SDP.Set

SDP.Set provides Set - class for basic set operations.

SetWith

class Nullable s => SetWith s o | s -> o where

SetWith is a class of data structures, that can represent sets.

SetWith doesn't provide data protection/validation before each first action. All functions (except setWith) works correctly only with correct sets. SetWith guarantee only that the returned data is correct. So if you need maximum reliability and security, use containers. But if you want simplicity, openness and a lot of non-set functions without extra conversions, then you are at the right place.

Note that function of type Compare o must follow basic order laws (comparability, transitivity, reflexivity and antisymmetry). With wrong comparator, the result may become implementation-dependent.

Minimal complete definition

intersectionWith, unionWith, differenceWith, lookupLTWith, lookupGTWith

Methods

setWith :: Compare o -> s -> s

Creates ordered set from linear structure.

default setWith :: Linear s o => Compare o -> s -> s

groupSetWith :: Compare o -> (o -> o -> o) -> s -> s

Creates set from linear structure using additional function for choice/merge equal elements.

default groupSetWith :: Linear s o => Compare o -> (o -> o -> o) -> s -> s

insertWith :: Compare o -> o -> s -> s

Adding element to set.

default insertWith :: Linear s o => Compare o -> o -> s -> s

deleteWith :: Compare o -> o -> s -> s

Deleting element from set.

default deleteWith :: Linear s o => Compare o -> o -> s -> s

intersectionWith :: Compare o -> s -> s -> s

Intersection of two sets.

differenceWith :: Compare o -> s -> s -> s

Difference (relative complement, aka A / B) of two sets.

symdiffWith :: Compare o -> s -> s -> s

Symmetric difference of two sets.

unionWith :: Compare o -> s -> s -> s

Union of two sets.

intersectionsWith :: Foldable f => Compare o -> f s -> s

Fold by intersectionWith.

differencesWith :: Foldable f => Compare o -> f s -> s

Fold by differenceWith.

unionsWith :: Foldable f => Compare o -> f s -> s

Fold by unionWith.

symdiffsWith :: Foldable f => Compare o -> f s -> s

Fold by symdiffWith.

isIntersectsWith :: Compare o -> s -> s -> Bool

Compares sets on intersection.

isDisjointWith :: Compare o -> s -> s -> Bool

Compares sets on disjoint.

memberWith :: Compare o -> o -> s -> Bool

Same as elem, but can work faster. By default, uses find.

default memberWith :: (t o ~~ s, Foldable t) => Compare o -> o -> s -> Bool

isSubsetWith :: Compare o -> s -> s -> Bool

Сhecks whether a first set is a subset of second.

default isSubsetWith :: (t o ~~ s, Foldable t) => Compare o -> s -> s -> Bool

subsets :: Ord o => s -> [s]

Generates a list of different subsets (including empty and equivalent).

default subsets :: (Linear s o, Ord o) => s -> [s]

lookupLTWith :: Compare o -> o -> s -> Maybe o

lookupLTWith trying to find lesser element in set.

lookupGTWith :: Compare o -> o -> s -> Maybe o

lookupGTWith trying to find greater element in set.

lookupGEWith :: Compare o -> o -> s -> Maybe o

lookupGEWith trying to find greater or equal element in set.

lookupLEWith :: Compare o -> o -> s -> Maybe o

lookupLEWith trying to find lesser or equal element in set.

Instances

SetWith [o] o

Defined in SDP.Set

Methods

setWith :: Compare o -> [o] -> [o]

groupSetWith :: Compare o -> (o -> o -> o) -> [o] -> [o]

insertWith :: Compare o -> o -> [o] -> [o]

deleteWith :: Compare o -> o -> [o] -> [o]

intersectionWith :: Compare o -> [o] -> [o] -> [o]

differenceWith :: Compare o -> [o] -> [o] -> [o]

symdiffWith :: Compare o -> [o] -> [o] -> [o]

unionWith :: Compare o -> [o] -> [o] -> [o]

intersectionsWith :: Foldable f => Compare o -> f [o] -> [o]

differencesWith :: Foldable f => Compare o -> f [o] -> [o]

