Data.Set.Ordered

This module provides OSet, an insertion-order-preserving set, with type class instances for Foldable and Data as well as a map function and other features. Semigroup and Monoid instances are provided on OSetL and OSetR which are left- and right-biased wrappers respectively.

This is intended to be API-compatible with OSet in unordered-containers but with a few extra type class instances.

Here's the quick-start guide to using this package:

module Main (main) where

import           Data.Set.Ordered ((|>), (|<), (|<>))
import qualified Data.Set.Ordered as OSet

main :: IO ()
main = do
    -- Create from list
    let s0 = OSet.fromList [1 :: Int, 2, 3, 4, 4, 3, 2, 1, -1, -2, -3]
    print s0 -- outputs: "fromList [1,2,3,4,-1,-2,-3]"

    -- Append
    let s1 = s0 |> 4
    print s1 -- outputs: "fromList [1,2,3,4,-1,-2,-3]"

    -- Prepend
    let s2 = 4 |< s0
    print s2 -- outputs: "fromList [4,1,2,3,-1,-2,-3]"

    -- Append
    let s3 = s0 |<> OSet.fromList [10, 10, 20, 20, 30, 30]
    print s3 -- outputs: "fromList [1,2,3,4,-1,-2,-3,10,20,30]"

    -- Map (but note that OSet is not a functor)
    let s4 = OSet.map (\x -> x * x) s3
    print s4 -- outputs: "fromList [1,4,9,16,100,400,900]"

    -- Filter
    let s5 = OSet.filter (>= 100) s4
    print s5 -- outputs: "fromList [100,400,900]"

There are cases where the developer's natural instinct would be to convert the OSet instance to a list using toList from Foldable. While this is possible, it will often be more efficient to use toSeq and operate on the sequence that way. You can even use view patterns to pattern-match on the resulting sequence:

module Main (main) where

import           Data.Sequence (ViewL(..), viewl)
import           Data.Set.Ordered (OSet)
import qualified Data.Set.Ordered as OSet

showFromLeft :: Show a => OSet a -> String
showFromLeft o = go (OSet.toSeq o)
    where
        go (viewl -> EmptyL) = ""
        go (viewl -> h :< t) = show h ++ go t
        go _ = error "Should not happen" -- suppress warning about non-exhaustive patterns

main :: IO ()
main = do
    let a = OSet.fromList [4 :: Int, 1, 3, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
    print $ showFromLeft a -- outputs: "4139025678"

Documentation

data OSet a

An OSet behaves much like a Set but remembers the order in which the elements were originally inserted.

Instances

Foldable OSet

Defined in Data.Set.Ordered

Methods

fold :: Monoid m => OSet m -> m

foldMap :: Monoid m => (a -> m) -> OSet a -> m

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

foldr' :: (a -> b -> b) -> b -> OSet a -> b

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

foldl' :: (b -> a -> b) -> b -> OSet a -> b

foldr1 :: (a -> a -> a) -> OSet a -> a

foldl1 :: (a -> a -> a) -> OSet a -> a

toList :: OSet a -> [a]

null :: OSet a -> Bool

length :: OSet a -> Int

elem :: Eq a => a -> OSet a -> Bool

maximum :: Ord a => OSet a -> a

minimum :: Ord a => OSet a -> a

sum :: Num a => OSet a -> a

product :: Num a => OSet a -> a

Eq a => Eq (OSet a)

Defined in Data.Set.Ordered

Methods

(==) :: OSet a -> OSet a -> Bool

(/=) :: OSet a -> OSet a -> Bool

(Data a, Ord a) => Data (OSet a)

Defined in Data.Set.Ordered

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> OSet a -> c (OSet a)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (OSet a)

toConstr :: OSet a -> Constr

dataTypeOf :: OSet a -> DataType

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (OSet a))

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (OSet a))

gmapT :: (forall b. Data b => b -> b) -> OSet a -> OSet a

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> OSet a -> r

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> OSet a -> r

gmapQ :: (forall d. Data d => d -> u) -> OSet a -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> OSet a -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> OSet a -> m (OSet a)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> OSet a -> m (OSet a)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> OSet a -> m (OSet a)

Ord a => Ord (OSet a)

Defined in Data.Set.Ordered

Methods

compare :: OSet a -> OSet a -> Ordering

(<) :: OSet a -> OSet a -> Bool

(<=) :: OSet a -> OSet a -> Bool

(>) :: OSet a -> OSet a -> Bool

(>=) :: OSet a -> OSet a -> Bool

max :: OSet a -> OSet a -> OSet a

min :: OSet a -> OSet a -> OSet a

Show a => Show (OSet a)

Defined in Data.Set.Ordered

Methods

showsPrec :: Int -> OSet a -> ShowS

show :: OSet a -> String

showList :: [OSet a] -> ShowS

Trivial sets

empty

Arguments

:: OSet a

set

\(O(1)\). The empty set.

singleton

Arguments

:: a

element

-> OSet a

set

\(O(1)\). A singleton set containing the given element.

