chickadee » srfi-113

SRFI-113: Sets and Bags

Sets and bags (also known as multisets) are unordered collections that can contain any Scheme object. Sets enforce the constraint that no two elements can be the same in the sense of the set's associated equality predicate; bags do not.

Installation

$ chicken-install srfi-113

or

$ chicken-install srfi-113 -test

if you want to run the tests for the egg in addition.

SRFI Description

For a full description of this SRFI, see the full SRFI document. This documentation covers the API only.

Although this version of SRFI-113 is based on the reference implementation, there is one notable difference. As SRFI-114 comparators have been deprecated in favour of SRFI-128 comparators, this egg uses SRFI-128 comparators whenever a comparator is needed. Thus, this egg depends on SRFI-128.

Set Procedures

Constructors

(set comparator element ...) procedure

Returns a newly allocated empty set. The comparator argument is a SRFI-128 comparator, which is used to control and distinguish the elements of the set. The elements are used to initialize the set.

(set-unfold comparator stop? mapper successor seed) procedure

Create a newly allocated set as if by set using comparator. If the result of applying the predicate stop? to seed is true, return the set. Otherwise, apply the procedure mapper to seed. The value that mapper returns is added to the set. Then get a new seed by applying the procedure successor to seed, and repeat this algorithm.

Predicates

(set? obj) procedure

Returns #t if obj is a set, and #f otherwise.

(set-contains? set element) procedure

Returns #t if element is a member of set and #f otherwise.

(set-empty? set) procedure

Returns #t if set has no elements and #f otherwise.

(set-disjoint? set1 set2) procedure

Returns #t if set1 and set2 have no elements in common and #f otherwise.

Accessors

(set-member set element default) procedure

Returns the element of set that is equal, in the sense of set's equality predicate, to element. If element is not a member of set, default is returned.

(set-element-comparator set) procedure

Returns the comparator used to compare the elements of set.

Updaters

(set-adjoin set element ...) procedure

The set-adjoin procedure returns a newly allocated set that uses the same comparator as set and contains all the values of set, and in addition each element unless it is already equal (in the sense of the comparator) to one of the existing or newly added members. It is an error to add an element to set that does not return #t when passed to the type test procedure of the comparator.

(set-adjoin! set element ...) procedure

The set-adjoin! procedure is the same as set-adjoin, except that it is permitted to mutate and return the set argument rather than allocating a new set.

(set-replace set element) procedure

The set-replace procedure returns a newly allocated set that uses the same comparator as set and contains all the values of set except as follows: If element is equal (in the sense of set's comparator) to an existing member of set, then that member is omitted and replaced by element. If there is no such element in set, then set is returned unchanged.

(set-replace! set element) procedure

The set-replace! procedure is the same as set-replace, except that it is permitted to mutate and return the set argument rather than allocating a new set.

(set-delete set element ...) procedure
(set-delete! set element ...) procedure
(set-delete-all set element-list) procedure
(set-delete-all! set element-list) procedure

The set-delete procedure returns a newly allocated set containing all the values of set except for any that are equal (in the sense of set's comparator) to one or more of the elements. Any element that is not equal to some member of the set is ignored.

The set-delete! procedure is the same as set-delete, except that it is permitted to mutate and return the set argument rather than allocating a new set.

The set-delete-all and set-delete-all! procedures are the same as set-delete and set-delete!, except that they accept a single argument which is a list of elements to be deleted.

(set-search! set element failure success) procedure

The set is searched for element. If it is not found, then the failure procedure is tail-called with two continuation arguments, insert and ignore, and is expected to tail-call one of them. If element is found, then the success procedure is tail-called with the matching element of set and two continuations, update and remove, and is expected to tail-call one of them.

The effects of the continuations are as follows (where obj is any Scheme object):

  • Invoking (insert obj) causes element to be inserted into set.
  • Invoking (ignore obj) causes set to remain unchanged.
  • Invoking (update new-element obj) causes new-element to be inserted into set in place of element.
  • Invoking (remove obj) causes the matching element of set to be removed from it.

