.
However, if the table contains several bindings for the same key,
they are passed to 
.ft B
f
.ft R
in reverse order of introduction, that is,
the most recent binding is passed first\&.
.sp
If the hash table was created in non\-randomized mode, the order
in which the bindings are enumerated is reproducible between
successive runs of the program, and even between minor versions
of OCaml\&.  For randomized hash tables, the order of enumeration
is entirely random\&.
.sp
The behavior is not specified if the hash table is modified
by 
.ft B
f
.ft R
during the iteration\&.

.sp

.I val length 
: 
.B ('a, 'b) t -> int
.sp

.ft B
Hashtbl\&.length tbl
.ft R
returns the number of bindings in 
.ft B
tbl
.ft R
\&.
It takes constant time\&.  Multiple bindings are counted once each, so
.ft B
Hashtbl\&.length
.ft R
gives the number of times 
.ft B
Hashtbl\&.iter
.ft R
calls its
first argument\&.

.sp

.I val randomize 
: 
.B unit -> unit
.sp
After a call to 
.ft B
Hashtbl\&.randomize()
.ft R
, hash tables are created in
randomized mode by default: 
.ft B
Hashtbl\&.create
.ft R
returns randomized
hash tables, unless the 
.ft B
~random:false
.ft R
optional parameter is given\&.
The same effect can be achieved by setting the 
.ft B
R
.ft R
parameter in
the 
.ft B
OCAMLRUNPARAM
.ft R
environment variable\&.
.sp
It is recommended that applications or Web frameworks that need to
protect themselves against the denial\-of\-service attack described
in 
.ft B
Hashtbl\&.create
.ft R
call 
.ft B
Hashtbl\&.randomize()
.ft R
at initialization
time before any domains are created\&.
.sp
Note that once 
.ft B
Hashtbl\&.randomize()
.ft R
was called, there is no way
to revert to the non\-randomized default behavior of 
.ft B
Hashtbl\&.create
.ft R
\&.
This is intentional\&.  Non\-randomized hash tables can still be
created using 
.ft B
Hashtbl\&.create ~random:false
.ft R
\&.

.sp
.B "Since"
4.00

.sp

.I val is_randomized 
: 
.B unit -> bool
.sp
Return 
.ft B
true
.ft R
if the tables are currently created in randomized mode
by default, 
.ft B
false
.ft R
otherwise\&.

.sp
.B "Since"
4.03

.sp

.I val rebuild 
: 
.B ?random:bool -> ('a, 'b) t -> ('a, 'b) t
.sp
Return a copy of the given hashtable\&.  Unlike 
.ft B
Hashtbl\&.copy
.ft R
,
.ft B
Hashtbl\&.rebuild
.ft R
.ft B
h
.ft R
re\-hashes all the (key, value) entries of
the original table 
.ft B
h
.ft R
\&.  The returned hash table is randomized if
.ft B
h
.ft R
was randomized, or the optional 
.ft B
random
.ft R
parameter is true, or
if the default is to create randomized hash tables; see
.ft B
Hashtbl\&.create
.ft R
for more information\&.
.sp

.ft B
Hashtbl\&.rebuild
.ft R
can safely be used to import a hash table built
by an old version of the 
.ft B
Hashtbl
.ft R
module, then marshaled to
persistent storage\&.  After unmarshaling, apply 
.ft B
Hashtbl\&.rebuild
.ft R
to produce a hash table for the current version of the 
.ft B
Hashtbl
.ft R
module\&.

.sp
.B "Since"
4.12

.sp
.I type statistics 
= {
 num_bindings : 
.B int
;  (* Number of bindings present in the table\&.
Same value as returned by 
.ft B
Hashtbl\&.length
.ft R
\&.
 *) 
 num_buckets : 
.B int
;  (* Number of buckets in the table\&.
 *) 
 max_bucket_length : 
.B int
;  (* Maximal number of bindings per bucket\&.
 *) 
 bucket_histogram : 
.B int array
;  (* Histogram of bucket sizes\&.  This array 
.ft B
histo
.ft R
has
length 
.ft B
max_bucket_length + 1
.ft R
\&.  The value of
.ft B
histo\&.(i)
.ft R
is the number of buckets whose size is 
.ft B
i
.ft R
\&.
 *) 
 }

.sp
.B "Since"
4.00

.sp

.I val stats 
: 
.B ('a, 'b) t -> statistics
.sp

.ft B
Hashtbl\&.stats tbl
.ft R
returns statistics about the table 
.ft B
tbl
.ft R
:
number of buckets, size of the biggest bucket, distribution of
buckets by size\&.

