Hash tables and hash functions.
Hash tables are hashed association tables, with in-place modification. Because most operations on a hash table modify their input, they're more commonly used in imperative code. The lookup of the value associated with a key (see find, find_opt) is normally very fast, often faster than the equivalent lookup in Map.
The functors Make and MakeSeeded can be used when performance or flexibility are key. The user provides custom equality and hash functions for the key type, and obtains a custom hash table type for this particular type of key.
Warning a hash table is only as good as the hash function. A bad hash function will turn the table into a degenerate association list, with linear time lookup instead of constant time lookup.
The polymorphic t hash table is useful in simpler cases or in interactive environments. It uses the polymorphic hash function defined in the OCaml runtime (at the time of writing, it's SipHash), as well as the polymorphic equality (=).
See the examples section.
Unsynchronized accesses
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 Mutex.t).
Generic interface
The type of hash tables from type 'a to type 'b.
val create : ?random:bool -> int -> ('a, 'b) tHashtbl.create n creates a new, empty hash table, with initial size n. For best results, n should be on the order of the expected number of elements that will be in the table. The table grows as needed, so n is just an initial guess.
The optional ~random parameter (a boolean) controls whether the internal organization of the hash table is randomized at each execution of Hashtbl.create or deterministic over all executions.
A hash table that is created with ~random set to false uses a fixed hash function (hash) 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.
A hash table that is created with ~random set to true uses the seeded hash function seeded_hash with a seed that is randomly chosen at hash table creation time. In effect, the hash function used is randomly selected among 2^{30} 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 fold or iter is no longer deterministic: elements are enumerated in different orders at different runs of the program.
If no ~random parameter is given, hash tables are created in non-random mode by default. This default can be changed either programmatically by calling randomize or by setting the R flag in the OCAMLRUNPARAM environment variable.
val clear : ('a, 'b) t -> unitEmpty a hash table. Use reset instead of clear to shrink the size of the bucket table to its initial size.
val reset : ('a, 'b) t -> unitEmpty a hash table and shrink the size of the bucket table to its initial size.
val copy : ('a, 'b) t -> ('a, 'b) tReturn a copy of the given hashtable.
val add : ('a, 'b) t -> 'a -> 'b -> unitHashtbl.add tbl key data adds a binding of key to data in table tbl.
Warning: Previous bindings for key are not removed, but simply hidden. That is, after performing remove tbl key, the previous binding for key, if any, is restored. (Same behavior as with association lists.)
If you desire the classic behavior of replacing elements, see replace.
val find : ('a, 'b) t -> 'a -> 'bHashtbl.find tbl x returns the current binding of x in tbl, or raises Not_found if no such binding exists.
val find_opt : ('a, 'b) t -> 'a -> 'b optionHashtbl.find_opt tbl x returns the current binding of x in tbl, or None if no such binding exists.
val find_all : ('a, 'b) t -> 'a -> 'b listHashtbl.find_all tbl x returns the list of all data associated with x in tbl. The current binding is returned first, then the previous bindings, in reverse order of introduction in the table.
val mem : ('a, 'b) t -> 'a -> boolHashtbl.mem tbl x checks if x is bound in tbl.
val remove : ('a, 'b) t -> 'a -> unitHashtbl.remove tbl x removes the current binding of x in tbl, restoring the previous binding if it exists. It does nothing if x is not bound in tbl.
val replace : ('a, 'b) t -> 'a -> 'b -> unitHashtbl.replace tbl key data replaces the current binding of key in tbl by a binding of key to data. If key is unbound in tbl, a binding of key to data is added to tbl. This is functionally equivalent to remove tbl key followed by add tbl key data.
val iter : ('a -> 'b -> unit) -> ('a, 'b) t -> unitHashtbl.iter f tbl applies f to all bindings in table tbl. f receives the key as first argument, and the associated value as second argument. Each binding is presented exactly once to f.
The order in which the bindings are passed to f is unspecified. However, if the table contains several bindings for the same key, they are passed to f in reverse order of introduction, that is, the most recent binding is passed first.
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.
The behavior is not specified if the hash table is modified by f during the iteration.
val filter_map_inplace : ('a -> 'b -> 'b option) -> ('a, 'b) t -> unitHashtbl.filter_map_inplace f tbl applies f to all bindings in table tbl and update each binding depending on the result of f. If f returns None, the binding is discarded. If it returns Some new_val, the binding is update to associate the key to new_val.