In all cases, two values are returned: the possibly updated set and obj.

The Whole Set

(set-size set) procedure

Returns the number of elements in set as an exact integer.

(set-find predicate set failure) procedure

Returns an arbitrarily chosen element of set that satisfies predicate, or the result of invoking failure with no arguments if there is none.

(set-count predicate set) procedure

Returns the number of elements of set that satisfy predicate as an exact integer.

(set-any? predicate set) procedure

Returns #t if any element of set satisfies predicate, or #f otherwise. Note that this differs from the SRFI 1 analogue because it does not return an element of the set.

(set-every? predicate set) procedure

Returns #t if every element of set satisfies predicate, or #f otherwise. Note that this differs from the SRFI 1 analogue because it does not return an element of the set.

Mapping and Folding

(set-map comparator proc set) procedure

Applies proc to each element of set in arbitrary order and returns a newly allocated set, created as if by (set comparator), which contains the results of the applications. For example:

(set-map string-ci-comparator symbol->string (set eq? 'foo 'bar 'baz))
     => (set string-ci-comparator "foo" "bar" "baz")

Note that, when proc defines a mapping that is not 1:1, some of the mapped objects may be equivalent in the sense of comparator's equality predicate, and in this case duplicate elements are omitted as in the set constructor. For example:

(set-map (lambda (x) (quotient x 2))
         integer-comparator
         (set integer-comparator 1 2 3 4 5))
 => (set integer-comparator 0 1 2)

If the elements are the same in the sense of eqv?, it is unpredictable which one will be preserved in the result.

(set-for-each proc set) procedure

Applies proc to set in arbitrary order, discarding the returned values. Returns an unspecified result.

(set-fold proc nil set) procedure

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, or nil if there was no invocation.

(set-filter predicate set) procedure

Returns a newly allocated set with the same comparator as set, containing just the elements of set that satisfy predicate.

(set-filter! predicate set) procedure

A linear update procedure that returns a set containing just the elements of set that satisfy predicate.

(set-remove predicate set) procedure

Returns a newly allocated set with the same comparator as set, containing just the elements of set that do not satisfy predicate.

(set-remove! predicate set) procedure

A linear update procedure that returns a set containing just the elements of set that do not satisfy predicate.

(set-partition predicate set) procedure

Returns two values: a newly allocated set with the same comparator as set that contains just the elements of set that satisfy predicate, and another newly allocated set, also with the same comparator, that contains just the elements of set that do not satisfy predicate.

(set-partition! predicate set) procedure

A linear update procedure that returns two sets containing the elements of set that do and do not, respectively, not satisfy predicate.

Copying and Conversion

(set-copy set) procedure

Returns a newly allocated set containing the elements of set, and using the same comparator.

(set->list set) procedure

Returns a newly allocated list containing the members of set in unspecified order.

(list->set comparator list) procedure

Returns a newly allocated set, created as if by set using comparator, that contains the elements of list. Duplicate elements (in the sense of the equality predicate) are omitted.

(list->set! set list) procedure

Returns a set that contains the elements of both set and list. Duplicate elements (in the sense of the equality predicate) are omitted.

Subsets

Note: The following three predicates do not obey the trichotomy law and therefore do not constitute a total order on sets.

(set=? set1 set2 ...) procedure

Returns #t if each set contains the same elements.

(set<? set1 set2 ...) procedure

Returns #t if each set other than the last is a proper subset of the following set, and #f otherwise.

(set>? set1 set2 ...) procedure

Returns #t if each set other than the last is a proper superset of the following set, and #f otherwise.

(set<=? set1 set2 ...) procedure

Returns #t if each set other than the last is a subset of the following set, and #f otherwise.

(set>=? set1 set2 ...) procedure

Returns #t if each set other than the last is a superset of the following set, and #f otherwise.