unionsWith :: Foldable f => Compare o -> f [o] -> [o]

symdiffsWith :: Foldable f => Compare o -> f [o] -> [o]

isIntersectsWith :: Compare o -> [o] -> [o] -> Bool

isDisjointWith :: Compare o -> [o] -> [o] -> Bool

memberWith :: Compare o -> o -> [o] -> Bool

isSubsetWith :: Compare o -> [o] -> [o] -> Bool

subsets :: [o] -> [[o]]

lookupLTWith :: Compare o -> o -> [o] -> Maybe o

lookupGTWith :: Compare o -> o -> [o] -> Maybe o

lookupGEWith :: Compare o -> o -> [o] -> Maybe o

lookupLEWith :: Compare o -> o -> [o] -> Maybe o

Unboxed e => SetWith (SBytes# e) e

Defined in SDP.Prim.SBytes

Methods

setWith :: Compare e -> SBytes# e -> SBytes# e

groupSetWith :: Compare e -> (e -> e -> e) -> SBytes# e -> SBytes# e

insertWith :: Compare e -> e -> SBytes# e -> SBytes# e

deleteWith :: Compare e -> e -> SBytes# e -> SBytes# e

intersectionWith :: Compare e -> SBytes# e -> SBytes# e -> SBytes# e

differenceWith :: Compare e -> SBytes# e -> SBytes# e -> SBytes# e

symdiffWith :: Compare e -> SBytes# e -> SBytes# e -> SBytes# e

unionWith :: Compare e -> SBytes# e -> SBytes# e -> SBytes# e

intersectionsWith :: Foldable f => Compare e -> f (SBytes# e) -> SBytes# e

differencesWith :: Foldable f => Compare e -> f (SBytes# e) -> SBytes# e

unionsWith :: Foldable f => Compare e -> f (SBytes# e) -> SBytes# e

symdiffsWith :: Foldable f => Compare e -> f (SBytes# e) -> SBytes# e

isIntersectsWith :: Compare e -> SBytes# e -> SBytes# e -> Bool

isDisjointWith :: Compare e -> SBytes# e -> SBytes# e -> Bool

memberWith :: Compare e -> e -> SBytes# e -> Bool

isSubsetWith :: Compare e -> SBytes# e -> SBytes# e -> Bool

subsets :: SBytes# e -> [SBytes# e]

lookupLTWith :: Compare e -> e -> SBytes# e -> Maybe e

lookupGTWith :: Compare e -> e -> SBytes# e -> Maybe e

lookupGEWith :: Compare e -> e -> SBytes# e -> Maybe e

lookupLEWith :: Compare e -> e -> SBytes# e -> Maybe e

SetWith (SArray# e) e

Defined in SDP.Prim.SArray

Methods

setWith :: Compare e -> SArray# e -> SArray# e

groupSetWith :: Compare e -> (e -> e -> e) -> SArray# e -> SArray# e

insertWith :: Compare e -> e -> SArray# e -> SArray# e

deleteWith :: Compare e -> e -> SArray# e -> SArray# e

intersectionWith :: Compare e -> SArray# e -> SArray# e -> SArray# e

differenceWith :: Compare e -> SArray# e -> SArray# e -> SArray# e

symdiffWith :: Compare e -> SArray# e -> SArray# e -> SArray# e

unionWith :: Compare e -> SArray# e -> SArray# e -> SArray# e

intersectionsWith :: Foldable f => Compare e -> f (SArray# e) -> SArray# e

differencesWith :: Foldable f => Compare e -> f (SArray# e) -> SArray# e

unionsWith :: Foldable f => Compare e -> f (SArray# e) -> SArray# e

symdiffsWith :: Foldable f => Compare e -> f (SArray# e) -> SArray# e

isIntersectsWith :: Compare e -> SArray# e -> SArray# e -> Bool

isDisjointWith :: Compare e -> SArray# e -> SArray# e -> Bool

memberWith :: Compare e -> e -> SArray# e -> Bool

isSubsetWith :: Compare e -> SArray# e -> SArray# e -> Bool

subsets :: SArray# e -> [SArray# e]

lookupLTWith :: Compare e -> e -> SArray# e -> Maybe e

lookupGTWith :: Compare e -> e -> SArray# e -> Maybe e

lookupGEWith :: Compare e -> e -> SArray# e -> Maybe e

lookupLEWith :: Compare e -> e -> SArray# e -> Maybe e

(SetWith1 rep e, Linear1 rep e, Ord (rep e), Bordered1 rep Int e) => SetWith (AnyChunks rep e) e

