Data.IxSet

Contents

Set type
Changes to set
Creation
Conversion
Size checking
Set operations
Indexing
Index creation helpers
Debugging and optimisation

Description

An efficient implementation of queryable sets.

Assume you have a type like:

 data Entry = Entry Author [Author] Updated Id Content
 newtype Updated = Updated EpochTime
 newtype Id = Id Int64
 newtype Content = Content String
 newtype Author = Author Email
 type Email = String

Decide what parts of your type you want indexed and make your type an instance of Indexable. Use ixFun and ixGen to build indexes:

 instance Indexable Entry where
     empty = ixSet 
               [ ixGen (Proxy :: Proxy Author)        -- out of order
               , ixGen (Proxy :: Proxy Id)
               , ixGen (Proxy :: Proxy Updated)
               , ixGen (Proxy :: Proxy Test)          -- bogus index
               ]

Use insert, delete, updateIx, deleteIx and empty to build up an IxSet collection:

 entries = foldr insert empty [e1,e2,e3,e4]
 entries' = foldr delete entries [e1,e3]
 entries'' = update e4 e5 entries

Use the query functions below to grab data from it:

 entries @= (Author "john@doe.com") @< (Updated t1)

Statement above will find all items in entries updated earlier than t1 by john@doe.com.

Text index

If you want to do add a text index create a calculated index. Then if you want all entries with either word1 or word2, you change the instance to:

 getWords (Entry _ _ _ _ (Content s)) = map Word $ words s

 instance Indexable Entry where
     empty = ixSet [ ...
                     ixFun getWords
                   ]

Now you can do this query to find entries with any of the words:

 entries @+ [Word "word1", Word "word2"]

And if you want all entries with both:

 entries @* [Word "word1", Word "word2"]

Find only the first author

If an Entry has multiple authors and you want to be able to query on the first author only, define a FirstAuthor datatype and create an index with this type. Now you can do:

 newtype FirstAuthor = FirstAuthor Email
   
 getFirstAuthor (Entry author _ _ _ _) = [FirstAuthor author]

 instance Indexable Entry where
     ...
     empty = ixSet [ ...
                     ixFun getFirstAuthor
                   ]

     entries @= (FirstAuthor "john@doe.com")  -- guess what this does

Synopsis

Set type

data IxSet a Source

Set with associatex indexes.

Instances

Typeable1 IxSet
(Data ctx a, Data ctx [a], Sat (ctx (IxSet a)), Sat (ctx [a]), Indexable a, Data a, Ord a) => Data ctx (IxSet a)
(Eq a, Ord a, Typeable a) => Eq (IxSet a)
Data a => Data (IxSet a)
(Eq a, Ord a, Typeable a) => Ord (IxSet a)
(Ord a, Read a, Typeable a, Indexable a) => Read (IxSet a)
(Ord a, Show a) => Show (IxSet a)
(Indexable a, Typeable a, Ord a) => Monoid (IxSet a)
(SafeCopy a, Ord a, Typeable a, Indexable a) => SafeCopy (IxSet a)

class Indexable a whereSource

Indexable class defines objects that can be members of IxSet.

Methods

empty :: IxSet aSource

Method empty defines what an empty IxSet for this particular type should look like. It should have all necessary indexes. Use ixSet function to create the set and fill it in with ixFun and ixGen.

data Proxy a Source

Constructors

Proxy

noCalcs :: t -> ()Source

Function to be used for calcs in inferIxSet when you don't want any calculated values.

inferIxSet :: String -> Name -> Name -> [Name] -> Q [Dec]Source

Template Haskell helper function for automatically building an Indexable instance from a data type, e.g.

 data Foo = Foo Int String

and

 $(inferIxSet "FooDB" ''Foo 'noCalcs [''Int,''String])

will build a type synonym

 type FooDB = IxSet Foo

with Int and String as indexes.

