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- Received: 2005/04/25
- Revised: 2005/05/09
- Revised: 2005/08/03
- Revised: 2005/08/10
- Draft extended: 2005/08/10 - 2005/09/09
- Revised: 2005/08/30
- Final: 2005/09/14

This SRFI defines basic hash tables. Hash tables are widely recognised as a fundamental data structure for a wide variety of applications. A hash table is a data structure that:

- provides a mapping from some set of keys to some set of values associated to those keys
- has no intrinsic order for the (key, value) associations it contains
- supports in-place modification as the primary means of setting the contents of a hash table
- provides key lookup and destructive update in amortised constant time, provided that a good hash function is used.

This SRFI aims to accomplish these goals:

- to provide a consistent, generic and widely applicable API for hash tables
- to improve code portability by providing a standard hash table facility with guaranteed behaviour
- to help the programmer by defining utility routines that account for the most common situations of using hash tables.

There is no single best way to make hash tables. The tables presented
in this SRFI aim at being both conceptually simple and usable for a wide
variety of applications. Even though a portable implementation is
provided, Scheme implementations can speed things up considerably by
e.g. providing an internal hash function for symbols. Moreover, almost
every Scheme implementation already has some kind of low-level hash
table functionality, because that's the natural way to implement
the global environment, and specifically, to provide support for
`string->symbol`. There might be some benefit in integration
between implementation-specific environment data types and the hash
table API presented here; however, these issues are left open.

This SRFI does not conform to the interface of maps presented in SRFI
44. Following SRFI 44 would seriously cripple the interface of hash
tables. The naming of the operations for maps in SRFI 44 goes against
common use and is unnatural. However, this SRFI has been written so
that it does not *prevent* a SRFI-44 API to hash tables. An
implementation supporting both SRFI 44 and this SRFI is encouraged to
provide a SRFI 44 interface to hash tables in addition to the one
presented here.

Hash tables are widely recognised as a fundamental data structure for many kinds of computational tasks. Thus far, there is no existing standard for Scheme hash tables; however, almost every non-minimal Scheme implementation provides some kind of hash table functionality.

Alas, although somewhat similar, these hash table APIs have many differences: some trivial, like the naming of certain functions; some complex, like revealing different aspects of the internal implementation to the user; some coarse, like requiring keys to be of some specific type(s); some subtle, like requiring the user to guess the size of the hash table in advance to get optimal performance. As a result, the existing hash table facilities cannot be used to write portable programs.

The primary aim of this SRFI is to establish a standard API for hash tables so that portable programs can be written that make efficient use of common hash table functionality. The SRFI resolves discrepancies that exist between the various hash table API's with respect to naming and semantics of hash table operations. A lot of effort has been put into making the the API consistent, simple and generic. The SRFI also defines some of the most common utility routines that would otherwise need to be written and rewritten for various applications.

Incorporating this SRFI as a standard feature in Scheme implementations makes it possible to write efficient and portable programs that use hash tables.

Names defined in this SRFI:

- Type constructors and predicate
- make-hash-table, hash-table?, alist->hash-table
- Reflective queries
- hash-table-equivalence-function, hash-table-hash-function
- Dealing with single elements
- hash-table-ref, hash-table-ref/default, hash-table-set!, hash-table-delete!, hash-table-exists?, hash-table-update!, hash-table-update!/default
- Dealing with the whole contents
- hash-table-size, hash-table-keys, hash-table-values, hash-table-walk, hash-table-fold, hash-table->alist, hash-table-copy, hash-table-merge!
- Hashing
- hash, string-hash, string-ci-hash, hash-by-identity

An implementation that does not provide `hash-table-ref`,
`hash-table-set!`, `hash-table-delete!`, `hash-table-update!`,
`hash-table-exists?`, and `hash-table-size` in amortised constant
time (when a good hash function is used), or fails to provide good hash
function definitions for `hash`, `string-hash`, `string-ci-hash`,
and `hash-by-identity`, does not conform to this SRFI.

Hash table implementations are allowed to rely on the fact that the hash value of a key in hash table does not change. In most cases, modifying a key in-place after it has been inserted into the hash table will violate this constraint and thus leads to unspecified behaviour.

Procedure: make-hash-table [ `equal?` [ `hash` [ `args` … ]]]
→ `hash-table`

Create a new hash table with no associations. `equal?` is a
predicate that should accept two keys and return a boolean telling
whether they denote the same key value; it defaults to `equal?`.

