Data.Edison.Coll.EnumSet

EdisonCore-1.3.1.1: A library of efficent, purely-functional data structures (Core Implementations)

Copyright | (c) David F. Place 2006
License | BSD
Maintainer | robdockins AT fastmail DOT fm
Stability | stable
Portability | GHC, Hugs (MPTC and FD)
Safe Haskell | None
Language | Haskell2010

Data.Edison.Coll.EnumSet

Contents

- Set type
- CollX operations
- OrdCollX operations
- SetX operations
- Coll operations
- OrdColl operations
- Set operations
- Bonus operations
- Documenation

Description

An efficient implementation of sets over small enumerations. The implementation of `EnumSet` is based on bit-wise operations.

For this implementation to work as expected at type `A`, there are a number of preconditions on the `Eq`, `Enum` and `Ord` instances.

The `Enum A` instance must create a bijection between the elements of type `A` and a finite subset of the naturals [0,1,2,3....]. As a corollary we must have:

    forall x y::A, fromEnum x == fromEnum y <==> x is indistinguishable from y

Also, the number of distinct elements of `A` must be less than or equal to the number of bits in `Word`.

The `Enum A` instance must be consistent with the `Eq A` instance. That is, we must have:

    forall x y::A, x == y <==> toEnum x == toEnum y

Additionally, for operations that require an `Ord A` context, we require that toEnum be monotonic with respect to comparison. That is, we must have:

    forall x y::A, x < y <==> toEnum x < toEnum y

Derived `Eq`, `Ord` and `Enum` instances will fulfill these conditions, if the enumerated type has sufficently few constructors.