Set-theory Operations

(set-union set1 set2 ...) procedure
(set-intersection set1 set2 ...) procedure
(set-difference set1 set2 ...) procedure
(set-xor set1 set2) procedure

Return a newly allocated set that is the union, intersection, asymmetric difference, or symmetric difference of the sets. Asymmetric difference is extended to more than two sets by taking the difference between the first set and the union of the others. Symmetric difference is not extended beyond two sets. Elements in the result set are drawn from the first set in which they appear.

(set-union! set1 set2 ...) procedure
(set-intersection! set1 set2 ...) procedure
(set-difference! set1 set2 ...) procedure
(set-xor! set1 set2) procedure

Linear update procedures returning a set that is the union, intersection, asymmetric difference, or symmetric difference of the sets. Asymmetric difference is extended to more than two sets by taking the difference between the first set and the union of the others. Symmetric difference is not extended beyond two sets. Elements in the result set are drawn from the first set in which they appear.

Bag Procedures

Bags are like sets, but can contain the same object more than once. However, if two elements that are the same in the sense of the equality predicate, but not in the sense of eqv?, are both included, it is not guaranteed that they will remain distinct when retrieved from the bag. It is an error for a single procedure to be invoked on bags with different comparators.

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 adjoining an element to a bag is effective even if the bag already contains the element. If two elements in a bag are the same in the sense of the bag's comparator, the implementation may in fact store just one of them.

The bag-union, bag-intersection, bag-difference, and bag-xor procedures (and their linear update analogues) behave as follows when both bags contain elements that are equal in the sense of the bags' comparator:

Constructors

(bag comparator element ...) procedure

Returns a newly allocated empty bag. The comparator argument is a SRFI-128 comparator, which is used to control and distinguish the elements of the bag. The elements are used to initialize the bag.

(bag-unfold comparator stop? mapper successor seed) procedure

Create a newly allocated bag as if by bag using comparator. If the result of applying the predicate stop? to seed is true, return the bag. Otherwise, apply the procedure mapper to seed. The value that mapper returns is added to the bag. Then get a new seed by applying the procedure successor to seed, and repeat this algorithm.

Predicates

(bag? obj) procedure

Returns #t if obj is a bag, and #f otherwise.

(bag-contains? bag element) procedure

Returns #t if element is a member of bag and #f otherwise.

(bag-empty? bag) procedure

Returns #t if bag has no elements and #f otherwise.

(bag-disjoint? bag1 bag2) procedure

Returns #t if bag1 and bag2 have no elements in common and #f otherwise.

Accessors

(bag-member bag element default) procedure

Returns the element of bag that is equal, in the sense of bag's equality predicate, to element. If element is not a member of bag, default is returned.

(bag-element-comparator bag) procedure

Returns the comparator used to compare the elements of bag.

Updaters

(bag-adjoin bag element ...) procedure

The bag-adjoin procedure returns a newly allocated bag that uses the same comparator as bag and contains all the values of bag, and in addition each element. It is an error to add an element to bag that does not return #t when passed to the type test procedure of the comparator.

(bag-adjoin! bag element ...) procedure

The bag-adjoin! procedure is the same as bag-adjoin, except that it is permitted to mutate and return the bag argument rather than allocating a new bag.

(bag-replace bag element) procedure

The bag-replace procedure returns a newly allocated bag that uses the same comparator as bag and contains all the values of bag. If there is no such element in bag, then bag is returned unchanged.

(bag-replace! bag element) procedure

The bag-replace! procedure is the same as bag-replace, except that it is permitted to mutate and return the bag argument rather than allocating a new bag.

(bag-delete bag element ...) procedure
(bag-delete! bag element ...) procedure
(bag-delete-all bag element-list) procedure
(bag-delete-all! bag element-list) procedure

The bag-delete procedure returns a newly allocated bag containing all the values of bag Any element that is not equal to some member of the bag is ignored.

The bag-delete! procedure is the same as bag-delete, except that it is permitted to mutate and return the bag argument rather than allocating a new bag.

The bag-delete-all and bag-delete-all!} procedures are the same as {{bag-delete and bag-delete!, except that they accept a single argument which is a list of elements to be deleted.