Insertion

(<|) infixr 5

Arguments

:: Ord a

=> a

element

-> OSet a

set

-> OSet a

set

\(O(log(N))\). Add an element to the left end of the sequence if the set does not already contain the element. Otherwise ignore the element.

(|<) infixr 5

Arguments

:: Ord a

=> a

element

-> OSet a

set

-> OSet a

set

\(O(log(N))\) if the element is not in the set, \(O(N)\) if the element is already in the set. Add an element to the left end of the sequence if the set does not already contain the element. Move the element to the left end of the sequence if the element is already present in the set.

(>|) infixl 5

Arguments

:: Ord a

=> OSet a

set

-> a

element

-> OSet a

set

\(O(log(N))\) if the element is not in the set, \(O(N)\) if the element is already in the set. Add an element to the right end of the sequence if the set does not already contain the element. Move the element to the right end of the sequence if the element is already present in the set.

(|>) infixl 5

Arguments

:: Ord a

=> OSet a

set

-> a

element

-> OSet a

set

\(O(log(N))\). Add an element to the right end of the sequence if the set does not already contain the element. Otherwise ignore the element.

(<>|) infixr 6

Arguments

:: Ord a

=> OSet a

set

-> OSet a

set

-> OSet a

set

\(O(N^2)\) worst case. Add elements from the right-hand set to the left-hand set. If elements occur in both sets, then this operation discards elements from the left-hand set and preserves those from the right.

(|<>) infixr 6

Arguments

:: Ord a

=> OSet a

set

-> OSet a

set

-> OSet a

set

\(O(Nlog(N))\) worst case. Add elements from the right-hand set to the left-hand set. If elements occur in both sets, then this operation discards elements from the right-hand set and preserves those from the left.

Query

member

Arguments

:: Ord a

=> a

element

-> OSet a

set

-> Bool

True if element is in set, False otherwise

\(O(log(N))\). Determine if the element is in the set.

notMember

Arguments

:: Ord a

=> a

element

-> OSet a

set

-> Bool

True if element is not in set, False otherwise

\(O(log(N))\). Determine if the element is not in the set.

size

Arguments

:: OSet a

set

-> Int

size

\(O(1)\). The number of elements in the set.

Deletion

(\\)

Arguments

:: Ord a

=> OSet a

set

-> OSet a

set

-> OSet a

set

\(O(N M)\). Find the set difference: r \\ s removes all M values in s from r with N values.

delete

Arguments

:: Ord a

=> a

element

-> OSet a

set

-> OSet a

set

\(O(log N)\). Delete an element from the set.

filter

Arguments

:: (a -> Bool)

predicate

-> OSet a

set

-> OSet a

set

\(O(N)\). Filter a set by returning a set whose elements satisfy the predicate.

Indexing

type Index = Int

A zero-based index with respect to insertion order.

elemAt

Arguments

:: OSet a

set

-> Index

index

-> Maybe a

element

\(O(log(min(i, N - i)))\). Return the element at the specified position, \(i\), counting from 0. If the specified position is out of range, this function returns Nothing.

findIndex

Arguments

:: Eq a

=> a

element

-> OSet a

set

-> Maybe Index

index

\(O(N)\). Finds the index of the leftmost element that matches the specified element or returns Nothing if no matching element can be found.

Conversion

fromList

Arguments

:: Ord a

=> [a]

elements

-> OSet a

set

\(O(N log(N))\). Create a set from a finite list of elements. If an element occurs multiple times in the original list, only the first occurrence is retained in the resulting set. The function toList, \(O(N)\), in Foldable can be used to return a list of the elements in the original insert order with duplicates removed.

toAscList

Arguments

:: OSet a

set

-> [a]

list

\(O(N)\). Convert the set to an ascending list of elements.

toSeq

Arguments

:: OSet a

set

-> Seq a

sequence

\(O(1)\). Return ordered sequence of elements in set. For obtaining a useful Functor instance this is recommended over toList due to its \(O(1)\) performance. Similarly, if you want to pattern-match on the OSet, obtain the sequence and use view patterns or pattern synonyms instead of converting to a list.

Miscellaneous

map

Arguments

:: Ord b

=> (a -> b)

function

-> OSet a

set

-> OSet b

set

\(O(N log(N))\). Return the set obtained by applying a function to each element of this set. Note that the resulting set may be smaller than the original. Along with the Ord constraint, this means that OSet cannot provide a lawful Functor instance.