{-# LANGUAGE UndecidableInstances, OverlappingInstances, FlexibleInstances,
MultiParamTypeClasses, TemplateHaskell, RankNTypes,
FunctionalDependencies, DeriveDataTypeable,
GADTs, CPP, ScopedTypeVariables #-}
module Data.IxSet
(
IxSet,
Indexable(..),
Proxy(..),
noCalcs,
inferIxSet,
ixSet,
ixFun,
ixGen,
IndexOp,
change,
insert,
delete,
updateIx,
deleteIx,
fromSet,
fromList,
toSet,
toList,
toAscList,
toDescList,
getOne,
getOneOr,
size,
null,
(&&&),
(|||),
union,
intersection,
(@=),
(@<),
(@>),
(@<=),
(@>=),
(@><),
(@>=<),
(@><=),
(@>=<=),
(@+),
(@*),
getEQ,
getLT,
getGT,
getLTE,
getGTE,
getRange,
groupBy,
groupAscBy,
groupDescBy,
flatten,
flattenWithCalcs,
stats
)
where
import Prelude hiding (null)
import Control.Arrow (first, second)
import Data.Generics (Data, gmapQ)
import qualified Data.Generics.SYB.WithClass.Basics as SYBWC
import qualified Data.IxSet.Ix as Ix
import Data.IxSet.Ix (Ix(Ix))
import qualified Data.List as List
import Data.Map (Map)
import qualified Data.Map as Map
import Data.Maybe (fromMaybe)
import Data.Monoid (Monoid(mempty, mappend))
import Data.SafeCopy (SafeCopy(..), contain, safeGet, safePut)
import Data.Set (Set)
import qualified Data.Set as Set
import Data.Typeable (Typeable, cast, typeOf)
import Language.Haskell.TH as TH
data Proxy a = Proxy
mkProxy :: a -> Proxy a
mkProxy _ = Proxy
asProxyType :: a -> Proxy a -> a
asProxyType a _ = a
data IxSet a = IxSet [Ix a]
deriving (Data, Typeable)
ixSet :: [Ix a] -> IxSet a
ixSet = IxSet
ixFun :: forall a b . (Ord b,Typeable b) => (a -> [b]) -> Ix a
ixFun f = Ix Map.empty f
ixGen :: forall a b . (Data a,Ord b,Typeable b) => Proxy b -> Ix a
ixGen _example = ixFun (flatten :: a -> [b])
showTypeOf :: (Typeable a) => a -> String
showTypeOf x = showsPrec 11 (typeOf x) []
instance (Eq a,Ord a,Typeable a) => Eq (IxSet a) where
IxSet (Ix a _:_) == IxSet (Ix b _:_) =
case cast b of
Just b' -> a==b'
Nothing -> error "trying to compare two sets with different types of first indexes, this is a bug in the library"
_ == _ = error "comparing sets without indexes, this is a bug in the library"
instance (Eq a,Ord a,Typeable a) => Ord (IxSet a) where
compare a b = compare (toSet a) (toSet b)
instance (SafeCopy a, Ord a, Typeable a, Indexable a) => SafeCopy (IxSet a) where
putCopy = contain . safePut . toList
getCopy = contain $ fmap fromList safeGet
instance ( SYBWC.Data ctx a
, SYBWC.Data ctx [a]
, SYBWC.Sat (ctx (IxSet a))
, SYBWC.Sat (ctx [a])
, SYBWC.Typeable1 IxSet
, Indexable a
, Data a
, Ord a
)
=> SYBWC.Data ctx (IxSet a) where
gfoldl _ f z ixset = z fromList `f` toList ixset
toConstr _ (IxSet _) = ixSetConstr
gunfold _ k z c = case SYBWC.constrIndex c of
1 -> k (z fromList)
_ -> error "IxSet.SYBWC.Data.gunfold unexpected match"
dataTypeOf _ _ = ixSetDataType
ixSetConstr :: SYBWC.Constr
ixSetConstr = SYBWC.mkConstr ixSetDataType "IxSet" [] SYBWC.Prefix
ixSetDataType :: SYBWC.DataType
ixSetDataType = SYBWC.mkDataType "IxSet" [ixSetConstr]
instance (Ord a,Show a) => Show (IxSet a) where
showsPrec prec = showsPrec prec . toSet
instance (Ord a,Read a,Typeable a,Indexable a) => Read (IxSet a) where
readsPrec n = map (first fromSet) . readsPrec n
class Indexable a where
empty :: IxSet a
noCalcs :: t -> ()