(bag-search! bag element failure success) procedure

The bag is searched for element. If it is not found, then the failure procedure is tail-called with two continuation arguments, insert and ignore, and is expected to tail-call one of them. If element is found, then the success procedure is tail-called with the matching element of bag and two continuations, update and remove, and is expected to tail-call one of them.

The effects of the continuations are as follows (where obj is any Scheme object):

  • Invoking (insert obj) causes element to be inserted into bag.
  • Invoking (ignore obj) causes bag to remain unchanged.
  • Invoking (update new-element obj) causes new-element to be inserted into bag in place of element.
  • Invoking (remove obj) causes the matching element of bag to be removed from it.

In all cases, two values are returned: the possibly updated bag and obj.

The Whole bag

(bag-size bag) procedure

Returns the number of elements in bag as an exact integer.

(bag-find predicate bag failure) procedure

Returns an arbitrarily chosen element of bag that satisfies predicate, or the result of invoking failure with no arguments if there is none.

(bag-count predicate bag) procedure

Returns the number of elements of bag that satisfy predicate as an exact integer.

(bag-any? predicate bag) procedure

Returns #t if any element of bag satisfies predicate, or #f otherwise. Note that this differs from the SRFI 1 analogue because it does not return an element of the bag.

(bag-every? predicate bag) procedure

Returns #t if every element of bag satisfies predicate, or #f otherwise. Note that this differs from the SRFI 1 analogue because it does not return an element of the bag.

Mapping and Folding

(bag-map comparator proc bag) procedure

Applies proc to each element of bag in arbitrary order and returns a newly allocated bag, created as if by (bag comparator), which contains the results of the applications. For example:

(bag-map string-ci-comparator symbol->string (bag eq? 'foo 'bar 'baz))
     => (bag string-ci-comparator "foo" "bar" "baz")
(bag-for-each proc bag) procedure

Applies proc to bag in arbitrary order, discarding the returned values. Returns an unspecified result.

(bag-fold proc nil bag) procedure

Invokes proc on each member of bag 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, or nil if there was no invocation.

(bag-filter predicate bag) procedure

Returns a newly allocated bag with the same comparator as bag, containing just the elements of bag that satisfy predicate.

(bag-filter! predicate bag) procedure

A linear update procedure that returns a bag containing just the elements of bag that satisfy predicate.

(bag-remove predicate bag) procedure

Returns a newly allocated bag with the same comparator as bag, containing just the elements of bag that do not satisfy predicate.

(bag-remove! predicate bag) procedure

A linear update procedure that returns a bag containing just the elements of bag that do not satisfy predicate.

(bag-partition predicate bag) procedure

Returns two values: a newly allocated bag with the same comparator as bag that contains just the elements of bag that satisfy predicate, and another newly allocated bag, also with the same comparator, that contains just the elements of bag that do not satisfy predicate.

(bag-partition! predicate bag) procedure

A linear update procedure that returns two bags containing the elements of bag that do and do not, respectively, not satisfy predicate.

Copying and Conversion

(bag-copy bag) procedure

Returns a newly allocated bag containing the elements of bag, and using the same comparator.

(bag->list bag) procedure

Returns a newly allocated list containing the members of bag in unspecified order.

(list->bag comparator list) procedure

Returns a newly allocated bag, created as if by bag using comparator, that contains the elements of list.

(list->bag! bag list) procedure

Returns a bag that contains the elements of both bag and list.

Subbags

(bag=? bag1 bag2 ...) procedure

Returns #t if each bag contains the same elements.

(bag<? bag1 bag2 ...) procedure

Returns #t if each bag other than the last is a proper subbag of the following bag, and #f otherwise.

(bag>? bag1 bag2 ...) procedure

Returns #t if each bag other than the last is a proper superbag of the following bag, and #f otherwise.

(bag<=? bag1 bag2 ...) procedure

Returns #t if each bag other than the last is a subbag of the following bag, and #f otherwise.