`hash` is a hash function, and defaults to an appropriate hash function
for the given `equal?` predicate (see section Hashing). However,
an acceptable default is not guaranteed to be given for any equivalence
predicate coarser than `equal?`, except for `string-ci=?`.[1] The function `hash` must be acceptable for `equal?`, so if
you use coarser equivalence than `equal?` other than `string-ci=?`,
you must always provide the function `hash` yourself.

[1] An
equivalence predicate `c1` is coarser than a equivalence predicate `c2`
iff there exist values `x` and `y` such that `(and (c1 x y) (not (c2 x
y)))`.

Implementations are allowed to use the rest `args` for
implementation-specific extensions. Be warned, though, that using these
extensions will make your program less portable.

Procedure: hash-table? `obj` → `boolean`

A predicate to test whether a given object `obj` is a hash table. The
hash table type should be disjoint from all other types, if possible.

Procedure: alist->hash-table `alist` [ `equal?` [ `hash`
[ `args` … ]]] → `hash-table`

Takes an association list

`alist` and creates a hash table
`hash-table` which maps the `car` of every element in `alist` to the
`cdr` of corresponding elements in `alist`. `equal?`, `hash`, and
`args` are interpreted as in `make-hash-table`. If some key occurs
multiple times in `alist`, the value in the first association will take
precedence over later ones. (Note: the choice of using `cdr` (instead
of `cadr`) for values tries to strike balance between the two
approaches: using `cadr` would render this procedure unusable for
`cdr` alists, but not vice versa.)

The rest `args` are passed to make-hash-table and can thus be used for
implementation-specific extensions.

Procedure: hash-table-equivalence-function `hash-table`

Returns the equivalence predicate used for keys of `hash-table`.

Procedure: hash-table-hash-function `hash-table`

Returns the hash function used for keys of `hash-table`.

Procedure: hash-table-ref `hash-table` `key` [ `thunk` ] → `value`

This procedure returns the `value` associated to `key` in `hash-table`.
If no `value` is associated to `key` and `thunk` is given, it is called
with no arguments and its value is returned; if `thunk` is not given, an
error is signalled.
Given a good hash function, this operation should have an (amortised)
complexity of O(1) with respect to the number of associations in
`hash-table`. (Note: this rules out implementation by association lists
or fixed-length hash tables.)

Procedure: hash-table-ref/default `hash-table` `key` `default` →
`value`

Evaluates to the same value as `(hash-table-ref hash-table key (lambda
() default))`.
Given a good hash function, this operation should have an (amortised)
complexity of O(1) with respect to the number of associations in
`hash-table`. (Note: this rules out implementation by association lists
or fixed-length hash tables.)

Procedure: hash-table-set! `hash-table` `key` `value` → undefined

This procedure sets the `value` associated to `key` in `hash-table`.
The previous association (if any) is removed.
Given a good hash function, this operation should have an (amortised)
complexity of O(1) with respect to the number of associations in
`hash-table`. (Note: this rules out implementation by association lists
or fixed-length hash tables.)

Procedure: hash-table-delete! `hash-table` `key` → undefined

This procedure removes any association to `key` in `hash-table`. It is
not an error if no association for that key exists; in this case,
nothing is done.
Given a good hash function, this operation should have an (amortised)
complexity of O(1) with respect to the number of associations in
`hash-table`. (Note: this rules out implementation by association lists
or fixed-length hash tables.)

Procedure: hash-table-exists? `hash-table` `key` → `boolean`

This predicate tells whether there is any association to `key` in
`hash-table`.
Given a good hash function, this operation should have an (amortised)
complexity of O(1) with respect to the number of associations in
`hash-table`. (Note: this rules out implementation by association lists
or fixed-length hash tables.)

Procedure: hash-table-update! `hash-table` `key` `function`
[ `thunk` ] → undefined

Semantically equivalent to, but may be implemented more efficiently than, the following code:

(hash-table-set! hash-table key (function (hash-table-ref hash-table key thunk)))

Procedure: hash-table-update!/default
`hash-table` `key` `function` `default` → undefined

Behaves as if it evaluates to `(hash-table-update! hash-table key
function (lambda () default))`.

Procedure: hash-table-size `hash-table` → `integer`

Returns the number of associations in `hash-table`. This operation
must have a complexity of O(1) with respect to the number of
associations in `hash-table`.

Procedure: hash-table-keys `hash-table` → `list`

Returns a list of keys in `hash-table`. The order of the keys is
unspecified.

Procedure: hash-table-values `hash-table` → `list`

Returns a list of values in `hash-table`. The order of the values is
unspecified, and is not guaranteed to match the order of keys in the
result of hash-table-keys.