Synopsis

- data Set a
- empty :: Set a
- singleton :: (Eq a, Enum a) => a -> Set a
- fromSeq :: (Eq a, Enum a, Sequence s) => s a -> Set a
- insert :: (Eq a, Enum a) => a -> Set a -> Set a
- insertSeq :: (Eq a, Enum a, Sequence s) => s a -> Set a -> Set a
- union :: Set a -> Set a -> Set a
- unionSeq :: (Eq a, Enum a, Sequence s) => s (Set a) -> Set a
- delete :: (Eq a, Enum a) => a -> Set a -> Set a
- deleteAll :: (Eq a, Enum a) => a -> Set a -> Set a
- deleteSeq :: (Eq a, Enum a, Sequence s) => s a -> Set a -> Set a
- null :: Set a -> Bool
- size :: Set a -> Int
- member :: (Eq a, Enum a) => a -> Set a -> Bool
- count :: (Eq a, Enum a) => a -> Set a -> Int
- strict :: Set a -> Set a
- deleteMin :: Enum a => Set a -> Set a
- deleteMax :: Enum a => Set a -> Set a
- unsafeInsertMin :: (Ord a, Enum a) => a -> Set a -> Set a
- unsafeInsertMax :: (Ord a, Enum a) => a -> Set a -> Set a
- unsafeFromOrdSeq :: (Ord a, Enum a, Sequence s) => s a -> Set a
- unsafeAppend :: (Ord a, Enum a) => Set a -> Set a -> Set a
- filterLT :: (Ord a, Enum a) => a -> Set a -> Set a
- filterLE :: (Ord a, Enum a) => a -> Set a -> Set a
- filterGT :: (Ord a, Enum a) => a -> Set a -> Set a
- filterGE :: (Ord a, Enum a) => a -> Set a -> Set a
- partitionLT_GE :: (Ord a, Enum a) => a -> Set a -> (Set a, Set a)
- partitionLE_GT :: (Ord a, Enum a) => a -> Set a -> (Set a, Set a)
- partitionLT_GT :: (Ord a, Enum a) => a -> Set a -> (Set a, Set a)
- intersection :: Set a -> Set a -> Set a
- difference :: Set a -> Set a -> Set a
- symmetricDifference :: Set a -> Set a -> Set a
- properSubset :: Set a -> Set a -> Bool
- subset :: Set a -> Set a -> Bool
- toSeq :: (Eq a, Enum a, Sequence s) => Set a -> s a
- lookup :: (Eq a, Enum a) => a -> Set a -> a
- lookupM :: (Eq a, Enum a, Monad m) => a -> Set a -> m a
- lookupAll :: (Eq a, Enum a, Sequence s) => a -> Set a -> s a
- lookupWithDefault :: (Eq a, Enum a) => a -> a -> Set a -> a
- fold :: (Eq a, Enum a) => (a -> c -> c) -> c -> Set a -> c
- fold' :: (Eq a, Enum a) => (a -> c -> c) -> c -> Set a -> c
- fold1 :: (Eq a, Enum a) => (a -> a -> a) -> Set a -> a
- fold1' :: (Eq a, Enum a) => (a -> a -> a) -> Set a -> a
- filter :: (Eq a, Enum a) => (a -> Bool) -> Set a -> Set a
- partition :: (Eq a, Enum a) => (a -> Bool) -> Set a -> (Set a, Set a)
- strictWith :: (a -> b) -> Set a -> Set a
- minView :: (Enum a, Monad m) => Set a -> m (a, Set a)
- minElem :: Enum a => Set a -> a
- maxView :: (Enum a, Monad m) => Set a -> m (a, Set a)
- maxElem :: Enum a => Set a -> a
- foldr :: (Ord a, Enum a) => (a -> b -> b) -> b -> Set a -> b
- foldr' :: (Ord a, Enum a) => (a -> b -> b) -> b -> Set a -> b
- foldl :: (Ord a, Enum a) => (c -> a -> c) -> c -> Set a -> c
- foldl' :: (Ord a, Enum a) => (c -> a -> c) -> c -> Set a -> c
- foldr1 :: (Ord a, Enum a) => (a -> a -> a) -> Set a -> a
- foldr1' :: (Ord a, Enum a) => (a -> a -> a) -> Set a -> a
- foldl1 :: (Ord a, Enum a) => (a -> a -> a) -> Set a -> a
- foldl1' :: (Ord a, Enum a) => (a -> a -> a) -> Set a -> a
- toOrdSeq :: (Ord a, Enum a, Sequence s) => Set a -> s a
- unsafeMapMonotonic :: Enum a => (a -> a) -> Set a -> Set a
- fromSeqWith :: (Eq a, Enum a, Sequence s) => (a -> a -> a) -> s a -> Set a
- fromOrdSeq :: (Ord a, Enum a, Sequence s) => s a -> Set a
- insertWith :: (Eq a, Enum a) => (a -> a -> a) -> a -> Set a -> Set a
- insertSeqWith :: (Eq a, Enum a, Sequence s) => (a -> a -> a) -> s a -> Set a -> Set a
- unionl :: Set a -> Set a -> Set a
- unionr :: Set a -> Set a -> Set a
- unionWith :: (a -> a -> a) -> Set a -> Set a -> Set a
- unionSeqWith :: (Eq a, Enum a, Sequence s) => (a -> a -> a) -> s (Set a) -> Set a
- intersectionWith :: (a -> a -> a) -> Set a -> Set a -> Set a
- map :: (Enum a, Enum b) => (a -> b) -> Set a -> Set b
- setCoerce :: (Enum a, Enum b) => Set a -> Set b
- complement :: (Eq a, Bounded a, Enum a) => Set a -> Set a
- toBits :: Set a -> Word
- fromBits :: Word -> Set a
- moduleName :: String

# Set type

data Set a #

A set of values `a` implemented as bitwise operations. Useful for members of class Enum with no more elements than there are bits in `Word`.