.sp
.B "Since"
4.00

.sp

.PP
.SS Hash tables and Sequences

.PP

.I val to_seq 
: 
.B ('a, 'b) t -> ('a * 'b) Seq.t
.sp
Iterate on the whole table\&.  The order in which the bindings
appear in the sequence is unspecified\&. However, if the table contains
several bindings for the same key, they appear in reversed order of
introduction, that is, the most recent binding appears first\&.
.sp
The behavior is not specified if the hash table is modified
during the iteration\&.

.sp
.B "Since"
4.07

.sp

.I val to_seq_keys 
: 
.B ('a, 'b) t -> 'a Seq.t
.sp
Same as 
.ft B
Seq\&.map fst (to_seq m)
.ft R


.sp
.B "Since"
4.07

.sp

.I val to_seq_values 
: 
.B ('a, 'b) t -> 'b Seq.t
.sp
Same as 
.ft B
Seq\&.map snd (to_seq m)
.ft R


.sp
.B "Since"
4.07

.sp

.I val add_seq 
: 
.B ('a, 'b) t -> ('a * 'b) Seq.t -> unit
.sp
Add the given bindings to the table, using 
.ft B
Hashtbl\&.add
.ft R


.sp
.B "Since"
4.07

.sp

.I val replace_seq 
: 
.B ('a, 'b) t -> ('a * 'b) Seq.t -> unit
.sp
Add the given bindings to the table, using 
.ft B
Hashtbl\&.replace
.ft R


.sp
.B "Since"
4.07

.sp

.I val of_seq 
: 
.B ('a * 'b) Seq.t -> ('a, 'b) t
.sp
Build a table from the given bindings\&. The bindings are added
in the same order they appear in the sequence, using 
.ft B
Hashtbl\&.replace_seq
.ft R
,
which means that if two pairs have the same key, only the latest one
will appear in the table\&.

.sp
.B "Since"
4.07

.sp

.PP
.SS Functorial interface

.PP

.PP
The functorial interface allows the use of specific comparison
and hash functions, either for performance/security concerns,
or because keys are not hashable/comparable with the polymorphic builtins\&.
.sp
For instance, one might want to specialize a table for integer keys:
.EX
.ft B
.br
\&      module IntHash =
.br
\&        struct
.br
\&          type t = int
.br
\&          let equal i j = i=j
.br
\&          let hash i = i land max_int
.br
\&        end
.br
\&
.br
\&      module IntHashtbl = Hashtbl\&.Make(IntHash)
.br
\&
.br
\&      let h = IntHashtbl\&.create 17 in
.br
\&      IntHashtbl\&.add h 12 "hello"
.br
\&    
.ft R
.EE
.sp
This creates a new module 
.ft B
IntHashtbl
.ft R
, with a new type 
.ft B
\&'a
.br
\&    IntHashtbl\&.t
.ft R
of tables from 
.ft B
int
.ft R
to 
.ft B
\&'a
.ft R
\&. In this example, 
.ft B
h
.ft R
contains 
.ft B
string
.ft R
values so its type is 
.ft B
string IntHashtbl\&.t
.ft R
\&.
.sp
Note that the new type 
.ft B
\&'a IntHashtbl\&.t
.ft R
is not compatible with
the type 
.ft B
(\&'a,\&'b) Hashtbl\&.t
.ft R
of the generic interface\&. For
example, 
.ft B
Hashtbl\&.length h
.ft R
would not type\-check, you must use
.ft B
IntHashtbl\&.length
.ft R
\&.
.PP
.I module type HashedType = 
.B sig end

.sp
The input signature of the functor 
.ft B
Hashtbl\&.Make
.ft R
\&.

.sp
.I module type S = 
.B sig end

.sp
The output signature of the functor 
.ft B
Hashtbl\&.Make
.ft R
\&.

