# ordsets

## Functions for Manipulating Sets as Ordered Lists

Sets are collections of elements with no duplicate elements.
An `ordset`

is a representation of a set, where an ordered
list is used to store the elements of the set. An ordered list
is more efficient than an unordered list.

This module provides exactly the same interface as the module
`sets`

but with a defined representation. One difference is
that while `sets`

considers two elements as different if they
do not match (`=:=`

), this module considers two elements as
different if and only if they do not compare equal (`==`

).

As returned by new/0.

#### Functions

### new() -> []

Returns a new empty ordered set.

### is_set(Ordset) -> boolean()

Returns `true`

if

is an ordered set of
elements, otherwise `false`

.

### size(Ordset) -> integer() >= 0

Returns the number of elements in

.

### to_list(Ordset) -> List

Returns the elements of

as a list.

### from_list(List) -> Ordset

Returns an ordered set of the elements in

.

### is_element(Element, Ordset) -> boolean()

Returns `true`

if

is an element of

, otherwise `false`

.

### add_element(Element, Ordset1) -> Ordset2

Returns a new ordered set formed from

with

inserted.

### del_element(Element, Ordset1) -> Ordset2

Returns

, but with

removed.

### union(Ordset1, Ordset2) -> Ordset3

Returns the merged (union) set of

and

.

### union(OrdsetList) -> Ordset

Returns the merged (union) set of the list of sets.

### intersection(Ordset1, Ordset2) -> Ordset3

Returns the intersection of

and

.

### intersection(OrdsetList) -> Ordset

Returns the intersection of the non-empty list of sets.

### is_disjoint(Ordset1, Ordset2) -> boolean()

Returns `true`

if

and

are disjoint (have no elements in common),
and `false`

otherwise.

### subtract(Ordset1, Ordset2) -> Ordset3

Returns only the elements of

which are not
also elements of

.

### is_subset(Ordset1, Ordset2) -> boolean()

Returns `true`

when every element of

is
also a member of

, otherwise `false`

.

### fold(Function, Acc0, Ordset) -> Acc1

Fold

over every element in

returning the final value of the accumulator.

### filter(Pred, Ordset1) -> Ordset2

Filter elements in

with boolean function

.