Defined in SDP.Templates.AnyChunks

Methods

setWith :: Compare e -> AnyChunks rep e -> AnyChunks rep e

groupSetWith :: Compare e -> (e -> e -> e) -> AnyChunks rep e -> AnyChunks rep e

insertWith :: Compare e -> e -> AnyChunks rep e -> AnyChunks rep e

deleteWith :: Compare e -> e -> AnyChunks rep e -> AnyChunks rep e

intersectionWith :: Compare e -> AnyChunks rep e -> AnyChunks rep e -> AnyChunks rep e

differenceWith :: Compare e -> AnyChunks rep e -> AnyChunks rep e -> AnyChunks rep e

symdiffWith :: Compare e -> AnyChunks rep e -> AnyChunks rep e -> AnyChunks rep e

unionWith :: Compare e -> AnyChunks rep e -> AnyChunks rep e -> AnyChunks rep e

intersectionsWith :: Foldable f => Compare e -> f (AnyChunks rep e) -> AnyChunks rep e

differencesWith :: Foldable f => Compare e -> f (AnyChunks rep e) -> AnyChunks rep e

unionsWith :: Foldable f => Compare e -> f (AnyChunks rep e) -> AnyChunks rep e

symdiffsWith :: Foldable f => Compare e -> f (AnyChunks rep e) -> AnyChunks rep e

isIntersectsWith :: Compare e -> AnyChunks rep e -> AnyChunks rep e -> Bool

isDisjointWith :: Compare e -> AnyChunks rep e -> AnyChunks rep e -> Bool

memberWith :: Compare e -> e -> AnyChunks rep e -> Bool

isSubsetWith :: Compare e -> AnyChunks rep e -> AnyChunks rep e -> Bool

subsets :: AnyChunks rep e -> [AnyChunks rep e]

lookupLTWith :: Compare e -> e -> AnyChunks rep e -> Maybe e

lookupGTWith :: Compare e -> e -> AnyChunks rep e -> Maybe e

lookupGEWith :: Compare e -> e -> AnyChunks rep e -> Maybe e

lookupLEWith :: Compare e -> e -> AnyChunks rep e -> Maybe e

(Index i, SetWith1 rep e, Linear1 rep e, Bordered1 rep Int e) => SetWith (AnyBorder rep i e) e

Defined in SDP.Templates.AnyBorder

Methods

setWith :: Compare e -> AnyBorder rep i e -> AnyBorder rep i e

groupSetWith :: Compare e -> (e -> e -> e) -> AnyBorder rep i e -> AnyBorder rep i e

insertWith :: Compare e -> e -> AnyBorder rep i e -> AnyBorder rep i e

deleteWith :: Compare e -> e -> AnyBorder rep i e -> AnyBorder rep i e

intersectionWith :: Compare e -> AnyBorder rep i e -> AnyBorder rep i e -> AnyBorder rep i e

differenceWith :: Compare e -> AnyBorder rep i e -> AnyBorder rep i e -> AnyBorder rep i e

symdiffWith :: Compare e -> AnyBorder rep i e -> AnyBorder rep i e -> AnyBorder rep i e

unionWith :: Compare e -> AnyBorder rep i e -> AnyBorder rep i e -> AnyBorder rep i e

intersectionsWith :: Foldable f => Compare e -> f (AnyBorder rep i e) -> AnyBorder rep i e

differencesWith :: Foldable f => Compare e -> f (AnyBorder rep i e) -> AnyBorder rep i e

unionsWith :: Foldable f => Compare e -> f (AnyBorder rep i e) -> AnyBorder rep i e

