 | EdisonCore-1.2.1: A library of efficient, purely-functional data structures (Core Implementations) | Contents | Index |
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| Data.Edison.Coll.EnumSet | | Portability | GHC, Hugs (MPTC and FD) | | Stability | stable | | Maintainer | robdockins AT fastmail DOT fm |
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| 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.
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| Synopsis |
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| 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 | | | 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 |
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| Set type
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| 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 a, Enum a, Arbitrary a) => Arbitrary (Set a) | | Eq (Set a) | | (Eq a, Enum a) => Monoid (Set a) | | (Ord a, Enum a) => Ord (Set a) | | (Eq a, Enum a, Read a) => Read (Set a) | | (Eq a, Enum a, Show a) => Show (Set a) | | (Eq a, Enum a) => Coll (Set a) a | | (Eq a, Enum a) => CollX (Set a) a | | (Ord a, Enum a) => OrdColl (Set a) a | | (Ord a, Enum a) => OrdCollX (Set a) a | | (Ord a, Enum a) => OrdSet (Set a) a | | (Ord a, Enum a) => OrdSetX (Set a) a | | (Eq a, Enum a) => Set (Set a) a | | (Eq a, Enum a) => SetX (Set a) a |
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| CollX operations
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| empty :: Set a |
| O(1). The empty set.
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| singleton :: (Eq a, Enum a) => a -> Set a |
| O(1). Create a singleton set.
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| fromSeq :: (Eq a, Enum a, Sequence s) => s a -> Set a |
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| 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.
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| insertSeq :: (Eq a, Enum a, Sequence s) => s a -> Set a -> Set a |
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| union :: Set a -> Set a -> Set a |
| O(1). The union of two sets.
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| unionSeq :: (Eq a, Enum a, Sequence s) => s (Set a) -> Set a |
| The union of a list of sets: (unions == foldl union empty).
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| delete :: (Eq a, Enum a) => a -> Set a -> Set a |
| O(1). Delete an element from a set.
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| deleteAll :: (Eq a, Enum a) => a -> Set a -> Set a |
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| deleteSeq :: (Eq a, Enum a, Sequence s) => s a -> Set a -> Set a |
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| null :: Set a -> Bool |
| O(1). Is this the empty set?
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| size :: Set a -> Int |
| O(1). The number of elements in the set.
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| member :: (Eq a, Enum a) => a -> Set a -> Bool |
| O(1). Is the element in the set?
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| count :: (Eq a, Enum a) => a -> Set a -> Int |
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| strict :: Set a -> Set a |
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| OrdCollX operations
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| deleteMin :: Enum a => Set a -> Set a |
| O(1). Delete the minimal element.
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| deleteMax :: Enum a => Set a -> Set a |
| O(1). Delete the maximal element.
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| unsafeInsertMin :: (Ord a, Enum a) => a -> Set a -> Set a |
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| unsafeInsertMax :: (Ord a, Enum a) => a -> Set a -> Set a |
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| unsafeFromOrdSeq :: (Ord a, Enum a, Sequence s) => s a -> Set a |
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| unsafeAppend :: (Ord a, Enum a) => Set a -> Set a -> Set a |
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| filterLT :: (Ord a, Enum a) => a -> Set a -> Set a |
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| filterLE :: (Ord a, Enum a) => a -> Set a -> Set a |
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| filterGT :: (Ord a, Enum a) => a -> Set a -> Set a |
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| filterGE :: (Ord a, Enum a) => a -> Set a -> Set a |
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| partitionLT_GE :: (Ord a, Enum a) => a -> Set a -> (Set a, Set a) |
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| partitionLE_GT :: (Ord a, Enum a) => a -> Set a -> (Set a, Set a) |
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| partitionLT_GT :: (Ord a, Enum a) => a -> Set a -> (Set a, Set a) |
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| SetX operations
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| intersection :: Set a -> Set a -> Set a |
| O(1). The intersection of two sets.
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| difference :: Set a -> Set a -> Set a |
| O(1). Difference of two sets.