Other comments for iter apply as well.
val fold : ('a -> 'b -> 'acc -> 'acc) -> ('a, 'b) t -> 'acc -> 'accHashtbl.fold f tbl init computes (f kN dN ... (f k1 d1 init)...), where k1 ... kN are the keys of all bindings in tbl, and d1 ... dN are the associated values. Each binding is presented exactly once to f.
The order in which the bindings are passed to f is unspecified. However, if the table contains several bindings for the same key, they are passed to f in reverse order of introduction, that is, the most recent binding is passed first.
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.
The behavior is not specified if the hash table is modified by f during the iteration.
val length : ('a, 'b) t -> intHashtbl.length tbl returns the number of bindings in tbl. It takes constant time. Multiple bindings are counted once each, so Hashtbl.length gives the number of times Hashtbl.iter calls its first argument.
val randomize : unit -> unitAfter a call to Hashtbl.randomize(), hash tables are created in randomized mode by default: create returns randomized hash tables, unless the ~random:false optional parameter is given. The same effect can be achieved by setting the R parameter in the OCAMLRUNPARAM environment variable.
It is recommended that applications or Web frameworks that need to protect themselves against the denial-of-service attack described in create call Hashtbl.randomize() at initialization time before any domains are created.
Note that once Hashtbl.randomize() was called, there is no way to revert to the non-randomized default behavior of create. This is intentional. Non-randomized hash tables can still be created using Hashtbl.create ~random:false.
val is_randomized : unit -> boolReturn true if the tables are currently created in randomized mode by default, false otherwise.
val rebuild : ?random:bool -> ('a, 'b) t -> ('a, 'b) tReturn a copy of the given hashtable. Unlike copy, rebuild h re-hashes all the (key, value) entries of the original table h. The returned hash table is randomized if h was randomized, or the optional random parameter is true, or if the default is to create randomized hash tables; see create for more information.
rebuild can safely be used to import a hash table built by an old version of the Hashtbl module, then marshaled to persistent storage. After unmarshaling, apply rebuild to produce a hash table for the current version of the Hashtbl module.
type statistics = {num_bindings : int;Number of bindings present in the table. Same value as returned by length.
num_buckets : int;Number of buckets in the table.
max_bucket_length : int;Maximal number of bindings per bucket.
bucket_histogram : int array;Histogram of bucket sizes. This array histo has length max_bucket_length + 1. The value of histo.(i) is the number of buckets whose size is i.
}Hashtbl.stats tbl returns statistics about the table tbl: number of buckets, size of the biggest bucket, distribution of buckets by size.
Hash tables and Sequences
val to_seq : ('a, 'b) t -> ('a * 'b) Seq.tIterate 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.
The behavior is not specified if the hash table is modified during the iteration.
val to_seq_keys : ('a, _) t -> 'a Seq.tSame as Seq.map fst (to_seq m)
val to_seq_values : (_, 'b) t -> 'b Seq.tSame as Seq.map snd (to_seq m)
val add_seq : ('a, 'b) t -> ('a * 'b) Seq.t -> unitAdd the given bindings to the table, using add
val replace_seq : ('a, 'b) t -> ('a * 'b) Seq.t -> unitAdd the given bindings to the table, using replace
val of_seq : ('a * 'b) Seq.t -> ('a, 'b) tBuild a table from the given bindings. The bindings are added in the same order they appear in the sequence, using replace_seq, which means that if two pairs have the same key, only the latest one will appear in the table.
Functorial interface
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.
For instance, one might want to specialize a table for integer keys:
module IntHash =
struct
type t = int
let equal i j = i=j
let hash i = i land max_int
end
module IntHashtbl = Hashtbl.Make(IntHash)
let h = IntHashtbl.create 17 in
IntHashtbl.add h 12 "hello"
This creates a new module IntHashtbl, with a new type 'a
IntHashtbl.t of tables from int to 'a. In this example, h contains string values so its type is string IntHashtbl.t.
Note that the new type 'a IntHashtbl.t is not compatible with the type ('a,'b) Hashtbl.t of the generic interface. For example, Hashtbl.length h would not type-check, you must use IntHashtbl.length.
The input signature of the functor Make.
module type S = sig ... endThe output signature of the functor Make.