symdiffsWith :: Foldable f => Compare e -> f (AnyBorder rep i e) -> AnyBorder rep i e

isIntersectsWith :: Compare e -> AnyBorder rep i e -> AnyBorder rep i e -> Bool

isDisjointWith :: Compare e -> AnyBorder rep i e -> AnyBorder rep i e -> Bool

memberWith :: Compare e -> e -> AnyBorder rep i e -> Bool

isSubsetWith :: Compare e -> AnyBorder rep i e -> AnyBorder rep i e -> Bool

subsets :: AnyBorder rep i e -> [AnyBorder rep i e]

lookupLTWith :: Compare e -> e -> AnyBorder rep i e -> Maybe e

lookupGTWith :: Compare e -> e -> AnyBorder rep i e -> Maybe e

lookupGEWith :: Compare e -> e -> AnyBorder rep i e -> Maybe e

lookupLEWith :: Compare e -> e -> AnyBorder rep i e -> Maybe e

type SetWith1 s o = SetWith (s o) o

SetWith contraint for (Type -> Type)-kind types.

type SetWith2 s i o = SetWith (s i o) o

SetWith contraint for (Type -> Type -> Type)-kind types.

Set

class Nullable s => Set s o | s -> o where

Set is a class of data structures, that can represent any sets. Set is intended for more specific sets than ordered linear structures. In particular, it may not work with an arbitrary comparator, and also (unlike the early implementation) does not impose restrictions on the element type.

Set, as well as SetWith, doesn't provide data protection/validation.

Minimal complete definition

Nothing

Methods

set :: s -> s

The same as setWith compare.

default set :: (SetWith s o, Ord o) => s -> s

insert :: o -> s -> s

Same as insert compare.

default insert :: (SetWith s o, Ord o) => o -> s -> s

delete :: o -> s -> s

Same as deleteWith compare.

default delete :: (SetWith s o, Ord o) => o -> s -> s

(/\) :: s -> s -> s

Same as intersectionWith compare.

default (/\) :: (SetWith s o, Ord o) => s -> s -> s

(\/) :: s -> s -> s

Same as unionWith compare.

default (\/) :: (SetWith s o, Ord o) => s -> s -> s

(\\) :: s -> s -> s

Same as differenceWith compare.

default (\\) :: (SetWith s o, Ord o) => s -> s -> s

(\^/) :: s -> s -> s

Same as symdiffWith compare.

default (\^/) :: (SetWith s o, Ord o) => s -> s -> s

(/?\) :: s -> s -> Bool

Same as isDisjointWith compare.

default (/?\) :: (SetWith s o, Ord o) => s -> s -> Bool

(\?/) :: s -> s -> Bool

Same as isIntersectsWith compare.

default (\?/) :: (SetWith s o, Ord o) => s -> s -> Bool

(\+/) :: s -> s -> Bool

Same as isSubsetWith compare.

default (\+/) :: (SetWith s o, Ord o) => s -> s -> Bool

intersections :: Foldable f => f s -> s

Same as intersectionsWith compare.

default intersections :: (Foldable f, SetWith s o, Ord o) => f s -> s

unions :: Foldable f => f s -> s

Same as unionsWith compare.

default unions :: (Foldable f, SetWith s o, Ord o) => f s -> s

differences :: Foldable f => f s -> s

Same as differencesWith compare.

default differences :: (Foldable f, SetWith s o, Ord o) => f s -> s

symdiffs :: Foldable f => f s -> s

Same as symdiffsWith compare'.

default symdiffs :: (Foldable f, SetWith s o, Ord o) => f s -> s

member :: o -> s -> Bool

Same as memberWith compare.

default member :: (SetWith s o, Ord o) => o -> s -> Bool

lookupLT :: Ord o => o -> s -> Maybe o

Same as lookupLTWith compare.

default lookupLT :: (SetWith s o, Ord o) => o -> s -> Maybe o

lookupGT :: Ord o => o -> s -> Maybe o

Same as lookupGTWith compare.

default lookupGT :: (SetWith s o, Ord o) => o -> s -> Maybe o

lookupLE :: Ord o => o -> s -> Maybe o

Same as lookupLEWith compare.

