## Hash tables

A hashtable is a data structure that associates keys with values. The hashtable has no intrinsic order for the (key, value) associations it contains, and supports in-place modification as the primary means of setting the contents of a hash table. Any object can be used as a key, provided a hash function and a suitable equivalence function is available. A hash function is a procedure that maps keys to exact integer objects.

The hashtable provides key lookup and destructive update in amortised constant time, provided that a good hash function is used. A hash function `h` is acceptable for an equivalence predicate `e` iff `(`e` `obj1` `obj2`)` implies `(= (`h` `obj1`) (`h` `obj2`))`. A hash function `h` is good for a equivalence predicate `e` if it distributes the resulting hash values for non-equal objects (by `e`) as uniformly as possible over the 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.

Kawa provides two complete sets of functions for hashtables:

- The functions specified by R6RS have names starting with `hashtable-`

- The functions specified by the older SRFI-69 specifiation have names starting with `hash-table-`

Both interfaces use the same underlying datatype, so it is possible to mix and match from both sets. That datatype implements `java.util.Map`. Freshly-written code should probably use the R6RS functions.

### R6RS hash tables

To use these hash table functions in your Kawa program you must first:

    (import (rnrs hashtables))

This section uses the `hashtable` parameter name for arguments that must be hashtables, and the `key` parameter name for arguments that must be hashtable keys.

Procedure: `make-eq-hashtable`

Procedure: `make-eq-hashtable` ``k``

> Return a newly allocated mutable hashtable that accepts arbitrary objects as keys, and compares those keys with `eq?`. If an argument is given, the initial capacity of the hashtable is set to approximately `k` elements.

Procedure: `make-eqv-hashtable`

Procedure: `make-eqv-hashtable` ``k``

> Return a newly allocated mutable hashtable that accepts arbitrary objects as keys, and compares those keys with `eqv?`. If an argument is given, the initial capacity of the hashtable is set to approximately `k` elements.

Procedure: `make-hashtable` ``hash-function`` ``equiv``

Procedure: `make-hashtable` ``hash-function`` ``equiv`` ``k``

> `hash-function` and `equiv` must be procedures. `hash-function` should accept a key as an argument and should return a non–negative exact integer object. `equiv` should accept two keys as arguments and return a single value. Neither procedure should mutate the hashtable returned by `make-hashtable`.

> The `make-hashtable` procedure returns a newly allocated mutable hashtable using `hash-function` as the hash function and `equiv` as the equivalence function used to compare keys. If a third argument is given, the initial capacity of the hashtable is set to approximately `k` elements.

> Both `hash-function` and `equiv` should behave like pure functions on the domain of keys. For example, the `string-hash` and `string=?` procedures are permissible only if all keys are strings and the contents of those strings are never changed so long as any of them continues to serve as a key in the hashtable. Furthermore, any pair of keys for which `equiv` returns true should be hashed to the same exact integer objects by `hash-function`.

> > Note: Hashtables are allowed to cache the results of calling the hash function and equivalence function, so programs cannot rely on the hash function being called for every lookup or update. Furthermore any hashtable operation may call the hash function more than once.

#### Procedures

Procedure: `hashtable?` ``obj``

> Return `#t` if `obj` is a hashtable, `#f` otherwise.

Procedure: `hashtable-size` ``hashtable``

> Return the number of keys contained in `hashtable` as an exact integer object.

Procedure: `hashtable-ref` ``hashtable`` ``key`` ``default``

> Return the value in `hashtable` associated with `key`. If `hashtable` does not contain an association for `key`, `default` is returned.

Procedure: `hashtable-set!` ``hashtable`` ``key`` ``obj``

> Change `hashtable` to associate `key` with `obj`, adding a new association or replacing any existing association for `key`, and returns unspecified values.

Procedure: `hashtable-delete!` ``hashtable`` ``key``

> Remove any association for `key` within `hashtable` and returns unspecified values.

Procedure: `hashtable-contains?` ``hashtable`` ``key``

> Return `#t` if `hashtable` contains an association for `key`, `#f` otherwise.

Procedure: `hashtable-update!` ``hashtable`` ``key`` ``proc`` ``default``

> `proc` should accept one argument, should return a single value, and should not mutate `hashtable`.

> The `hashtable-update!` procedure applies `proc` to the value in `hashtable` associated with `key`, or to `default` if `hashtable` does not contain an association for `key`. The `hashtable` is then changed to associate `key` with the value returned by `proc`.

> The behavior of `hashtable-update!` is equivalent to the following code, but is may be (and is in Kawa) implemented more efficiently in cases where the implementation can avoid multiple lookups of the same key:

>     (hashtable-set!
>       hashtable key
>       (proc (hashtable-ref
>              hashtable key default)))

Procedure: `hashtable-copy` ``hashtable``

Procedure: `hashtable-copy` ``hashtable`` ``mutable``

> Return a copy of `hashtable`. If the `mutable` argument is provided and is true, the returned hashtable is mutable; otherwise it is immutable.