Functor building an implementation of the hashtable structure. The functor Hashtbl.Make returns a structure containing a type key of keys and a type 'a t of hash tables associating data of type 'a to keys of type key. The operations perform similarly to those of the generic interface, but use the hashing and equality functions specified in the functor argument H instead of generic equality and hashing. Since the hash function is not seeded, the create operation of the result structure always returns non-randomized hash tables.
Functor building an implementation of the hashtable structure. The functor Hashtbl.MakeSeeded returns a structure containing a type key of keys and a type 'a t of hash tables associating data of type 'a to keys of type key. The operations perform similarly to those of the generic interface, but use the seeded hashing and equality functions specified in the functor argument H instead of generic equality and hashing. The create operation of the result structure supports the ~random optional parameter and returns randomized hash tables if ~random:true is passed or if randomization is globally on (see Hashtbl.randomize).
The polymorphic hash functions
Hashtbl.hash x associates a nonnegative integer to any value of any type. It is guaranteed that if x = y or Stdlib.compare x y = 0, then hash x = hash y. Moreover, hash always terminates, even on cyclic structures.
val seeded_hash : int -> 'a -> intA variant of hash that is further parameterized by an integer seed.
val hash_param : int -> int -> 'a -> intHashtbl.hash_param meaningful total x computes a hash value for x, with the same properties as for hash. The two extra integer parameters meaningful and total give more precise control over hashing. Hashing performs a breadth-first, left-to-right traversal of the structure x, stopping after meaningful meaningful nodes were encountered, or total nodes (meaningful or not) were encountered. If total 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 meaningful and total 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 meaningful and total govern the tradeoff between accuracy and speed. As default choices, hash and seeded_hash take meaningful = 10 and total = 100.
val seeded_hash_param : int -> int -> int -> 'a -> intA variant of hash_param that is further parameterized by an integer seed. Usage: Hashtbl.seeded_hash_param meaningful total seed x.
Examples
Basic Example
(* 0...99 *)
let seq = Seq.ints 0 |> Seq.take 100
(* build from Seq.t *)
# let tbl =
seq
|> Seq.map (fun x -> x, string_of_int x)
|> Hashtbl.of_seq
val tbl : (int, string) Hashtbl.t = <abstr>
# Hashtbl.length tbl
- : int = 100
# Hashtbl.find_opt tbl 32
- : string option = Some "32"
# Hashtbl.find_opt tbl 166
- : string option = None
# Hashtbl.replace tbl 166 "one six six"
- : unit = ()
# Hashtbl.find_opt tbl 166
- : string option = Some "one six six"
# Hashtbl.length tbl
- : int = 101
Counting Elements
Given a sequence of elements (here, a Seq.t), 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.
Here we illustrate that principle using a sequence of (ascii) characters (type char). We use a custom Char_tbl specialized for char.
# module Char_tbl = Hashtbl.Make(struct
type t = char
let equal = Char.equal
let hash = Hashtbl.hash
end)
(* count distinct occurrences of chars in [seq] *)
# let count_chars (seq : char Seq.t) : _ list =
let counts = Char_tbl.create 16 in
Seq.iter
(fun c ->
let count_c =
Char_tbl.find_opt counts c
|> Option.value ~default:0
in
Char_tbl.replace counts c (count_c + 1))
seq;
(* turn into a list *)
Char_tbl.fold (fun c n l -> (c,n) :: l) counts []
|> List.sort (fun (c1,_)(c2,_) -> Char.compare c1 c2)
val count_chars : Char_tbl.key Seq.t -> (Char.t * int) list = <fun>
(* basic seq from a string *)
# let seq = String.to_seq "hello world, and all the camels in it!"
val seq : char Seq.t = <fun>
# count_chars seq
- : (Char.t * int) list =
[(' ', 7); ('!', 1); (',', 1); ('a', 3); ('c', 1); ('d', 2); ('e', 3);
('h', 2); ('i', 2); ('l', 6); ('m', 1); ('n', 2); ('o', 2); ('r', 1);
('s', 1); ('t', 2); ('w', 1)]
(* "abcabcabc..." *)
# let seq2 =
Seq.cycle (String.to_seq "abc") |> Seq.take 31
val seq2 : char Seq.t = <fun>
# String.of_seq seq2
- : String.t = "abcabcabcabcabcabcabcabcabcabca"
# count_chars seq2
- : (Char.t * int) list = [('a', 11); ('b', 10); ('c', 10)]