default lookupLE :: (SetWith s o, Ord o) => o -> s -> Maybe o

lookupGE :: Ord o => o -> s -> Maybe o

Same as lookupGEWith compare.

default lookupGE :: (SetWith s o, Ord o) => o -> s -> Maybe o

Instances

Ord o => Set [o] o

Defined in SDP.Set

Methods

set :: [o] -> [o]

insert :: o -> [o] -> [o]

delete :: o -> [o] -> [o]

(/\) :: [o] -> [o] -> [o]

(\/) :: [o] -> [o] -> [o]

(\\) :: [o] -> [o] -> [o]

(\^/) :: [o] -> [o] -> [o]

(/?\) :: [o] -> [o] -> Bool

(\?/) :: [o] -> [o] -> Bool

(\+/) :: [o] -> [o] -> Bool

intersections :: Foldable f => f [o] -> [o]

unions :: Foldable f => f [o] -> [o]

differences :: Foldable f => f [o] -> [o]

symdiffs :: Foldable f => f [o] -> [o]

member :: o -> [o] -> Bool

lookupLT :: o -> [o] -> Maybe o

lookupGT :: o -> [o] -> Maybe o

lookupLE :: o -> [o] -> Maybe o

lookupGE :: o -> [o] -> Maybe o

(Unboxed e, Ord e) => Set (SBytes# e) e

Defined in SDP.Prim.SBytes

Methods

set :: SBytes# e -> SBytes# e

insert :: e -> SBytes# e -> SBytes# e

delete :: e -> SBytes# e -> SBytes# e

(/\) :: SBytes# e -> SBytes# e -> SBytes# e

(\/) :: SBytes# e -> SBytes# e -> SBytes# e

(\\) :: SBytes# e -> SBytes# e -> SBytes# e

(\^/) :: SBytes# e -> SBytes# e -> SBytes# e

(/?\) :: SBytes# e -> SBytes# e -> Bool

(\?/) :: SBytes# e -> SBytes# e -> Bool

(\+/) :: SBytes# e -> SBytes# e -> Bool

intersections :: Foldable f => f (SBytes# e) -> SBytes# e

unions :: Foldable f => f (SBytes# e) -> SBytes# e

differences :: Foldable f => f (SBytes# e) -> SBytes# e

symdiffs :: Foldable f => f (SBytes# e) -> SBytes# e

member :: e -> SBytes# e -> Bool

lookupLT :: e -> SBytes# e -> Maybe e

lookupGT :: e -> SBytes# e -> Maybe e

lookupLE :: e -> SBytes# e -> Maybe e

lookupGE :: e -> SBytes# e -> Maybe e

Ord e => Set (SArray# e) e

Defined in SDP.Prim.SArray

Methods

set :: SArray# e -> SArray# e

insert :: e -> SArray# e -> SArray# e

delete :: e -> SArray# e -> SArray# e

(/\) :: SArray# e -> SArray# e -> SArray# e

(\/) :: SArray# e -> SArray# e -> SArray# e

(\\) :: SArray# e -> SArray# e -> SArray# e

(\^/) :: SArray# e -> SArray# e -> SArray# e

(/?\) :: SArray# e -> SArray# e -> Bool

(\?/) :: SArray# e -> SArray# e -> Bool

(\+/) :: SArray# e -> SArray# e -> Bool

intersections :: Foldable f => f (SArray# e) -> SArray# e

unions :: Foldable f => f (SArray# e) -> SArray# e

differences :: Foldable f => f (SArray# e) -> SArray# e

symdiffs :: Foldable f => f (SArray# e) -> SArray# e

member :: e -> SArray# e -> Bool

lookupLT :: e -> SArray# e -> Maybe e

lookupGT :: e -> SArray# e -> Maybe e

lookupLE :: e -> SArray# e -> Maybe e

lookupGE :: e -> SArray# e -> Maybe e

(Nullable (AnyChunks rep e), SetWith1 (AnyChunks rep) e, Ord e) => Set (AnyChunks rep e) e