Instances

Eq (Set a) # |
Methods (==) :: Set a -> Set a -> Bool # (/=) :: Set a -> Set a -> Bool #
(Ord a, Enum a) => Ord (Set a) # |
Methods compare :: Set a -> Set a -> Ordering # (<) :: Set a -> Set a -> Bool # (<=) :: Set a -> Set a -> Bool # (>) :: Set a -> Set a -> Bool # (>=) :: Set a -> Set a -> Bool # max :: Set a -> Set a -> Set a # min :: Set a -> Set a -> Set a #
(Eq a, Enum a, Read a) => Read (Set a) # |
Methods readsPrec :: Int -> ReadS (Set a) # readList :: ReadS [Set a] # readPrec :: ReadPrec (Set a) # readListPrec :: ReadPrec [Set a] #
(Eq a, Enum a, Show a) => Show (Set a) # |
Methods showsPrec :: Int -> Set a -> ShowS # show :: Set a -> String # showList :: [Set a] -> ShowS #
(Eq a, Enum a) => Monoid (Set a) # |
Methods mempty :: Set a # mappend :: Set a -> Set a -> Set a # mconcat :: [Set a] -> Set a #
(Eq a, Enum a, Arbitrary a) => Arbitrary (Set a) # |
Methods arbitrary :: Gen (Set a) # shrink :: Set a -> [Set a] #
(Eq a, Enum a, CoArbitrary a) => CoArbitrary (Set a) # |
Methods coarbitrary :: Set a -> Gen b -> Gen b #
(Eq a, Enum a) => CollX (Set a) a # |
Methods singleton :: a -> Set a # fromSeq :: Sequence seq => seq a -> Set a # unionSeq :: Sequence seq => seq (Set a) -> Set a # insert :: a -> Set a -> Set a # insertSeq :: Sequence seq => seq a -> Set a -> Set a # delete :: a -> Set a -> Set a # deleteAll :: a -> Set a -> Set a # deleteSeq :: Sequence seq => seq a -> Set a -> Set a # null :: Set a -> Bool # size :: Set a -> Int # member :: a -> Set a -> Bool # count :: a -> Set a -> Int # strict :: Set a -> Set a # structuralInvariant :: Set a -> Bool # instanceName :: Set a -> String #
(Ord a, Enum a) => OrdCollX (Set a) a # |
Methods deleteMin :: Set a -> Set a # deleteMax :: Set a -> Set a # unsafeInsertMin :: a -> Set a -> Set a # unsafeInsertMax :: a -> Set a -> Set a # unsafeFromOrdSeq :: Sequence seq => seq a -> Set a # unsafeAppend :: Set a -> Set a -> Set a # filterLT :: a -> Set a -> Set a # filterLE :: a -> Set a -> Set a # filterGT :: a -> Set a -> Set a # filterGE :: a -> Set a -> Set a # partitionLT_GE :: a -> Set a -> (Set a, Set a) # partitionLE_GT :: a -> Set a -> (Set a, Set a) # partitionLT_GT :: a -> Set a -> (Set a, Set a) #
(Eq a, Enum a) => SetX (Set a) a # |
Methods intersection :: Set a -> Set a -> Set a # difference :: Set a -> Set a -> Set a # symmetricDifference :: Set a -> Set a -> Set a # properSubset :: Set a -> Set a -> Bool # subset :: Set a -> Set a -> Bool #
(Ord a, Enum a) => OrdSetX (Set a) a # |
(Eq a, Enum a) => Coll (Set a) a # |
Methods toSeq :: Sequence seq => Set a -> seq a # lookup :: a -> Set a -> a # lookupM :: Monad m => a -> Set a -> m a # lookupAll :: Sequence seq => a -> Set a -> seq a # lookupWithDefault :: a -> a -> Set a -> a # fold :: (a -> b -> b) -> b -> Set a -> b # fold' :: (a -> b -> b) -> b -> Set a -> b # fold1 :: (a -> a -> a) -> Set a -> a # fold1' :: (a -> a -> a) -> Set a -> a # filter :: (a -> Bool) -> Set a -> Set a # partition :: (a -> Bool) -> Set a -> (Set a, Set a) # strictWith :: (a -> b) -> Set a -> Set a #
(Ord a, Enum a) => OrdColl (Set a) a # |
Methods minView :: Monad m => Set a -> m (a, Set a) # minElem :: Set a -> a # maxView :: Monad m => Set a -> m (a, Set a) # maxElem :: Set a -> a # foldr :: (a -> b -> b) -> b -> Set a -> b # foldr' :: (a -> b -> b) -> b -> Set a -> b # foldl :: (b -> a -> b) -> b -> Set a -> b # foldl' :: (b -> a -> b) -> b -> Set a -> b # foldr1 :: (a -> a -> a) -> Set a -> a # foldr1' :: (a -> a -> a) -> Set a -> a # foldl1 :: (a -> a -> a) -> Set a -> a # foldl1' :: (a -> a -> a) -> Set a -> a # toOrdSeq :: Sequence seq => Set a -> seq a # unsafeMapMonotonic :: (a -> a) -> Set a -> Set a #
(Eq a, Enum a) => Set (Set a) a # |
Methods fromSeqWith :: Sequence seq => (a -> a -> a) -> seq a -> Set a # insertWith :: (a -> a -> a) -> a -> Set a -> Set a # insertSeqWith :: Sequence seq => (a -> a -> a) -> seq a -> Set a -> Set a # unionl :: Set a -> Set a -> Set a # unionr :: Set a -> Set a -> Set a # unionWith :: (a -> a -> a) -> Set a -> Set a -> Set a # unionSeqWith :: Sequence seq => (a -> a -> a) -> seq (Set a) -> Set a # intersectionWith :: (a -> a -> a) -> Set a -> Set a -> Set a #
(Ord a, Enum a) => OrdSet (Set a) a # |

