Data.Edison.Coll.EnumSet
 Portability GHC, Hugs (MPTC and FD) Stability stable Maintainer robdockins AT fastmail DOT fm
 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 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
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 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
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
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