Defined in SDP.Templates.AnyChunks

Methods

set :: AnyChunks rep e -> AnyChunks rep e

insert :: e -> AnyChunks rep e -> AnyChunks rep e

delete :: e -> AnyChunks rep e -> AnyChunks rep e

(/\) :: AnyChunks rep e -> AnyChunks rep e -> AnyChunks rep e

(\/) :: AnyChunks rep e -> AnyChunks rep e -> AnyChunks rep e

(\\) :: AnyChunks rep e -> AnyChunks rep e -> AnyChunks rep e

(\^/) :: AnyChunks rep e -> AnyChunks rep e -> AnyChunks rep e

(/?\) :: AnyChunks rep e -> AnyChunks rep e -> Bool

(\?/) :: AnyChunks rep e -> AnyChunks rep e -> Bool

(\+/) :: AnyChunks rep e -> AnyChunks rep e -> Bool

intersections :: Foldable f => f (AnyChunks rep e) -> AnyChunks rep e

unions :: Foldable f => f (AnyChunks rep e) -> AnyChunks rep e

differences :: Foldable f => f (AnyChunks rep e) -> AnyChunks rep e

symdiffs :: Foldable f => f (AnyChunks rep e) -> AnyChunks rep e

member :: e -> AnyChunks rep e -> Bool

lookupLT :: e -> AnyChunks rep e -> Maybe e

lookupGT :: e -> AnyChunks rep e -> Maybe e

lookupLE :: e -> AnyChunks rep e -> Maybe e

lookupGE :: e -> AnyChunks rep e -> Maybe e

(SetWith1 (AnyBorder rep i) e, Nullable (AnyBorder rep i e), Ord e) => Set (AnyBorder rep i e) e

Defined in SDP.Templates.AnyBorder

Methods

set :: AnyBorder rep i e -> AnyBorder rep i e

insert :: e -> AnyBorder rep i e -> AnyBorder rep i e

delete :: e -> AnyBorder rep i e -> AnyBorder rep i e

(/\) :: AnyBorder rep i e -> AnyBorder rep i e -> AnyBorder rep i e

(\/) :: AnyBorder rep i e -> AnyBorder rep i e -> AnyBorder rep i e

(\\) :: AnyBorder rep i e -> AnyBorder rep i e -> AnyBorder rep i e

(\^/) :: AnyBorder rep i e -> AnyBorder rep i e -> AnyBorder rep i e

(/?\) :: AnyBorder rep i e -> AnyBorder rep i e -> Bool

(\?/) :: AnyBorder rep i e -> AnyBorder rep i e -> Bool

(\+/) :: AnyBorder rep i e -> AnyBorder rep i e -> Bool

intersections :: Foldable f => f (AnyBorder rep i e) -> AnyBorder rep i e

unions :: Foldable f => f (AnyBorder rep i e) -> AnyBorder rep i e

differences :: Foldable f => f (AnyBorder rep i e) -> AnyBorder rep i e

symdiffs :: Foldable f => f (AnyBorder rep i e) -> AnyBorder rep i e

member :: e -> AnyBorder rep i e -> Bool

lookupLT :: e -> AnyBorder rep i e -> Maybe e

lookupGT :: e -> AnyBorder rep i e -> Maybe e

lookupLE :: e -> AnyBorder rep i e -> Maybe e

lookupGE :: e -> AnyBorder rep i e -> Maybe e

type Set1 s o = Set (s o) o

Set contraint for (Type -> Type)-kind types.

type Set2 s i o = Set (s i o) o

Set contraint for (Type -> Type -> Type)-kind types.

Rank 2 quantified constraints

GHC 8.6.1+ only

type SetWith' s = forall o. SetWith (s o) o

SetWith quantified contraint for (Type -> Type)-kind types.

type SetWith'' s = forall i o. SetWith (s i o) o

SetWith quantified contraint for (Type -> Type -> Type)-kind types.

type Set' s = forall o. Set (s o) o

Set quantified contraint for (Type -> Type)-kind types.

type Set'' s = forall i o. Set (s i o) o

Set quantified contraint for (Type -> Type -> Type)-kind types.