.sp
.I module Make : 
.B functor (H : HashedType) -> sig end

.sp
Functor building an implementation of the hashtable structure\&.
The functor 
.ft B
Hashtbl\&.Make
.ft R
returns a structure containing
a type 
.ft B
key
.ft R
of keys and a type 
.ft B
\&'a t
.ft R
of hash tables
associating data of type 
.ft B
\&'a
.ft R
to keys of type 
.ft B
key
.ft R
\&.
The operations perform similarly to those of the generic
interface, but use the hashing and equality functions
specified in the functor argument 
.ft B
H
.ft R
instead of generic
equality and hashing\&.  Since the hash function is not seeded,
the 
.ft B
create
.ft R
operation of the result structure always returns
non\-randomized hash tables\&.

.sp
.I module type SeededHashedType = 
.B sig end

.sp
The input signature of the functor 
.ft B
Hashtbl\&.MakeSeeded
.ft R
\&.

.sp
.B "Since"
4.00

.sp
.I module type SeededS = 
.B sig end

.sp
The output signature of the functor 
.ft B
Hashtbl\&.MakeSeeded
.ft R
\&.

.sp
.B "Since"
4.00

.sp
.I module MakeSeeded : 
.B functor (H : SeededHashedType) -> sig end

.sp
Functor building an implementation of the hashtable structure\&.
The functor 
.ft B
Hashtbl\&.MakeSeeded
.ft R
returns a structure containing
a type 
.ft B
key
.ft R
of keys and a type 
.ft B
\&'a t
.ft R
of hash tables
associating data of type 
.ft B
\&'a
.ft R
to keys of type 
.ft B
key
.ft R
\&.
The operations perform similarly to those of the generic
interface, but use the seeded hashing and equality functions
specified in the functor argument 
.ft B
H
.ft R
instead of generic
equality and hashing\&.  The 
.ft B
create
.ft R
operation of the
result structure supports the 
.ft B
~random
.ft R
optional parameter
and returns randomized hash tables if 
.ft B
~random:true
.ft R
is passed
or if randomization is globally on (see 
.ft B
Hashtbl\&.randomize
.ft R
)\&.

.sp
.B "Since"
4.00

.sp

.PP
.SS The polymorphic hash functions

.PP

.I val hash 
: 
.B 'a -> int
.sp

.ft B
Hashtbl\&.hash x
.ft R
associates a nonnegative integer to any value of
any type\&. It is guaranteed that
if 
.ft B
x = y
.ft R
or 
.ft B
Stdlib\&.compare x y = 0
.ft R
, then 
.ft B
hash x = hash y
.ft R
\&.
Moreover, 
.ft B
hash
.ft R
always terminates, even on cyclic structures\&.

.sp

.I val seeded_hash 
: 
.B int -> 'a -> int
.sp
A variant of 
.ft B
Hashtbl\&.hash
.ft R
that is further parameterized by
an integer seed\&.

.sp
.B "Since"
4.00

.sp

.I val hash_param 
: 
.B int -> int -> 'a -> int
.sp

.ft B
Hashtbl\&.hash_param meaningful total x
.ft R
computes a hash value for 
.ft B
x
.ft R
,
with the same properties as for 
.ft B
hash
.ft R
\&. The two extra integer
parameters 
.ft B
meaningful
.ft R
and 
.ft B
total
.ft R
give more precise control over
hashing\&. Hashing performs a breadth\-first, left\-to\-right traversal
of the structure 
.ft B
x
.ft R
, stopping after 
.ft B
meaningful
.ft R
meaningful nodes
were encountered, or 
.ft B
total
.ft R
nodes (meaningful or not) were
encountered\&.  If 
.ft B
total
.ft R
as specified by the user exceeds a certain
value, currently 256, then it is capped to that value\&.
Meaningful nodes are: integers; floating\-point
numbers; strings; characters; booleans; and constant
constructors\&. Larger values of 
.ft B
meaningful
.ft R
and 
.ft B
total
.ft R
means that
more nodes are taken into account to compute the final hash value,
and therefore collisions are less likely to happen\&.  However,
hashing takes longer\&. The parameters 
.ft B
meaningful
.ft R
and 
.ft B
total
.ft R
govern the tradeoff between accuracy and speed\&.  As default
choices, 
.ft B
Hashtbl\&.hash
.ft R
and 
.ft B
Hashtbl\&.seeded_hash
.ft R
take
.ft B
meaningful = 10
.ft R
and 
.ft B
total = 100
.ft R
\&.

.sp

.I val seeded_hash_param 
: 
.B int -> int -> int -> 'a -> int
.sp
A variant of 
.ft B
Hashtbl\&.hash_param
.ft R
that is further parameterized by
an integer seed\&.  Usage:
.ft B
Hashtbl\&.seeded_hash_param meaningful total seed x
.ft R
\&.

