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4.15 Hash Tables

Hash Tables in The Racket Guide introduces hash tables.

A hash table (or simply hash) maps each of its keys to a single value. For a given hash table, keys are equivalent via equal?, equal-always?, eqv?, or eq?, and keys are retained either strongly, weakly (see Weak Boxes), or like ephemerons. A hash table is also either mutable or immutable. Immutable hash tables support effectively constant-time access and update, just like mutable hash tables; the constant on immutable operations is usually larger, but the functional nature of immutable hash tables can pay off in certain algorithms. Use immutable? to check whether a hash table is immutable.

Immutable hash tables actually provide O(log N) access and update. Since N is limited by the address space so that log N is limited to less than 30 or 62 (depending on the platform), log N can be treated reasonably as a constant.

For equal?-based hashing, the built-in hash functions on strings, pairs, lists, vectors, prefab or transparent structures, etc., take time proportional to the size of the value. The hash code for a compound data structure, such as a list or vector, depends on hashing each item of the container, but the depth of such recursive hashing is limited (to avoid potential problems with cyclic data). For a non-list pair, both car and cdr hashing is treated as a deeper hash, but the cdr of a list is treated as having the same hashing depth as the list.

A hash table can be used as a two-valued sequence (see Sequences). The keys and values of the hash table serve as elements of the sequence (i.e., each element is a key and its associated value). If a mapping is added to or removed from the hash table during iteration, then an iteration step may fail with exn:fail:contract, or the iteration may skip or duplicate keys and values. See also in-hash, in-hash-keys, in-hash-values, and in-hash-pairs.

Two hash tables cannot be equal? unless they have the same mutability, use the same key-comparison procedure (equal?, equal-always?, eqv?, or eq?), both hold keys strongly, weakly, or like ephemerons. Empty immutable hash tables are eq? when they are equal?.

Changed in version 7.2.0.9 of package base: Made empty immutable hash tables eq? when they are equal?.

Caveats concerning concurrent modification: A mutable hash table can be manipulated with hash-ref, hash-set!, and hash-remove! concurrently by multiple threads, and the operations are protected by a table-specific semaphore as needed. Several caveats apply, however:

• If a thread is terminated while applying hash-ref, hash-ref-key, hash-set!, hash-remove!, hash-ref!, hash-update!, or hash-clear! to a hash table that uses equal?, equal-always?, or eqv? key comparisons, all current and future operations on the hash table may block indefinitely.

• The hash-map, hash-for-each, and hash-clear! procedures do not use the table’s semaphore to guard the traversal as a whole (if a traversal is needed, in the case of hash-clear!). Changes by one thread to a hash table can affect the keys and values seen by another thread part-way through its traversal of the same hash table.

• The hash-update! and hash-ref! functions use a table’s semaphore independently for the hash-ref and hash-set! parts of their functionality, which means that the update as a whole is not “atomic.”

• Adding a mutable hash table as a key in itself is trouble on the grounds that the key is being mutated (see the caveat below), but it is also a kind of concurrent use of the hash table: computing a hash table’s hash code may require waiting on the table’s semaphore, but the semaphore is already held for modifying the hash table, so the hash-table addition can block indefinitely.

Caveat concerning mutable keys: If a key in an equal?-based hash table is mutated (e.g., a key string is modified with string-set!), then the hash table’s behavior for insertion and lookup operations becomes unpredictable.

A literal or printed hash table starts with #hash, #hashalw, #hasheqv, or #hasheq. See Reading Hash Tables for information on reading hash tables and Printing Hash Tables for information on printing hash tables.

See also immutable-hash? and mutable-hash?.

Added in version 8.5.0.3 of package base.

Returns

if

retains its keys strongly,

if it retains keys weakly or like

.

Added in version 8.0.0.10 of package base.

Returns

if

retains its keys weakly,

if it retains keys strongly or like

.

Returns

if

retains its keys like

,

if it retains keys strongly or merely weakly.

Added in version 8.0.0.10 of package base.

Creates an immutable hash table with each given

mapped to the following

; each

must have a

, so the total number of arguments to

must be even.

The hash procedure creates a table where keys are compared with equal?, hashalw creates a table where keys are compared with equal-always?, hasheq procedure creates a table where keys are compared with eq?, hasheqv procedure creates a table where keys are compared with eqv?.

The key to val mappings are added to the table in the order that they appear in the argument list, so later mappings can hide earlier mappings if the keys are equal.

Changed in version 8.5.0.3 of package base: Added hashalw.

Creates a mutable hash table that holds keys strongly.

The make-hash procedure creates a table where keys are compared with equal?, make-hasheq procedure creates a table where keys are compared with eq?, make-hasheqv procedure creates a table where keys are compared with eqv?, and make-hashalw creates a table where keys are compared with equal-always?.

