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A set of unique values. The values can be any type, as the implementation is based on EveryDict

type EverySet a
= EverySet (EveryDict a ())

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

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

is a set of strings.

empty : EverySet a

Create an empty set.

singleton : a -> EverySet a

Create a set with one value.

insert : a -> EverySet a -> EverySet a

Insert a value into a set.

remove : a -> EverySet a -> EverySet a

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

isEmpty : EverySet a -> Bool

Determine if a set is empty.

member : a -> EverySet a -> Bool

Determine if a value is in a set.

size : EverySet a -> Int

Determine the number of elements in a set.

union : EverySet a -> EverySet a -> EverySet a

Get the union of two sets. Keep all values.

intersect : EverySet a -> EverySet a -> EverySet a

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

diff : EverySet a -> EverySet a -> EverySet a

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

toList : EverySet a -> List a

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

fromList : List a -> EverySet a

Convert a list into a set, removing any duplicates.

map : (a -> a2) -> EverySet a -> EverySet a2

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

foldl : (a -> b -> b) -> b -> EverySet a -> b

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

foldr : (a -> b -> b) -> b -> EverySet a -> b

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

filter : (a -> Bool) -> EverySet a -> EverySet a

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

partition : (a -> Bool) -> EverySet a -> ( EverySet a, EverySet a )

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

```
module EverySet
exposing
( EverySet
, diff
, empty
, filter
, foldl
, foldr
, fromList
, insert
, intersect
, isEmpty
, map
, member
, partition
, remove
, singleton
, size
, toList
, union
)
{-| A set of unique values. The values can be any type, as the implementation is
based on [EveryDict](http://package.elm-lang.org/packages/eeue56/elm-all-dict/latest)
# Sets
@docs EverySet
# 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 EveryDict exposing (EveryDict)
{-| Represents a set of unique values. So `(Set Int)` is a set of integers and
`(Set String)` is a set of strings.
-}
type EverySet a
= EverySet (EveryDict a ())
{-| Create an empty set.
-}
empty : EverySet a
empty =
EverySet EveryDict.empty
{-| Create a set with one value.
-}
singleton : a -> EverySet a
singleton k =
EverySet <| EveryDict.singleton k ()
{-| Insert a value into a set.
-}
insert : a -> EverySet a -> EverySet a
insert k (EverySet d) =
EverySet <| EveryDict.insert k () d
{-| Remove a value from a set. If the value is not found, no changes are made.
-}
remove : a -> EverySet a -> EverySet a
remove k (EverySet d) =
EverySet <| EveryDict.remove k d
{-| Determine if a set is empty.
-}
isEmpty : EverySet a -> Bool
isEmpty (EverySet d) =
EveryDict.isEmpty d
{-| Determine if a value is in a set.
-}
member : a -> EverySet a -> Bool
member k (EverySet d) =
EveryDict.member k d
{-| Determine the number of elements in a set.
-}
size : EverySet a -> Int
size (EverySet d) =
EveryDict.size d
{-| Get the union of two sets. Keep all values.
-}
union : EverySet a -> EverySet a -> EverySet a
union (EverySet d1) (EverySet d2) =
EverySet <| EveryDict.union d1 d2
{-| Get the intersection of two sets. Keeps values that appear in both sets.
-}
intersect : EverySet a -> EverySet a -> EverySet a
intersect (EverySet d1) (EverySet d2) =
EverySet <| EveryDict.intersect d1 d2
{-| Get the difference between the first set and the second. Keeps values
that do not appear in the second set.
-}
diff : EverySet a -> EverySet a -> EverySet a
diff (EverySet d1) (EverySet d2) =
EverySet <| EveryDict.diff d1 d2
{-| Convert a set into a list, sorted from lowest to highest.
-}
toList : EverySet a -> List a
toList (EverySet d) =
EveryDict.keys d
{-| Convert a list into a set, removing any duplicates.
-}
fromList : List a -> EverySet a
fromList xs =
List.foldl insert empty xs
{-| Fold over the values in a set, in order from lowest to highest.
-}
foldl : (a -> b -> b) -> b -> EverySet a -> b
foldl f b (EverySet d) =
EveryDict.foldl (\k _ b -> f k b) b d
{-| Fold over the values in a set, in order from highest to lowest.
-}
foldr : (a -> b -> b) -> b -> EverySet a -> b
foldr f b (EverySet d) =
EveryDict.foldr (\k _ b -> f k b) b d
{-| Map a function onto a set, creating a new set with no duplicates.
-}
map : (a -> a2) -> EverySet a -> EverySet a2
map f s =
fromList (List.map f (toList s))
{-| Create a new set consisting only of elements which satisfy a predicate.
-}
filter : (a -> Bool) -> EverySet a -> EverySet a
filter p (EverySet d) =
EverySet <| EveryDict.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 : (a -> Bool) -> EverySet a -> ( EverySet a, EverySet a )
partition p (EverySet d) =
let
( p1, p2 ) =
EveryDict.partition (\k _ -> p k) d
in
( EverySet p1, EverySet p2 )
```