.sp
.B "Since"
4.00

.sp

.PP
.SS Examples
.sp
.SS Basic Example
.sp

.EX
.ft B
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\&    (* 0\&.\&.\&.99 *)
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\&    let seq = Seq\&.ints 0 |> Seq\&.take 100
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\&
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\&    (* build from Seq\&.t *)
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\&    # let tbl =
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\&        seq
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\&        |> Seq\&.map (fun x \-> x, string_of_int x)
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\&        |> Hashtbl\&.of_seq
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\&    val tbl : (int, string) Hashtbl\&.t = <abstr>
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\&
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\&    # Hashtbl\&.length tbl
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\&    \- : int = 100
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\&
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\&    # Hashtbl\&.find_opt tbl 32
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\&    \- : string option = Some "32"
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\&
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\&    # Hashtbl\&.find_opt tbl 166
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\&    \- : string option = None
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\&
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\&    # Hashtbl\&.replace tbl 166 "one six six"
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\&    \- : unit = ()
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\&
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\&    # Hashtbl\&.find_opt tbl 166
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\&    \- : string option = Some "one six six"
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\&
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\&    # Hashtbl\&.length tbl
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\&    \- : int = 101
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\&    
.ft R
.EE
.sp
.SS Counting Elements
.sp
Given a sequence of elements (here, a 
.ft B
Seq\&.t
.ft R
), we want to count how many
times each distinct element occurs in the sequence\&. A simple way to do this,
assuming the elements are comparable and hashable, is to use a hash table
that maps elements to their number of occurrences\&.
.sp
Here we illustrate that principle using a sequence of (ascii) characters
(type 
.ft B
char
.ft R
)\&.
We use a custom 
.ft B
Char_tbl
.ft R
specialized for 
.ft B
char
.ft R
\&.
.sp

.EX
.ft B
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\&    # module Char_tbl = Hashtbl\&.Make(struct
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\&        type t = char
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\&        let equal = Char\&.equal
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\&        let hash = Hashtbl\&.hash
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\&      end)
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\&
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\&    (*  count distinct occurrences of chars in [seq] *)
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\&    # let count_chars (seq : char Seq\&.t) : _ list =
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\&        let counts = Char_tbl\&.create 16 in
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\&        Seq\&.iter
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\&          (fun c \->
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\&            let count_c =
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\&              Char_tbl\&.find_opt counts c
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\&              |> Option\&.value ~default:0
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\&            in
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\&            Char_tbl\&.replace counts c (count_c + 1))
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\&          seq;
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\&        (* turn into a list *)
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\&        Char_tbl\&.fold (fun c n l \-> (c,n) :: l) counts []
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\&          |> List\&.sort (fun (c1,_)(c2,_) \-> Char\&.compare c1 c2)
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\&    val count_chars : Char_tbl\&.key Seq\&.t \-> (Char\&.t * int) list = <fun>
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\&
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\&    (* basic seq from a string *)
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\&    # let seq = String\&.to_seq "hello world, and all the camels in it!"
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\&    val seq : char Seq\&.t = <fun>
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\&
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\&    # count_chars seq
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\&    \- : (Char\&.t * int) list =
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\&    [(\&' \&', 7); (\&'!\&', 1); (\&',\&', 1); (\&'a\&', 3); (\&'c\&', 1); (\&'d\&', 2); (\&'e\&', 3);
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\&     (\&'h\&', 2); (\&'i\&', 2); (\&'l\&', 6); (\&'m\&', 1); (\&'n\&', 2); (\&'o\&', 2); (\&'r\&', 1);
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\&     (\&'s\&', 1); (\&'t\&', 2); (\&'w\&', 1)]
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\&
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\&    (* "abcabcabc\&.\&.\&." *)
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\&    # let seq2 =
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\&        Seq\&.cycle (String\&.to_seq "abc") |> Seq\&.take 31
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\&    val seq2 : char Seq\&.t = <fun>
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\&
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\&    # String\&.of_seq seq2
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\&    \- : String\&.t = "abcabcabcabcabcabcabcabcabcabca"
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\&
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\&    # count_chars seq2
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\&    \- : (Char\&.t * int) list = [(\&'a\&', 11); (\&'b\&', 10); (\&'c\&', 10)]
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\&
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\&  
.ft R
.EE
.PP