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| symmetricDifference :: Set a -> Set a -> Set a |
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| properSubset :: Set a -> Set a -> Bool |
| O(1). Is this a proper subset? (ie. a subset but not equal).
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| subset :: Set a -> Set a -> Bool |
| O(1). Is this a subset?
(s1 subset s2) tells whether s1 is a subset of s2.
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| Coll operations
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| toSeq :: (Eq a, Enum a, Sequence s) => Set a -> s a |
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| lookup :: (Eq a, Enum a) => a -> Set a -> a |
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| lookupM :: (Eq a, Enum a, Monad m) => a -> Set a -> m a |
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| lookupAll :: (Eq a, Enum a, Sequence s) => a -> Set a -> s a |
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| lookupWithDefault :: (Eq a, Enum a) => a -> a -> Set a -> a |
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| fold :: (Eq a, Enum a) => (a -> c -> c) -> c -> Set a -> c |
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| fold' :: (Eq a, Enum a) => (a -> c -> c) -> c -> Set a -> c |
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| fold1 :: (Eq a, Enum a) => (a -> a -> a) -> Set a -> a |
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| fold1' :: (Eq a, Enum a) => (a -> a -> a) -> Set a -> a |
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| filter :: (Eq a, Enum a) => (a -> Bool) -> Set a -> Set a |
| O(n). Filter all elements that satisfy the predicate.
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| 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.
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| strictWith :: (a -> b) -> Set a -> Set a |
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| OrdColl operations
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| minView :: (Enum a, Monad m) => Set a -> m (a, Set a) |
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| minElem :: Enum a => Set a -> a |
| O(1). The minimal element of a set.
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| maxView :: (Enum a, Monad m) => Set a -> m (a, Set a) |
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| maxElem :: Enum a => Set a -> a |
| O(1). The maximal element of a set.
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| foldr :: (Ord a, Enum a) => (a -> b -> b) -> b -> Set a -> b |
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| foldr' :: (Ord a, Enum a) => (a -> b -> b) -> b -> Set a -> b |
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| foldl :: (Ord a, Enum a) => (c -> a -> c) -> c -> Set a -> c |
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| foldl' :: (Ord a, Enum a) => (c -> a -> c) -> c -> Set a -> c |
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| foldr1 :: (Ord a, Enum a) => (a -> a -> a) -> Set a -> a |
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| foldr1' :: (Ord a, Enum a) => (a -> a -> a) -> Set a -> a |
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| foldl1 :: (Ord a, Enum a) => (a -> a -> a) -> Set a -> a |
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| foldl1' :: (Ord a, Enum a) => (a -> a -> a) -> Set a -> a |
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| toOrdSeq :: (Ord a, Enum a, Sequence s) => Set a -> s a |
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| unsafeMapMonotonic :: Enum a => (a -> a) -> Set a -> Set a |
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| Set operations
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| fromSeqWith :: (Eq a, Enum a, Sequence s) => (a -> a -> a) -> s a -> Set a |
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| insertWith :: (Eq a, Enum a) => (a -> a -> a) -> a -> Set a -> Set a |
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| insertSeqWith :: (Eq a, Enum a, Sequence s) => (a -> a -> a) -> s a -> Set a -> Set a |
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| unionl :: Set a -> Set a -> Set a |
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| unionr :: Set a -> Set a -> Set a |
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| unionWith :: (a -> a -> a) -> Set a -> Set a -> Set a |
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| unionSeqWith :: (Eq a, Enum a, Sequence s) => (a -> a -> a) -> s (Set a) -> Set a |
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| intersectionWith :: (a -> a -> a) -> Set a -> Set a -> Set a |
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| Bonus operations
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| 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
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| 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.
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| 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.
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| toBits :: Set a -> Word |
| O(1) Get the underlying bit-encoded representation.
This method is operationally a no-op.
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| fromBits :: Word -> Set a |
| O(1) Create an EnumSet from a bit-encoded representation.
This method is operationally a no-op.
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| Documenation
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| Produced by Haddock version 0.8 |