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A set of unique values. The values can be any comparable type. This
includes `Int`

, `Float`

, `Time`

, `Char`

, `String`

, and tuples or lists
of comparable types.

type alias Set comparable =
Dict comparable ()

Represents a set of unique values. So `(Set Int)`

is a set of integers and
`(Set String)`

is a set of strings.

empty : Set comparable

Create an empty set.

singleton : comparable -> Set comparable

Create a set with one value.

insert : comparable -> Set comparable -> Set comparable

Insert a value into a set.

remove : comparable -> Set comparable -> Set comparable

Remove a value from a set. If the value is not found, no changes are made.

isEmpty : Set comparable -> Bool

Determine if a set is empty.

member : comparable -> Set comparable -> Bool

Determine if a value is in a set.

size : Set comparable -> Int

Determine the number of elements in a set.

union : Set comparable -> Set comparable -> Set comparable

Get the union of two sets. Keep all values.

intersect : Set comparable -> Set comparable -> Set comparable

Get the intersection of two sets. Keeps values that appear in both sets.

diff : Set comparable -> Set comparable -> Set comparable

Get the difference between the first set and the second. Keeps values that do not appear in the second set.

toList : Set comparable -> List comparable

Convert a set into a list, sorted from lowest to highest.

fromList : List comparable -> Set comparable

Convert a list into a set, removing any duplicates.

map : (comparable -> comparable') -> Set comparable -> Set comparable'

Map a function onto a set, creating a new set with no duplicates.

foldl : (comparable -> b -> b) -> b -> Set comparable -> b

Fold over the values in a set, in order from lowest to highest.

foldr : (comparable -> b -> b) -> b -> Set comparable -> b

Fold over the values in a set, in order from highest to lowest.

filter : (comparable -> Bool) -> Set comparable -> Set comparable

Create a new set consisting only of elements which satisfy a predicate.

partition : (comparable -> Bool) -> Set comparable -> ( Set comparable, Set comparable )

Create two new sets; the first consisting of elements which satisfy a predicate, the second consisting of elements which do not.

```
module CollectionsNg.Set
exposing
( Set
, empty
, singleton
, insert
, remove
, isEmpty
, member
, size
, foldl
, foldr
, map
, filter
, partition
, union
, intersect
, diff
, toList
, fromList
)
{-| A set of unique values. The values can be any comparable type. This
includes `Int`, `Float`, `Time`, `Char`, `String`, and tuples or lists
of comparable types.
# Sets
@docs Set
# Build
@docs empty, singleton, insert, remove
# Query
@docs isEmpty, member, size
# Combine
@docs union, intersect, diff
# Lists
@docs toList, fromList
# Transform
@docs map, foldl, foldr, filter, partition
-}
import CollectionsNg.Dict as Dict exposing (Dict)
{-| Represents a set of unique values. So `(Set Int)` is a set of integers and
`(Set String)` is a set of strings.
-}
type alias Set comparable =
Dict comparable ()
{-| Create an empty set.
-}
empty : Set comparable
empty =
Dict.empty
{-| Create a set with one value.
-}
singleton : comparable -> Set comparable
singleton k =
Dict.singleton k ()
{-| Insert a value into a set.
-}
insert : comparable -> Set comparable -> Set comparable
insert k d =
Dict.insert k () d
{-| Remove a value from a set. If the value is not found, no changes are made.
-}
remove : comparable -> Set comparable -> Set comparable
remove k d =
Dict.remove k d
{-| Determine if a set is empty.
-}
isEmpty : Set comparable -> Bool
isEmpty d =
Dict.isEmpty d
{-| Determine if a value is in a set.
-}
member : comparable -> Set comparable -> Bool
member k d =
Dict.member k d
{-| Determine the number of elements in a set.
-}
size : Set comparable -> Int
size d =
Dict.size d
{-| Get the union of two sets. Keep all values.
-}
union : Set comparable -> Set comparable -> Set comparable
union d1 d2 =
Dict.union d1 d2
{-| Get the intersection of two sets. Keeps values that appear in both sets.
-}
intersect : Set comparable -> Set comparable -> Set comparable
intersect d1 d2 =
Dict.intersect d1 d2
{-| Get the difference between the first set and the second. Keeps values
that do not appear in the second set.
-}
diff : Set comparable -> Set comparable -> Set comparable
diff d1 d2 =
Dict.diff d1 d2
{-| Convert a set into a list, sorted from lowest to highest.
-}
toList : Set comparable -> List comparable
toList d =
Dict.keys d
{-| Convert a list into a set, removing any duplicates.
-}
fromList : List comparable -> Set comparable
fromList xs =
List.foldl insert empty xs
{-| Fold over the values in a set, in order from lowest to highest.
-}
foldl : (comparable -> b -> b) -> b -> Set comparable -> b
foldl f b d =
Dict.foldr (\k _ b -> f k b) b d
{-| Fold over the values in a set, in order from highest to lowest.
-}
foldr : (comparable -> b -> b) -> b -> Set comparable -> b
foldr f b d =
Dict.foldr (\k _ b -> f k b) b d
{-| Map a function onto a set, creating a new set with no duplicates.
-}
map : (comparable -> comparable') -> Set comparable -> Set comparable'
map f s =
fromList (List.map f (toList s))
{-| Create a new set consisting only of elements which satisfy a predicate.
-}
filter : (comparable -> Bool) -> Set comparable -> Set comparable
filter p d =
Dict.filter (\k _ -> p k) d
{-| Create two new sets; the first consisting of elements which satisfy a
predicate, the second consisting of elements which do not.
-}
partition : (comparable -> Bool) -> Set comparable -> ( Set comparable, Set comparable )
partition p d =
Dict.partition (\k _ -> p k) d
```