The table is initialized with the content of assocs. In each element of assocs, the car is a key, and the cdr is the corresponding value. The mappings are added to the table in the order that they appear in assocs, so later mappings can hide earlier mappings.

See also make-custom-hash.

Examples:

> (make-hash)

'#hash()

> (make-hash '([0 . 1] [42 . "meaning of life"] [2 . 3]))

'#hash((0 . 1) (2 . 3) (42 . "meaning of life"))

> (make-hash '([0 . 1] [1 . 2] [0 . 3]))

'#hash((0 . 3) (1 . 2))

> (make-hash (list (cons 0 1) (cons 'apple 'orange) (cons #t #f)))

'#hash((#t . #f) (0 . 1) (apple . orange))

> (make-hash '((0 1) (1 2) (2 3)))

'#hash((0 . (1)) (1 . (2)) (2 . (3)))

> (make-hash (list (cons + -)))

'#hash((#<procedure:+> . #<procedure:->))

Changed in version 8.5.0.3 of package base: Added make-hashalw.

Beware that values in a weak hash table are retained normally. If a value in the table refers back to its key, then the table will retain the value and therefore the key; the mapping will never be removed from the table even if the key becomes otherwise inaccessible. To avoid that problem, use an ephemeron hash table as created by make-ephemeron-hash, make-ephemeron-hashalw, make-ephemeron-hasheqv, or make-ephemeron-hasheq. For values that do not refer to keys, there is a modest extra cost to using an ephemeron hash table instead of a weak hash table, but prefer an ephemeron hash table when in doubt.

Changed in version 8.5.0.3 of package base: Added make-weak-hashalw.

Using an ephemeron hash table is like using a weak hash table and mapping each key to a ephemeron that pairs the key and value. An advantage of an ephemeron hash table is that the value need not be extracted with ephemeron-value from the result of functions like hash-ref. An ephemeron hash table might also be represented more compactly than a weak hash table with explicit ephemeron values.

Added in version 8.0.0.10 of package base.
Changed in version 8.5.0.3: Added make-ephemeron-hashalw.

Changed in version 8.5.0.3 of package base: Added make-immutable-hashalw.

Maps key to v in ht, overwriting any existing mapping for key.

See also the caveats concerning concurrent modification and the caveat concerning mutable keys above.

Maps each key to each v in ht, overwriting any existing mapping for each key. Mappings are added from the left, so later mappings overwrite earlier mappings.

See also the caveats concerning concurrent modification and the caveat concerning mutable keys above.

Functionally extends ht by mapping key to v, overwriting any existing mapping for key, and returning the extended hash table.

See also the caveat concerning mutable keys above.

Functionally extends ht by mapping each key to v, overwriting any existing mapping for each key, and returning the extended hash table. Mappings are added from the left, so later mappings overwrite earlier mappings.

See also the caveat concerning mutable keys above.

Returns the value for key in ht. If no value is found for key, then failure-result determines the result:

• If failure-result is a procedure, it is called (through a tail call) with no arguments to produce the result.

• Otherwise, failure-result is returned as the result.

Examples:

See also the caveats concerning concurrent modification and the caveat concerning mutable keys above.

Returns the key held by

that is equivalent to

according to

’s key-comparison function. If no key is found, then

is used as in

to determine the result.

If ht is not an impersonator, then the returned key, assuming it is found, will be eq?-equivalent to the one actually retained by ht:

Examples:

If a mutable hash is updated multiple times using keys that are not eq?-equivalent but are equivalent according to the hash’s key-comparison procedure, the hash retains the first one:

Examples:

Conversely, an immutable hash retains the key that was most-recently used to update it:

If ht is an impersonator, then the returned key will be determined as described in the documentation to impersonate-hash.

See also the caveats concerning concurrent modification and the caveat concerning mutable keys above.

Added in version 7.4.0.3 of package base.

Returns the value for

in

. If no value is found for

, then

determines the result as in

(i.e., it is either a thunk that computes a value or a plain value), and this result is stored in

for the

. (Note that if

is a thunk, it is not invoked in tail position.)

See also the caveats concerning concurrent modification and the caveat concerning mutable keys above.

Returns #t if ht contains a value for the given key, #f otherwise.

Updates the value mapped by key in ht by applying updater to the value. The value returned by updater becomes the new mapping for key, overwriting the original value in ht.

Examples:

The optional failure-result argument is used when no mapping exists for key already, in the same manner as in hash-ref.

Examples:

See also the caveats concerning concurrent modification and the caveat concerning mutable keys above.

Functionally updates the value mapped by key in ht by applying updater to the value and returning a new hash table. The value returned by updater becomes the new mapping for key in the returned hash table.

Examples:

The optional failure-result argument is used when no mapping exists for key already, in the same manner as in hash-ref.

