# 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 (`==`

).

#### DATA TYPES

ordered_set() as returned by new/0

#### Functions

### new() -> Ordset

`Ordset = ordered_set()`

Returns a new empty ordered set.

### is_set(Ordset) -> bool()

`Ordset = term()`

Returns `true`

if `Ordset`

is an ordered set of
elements, otherwise `false`

.

### size(Ordset) -> int()

`Ordset = term()`

Returns the number of elements in `Ordset`

.

### to_list(Ordset) -> List

`Ordset = ordered_set()`

`List = [term()]`

Returns the elements of `Ordset`

as a list.

### from_list(List) -> Ordset

`List = [term()]`

`Ordset = ordered_set()`

Returns an ordered set of the elements in `List`

.

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

`Element = term()`

`Ordset = ordered_set()`

Returns `true`

if `Element`

is an element of
`Ordset`

, otherwise `false`

.

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

`Element = term()`

`Ordset1 = Ordset2 = ordered_set()`

Returns a new ordered set formed from `Ordset1`

with
`Element`

inserted.

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

`Element = term()`

`Ordset1 = Ordset2 = ordered_set()`

Returns `Ordset1`

, but with `Element`

removed.

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

`Ordset1 = Ordset2 = Ordset3 = ordered_set()`

Returns the merged (union) set of `Ordset1`

and
`Ordset2`

.

### union(OrdsetList) -> Ordset

`OrdsetList = [ordered_set()]`

`Ordset = ordered_set()`

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

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

`Ordset1 = Ordset2 = Ordset3 = ordered_set()`

Returns the intersection of `Ordset1`

and
`Ordset2`

.

### intersection(OrdsetList) -> Ordset

`OrdsetList = [ordered_set()]`

`Ordset = ordered_set()`

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

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

`Ordset1 = Ordset2 = ordered_set()`

Returns `true`

if `Ordset1`

and
`Ordset2`

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

otherwise.

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

`Ordset1 = Ordset2 = Ordset3 = ordered_set()`

Returns only the elements of `Ordset1`

which are not
also elements of `Ordset2`

.

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

`Ordset1 = Ordset2 = ordered_set()`

Returns `true`

when every element of `Ordset`

1 is
also a member of `Ordset2`

, otherwise `false`

.

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

`Function = fun (E, AccIn) -> AccOut`

`Acc0 = Acc1 = AccIn = AccOut = term()`

`Ordset = ordered_set()`

Fold `Function`

over every element in `Ordset`

returning the final value of the accumulator.

### filter(Pred, Ordset1) -> Set2

`Pred = fun (E) -> bool()`

`Set1 = Set2 = ordered_set()`

Filter elements in `Set1`

with boolean function
`Fun`

.