# CollX operations

empty :: Set a #

O(1). The empty set.

singleton :: (Eq a, Enum a) => a -> Set a #

O(1). Create a singleton set.

fromSeq :: (Eq a, Enum a, Sequence s) => s a -> Set a #

insert :: (Eq a, Enum a) => a -> Set a -> Set a #

O(1). Insert an element in a set. If the set already contains an element equal to the given value, it is replaced with the new value.

insertSeq :: (Eq a, Enum a, Sequence s) => s a -> Set a -> Set a #

union :: Set a -> Set a -> Set a #

O(1). The union of two sets.

unionSeq :: (Eq a, Enum a, Sequence s) => s (Set a) -> Set a #

The union of a list of sets: (``unions` == `foldl` `union` `empty``).

delete :: (Eq a, Enum a) => a -> Set a -> Set a #

O(1). Delete an element from a set.

deleteAll :: (Eq a, Enum a) => a -> Set a -> Set a #

deleteSeq :: (Eq a, Enum a, Sequence s) => s a -> Set a -> Set a #

null :: Set a -> Bool #

O(1). Is this the empty set?

size :: Set a -> Int #

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

member :: (Eq a, Enum a) => a -> Set a -> Bool #

O(1). Is the element in the set?

count :: (Eq a, Enum a) => a -> Set a -> Int #

strict :: Set a -> Set a #

# OrdCollX operations

deleteMin :: Enum a => Set a -> Set a #

O(1). Delete the minimal element.

deleteMax :: Enum a => Set a -> Set a #

O(1). Delete the maximal element.

unsafeInsertMin :: (Ord a, Enum a) => a -> Set a -> Set a #

unsafeInsertMax :: (Ord a, Enum a) => a -> Set a -> Set a #

unsafeFromOrdSeq :: (Ord a, Enum a, Sequence s) => s a -> Set a #

unsafeAppend :: (Ord a, Enum a) => Set a -> Set a -> Set a #

filterLT :: (Ord a, Enum a) => a -> Set a -> Set a #

filterLE :: (Ord a, Enum a) => a -> Set a -> Set a #

filterGT :: (Ord a, Enum a) => a -> Set a -> Set a #

filterGE :: (Ord a, Enum a) => a -> Set a -> Set a #

partitionLT_GE :: (Ord a, Enum a) => a -> Set a -> (Set a, Set a) #

partitionLE_GT :: (Ord a, Enum a) => a -> Set a -> (Set a, Set a) #

partitionLT_GT :: (Ord a, Enum a) => a -> Set a -> (Set a, Set a) #

# SetX operations

intersection :: Set a -> Set a -> Set a #

O(1). The intersection of two sets.

difference :: Set a -> Set a -> Set a #

O(1). Difference of two sets.

symmetricDifference :: Set a -> Set a -> Set a #

properSubset :: Set a -> Set a -> Bool #

O(1). Is this a proper subset? (ie. a subset but not equal).

subset :: Set a -> Set a -> Bool #

O(1). Is this a subset? `(s1 `subset` s2)` tells whether `s1` is a subset of `s2`.