Examples:

See also the caveat concerning mutable keys above.

Removes any existing mapping for key in ht.

See also the caveats concerning concurrent modification and the caveat concerning mutable keys above.

Functionally removes any existing mapping for

in

, returning

(i.e., a result

to

) if

is not present in

.

See also the caveat concerning mutable keys above.

Removes all mappings from ht.

If ht is not an impersonator, then all mappings are removed in constant time. If ht is an impersonator, then each key is removed one-by-one using hash-remove!.

See also the caveats concerning concurrent modification and the caveat concerning mutable keys above.

Functionally removes all mappings from ht.

If ht is not a chaperone, then clearing is equivalent to creating a new hash table, and the operation is performed in constant time. If ht is a chaperone, then each key is removed one-by-one using hash-remove.

Produces an empty

with the same key-comparison procedure as

, with either the given

or the same kind as the given

.

If kind is not supplied or #f, produces a hash table of the same kind and mutability as the given ht. If kind is 'immutable, 'mutable, 'weak, or 'ephemeron, produces a table that’s immutable, mutable with strongly-held keys, mutable with weakly-held keys, or mutable with ephemeron-held keys respectively.

Changed in version 8.5.0.2 of package base: Added the kind argument.

Applies the procedure proc to each element in ht in an unspecified order, accumulating the results into a list. The procedure proc is called each time with a key and its value, and the procedure’s individual results appear in order in the result list.

If a hash table is extended with new keys (either through proc or by another thread) while a hash-map or hash-for-each traversal is in process, arbitrary key–value pairs can be dropped or duplicated in the traversal. Key mappings can be deleted or remapped (by any thread) with no adverse affects; the change does not affect a traversal if the key has been seen already, otherwise the traversal skips a deleted key or uses the remapped key’s new value.

See also the caveats concerning concurrent modification above.

If try-order? is true, then the order of keys and values passed to proc is normalized under certain circumstances—including when every key is one of the following and with the following order (earlier bullets before later):

• booleans sorted #f before #t;

• characters sorted by char<?;

• real numbers sorted by <;

• symbols sorted with uninterned symbols before unreadable symbols before interned symbols, then sorted by symbol<?;

• keywords sorted by keyword<?;

• strings sorted by string<?;

• byte strings sorted by bytes<?;

• null;

• #<void>; and

• eof.

Changed in version 6.3 of package base: Added the try-order? argument.
Changed in version 7.1.0.7: Added guarantees for try-order?.

Examples:

Applies the procedure proc to each element in ht in an unspecified order, accumulating the results into a new hash with the same key-comparison procedure as ht, with either the given kind or the same kind as the given ht.

If kind is not supplied or #f, produces a hash table of the same kind and mutability as the given ht. If kind is 'immutable, 'mutable, 'weak, or 'ephemeron, produces a table that’s immutable, mutable with strongly-held keys, mutable with weakly-held keys, or mutable with ephemeron-held keys respectively.

Examples:

'#hash((a . "APPLE") (b . "BANANA"))

> frozen-capital

'#hash((a . "APPLE") (b . "BANANA"))

> (immutable? frozen-capital)

#t

Added in version 8.5.0.2 of package base.

Returns a list of the keys of ht in an unspecified order.

If

is true, then the order of keys is normalized under certain circumstances. See

for further explanations on

and on information about modifying

during

.

Changed in version 8.3.0.11 of package base: Added the try-order? argument.

Returns a list of the values of ht in an unspecified order.

If

is true, then the order of values is normalized under certain circumstances, based on the ordering of the associated keys. See

for further explanations on

and on information about modifying

during

.

Changed in version 8.3.0.11 of package base: Added the try-order? argument.

Returns a list of the key–value pairs of ht in an unspecified order.

If

is true, then the order of keys and values is normalized under certain circumstances. See

for further explanations on

and on information about modifying

during

.

Changed in version 8.3.0.11 of package base: Added the try-order? argument.

Returns

if the keys of

are a subset of or the same as the keys of

. The hash tables must both use the same key-comparison function (

,

,

, or

), otherwise the

exception is raised.

Using hash-keys-subset? on immutable hash tables can be much faster than iterating through the keys of ht1 to make sure that each is in ht2.

Added in version 6.5.0.8 of package base.

Applies proc to each element in ht (for the side-effects of proc) in an unspecified order. The procedure proc is called each time with a key and its value.

See

for information about

and about modifying

within

.

Changed in version 6.3 of package base: Added the try-order? argument.
Changed in version 7.1.0.7: Added guarantees for try-order?.

Returns the number of keys mapped by ht.

For the CS implementation of Racket, the result is always computed in constant time and atomically. For the BC implementation of Racket, the result is computed in constant time and atomically only if ht does not retain keys weakly or like an ephemeron, otherwise, a traversal is required to count the keys.