noCalcs _ = ()
inferIxSet :: String -> TH.Name -> TH.Name -> [TH.Name] -> Q [Dec]
inferIxSet _ _ _ [] = error "inferIxSet needs at least one index"
inferIxSet ixset typeName calName entryPoints
= do calInfo <- reify calName
typeInfo <- reify typeName
let (context,binders) = case typeInfo of
#if MIN_VERSION_template_haskell(2,11,0)
TyConI (DataD ctxt _ nms _ _ _) -> (ctxt,nms)
TyConI (NewtypeD ctxt _ nms _ _ _) -> (ctxt,nms)
#else
TyConI (DataD ctxt _ nms _ _) -> (ctxt,nms)
TyConI (NewtypeD ctxt _ nms _ _) -> (ctxt,nms)
#endif
TyConI (TySynD _ nms _) -> ([],nms)
_ -> error "IxSet.inferIxSet typeInfo unexpected match"
names = map tyVarBndrToName binders
typeCon = List.foldl' appT (conT typeName) (map varT names)
#if MIN_VERSION_template_haskell(2,4,0)
mkCtx = classP
#else
mkType con = foldl appT (conT con)
mkCtx = mkType
#endif
dataCtxConQ = [mkCtx ''Data [varT name] | name <- names]
fullContext = do
dataCtxCon <- sequence dataCtxConQ
return (context ++ dataCtxCon)
case calInfo of
#if MIN_VERSION_template_haskell(2,11,0)
VarI _ t _ ->
#else
VarI _ t _ _ ->
#endif
let calType = getCalType t
getCalType (ForallT _names _ t') = getCalType t'
getCalType (AppT (AppT ArrowT _) t') = t'
getCalType t' = error ("Unexpected type in getCalType: " ++ pprint t')
mkEntryPoint n = (conE 'Ix) `appE`
(sigE (varE 'Map.empty) (forallT binders (return context) $
appT (appT (conT ''Map) (conT n))
(appT (conT ''Set) typeCon))) `appE`
(varE 'flattenWithCalcs `appE` varE calName)
in do i <- instanceD (fullContext)
(conT ''Indexable `appT` typeCon)
[valD (varP 'empty) (normalB [| ixSet $(listE (map mkEntryPoint entryPoints)) |]) []]
let ixType = appT (conT ''IxSet) typeCon
ixType' <- tySynD (mkName ixset) binders ixType
return $ [i, ixType'] -- ++ d
_ -> error "IxSet.inferIxSet calInfo unexpected match"
-- | Version of 'instanceD' that takes in a Q [Dec] instead of a [Q Dec]
-- and filters out signatures from the list of declarations.
instanceD' :: CxtQ -> TypeQ -> Q [Dec] -> DecQ
instanceD' ctxt ty decs =
do decs' <- decs
let decs'' = filter (not . isSigD) decs'
instanceD ctxt ty (map return decs'')
-- | Returns true if the Dec matches a SigD constructor.
isSigD :: Dec -> Bool
isSigD (SigD _ _) = True
isSigD _ = False
#if MIN_VERSION_template_haskell(2,4,0)
tyVarBndrToName :: TyVarBndr -> Name
tyVarBndrToName (PlainTV nm) = nm
tyVarBndrToName (KindedTV nm _) = nm
#else
tyVarBndrToName :: a -> a
tyVarBndrToName = id
#endif
-- modification operations
type IndexOp =
forall k a. (Ord k,Ord a) => k -> a -> Map k (Set a) -> Map k (Set a)
-- | 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']@.
flatten :: (Typeable a, Data a, Typeable b) => a -> [b]
flatten x = case cast x of
Just y -> case cast (y :: String) of
Just v -> [v]
Nothing -> []
Nothing -> case cast x of
Just v -> v : concat (gmapQ flatten x)
Nothing -> concat (gmapQ flatten x)
-- | 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']@.
flattenWithCalcs :: (Data c,Typeable a, Data a, Typeable b) => (a -> c) -> a -> [b]
flattenWithCalcs calcs x = flatten (x,calcs x)
-- | Higher order operator for modifying 'IxSet's. Use this when your
-- final function should have the form @a -> 'IxSet' a -> 'IxSet' a@,
-- e.g. 'insert' or 'delete'.