# Coll operations

toSeq :: (Eq a, Enum a, Sequence s) => Set a -> s a #

lookup :: (Eq a, Enum a) => a -> Set a -> a #

lookupM :: (Eq a, Enum a, Monad m) => a -> Set a -> m a #

lookupAll :: (Eq a, Enum a, Sequence s) => a -> Set a -> s a #

lookupWithDefault :: (Eq a, Enum a) => a -> a -> Set a -> a #

fold :: (Eq a, Enum a) => (a -> c -> c) -> c -> Set a -> c #

fold' :: (Eq a, Enum a) => (a -> c -> c) -> c -> Set a -> c #

fold1 :: (Eq a, Enum a) => (a -> a -> a) -> Set a -> a #

fold1' :: (Eq a, Enum a) => (a -> a -> a) -> Set a -> a #

filter :: (Eq a, Enum a) => (a -> Bool) -> Set a -> Set a #

O(n). Filter all elements that satisfy the predicate.

partition :: (Eq a, Enum a) => (a -> Bool) -> Set a -> (Set a, Set a) #

O(n). Partition the set into two sets, one with all elements that satisfy the predicate and one with all elements that don't satisfy the predicate. See also `split`.

strictWith :: (a -> b) -> Set a -> Set a #

# OrdColl operations

minView :: (Enum a, Monad m) => Set a -> m (a, Set a) #

minElem :: Enum a => Set a -> a #

O(1). The minimal element of a set.

maxView :: (Enum a, Monad m) => Set a -> m (a, Set a) #

maxElem :: Enum a => Set a -> a #

O(1). The maximal element of a set.

foldr :: (Ord a, Enum a) => (a -> b -> b) -> b -> Set a -> b #

foldr' :: (Ord a, Enum a) => (a -> b -> b) -> b -> Set a -> b #

foldl :: (Ord a, Enum a) => (c -> a -> c) -> c -> Set a -> c #

foldl' :: (Ord a, Enum a) => (c -> a -> c) -> c -> Set a -> c #

foldr1 :: (Ord a, Enum a) => (a -> a -> a) -> Set a -> a #

foldr1' :: (Ord a, Enum a) => (a -> a -> a) -> Set a -> a #

foldl1 :: (Ord a, Enum a) => (a -> a -> a) -> Set a -> a #

foldl1' :: (Ord a, Enum a) => (a -> a -> a) -> Set a -> a #

toOrdSeq :: (Ord a, Enum a, Sequence s) => Set a -> s a #

unsafeMapMonotonic :: Enum a => (a -> a) -> Set a -> Set a #

# Set operations

fromSeqWith :: (Eq a, Enum a, Sequence s) => (a -> a -> a) -> s a -> Set a #

fromOrdSeq :: (Ord a, Enum a, Sequence s) => s a -> Set a #

insertWith :: (Eq a, Enum a) => (a -> a -> a) -> a -> Set a -> Set a #

insertSeqWith :: (Eq a, Enum a, Sequence s) => (a -> a -> a) -> s a -> Set a -> Set a #

unionl :: Set a -> Set a -> Set a #

unionr :: Set a -> Set a -> Set a #

unionWith :: (a -> a -> a) -> Set a -> Set a -> Set a #

unionSeqWith :: (Eq a, Enum a, Sequence s) => (a -> a -> a) -> s (Set a) -> Set a #

intersectionWith :: (a -> a -> a) -> Set a -> Set a -> Set a #

# Bonus operations

map :: (Enum a, Enum b) => (a -> b) -> Set a -> Set b #

O(n). ``map` f s` is the set obtained by applying `f` to each element of `s`.

It's worth noting that the size of the result may be smaller if, for some `(x,y)`, `x /= y && f x == f y`

setCoerce :: (Enum a, Enum b) => Set a -> Set b #

O(1) Changes the type of the elements in the set without changing the representation. Equivalant to `map (toEnum . fromEnum)`, and to `(fromBits . toBits)`. This method is operationally a no-op.

complement :: (Eq a, Bounded a, Enum a) => Set a -> Set a #

O(1). The complement of a set with its universe set. `complement` can be used with bounded types for which the universe set will be automatically created.

toBits :: Set a -> Word #

O(1) Get the underlying bit-encoded representation. This method is operationally a no-op.

fromBits :: Word -> Set a #

O(1) Create an EnumSet from a bit-encoded representation. This method is operationally a no-op.

# Documenation

moduleName :: String #