Set

_Set_
_set_

This collection provides two files:

 _set.ss_: functional sets, with elements compared via `equal?'
 _seteq.ss_: functional sets, with elements compared via `eq?'

The data structures of this library are immutable.

This library was inspired by SRFI 1 [1] and GHC [2].

[1] SRFI-1. http://srfi.schemers.org/srfi-1/srfi-1.html
[2] Data.Set. http://www.haskell.org/ghc/docs/latest/html/libraries/containers/Data-Set.html

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> type (setof a)

Sets of elements of type a, compared via `equal?'.

> type (seteqof a)

Sets of elements of type a, compared via `eq?'.

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Both set.ss and seteq.ss provide exactly the same bindings.

> (set? x) :: any -> boolean

Determines whether a value is of the set type provided by this module.

> (list->set ls) :: (listof a) -> (set[eq]of a)

Produces a set of the elements in the given list.

> (set->list s) :: (set[eq]of a) -> (listof a)

Produces a list of the elements in the given set.

> empty :: (set[eq]of a)

An empty set.

> (intersection s [ss ...]) :: (set[eq]of a) [(set[eq]of a) ...] -> (set[eq]of a)

Produces the intersection of the given sets.

> (intersections ss) :: (nelistof (set[eq]of a)) -> (set[eq]of a)

Produces the intersection of the given list of sets.

> (difference s [ss ...]) :: (set[eq]of a) [(set[eq]of a) ...] -> (set[eq]of a)

Produces the set difference of the given sets, left-associatively.

> (differences ss) :: (listof (set[eq]of a)) -> (set[eq]of a)

Produces the set difference of the given list of sets, left-associatively.

> (union [ss ...]) :: [(set[eq]of a) ...] -> (set[eq]of a)

Produces the union of the given sets.

> (unions ss) :: (listof (set[eq]of a)) -> (set[eq]of a)

Produces the union of the given list of sets.

> (xor s [ss ...]) :: (set[eq]of a) [(set[eq]of a) ...] -> (set[eq]of a)

Produces the exclusive union of the given sets. This operation is
associative and extends to the n-ary case -- the elements that
appear in an odd number of the sets.