# 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 the same interface as the `sets(3)` module 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 (`==`).

### ordset(T) = [T]

As returned by `new/0`.

#### Functions

• `Element = E`
• `Ordset1 = ordset(T)`
• `Ordset2 = ordset(T | E)`

Returns a new ordered set formed from `Ordset1` with `Element` inserted.

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

• `Element = term()`
• `Ordset1 = Ordset2 = ordset(T)`

Returns `Ordset1`, but with `Element` removed.

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

• `Pred = fun((Element :: T) -> boolean())`
• `Ordset1 = Ordset2 = ordset(T)`

Filters elements in `Ordset1` with boolean function `Pred`.

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

• ```Function =     fun((Element :: T, AccIn :: term()) -> AccOut :: term())```
• `Ordset = ordset(T)`
• `Acc0 = Acc1 = term()`

Folds `Function` over every element in `Ordset` and returns the final value of the accumulator.

### from_list(List) -> Ordset

• `List = [T]`
• `Ordset = ordset(T)`

Returns an ordered set of the elements in `List`.

### intersection(OrdsetList) -> Ordset

• `OrdsetList = [ordset(term()), ...]`
• `Ordset = ordset(term())`

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

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

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

Returns the intersection of `Ordset1` and `Ordset2`.

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

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

Returns `true` if `Ordset1` and `Ordset2` are disjoint (have no elements in common), otherwise `false`.

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

• `Element = term()`
• `Ordset = ordset(term())`

Returns `true` if `Element` is an element of `Ordset`, otherwise `false`.

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

• `Ordset = term()`

Returns `true` if `Ordset` is an ordered set of elements, otherwise `false`.

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

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

Returns `true` when every element of `Ordset1` is also a member of `Ordset2`, otherwise `false`.

### new() -> []

Returns a new empty ordered set.

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

• `Ordset = ordset(term())`

Returns the number of elements in `Ordset`.

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

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

Returns only the elements of `Ordset1` that are not also elements of `Ordset2`.

### to_list(Ordset) -> List

• `Ordset = ordset(T)`
• `List = [T]`

Returns the elements of `Ordset` as a list.

### union(OrdsetList) -> Ordset

• `OrdsetList = [ordset(T)]`
• `Ordset = ordset(T)`

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

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

• `Ordset1 = ordset(T1)`
• `Ordset2 = ordset(T2)`
• `Ordset3 = ordset(T1 | T2)`

Returns the merged (union) set of `Ordset1` and `Ordset2`.