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Sets­Cowan

cowan
2010-09-24 01:41:06
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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 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 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 each element of set in arbitrary order and constructs and returns a new set containing the values of the applications.

(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 argument 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.

(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' 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 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 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 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.

(vector->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 vector.

The other integer set procedures 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.

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.