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== Sets, bags, and integer sets ==

Sets and bags (multisets) are mutable collections that can contain any Scheme object.  Integer sets are mutable collections that can contain non-negative integers from 0 to a value ''n'' that is specified when the integer set is created.

Sets and bags (multisets) are intended to be a thin veneer over hashtables, and integer sets are a thin veneer over bit vectors.  Consequently, the `-member?`, `-add!`, and `-remove!` procedures are required to have an amortized cost of O(1).

== Basic set procedures ==

`(make-set `''proc''`)`

Constructs and returns a new empty set.  ''Proc'' is the equality procedure for the set, which must be consistent with `eq?`.  If ''proc'' is other than `eq?`, `eqv?`, `equal`, or `string-ci=?`, the implementation MAY signal an error.

`(set `''element''` ...)`

Constructs and returns a new set containing the ''elements''.

`(copy-set `''set''`)`

Constructs and returns a new set containing the elements of ''set''.

`(set? `''obj''`)`

Returns `#t` if ''obj'' is a set, and `#f` otherwise.

`(set-length? `''set''`)`

Returns the number of elements in ''set''.

`(set-member? `''set''` `''element''`)`

Returns `#t` if ''element'' is a member of ''set'' and `#f` otherwise.

`(set-add! `''set''` `''element''`)`

Adds ''element'' to ''set'' unless it is already a member.  Returns unspecified values.

`(set-remove! `''set''` `''element''`)`

Removes ''element'' from ''set'' unless it is not a member.  Returns unspecified values.

`(set-map `''proc''` `''set'' ...`)`

Applies ''proc'' to the ''sets'' and constructs and returns a new set containing the values of the applications.

`(set-for-each `''proc''` `''set'' ...`)`

Applies ''proc'' to the ''sets'', discarding the returned values.  Returns unspecified results.

`(set->list `''set''`)`

Constructs and returns a new list containing the members of ''set'' in unspecified order.

`(list->set `''list''`)`

Constructs and returns a new set containing the elements of ''list''.

`(set->vector `''set''`)`

Constructs and returns a new vector containing the elements of ''set'' in unspecified order.

`(vector->set `''vector''`)`

Constructs and returns a new set containing the elements of ''vector''.

== Advanced set procedures ==

`(set<= `''set'' ...`)`

Returns `#t` if each ''set'' other than the last is a subset of the following ''set'', and `#f` otherwise.  All the ''sets'' must share the same equality predicate.

`(set= `''set'' ...`)`

Returns `#t` if each ''set'' contains the same elements.  All the ''sets'' must share the same equality predicate.

`(set-union `''set'' ...`)`

Constructs and returns a new set that is the union of the ''sets''.

`(set-intersection `''set'' ...`)`

Constructs and returns a new set that is the intersection of the ''sets''.

`(set-difference `''set'' ...`)`

Constructs and returns a new set that is the difference of the ''sets''.

`(set-xor `''set'' ...`)`

Constructs and returns a new set that is the xor (symmetric difference) of the ''sets''.

`(set-union! `''set''` `''other-set'' ...`)`

Mutates ''set'' to a new set that is the union of ''set'' and the ''other-sets''.

`(set-intersection! `''set''` `''other-set'' ...`)`

Mutates ''set'' to a new set that is the difference of ''set'' and the ''other-sets''.

`(set-difference! `''set''` `''other-set'' ...`)`

Mutates ''set'' to a new set that is the difference of ''set'' and the ''other-sets''.

`(set-xor! `''set''` `''other-set'' ...`)`

Mutates ''set'' to a new set that is the xor (symmetric difference) of ''set'' and the ''other-sets''.

== Bag procedures ==

The procedures for creating and manipulating bags are the same as those for sets, except that `set` is replaced by `bag` in their names, and that adding an element to a bag is effective even if the bag already contains the element.

== Integer set procedures ==

`(make-integer-set `''n''`)`

Constructs and returns a new empty integer set.  The possible elements of the set are the exact integers from 0 to ''n'' - 1.

`(integer-set `''n''` `''element'' ...`)`

Constructs and returns a new integer set.  The possible elements of the set are the exact integers from 0 to ''n'' - 1. The set is initialized to contain the ''elements''.

`(list->integer-set `''n''` `''list''`)`

Constructs and returns a new integer set.  The possible elements of the set are the exact integers from 0 to ''n'' - 1. The set is initialized to contain the elements of ''list''.

`(vector->integer-set `''n''` `''list''`)`

Constructs and returns a new integer set.  The possible elements of the set are the exact integers from 0 to ''n'' - 1. The set is initialized to contain the elements of ''vector''.

The other integer set procedures are the same as those for sets, except that `set` is replaced by `integer-set` in their names.  

== Conversions ==

`set->bag`, `bag->set`, `integer-set->bag`, and `integer-set->set` take one argument and do the obvious thing.  `bag->integer-set` and `set->integer-set` take two arguments, ''n'' and the set or bag, and also do the obvious thing.

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2010-09-21 06:41:14