wiki:SetsCowan

Version 12 (modified by cowan, 5 years ago) (diff)

Minor rewording

Sets, bags, integer sets, and enumeration 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. Enumeration sets are mutable collections that can contain symbols chosen from a set of symbols represented by an enumeration type.

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

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

Set procedures

(make-set =)

Returns a newly allocated 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 ...)

Returns a newly allocated set with equality procedure = and containing the elements.

(set-copy set)

Returns a newly allocated 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 an unspecified value.

(set-remove! set element)

Removes element from set unless it is not a member. Returns an unspecified value.

(set-map proc set)

Applies proc to each element of set in arbitrary order and returns a newly allocated 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)

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

(list->set list)

Returns a newly allocated set containing the elements of list.

(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 ...)

Returns a newly allocated set that is the union of set and the other-sets.

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

Returns a newly allocated set that is the intersection of set and the other-sets.

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

Returns a newly allocated set that is the difference of set and the union of the other-sets.

(set-xor set other-set ...)

Returns a newly allocated 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 allocated integer set is returned, it has the same limit as the source sets.

(make-integer-set limit)

Returns a newly allocated 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. The set is empty.

(make-universal-integer-set limit)

Returns a newly allocated 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. The set contains all possible elements.

(integer-set limit element ...)

Returns a newly allocated 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)

Returns a newly allocated 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.

Enumeration sets

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

(make-enum-type symbol-list)

Returns a newly allocated enumeration type suitable for constructing enumeration sets whose members are the symbols in symbol-list. These symbols are said to be in the enumeration type.

(make-enum-set enum-type)

Returns a newly allocated enumeration set. The possible elements of the set are the symbols in enum-type. The set is empty.

(make-universal-enum-set enum-type)

Returns a newly allocated enumeration set. The possible elements of the set are the symbols in enum-type. The set contains all possible elements.

(enum-set enum-type element ...)

Returns a newly allocated enumeration set. The possible elements of the set are the symbols in enum-type. The set is initialized to contain the elements.

(list->enum-set enum-type list)

Returns a newly allocated enumeration set. The possible elements of the set are the symbols in enum-type. The set is initialized to contain the elements of list.

(enum-set-complement enum-set)

Returns a newly allocated enumeration set that is the complement of enum-set.

(enum-set-complement! enum-set)

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

(enum-set-projection enum-set-1 enum-set-2)

Returns a newly allocated enumeration set of the same enumeration type as enum-set-2. The elements of the enumeration set are the symbols belonging to enum-set-1, ignoring any symbols which are not in the enumeration type of enum-set-2.

(define-enumeration <type-name> (<symbol> ...) <constructor>)

Defines a newly allocated enumeration type and provides macros for constructing its members and sets. It is a definition and can appear anywhere that other definitions can appear. The <symbol>s are in the enumeration type. Issue: do we need define-enumeration?

The identifier <type-name> is bound to a syntax definition which accepts a symbol as its argument and returns the symbol if it is in the enumeration type. It is a syntax error if the symbol is not in the enumeration type.

The identifier <constructor> is bound to a syntax definition which accepts symbols as its arguments and returns an enumeration set containing those symbols. It is a syntax error if any of the symbols are not in the enumeration type.

Conversions

The basic set is used as the pivot between different kinds of specialized sets. In particular, set->bag, set->integer-set, set->bag, bag->set, integer-set->set, and enum-set->set take one argument and do the obvious thing. set->integer-set takes two arguments, limit and the set. `set->enum-set also takes two arguments, enum-type and the set.