Procedure: hash-table-walk `hash-table` `proc` → unspecified

`proc` should be a function taking two arguments, a `key` and a `value`.
This procedure calls `proc` for each association in `hash-table`, giving
the key of the association as `key` and the value of the association as
`value`. The results of `proc` are discarded. The order in which
`proc` is called for the different associations is unspecified.

(Note: in some implementations, there is a procedure called
`hash-table-map` which does the same as this procedure. However, in
other implementations, `hash-table-map` does something else. In no
implementation that I know of, `hash-table-map` does a real functorial
map that lifts an ordinary function to the domain of hash tables.
Because of these reasons, `hash-table-map` is left outside this SRFI.)

Procedure: hash-table-fold `hash-table` `f` `init-value`
→ `final-value`

This procedure calls `f` for every association in `hash-table` with
three arguments: the key of the association `key`, the value of the
association `value`, and an accumulated value

, `val`. `val` is
`init-value` for the first invocation of `f`, and for subsequent
invocations of `f`, the return value of the previous invocation of `f`.
The value `final-value` returned by `hash-table-fold` is the return
value of the last invocation of `f`. The order in which `f` is called
for different associations is unspecified.

Procedure: hash-table->alist `hash-table` → `alist`

Returns an association list such that the `car` of each element in
`alist` is a key in `hash-table` and the corresponding `cdr` of each
element in `alist` is the value associated to the key in `hash-table`.
The order of the elements is unspecified.

The following should always produce a hash table with the same mappings
as a hash table `h`:

(alist->hash-table (hash-table->alist h) (hash-table-equivalence-function h) (hash-table-hash-function h))

Procedure: hash-table-copy `hash-table` → `hash-table`

Returns a new hash table with the same equivalence predicate, hash
function and mappings as in `hash-table`.

Procedure: hash-table-merge! `hash-table1` `hash-table2` →
`hash-table`

Adds all mappings in `hash-table2` into `hash-table1` and returns the
resulting hash table. This function may modify `hash-table1`
destructively.

Hashing means the act of taking some value and producing a number from
the value. A hash function is a function that does this. Every
equivalence predicate `e` has a set of `acceptable` hash functions for
that predicate; a hash funtion `hash` is acceptable iff `(e obj1
obj2)` → `(= (hash obj1) (hash obj2))`.

A hash function `h` is `good` for a equivalence predicate `e` if it
distributes the result numbers (`hash values`) for non-equal objects (by
`e`) as uniformly as possible over the numeric range of hash values,
especially in the case when some (non-equal) objects resemble each other
by e.g. having common subsequences. This definition is vague but should
be enough to assert that e.g. a constant function is *not* a good hash
function.

When the definition of make-hash-table above talks about an
appropriate

hashing function for `e`, it means a hashing function that
gives decent performance (for the hashing operation) while being both
acceptable and good for `e`. This definition, too, is intentionally
vague.

Procedure: hash `object` [ `bound` ] → `integer`

Produces a hash value for `object` in the range ( 0, `bound` (. If
`bound` is not given, the implementation is free to choose any bound,
given that the default bound is greater than the size of any imaginable
hash table in a normal application. (This is so that the implementation
may choose some very big value in fixnum range for the default bound.)
This hash function is acceptable for `equal?`.

Procedure: string-hash `string` [ `bound` ] → `integer`

The same as hash, except that the argument `string` must be a string.

Procedure: string-ci-hash `string` [ `bound` ] → `integer`

The same as string-hash, except that the case of characters in
`string` does not affect the hash value produced.

Procedure: hash-by-identity `object` [ `bound` ] → `integer`

The same as hash, except that this function is only guaranteed to be
acceptable for `eq?`. The reason for providing this function is that
it might be implemented significantly more efficiently than `hash`.
Implementations are encouraged to provide this function as a builtin.

This implementation relies on SRFI-9 for distinctness of the hash table type, and on SRFI-23 for error reporting. Otherwise, the implementation is pure R5RS.

