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Source for wiki SetsCowan version 8

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cowan

comment

Add integer set complement procedures

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66.108.19.185

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SetsCowan

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text

== 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 exact integers from 0 to a maximum value 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).

Sets, bags, and integer sets are mutually disjoint and disjoint from other types of Scheme objects.

== Basic set procedures ==

`(make-set `''=''`)`

Constructs and returns a new empty set.  ''='' is the equality procedure for the set, which must be consistent with `eq?`.  If ''='' is other than `eq?`, `equal`, `string=?`, or `string-ci=?`, the implementation MAY signal an error.  '''Issue: possibly add '''`eqv?`''' to this list if hash tables support it.'''

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

Constructs and returns a new set with equality procedure ''='' and containing the ''elements''.

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

Constructs and returns a new set containing the elements of ''set'', with the same equality procedure.

`(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 each element of ''set'' in arbitrary order and constructs and returns a new set with the same equality predicate containing the values of the applications.  '''Issue: Should we provide this at all?  The fold is sufficient.'''

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

Applies ''proc'' to ''set'' in arbitrary order, discarding the returned values.  Returns unspecified results.

`(set-fold `''proc''` `''nil''` `''set''`)`

Invokes ''proc'' on each member of ''set'' in arbitrary order, passing the result of the previous invocation as a second argument.  For the first invocation, ''nil'' is used as the second argument.  Returns the result of the last invocation.

`(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''.

== Advanced set procedures ==

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

Returns `#t` if each ''set'' contains the same elements.

`(set<? `''set'' ...`)`

Returns `#t` if each ''set'' other than the last is a proper subset of the following ''set'', and `#f` otherwise.

`(set>? `''set'' ...`)`

Returns `#t` if each ''set'' other than the last is a proper superset of the following ''set'', and `#f` otherwise.

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

Returns `#t` if each ''set'' other than the last is a subset of the following ''set'', and `#f` otherwise.

`(set>=? `''set'' ...`)`

Returns `#t` if each ''set'' other than the last is a superset of the following ''set'', and `#f` otherwise.

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

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

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

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

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

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

`(set-xor `''set''` `''other-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 intersection 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 union of 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.

`(bag-count `''bag''` `''element''`)`

Returns an exact integer representing the number of times that ''element'' appears in ''bag''.

== Integer set procedures ==

Except as noted below, the procedures for creating and manipulating integer sets are the same as those for sets, except that `set` is replaced by `integer-set` in their names.  Wherever a newly constructed integer set is returned, it has the same limit as the source set.

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

Constructs and returns a new empty integer set.  The possible elements of the set are the exact integers from 0 to ''limit'' - 1, where ''limit'' is an exact non-negative integer.

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

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

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

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

`(integer-set-complement `''integer-set''`)`

Returns a newly allocated integer set that is the complement of ''integer-set''.

`(integer-set-complement! `''integer-set''`)`

Mutates ''integer-set'' to a new set that is the complement of ''integer-set''.


== 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, ''limit'' and the set or bag, and also do the obvious thing.

time

2012-04-04 12:37:14