Procedure: `hashtable-clear!` ``hashtable``

Procedure: `hashtable-clear!` ``hashtable`` ``k``

> Remove all associations from `hashtable` and returns unspecified values.

> If a second argument is given, the current capacity of the hashtable is reset to approximately `k` elements.

Procedure: `hashtable-keys` ``hashtable``

> Return a vector of all keys in `hashtable`. The order of the vector is unspecified.

Procedure: `hashtable-entries` ``hashtable``

> Return two values, a vector of the keys in `hashtable`, and a vector of the corresponding values.

> Example:

>     (let ((h (make-eqv-hashtable)))
>       (hashtable-set! h 1 'one)
>       (hashtable-set! h 2 'two)
>       (hashtable-set! h 3 'three)
>       (hashtable-entries h))
>     ⇒ #(1 2 3) #(one two three) ; two return values

> the order of the entries in the result vectors is not known.

#### Inspection

Procedure: `hashtable-equivalence-function` ``hashtable``

> Return the equivalence function used by `hashtable` to compare keys. For hashtables created with `make-eq-hashtable` and `make-eqv-hashtable`, returns `eq?` and `eqv?` respectively.

Procedure: `hashtable-hash-function` ``hashtable``

> Return the hash function used by `hashtable`. For hashtables created by `make-eq-hashtable` or `make-eqv-hashtable`, `#f` is returned.

Procedure: `hashtable-mutable?` ``hashtable``

> Return `#t` if `hashtable` is mutable, otherwise `#f`.

#### Hash functions

The `equal-hash`, `string-hash`, and `string-ci-hash` procedures of this section are acceptable as the hash functions of a hashtable only if the keys on which they are called are not mutated while they remain in use as keys in the hashtable.

Procedure: `equal-hash` ``obj``

> Return an integer hash value for `obj`, based on its structure and current contents. This hash function is suitable for use with `equal?` as an equivalence function.

> > Note: Like `equal?`, the `equal-hash` procedure must always terminate, even if its arguments contain cycles.

Procedure: `string-hash` ``string``

> Return an integer hash value for `string`, based on its current contents. This hash function is suitable for use with `string=?` as an equivalence function.

Procedure: `string-ci-hash` ``string``

> Return an integer hash value for `string` based on its current contents, ignoring case. This hash function is suitable for use with `string-ci=?` as an equivalence function.

Procedure: `symbol-hash` ``symbol``

> Return an integer hash value for `symbol`.

### SRFI-69 hash tables

To use these hash table functions in your Kawa program you must first:

    (require 'srfi-69)

or

    (require 'hash-table)

or

    (import (srfi 69 basic-hash-tables))

#### Type constructors and predicate

Procedure: `make-hash-table` [ `equal?` [ `hash` [ `size-hint`]]] `→` `hash-table`

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

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

> The `size-hint` parameter can be used to suggested an approriate initial size. This option is not part of the SRFI-69 specification (though it is handled by the reference implementation), so specifying that option might be unportable.

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

> A predicate to test whether a given object `obj` is a hash table.

Procedure: `alist->hash-table` `alist` [ `equal?` [ `hash` [ `size-hint`]]] `→` `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`. The `equal?`, `hash`, and `size-hint` parameters 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.)

#### Reflective queries

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`.

#### Dealing with single elements

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`.

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.

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

> 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.

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

> This procedure removes any association to `key` in `hash-table`. It is not an error if no association for the `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.

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.

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

> 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` `→` `void`

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

#### Dealing with the whole contents

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

> Returns the number of associations in `hash-table`. This operation takes constant time.

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` `→` `void`

> `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.

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`. The `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.

#### Hash functions

The Kawa implementation always calls these hash functions with a single parameter, and expects the result to be within the entire (32-bit signed) `int` range, for compatibility with standard `hashCode` methods.

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

> Produces a hash value for object in the range from 0 (inclusive) tp to `bound` (exclusive).

> If `bound` is not given, the Kawa implementation returns a value within the range `(- (expt 2 32))` (inclusive) to `(- (expt 2 32) 1)` (inclusive). It does this by calling the standard `hashCode` method, and returning the result as is. (If the `object` is the Java `null` value, 0 is returned.) 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. (The Kawa implementation returns the same as the `hash` function.)

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. (The Kawa implementation returns the same the `hash` function applied to the lower-cased `string`.)

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

> The same as `hash`, except that this function is only guaranteed to be acceptable for `eq?`. Kawa uses the `identityHashCode` method of `java.lang.System`.