change :: (Typeable a,Indexable a,Ord a) =>
IndexOp -> a -> IxSet a -> IxSet a
change op x (IxSet indexes) =
IxSet v
where
v = zipWith update (True:repeat False) indexes
update firstindex (Ix index flatten2) = Ix index' flatten2
where
key = (undefined :: Map key (Set a) -> key) index
ds = flatten2 x
ii m dkey = op dkey x m
index' = if firstindex && List.null ds
then error $ "Happstack.Data.IxSet.change: all values must appear in first declared index " ++ showTypeOf key ++ " of " ++ showTypeOf x
else List.foldl' ii index ds -- handle multiple values
insertList :: (Typeable a,Indexable a,Ord a)
=> [a] -> IxSet a -> IxSet a
insertList xs (IxSet indexes) =
IxSet v
where
v = zipWith update (True:repeat False) indexes
update firstindex (Ix index flatten2) = Ix index' flatten2
where
key = (undefined :: Map key (Set a) -> key) index
flattencheck x
| firstindex = case flatten2 x of
[] -> error $ "Happstack.Data.IxSet.change: all values must appear in first declared index " ++ showTypeOf key ++ " of " ++ showTypeOf x
res -> res
| otherwise = flatten2 x
dss = [(k,x) | x <- xs, k <- flattencheck x]
index' = Ix.insertList dss index
insertMapOfSets :: (Typeable a, Ord a,Indexable a,Typeable key,Ord key)
=> Map key (Set a) -> IxSet a -> IxSet a
insertMapOfSets originalindex (IxSet indexes) =
IxSet v
where
v = map update indexes
xs = concatMap Set.toList (Map.elems originalindex)
update (Ix index flatten2) = Ix index' flatten2
where
dss = [(k,x) | x <- xs, k <- flatten2 x]
{- We try to be really clever here. The originalindex is a Map of Sets
from original index. We want to reuse it as much as possible. If there
was a guarantee that each element is present at at most one index we
could reuse originalindex as it is. But there can be more, so we need to
add remaining ones. Anyway we try to reuse old structure and keep
new allocations low as much as possible.
-}
index' = case cast originalindex of
Just originalindex' ->
let dssf = filter (\(k,_v) -> not (Map.member k originalindex')) dss
in Ix.insertList dssf originalindex'
Nothing -> Ix.insertList dss index
-- | Inserts an item into the 'IxSet'. If your data happens to have
-- a primary key this function might not be what you want. See
-- 'updateIx'.
insert :: (Typeable a, Ord a,Indexable a) => a -> IxSet a -> IxSet a
insert = change Ix.insert
-- | Removes an item from the 'IxSet'.
delete :: (Typeable a, Ord a,Indexable a) => a -> IxSet a -> IxSet a
delete = change Ix.delete
-- | 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.
updateIx :: (Indexable a, Ord a, Typeable a, Typeable k)
=> k -> a -> IxSet a -> IxSet a
updateIx i new ixset = insert new $
maybe ixset (flip delete ixset) $
getOne $ ixset @= i
-- | 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.
deleteIx :: (Indexable a, Ord a, Typeable a, Typeable k)
=> k -> IxSet a -> IxSet a
deleteIx i ixset = maybe ixset (flip delete ixset) $
getOne $ ixset @= i
-- conversion operations
-- | Converts an 'IxSet' to a 'Set' of its elements.
toSet :: Ord a => IxSet a -> Set a
toSet (IxSet (Ix ix _:_)) = List.foldl' Set.union Set.empty (Map.elems ix)
toSet (IxSet []) = Set.empty
-- | Converts a 'Set' to an 'IxSet'.
fromSet :: (Indexable a, Ord a, Typeable a) => Set a -> IxSet a
fromSet = fromList . Set.toList
-- | Converts a list to an 'IxSet'.
fromList :: (Indexable a, Ord a, Typeable a) => [a] -> IxSet a
fromList list = insertList list empty
-- | Returns the number of unique items in the 'IxSet'.
size :: Ord a => IxSet a -> Int
size = Set.size . toSet
-- | Converts an 'IxSet' to its list of elements.
toList :: Ord a => IxSet a -> [a]
toList = Set.toList . toSet
-- | 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.
toAscList :: forall k a. (Indexable a, Typeable a, Typeable k) => Proxy k -> IxSet a -> [a]
toAscList _ ixset = concatMap snd (groupAscBy ixset :: [(k, [a])])
-- | 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.
toDescList :: forall k a. (Indexable a, Typeable a, Typeable k) => Proxy k -> IxSet a -> [a]
toDescList _ ixset = concatMap snd (groupDescBy ixset :: [(k, [a])])
-- | 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'.
getOne :: Ord a => IxSet a -> Maybe a
getOne ixset = case toList ixset of
[x] -> Just x
_ -> Nothing
-- | Like 'getOne' with a user-provided default.
getOneOr :: Ord a => a -> IxSet a -> a
getOneOr def = fromMaybe def . getOne
-- | Return 'True' if the 'IxSet' is empty, 'False' otherwise.
null :: IxSet a -> Bool
null (IxSet (Ix ix _:_)) = Map.null ix
null (IxSet []) = True
-- set operations
-- | An infix 'intersection' operation.