WARNING: The type specified as the first index must be a type which appears in all values in the IxSet or toList, toSet and serialization will not function properly. You will be warned not to do this by runtime error. You can always use the element type itself. For example:

 $(inferIxSet "FooDB" ''Foo 'noCalcs [''Foo, ''Int, ''String])

ixSet :: [Ix a] -> IxSet aSource

Create an IxSet using a list of indexes. Useful in Indexable empty method. Use ixFun and ixGen as list elements.

 instance Indexable Type where
     empty = ixSet [ ...
                     ixFun getIndex1
                     ixGen (Proxy :: Proxy Index2Type)
                   ]

First index in the list must contain all objects in set, doing otherwise result in runtime error.

ixFun :: forall a b. (Ord b, Typeable b) => (a -> [b]) -> Ix aSource

Create a functional index. Provided function should return a list of indexes where value should be found.

 getIndexes value = [...indexes...]

 instance Indexable Type where
     empty = ixSet [ ixFun getIndexes ]

This is the recommended way to create indexes.

ixGen :: forall a b. (Data a, Ord b, Typeable b) => Proxy b -> Ix aSource

Create a generic index. Provided example is used only as type source so you may use a Proxy. The ixGen uses flatten to traverse value using its Data instance.

 instance Indexable Type where
     empty = ixSet [ ixGen (Proxy :: Proxy Type) ]

In production systems consider using ixFun in place of ixGen as the former one is much faster.

Changes to set

type IndexOp = forall k a. (Ord k, Ord a) => k -> a -> Map k (Set a) -> Map k (Set a)Source

change :: (Typeable a, Indexable a, Ord a) => IndexOp -> a -> IxSet a -> IxSet aSource

Higher order operator for modifying IxSets. Use this when your final function should have the form a -> IxSet a -> IxSet a, e.g. insert or delete.

insert :: (Typeable a, Ord a, Indexable a) => a -> IxSet a -> IxSet aSource

Inserts an item into the IxSet. If your data happens to have primary key this function might not be what you want. See updateIx.

delete :: (Typeable a, Ord a, Indexable a) => a -> IxSet a -> IxSet aSource

Removes an item from the IxSet.

updateIx :: (Indexable a, Ord a, Typeable a, Typeable k) => k -> a -> IxSet a -> IxSet aSource

Will replace the item with index k. Only works if there is at most one item with that index in the IxSet. Will not change IxSet if you have more then 1 item with given index.

deleteIx :: (Indexable a, Ord a, Typeable a, Typeable k) => k -> IxSet a -> IxSet aSource

Will delete the item with index k. Only works if there is at most one item with that index in the IxSet. Will not change IxSet if you have more then 1 item with given index.

Creation

fromSet :: (Indexable a, Ord a, Typeable a) => Set a -> IxSet aSource

Converts a Set to an IxSet.

fromList :: (Indexable a, Ord a, Typeable a) => [a] -> IxSet aSource

Converts a list to an IxSet.

Conversion

toSet :: Ord a => IxSet a -> Set aSource

Converts an IxSet to a Set of its elements.

toList :: Ord a => IxSet a -> [a]Source

Converts an IxSet to its list of elements.

toAscList :: forall k a. (Indexable a, Typeable a, Typeable k) => Proxy k -> IxSet a -> [a]Source

Converts an IxSet to its list of elements.

List will be sorted in ascending order by the index k.

The list may contain duplicate entries if a single value produces multiple keys.

toDescList :: forall k a. (Indexable a, Typeable a, Typeable k) => Proxy k -> IxSet a -> [a]Source

Converts an IxSet to its list of elements.

List will be sorted in descending order by the index k.

The list may contain duplicate entries if a single value produces multiple keys.

getOne :: Ord a => IxSet a -> Maybe aSource

If the IxSet is a singleton it will return the one item stored in it. If IxSet is empty or has many elements this function returns Nothing.

getOneOr :: Ord a => a -> IxSet a -> aSource

Like getOne with a user provided default.

Size checking

size :: Ord a => IxSet a -> Int Source

Returns the number of unique items in the IxSet.

null :: IxSet a -> Bool Source

Return True if the IxSet is empty, False otherwise.

Set operations

(&&&) :: (Ord a, Typeable a, Indexable a) => IxSet a -> IxSet a -> IxSet aSource

An infix intersection operation.

(|||) :: (Ord a, Typeable a, Indexable a) => IxSet a -> IxSet a -> IxSet aSource

An infix union operation.

union :: (Ord a, Typeable a, Indexable a) => IxSet a -> IxSet a -> IxSet aSource

Takes the union of the two IxSets.

intersection :: (Ord a, Typeable a, Indexable a) => IxSet a -> IxSet a -> IxSet aSource

Takes the intersection of the two IxSets.

Indexing

(@=) :: (Indexable a, Typeable a, Ord a, Typeable k) => IxSet a -> k -> IxSet aSource

Infix version of getEQ.

(@<) :: (Indexable a, Typeable a, Ord a, Typeable k) => IxSet a -> k -> IxSet aSource

Infix version of getLT.

(@>) :: (Indexable a, Typeable a, Ord a, Typeable k) => IxSet a -> k -> IxSet aSource

Infix version of getGT.