Returns #f if ht contains no elements, otherwise it returns an integer that is an index to the first element in the hash table; “first” refers to an unspecified ordering of the table elements, and the index values are not necessarily consecutive integers.

For a mutable ht, this index is guaranteed to refer to the first item only as long as no items are added to or removed from ht. More generally, an index is guaranteed to be a valid hash index for a given hash table only as long it comes from hash-iterate-first or hash-iterate-next, and only as long as the hash table is not modified. In the case of a hash table with weakly held keys or keys held like ephemerons, the hash table can be implicitly modified by the garbage collector (see Garbage Collection) when it discovers that the key is not reachable.

Returns either an integer that is an index to the element in ht after the element indexed by pos (which is not necessarily one more than pos) or #f if pos refers to the last element in ht.

If pos is not a valid hash index of ht, then the result may be #f or it may be the next later index that remains valid. The latter result is guaranteed if a hash table has been modified only by the removal of keys.

Changed in version 7.0.0.10 of package base: Handle an invalid index by returning #f instead of raising exn:fail:contract.

Returns the key for the element in ht at index pos.

If pos is not a valid hash index for ht, the result is bad-index-v if provided, otherwise the exn:fail:contract exception is raised.

Changed in version 7.0.0.10 of package base: Added the optional bad-index-v argument.

Returns the value for the element in ht at index pos.

If pos is not a valid hash index for ht, the result is bad-index-v if provided, otherwise the exn:fail:contract exception is raised.

Changed in version 7.0.0.10 of package base: Added the optional bad-index-v argument.

Returns a pair containing the key and value for the element in ht at index pos.

If pos is not a valid hash index for ht, the result is (cons bad-index-v bad-index-v) if bad-index-v is provided, otherwise the exn:fail:contract exception is raised.

Added in version 6.4.0.5 of package base.
Changed in version 7.0.0.10: Added the optional bad-index-v argument.

Returns the key and value for the element in ht at index pos.

If pos is not a valid hash index for ht, the result is (values bad-index-v bad-index-v) if bad-index-v is provided, otherwise the exn:fail:contract exception is raised.

Added in version 6.4.0.5 of package base.
Changed in version 7.0.0.10: Added the optional bad-index-v argument.

Returns a mutable hash table with the same mappings, same key-comparison mode, and same key-holding strength as ht.

Computes the union of ht0 with each hash table ht by functional update, adding each element of each ht to ht0 in turn. For each key k and value v, if a mapping from k to some value v0 already exists, it is replaced with a mapping from k to (combine/key k v0 v).

Examples:

'#hash((1 . one) (2 . two) (3 . three))

'#hash((1 . (one uno eins un)) (2 . (two dos zwei deux)))

Computes the union of ht0 with each hash table ht by mutable update, adding each element of each ht to ht0 in turn. For each key k and value v, if a mapping from k to some value v0 already exists, it is replaced with a mapping from k to (combine/key k v0 v).

Examples:

Constructs the hash table which is the intersection of

with every hash table

. In the resulting hash table, a key

is mapped to a combination of the values to which

is mapped in each of the hash tables. The final values are computed by stepwise combination of the values appearing in each of the hash tables by applying

, where

is the value to which

is mapped in the

-th hash table

, and

is the accumulation of the values from the previous steps. The comparison predicate of the first argument (

,

,

,

) determines the one for the result.

Examples:

'#hash((a . 5) (b . 7))

'#hash((a . 5) (b . -3))

Added in version 7.9.0.1 of package base.

Filters the

based on a predicate

applied to both its keys and values. This function constructs a new hash table that includes only those key-value pairs from the input

for which the predicate

returns true when applied simultaneously to the keys and values of

. The output hash table retains the mutability and the key comparison predicate (e.g.,

,

,

) of the input hash table

, ensuring that the structural and operational properties of the original hash are preserved in the output.

Examples:

'#hash((1 . 2) (2 . 4))

> (hash-filter (make-hash) (λ (k v) (< k 3)))

'#hash()

'#hasheq((#t . "true"))

'#hash(((1 2) . pair))

'#hash(("three" . 3))

Added in version 8.13.0.4 of package base.

Filters the

based on a predicate

applied to its keys. This function constructs a new hash table that includes only those key-value pairs from the input

for which the predicate

returns true when applied to the keys. Similar to

, the output hash table maintains the mutability and key comparator of the input hash table, ensuring that the structural and operational properties of the original hash are retained.

Examples:

Added in version 8.12.0.9 of package base.

Filters the

based on a predicate

applied to its values. This function returns a new hash table containing only the key-value pairs for which the predicate

returns true when applied to the values of

. The resulting hash table retains the mutability and the key comparison predicate (e.g.,

,

,

,

) of the input hash table

.

Examples:

Added in version 8.12.0.9 of package base.

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