(&&&) :: (Ord a, Typeable a, Indexable a) => IxSet a -> IxSet a -> IxSet a
(&&&) = intersection
-- | An infix 'union' operation.
(|||) :: (Ord a, Typeable a, Indexable a) => IxSet a -> IxSet a -> IxSet a
(|||) = union
infixr 5 &&&
infixr 5 |||
-- | Takes the union of the two 'IxSet's.
union :: (Ord a, Typeable a, Indexable a) => IxSet a -> IxSet a -> IxSet a
union (IxSet x1) (IxSet x2) = IxSet indexes'
where
indexes' = zipWith union' x1 x2
union' (Ix a f) (Ix b _) =
case cast b of
Nothing -> error "IxSet.union: indexes out of order"
Just b' -> Ix (Ix.union a b') f
-- | Takes the intersection of the two 'IxSet's.
intersection :: (Ord a, Typeable a, Indexable a) => IxSet a -> IxSet a -> IxSet a
intersection (IxSet x1) (IxSet x2) = IxSet indexes'
where
indexes' = zipWith intersection' x1 x2
intersection' (Ix a f) (Ix b _) =
case cast b of
Nothing -> error "IxSet.intersection: indexes out of order"
Just b' -> Ix (Ix.intersection a b') f
-- query operators
-- | Infix version of 'getEQ'.
(@=) :: (Indexable a, Typeable a, Ord a, Typeable k)
=> IxSet a -> k -> IxSet a
ix @= v = getEQ v ix
-- | Infix version of 'getLT'.
(@<) :: (Indexable a, Typeable a, Ord a, Typeable k)
=> IxSet a -> k -> IxSet a
ix @< v = getLT v ix
-- | Infix version of 'getGT'.
(@>) :: (Indexable a, Typeable a, Ord a, Typeable k)
=> IxSet a -> k -> IxSet a
ix @> v = getGT v ix
-- | Infix version of 'getLTE'.
(@<=) :: (Indexable a, Typeable a, Ord a, Typeable k)
=> IxSet a -> k -> IxSet a
ix @<= v = getLTE v ix
-- | Infix version of 'getGTE'.
(@>=) :: (Indexable a, Typeable a, Ord a, Typeable k)
=> IxSet a -> k -> IxSet a
ix @>= v = getGTE v ix
-- | Returns the subset with indexes in the open interval (k,k).
(@><) :: (Indexable a, Typeable a, Ord a, Typeable k)
=> IxSet a -> (k, k) -> IxSet a
ix @>< (v1,v2) = getLT v2 $ getGT v1 ix
-- | Returns the subset with indexes in [k,k).
(@>=<) :: (Indexable a, Typeable a, Ord a, Typeable k)
=> IxSet a -> (k, k) -> IxSet a
ix @>=< (v1,v2) = getLT v2 $ getGTE v1 ix
-- | Returns the subset with indexes in (k,k].
(@><=) :: (Indexable a, Typeable a, Ord a, Typeable k)
=> IxSet a -> (k, k) -> IxSet a
ix @><= (v1,v2) = getLTE v2 $ getGT v1 ix
-- | Returns the subset with indexes in [k,k].
(@>=<=) :: (Indexable a, Typeable a, Ord a, Typeable k)
=> IxSet a -> (k, k) -> IxSet a
ix @>=<= (v1,v2) = getLTE v2 $ getGTE v1 ix
-- | Creates the subset that has an index in the provided list.
(@+) :: (Indexable a, Typeable a, Ord a, Typeable k)
=> IxSet a -> [k] -> IxSet a
ix @+ list = List.foldl' union empty $ map (ix @=) list
-- | Creates the subset that matches all the provided indexes.