(define *default-bound* (- (expt 2 29) 3)) (define (%string-hash s ch-conv bound) (let ((hash 31) (len (string-length s))) (do ((index 0 (+ index 1))) ((>= index len) (modulo hash bound)) (set! hash (modulo (+ (* 37 hash) (char->integer (ch-conv (string-ref s index)))) *default-bound*))))) (define (string-hash s . maybe-bound) (let ((bound (if (null? maybe-bound) *default-bound* (car maybe-bound)))) (%string-hash s (lambda (x) x) bound))) (define (string-ci-hash s . maybe-bound) (let ((bound (if (null? maybe-bound) *default-bound* (car maybe-bound)))) (%string-hash s char-downcase bound))) (define (symbol-hash s . maybe-bound) (let ((bound (if (null? maybe-bound) *default-bound* (car maybe-bound)))) (%string-hash (symbol->string s) (lambda (x) x) bound))) (define (hash obj . maybe-bound) (let ((bound (if (null? maybe-bound) *default-bound* (car maybe-bound)))) (cond ((integer? obj) (modulo obj bound)) ((string? obj) (string-hash obj bound)) ((symbol? obj) (symbol-hash obj bound)) ((real? obj) (modulo (+ (numerator obj) (denominator obj)) bound)) ((number? obj) (modulo (+ (hash (real-part obj)) (* 3 (hash (imag-part obj)))) bound)) ((char? obj) (modulo (char->integer obj) bound)) ((vector? obj) (vector-hash obj bound)) ((pair? obj) (modulo (+ (hash (car obj)) (* 3 (hash (cdr obj)))) bound)) ((null? obj) 0) ((not obj) 0) ((procedure? obj) (error "hash: procedures cannot be hashed" obj)) (else 1)))) (define hash-by-identity hash) (define (vector-hash v bound) (let ((hashvalue 571) (len (vector-length v))) (do ((index 0 (+ index 1))) ((>= index len) (modulo hashvalue bound)) (set! hashvalue (modulo (+ (* 257 hashvalue) (hash (vector-ref v index))) *default-bound*))))) (define %make-hash-node cons) (define %hash-node-set-value! set-cdr!) (define %hash-node-key car) (define %hash-node-value cdr) (define-record-type <srfi-hash-table> (%make-hash-table size hash compare associate entries) hash-table? (size hash-table-size hash-table-set-size!) (hash hash-table-hash-function) (compare hash-table-equivalence-function) (associate hash-table-association-function) (entries hash-table-entries hash-table-set-entries!)) (define *default-table-size* 64) (define (appropriate-hash-function-for comparison) (or (and (eq? comparison eq?) hash-by-identity) (and (eq? comparison string=?) string-hash) (and (eq? comparison string-ci=?) string-ci-hash) hash)) (define (make-hash-table . args) (let* ((comparison (if (null? args) equal? (car args))) (hash (if (or (null? args) (null? (cdr args))) (appropriate-hash-function-for comparison) (cadr args))) (size (if (or (null? args) (null? (cdr args)) (null? (cddr args))) *default-table-size* (caddr args))) (association (or (and (eq? comparison eq?) assq) (and (eq? comparison eqv?) assv) (and (eq? comparison equal?) assoc) (letrec ((associate (lambda (val alist) (cond ((null? alist) #f) ((comparison val (caar alist)) (car alist)) (else (associate val (cdr alist))))))) associate)))) (%make-hash-table 0 hash comparison association (make-vector size '())))) (define (make-hash-table-maker comp hash) (lambda args (apply make-hash-table (cons comp (cons hash args))))) (define make-symbol-hash-table (make-hash-table-maker eq? symbol-hash)) (define make-string-hash-table (make-hash-table-maker string=? string-hash)) (define make-string-ci-hash-table (make-hash-table-maker string-ci=? string-ci-hash)) (define make-integer-hash-table (make-hash-table-maker = modulo)) (define (%hash-table-hash hash-table key) ((hash-table-hash-function hash-table) key (vector-length (hash-table-entries hash-table)))) (define (%hash-table-find entries associate hash key) (associate key (vector-ref entries hash))) (define (%hash-table-add! entries hash key value) (vector-set! entries hash (cons (%make-hash-node key value) (vector-ref entries hash)))) (define (%hash-table-delete! entries compare hash key) (let ((entrylist (vector-ref entries hash))) (cond ((null? entrylist) #f) ((compare key (caar entrylist)) (vector-set! entries hash (cdr entrylist)) #t) (else (let loop ((current (cdr entrylist)) (previous entrylist)) (cond ((null? current) #f) ((compare key (caar current)) (set-cdr! previous (cdr current)) #t) (else (loop (cdr current) current)))))))) (define (%hash-table-walk proc entries) (do ((index (- (vector-length entries) 1) (- index 1))) ((< index 0)) (for-each proc (vector-ref entries index)))) (define (%hash-table-maybe-resize! hash-table) (let* ((old-entries (hash-table-entries hash-table)) (hash-length (vector-length old-entries))) (if (> (hash-table-size hash-table) hash-length) (let* ((new-length (* 2 hash-length)) (new-entries (make-vector new-length '())) (hash (hash-table-hash-function hash-table))) (%hash-table-walk (lambda (node) (%hash-table-add! new-entries (hash (%hash-node-key node) new-length) (%hash-node-key node) (%hash-node-value node))) old-entries) (hash-table-set-entries! hash-table new-entries))))) (define (hash-table-ref hash-table key . maybe-default) (cond ((%hash-table-find (hash-table-entries hash-table) (hash-table-association-function hash-table) (%hash-table-hash hash-table key) key) => %hash-node-value) ((null? maybe-default) (error "hash-table-ref: no value associated with" key)) (else ((car maybe-default))))) (define (hash-table-ref/default hash-table key default) (hash-table-ref hash-table key (lambda () default))) (define (hash-table-set! hash-table key value) (let ((hash (%hash-table-hash hash-table key)) (entries (hash-table-entries hash-table))) (cond ((%hash-table-find entries (hash-table-association-function hash-table) hash key) => (lambda (node) (%hash-node-set-value! node value))) (else (%hash-table-add! entries hash key value) (hash-table-set-size! hash-table (+ 1 (hash-table-size hash-table))) (%hash-table-maybe-resize! hash-table))))) (define (hash-table-update! hash-table key function . maybe-default) (let ((hash (%hash-table-hash hash-table key)) (entries (hash-table-entries hash-table))) (cond ((%hash-table-find entries (hash-table-association-function hash-table) hash key) => (lambda (node) (%hash-node-set-value! node (function (%hash-node-value node))))) ((null? maybe-default) (error "hash-table-update!: no value exists for key" key)) (else (%hash-table-add! entries hash key (function ((car maybe-default)))) (hash-table-set-size! hash-table (+ 1 (hash-table-size hash-table))) (%hash-table-maybe-resize! hash-table))))) (define (hash-table-update!/default hash-table key function default) (hash-table-update! hash-table key function (lambda () default))) (define (hash-table-delete! hash-table key) (if (%hash-table-delete! (hash-table-entries hash-table) (hash-table-equivalence-function hash-table) (%hash-table-hash hash-table key) key) (hash-table-set-size! hash-table (- (hash-table-size hash-table) 1)))) (define (hash-table-exists? hash-table key) (and (%hash-table-find (hash-table-entries hash-table) (hash-table-association-function hash-table) (%hash-table-hash hash-table key) key) #t)) (define (hash-table-walk hash-table proc) (%hash-table-walk (lambda (node) (proc (%hash-node-key node) (%hash-node-value node))) (hash-table-entries hash-table))) (define (hash-table-fold hash-table f acc) (hash-table-walk hash-table (lambda (key value) (set! acc (f key value acc)))) acc) (define (alist->hash-table alist . args) (let* ((comparison (if (null? args) equal? (car args))) (hash (if (or (null? args) (null? (cdr args))) (appropriate-hash-function-for comparison) (cadr args))) (size (if (or (null? args) (null? (cdr args)) (null? (cddr args))) (max *default-table-size* (* 2 (length alist))) (caddr args))) (hash-table (make-hash-table comparison hash size))) (for-each (lambda (elem) (hash-table-update!/default hash-table (car elem) (lambda (x) x) (cdr elem))) alist) hash-table)) (define (hash-table->alist hash-table) (hash-table-fold hash-table (lambda (key val acc) (cons (cons key val) acc)) '())) (define (hash-table-copy hash-table) (let ((new (make-hash-table (hash-table-equivalence-function hash-table) (hash-table-hash-function hash-table) (max *default-table-size* (* 2 (hash-table-size hash-table)))))) (hash-table-walk hash-table (lambda (key value) (hash-table-set! new key value))) new)) (define (hash-table-merge! hash-table1 hash-table2) (hash-table-walk hash-table2 (lambda (key value) (hash-table-set! hash-table1 key value))) hash-table1) (define (hash-table-keys hash-table) (hash-table-fold hash-table (lambda (key val acc) (cons key acc)) '())) (define (hash-table-values hash-table) (hash-table-fold hash-table (lambda (key val acc) (cons val acc)) '()))

Copyright © Panu Kalliokoski (2005). All Rights Reserved.

Permission is hereby granted, free of charge, to any person obtaining a
copy of this software and associated documentation files (the
Software

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Editor: David Van Horn Last modified: Wed Sep 14 09:54:51 EDT 2005