(bag>=? bag1 bag2 ...) procedure

Returns #t if each bag other than the last is a superbag of the following bag, and #f otherwise.

Bag-theory Operations

(bag-union bag1 bag2 ...) procedure
(bag-intersection bag1 bag2 ...) procedure
(bag-difference bag1 bag2 ...) procedure
(bag-xor bag1 bag2) procedure

Return a newly allocated bag that is the union, intersection, asymmetric difference, or symmetric difference of the bags. Asymmetric difference is extended to more than two bags by taking the difference between the first bag and the union of the others. Symmetric difference is not extended beyond two bags.

(bag-union! bag1 bag2 ...) procedure
(bag-intersection! bag1 bag2 ...) procedure
(bag-difference! bag1 bag2 ...) procedure
(bag-xor! bag1 bag2) procedure

Linear update procedures returning a bag that is the union, intersection, asymmetric difference, or symmetric difference of the bags. Asymmetric difference is extended to more than two bags by taking the difference between the first bag and the union of the others. Symmetric difference is not extended beyond two bags.

Additional bag procedures

(bag-sum bag1 bag2 ...) procedure
(bag-sum! bag1 bag2) procedure

The bag-sum procedure returns a newly allocated bag containing all the unique elements in all the bags, such that the count of each unique element in the result is equal to the sum of the counts of that element in the arguments. It differs from bag-union by treating identical elements as potentially distinct rather than attempting to match them up.

The bag-sum! procedure is equivalent except that it is linear-update.

(bag-product n bag) procedure
(bag-product! n bag) procedure

The bag-product procedure returns a newly allocated bag containing all the unique elements in bag, where the count of each unique element in the bag is equal to the count of that element in bag multiplied by n.

The bag-product! procedure is equivalent except that it is linear-update.

(bag-unique-size bag) procedure
Returns the number of unique elements of {{bag}}.
(bag-element-count bag element) procedure

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

bag-for-each-unique proc bag) procedure

Applies proc to each unique element of bag in arbitrary order, passing the element and the number of times it occurs in bag, and discarding the returned values. Returns an unspecified result.

(bag-fold-unique proc nil bag) procedure

Invokes proc on each unique element of bag in arbitrary order, passing the number of occurrences as a second argument and the result of the previous invocation as a third argument. For the first invocation, nil is used as the third argument. Returns the result of the last invocation.

(bag-increment! bag element count) procedure
(bag-decrement! bag element count) procedure

Linear update procedures that return a bag with the same elements as bag, but with the element count of element in bag increased or decreased by the exact integer count (but not less than zero).

(bag->set bag) procedure
(set->bag set) procedure
(set->bag! bag set) procedure

The bag->set procedure returns a newly allocated set containing the unique elements (in the sense of the equality predicate) of bag. The set->bag procedure returns a newly allocated bag containing the elements of set. The set->bag! procedure returns a bag containing the elements of both bag and set. In all cases, the comparator of the result is the same as the comparator of the argument or arguments.

(bag->alist bag) procedure
(alist->bag comparator alist) procedure

The bag->alist procedure returns a newly allocated alist whose keys are the unique elements of bag and whose values are the number of occurrences of each element. The alist->bag returning a newly allocated bag based on comparator, where the keys of alist specify the elements and the corresponding values of alist specify how many times they occur.

Comparators

The following comparators are used to compare sets or bags, and allow sets of

sets, bags of sets, etc.

set-comparator constant
bag-comparator constant

Note: that these comparators do not provide comparison procedures, as there is no ordering between sets or bags. It is an error to compare sets or bags with different element comparators.

Repository

Github

Version History

0.7
Adds fix to (set/bag) sob-map argument order
0.6
Fix for single argument case of set-union
0.5
Removes hardcoded .so in setup
0.4
Adds standard README.org to SRFIs
0.3
Packages egg without extraneous files
0.2
Fixes setup file on Windows
0.1
Initial release.

License

Copyright (C) John Cowan (2015). 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"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

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