# 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 (`==`

).

#### Functions

### new() -> []

Returns a new empty ordered set.

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

`Ordset = term()`

Returns `true`

if

is an ordered set of
elements, otherwise `false`

.

### from_list(List) -> Ordset

`List = [T]`

`Ordset = ordset(T)`

Returns an ordered set of the elements in

.

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

`Element = term()`

`Ordset = ordset(term())`

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

`Element = term()`

`Ordset1 = Ordset2 = ordset(T)`

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

`Ordset1 = Ordset2 = Ordset3 = ordset(term())`

Returns the intersection of

and

.

### intersection(OrdsetList) -> Ordset

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

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

`Ordset1 = Ordset2 = ordset(term())`

Returns `true`

if

and

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

otherwise.

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

`Ordset1 = Ordset2 = Ordset3 = ordset(term())`

Returns only the elements of

which are not
also elements of

.

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

`Ordset1 = Ordset2 = ordset(term())`

Returns `true`

when every element of

is
also a member of

, otherwise `false`

.

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

`Function =`

fun((Element :: T, AccIn :: term()) -> AccOut :: term())`Ordset = ordset(T)`

`Acc0 = Acc1 = term()`

Fold

over every element in

returning the final value of the accumulator.

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

`Pred = fun((Element :: T) -> boolean())`

`Ordset1 = Ordset2 = ordset(T)`

Filter elements in

with boolean function

.