(@*) :: (Indexable a, Typeable a, Ord a, Typeable k)
=> IxSet a -> [k] -> IxSet a
ix @* list = List.foldl' intersection ix $ map (ix @=) list
-- | 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.
getEQ :: (Indexable a, Typeable a, Ord a, Typeable k)
=> k -> IxSet a -> IxSet a
getEQ = getOrd EQ
-- | 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.
getLT :: (Indexable a, Typeable a, Ord a, Typeable k)
=> k -> IxSet a -> IxSet a
getLT = getOrd LT
-- | 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.
getGT :: (Indexable a, Typeable a, Ord a, Typeable k)
=> k -> IxSet a -> IxSet a
getGT = getOrd GT
-- | 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.
getLTE :: (Indexable a, Typeable a, Ord a, Typeable k)
=> k -> IxSet a -> IxSet a
getLTE = getOrd2 True True False
-- | 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.
getGTE :: (Indexable a, Typeable a, Ord a, Typeable k)
=> k -> IxSet a -> IxSet a
getGTE = getOrd2 False True True
-- | 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.
getRange :: (Indexable a, Typeable k, Ord a, Typeable a)
=> k -> k -> IxSet a -> IxSet a
getRange k1 k2 ixset = getGTE k1 (getLT k2 ixset)
-- | Returns lists of elements paired with the indexes determined by
-- type inference.
groupBy :: (Typeable k,Typeable t) => IxSet t -> [(k, [t])]
groupBy (IxSet indexes) = collect indexes
where
collect [] = [] -- FIXME: should be an error
collect (Ix index _:is) = maybe (collect is) f (cast index)
f = map (second Set.toList) . Map.toList
-- | 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.
groupAscBy :: (Typeable k,Typeable t) => IxSet t -> [(k, [t])]
groupAscBy (IxSet indexes) = collect indexes
where
collect [] = [] -- FIXME: should be an error
collect (Ix index _:is) = maybe (collect is) f (cast index)
f = map (second Set.toAscList) . Map.toAscList
-- | 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]'.
groupDescBy :: (Typeable k,Typeable t) => IxSet t -> [(k, [t])]
groupDescBy (IxSet indexes) = collect indexes
where
collect [] = [] -- FIXME: should be an error
collect (Ix index _:is) = maybe (collect is) f (cast index)
f = map (second Set.toAscList) . Map.toDescList
--query impl function
-- | A function for building up selectors on 'IxSet's. Used in the
-- various get* functions. The set must be indexed over key type,
-- doing otherwise results in runtime error.
getOrd :: (Indexable a, Ord a, Typeable a, Typeable k)
=> Ordering -> k -> IxSet a -> IxSet a
getOrd LT = getOrd2 True False False
getOrd EQ = getOrd2 False True False
getOrd GT = getOrd2 False False True
-- | A function for building up selectors on 'IxSet's. Used in the
-- various get* functions. The set must be indexed over key type,
-- doing otherwise results in runtime error.
getOrd2 :: (Indexable a, Ord a, Typeable a, Typeable k)
=> Bool -> Bool -> Bool -> k -> IxSet a -> IxSet a
getOrd2 inclt inceq incgt v ixset@(IxSet indexes) = collect indexes
where
collect [] = error $ "IxSet: there is no index " ++ showTypeOf v ++
" in " ++ showTypeOf ixset
collect (Ix index _:is) = maybe (collect is) f $ cast v
where
f v'' = insertMapOfSets result empty
where
(lt',eq',gt') = Map.splitLookup v'' index
ltgt = Map.unionWith Set.union lt gt
result = case eq of
Just eqset -> Map.insertWith Set.union v'' eqset ltgt
Nothing -> ltgt
lt = if inclt
then lt'
else Map.empty
gt = if incgt
then gt'
else Map.empty
eq = if inceq
then eq'
else Nothing
{--
Optimization todo:
* can we avoid rebuilding the collection every time we query?
does laziness take care of everything?
* nicer operators?
* nice way to do updates that doesn't involve reinserting the entire data
* can we index on xpath rather than just type?
--}
instance (Indexable a, Typeable a, Ord a) => Monoid (IxSet a) where
mempty = empty
mappend = union
-- | 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.
stats :: (Ord a) => IxSet a -> (Int,Int,Int,Int)
stats (IxSet indexes) = (no_elements,no_indexes,no_keys,no_values)
where
no_elements = size (IxSet indexes)
no_indexes = length indexes
no_keys = sum [Map.size m | Ix m _ <- indexes]
no_values = sum [sum [Set.size s | s <- Map.elems m] | Ix m _ <- indexes]