(@<=) :: (Indexable a, Typeable a, Ord a, Typeable k) => IxSet a -> k -> IxSet aSource

Infix version of getLTE.

(@>=) :: (Indexable a, Typeable a, Ord a, Typeable k) => IxSet a -> k -> IxSet aSource

Infix version of getGTE.

(@><) :: (Indexable a, Typeable a, Ord a, Typeable k) => IxSet a -> (k, k) -> IxSet aSource

Returns the subset with indexes in the open interval (k,k).

(@>=<) :: (Indexable a, Typeable a, Ord a, Typeable k) => IxSet a -> (k, k) -> IxSet aSource

Returns the subset with indexes in [k,k).

(@><=) :: (Indexable a, Typeable a, Ord a, Typeable k) => IxSet a -> (k, k) -> IxSet aSource

Returns the subset with indexes in (k,k].

(@>=<=) :: (Indexable a, Typeable a, Ord a, Typeable k) => IxSet a -> (k, k) -> IxSet aSource

Returns the subset with indexes in [k,k].

(@+) :: (Indexable a, Typeable a, Ord a, Typeable k) => IxSet a -> [k] -> IxSet aSource

Creates the subset that has an index in the provided list.

(@*) :: (Indexable a, Typeable a, Ord a, Typeable k) => IxSet a -> [k] -> IxSet aSource

Creates the subset that matches all the provided indexes.

getEQ :: (Indexable a, Typeable a, Ord a, Typeable k) => k -> IxSet a -> IxSet aSource

Returns the subset with an index equal to the provided key. The set must be indexed over key type, doing otherwise results in runtime error.

getLT :: (Indexable a, Typeable a, Ord a, Typeable k) => k -> IxSet a -> IxSet aSource

Returns the subset with an index less than the provided key. The set must be indexed over key type, doing otherwise results in runtime error.

getGT :: (Indexable a, Typeable a, Ord a, Typeable k) => k -> IxSet a -> IxSet aSource

Returns the subset with an index greater than the provided key. The set must be indexed over key type, doing otherwise results in runtime error.

getLTE :: (Indexable a, Typeable a, Ord a, Typeable k) => k -> IxSet a -> IxSet aSource

Returns the subset with an index less than or equal to the provided key. The set must be indexed over key type, doing otherwise results in runtime error.

getGTE :: (Indexable a, Typeable a, Ord a, Typeable k) => k -> IxSet a -> IxSet aSource

Returns the subset with an index greater than or equal to the provided key. The set must be indexed over key type, doing otherwise results in runtime error.

getRange :: (Indexable a, Typeable k, Ord a, Typeable a) => k -> k -> IxSet a -> IxSet aSource

Returns the subset with an index within the interval provided. The bottom of the interval is closed and the top is open, i. e. [k1;k2). The set must be indexed over key type, doing otherwise results in runtime error.

groupBy :: (Typeable k, Typeable t) => IxSet t -> [(k, [t])]Source

Returns lists of elements paired with the indexes determined by type inference.

groupAscBy :: (Typeable k, Typeable t) => IxSet t -> [(k, [t])]Source

Returns lists of elements paired with the indexes determined by type inference.

The resulting list will be sorted in ascending order by k. The values in '[t]' will be sorted in ascending order as well.

groupDescBy :: (Typeable k, Typeable t) => IxSet t -> [(k, [t])]Source

Returns lists of elements paired with the indexes determined by type inference.

The resulting list will be sorted in descending order by k.

NOTE: The values in '[t]' are currently sorted in ascending order. But this may change if someone bothers to add Set.toDescList. So do not rely on the sort order of '[t]'.

Index creation helpers

flatten :: (Typeable a, Data a, Typeable b) => a -> [b]Source

Generically traverses the argument to find all occurences of values of type b and returns them as a list.

This function properly handles String as String not as [Char].

flattenWithCalcs :: (Data c, Typeable a, Data a, Typeable b) => (a -> c) -> a -> [b]Source

Generically traverses the argument and calculated values to find all occurences of values of type b and returns them as a list. Equivalent to:

 flatten (x,calcs x)

This function properly handles String as String not as [Char].

Debugging and optimisation

stats :: Ord a => IxSet a -> (Int, Int, Int, Int)Source

Statistics about IxSet. This function returns quadruple consisting of 1. total number of elements in the set 2. number of declared indexes 3. number of keys in all indexes 4. number of values in all keys in all indexes. This can aid you in debugging and optimisation.