@@ -1,10 +1,11 @@
1+{-# OPTIONS_GHC -Wno-missing-export-lists #-}
1{-# LANGUAGE AllowAmbiguousTypes #-}
3{-# LANGUAGE AllowAmbiguousTypes #-}
2{-# LANGUAGE BangPatterns #-}
4{-# LANGUAGE BangPatterns #-}
3{-# LANGUAGE CPP #-}
5{-# LANGUAGE CPP #-}
4{-# LANGUAGE DataKinds #-}
6{-# LANGUAGE DataKinds #-}
5{-# LANGUAGE GADTs #-}
7{-# LANGUAGE GADTs #-}
6{-# LANGUAGE InstanceSigs #-}
8{-# LANGUAGE InstanceSigs #-}
7−{-# LANGUAGE KindSignatures #-}
8{-# LANGUAGE MagicHash #-}
9{-# LANGUAGE MagicHash #-}
9{-# LANGUAGE PolyKinds #-}
10{-# LANGUAGE PolyKinds #-}
10{-# LANGUAGE Rank2Types #-}
11{-# LANGUAGE Rank2Types #-}
@@ -18,7 +19,12 @@
19-- {-# OPTIONS_GHC -ddump-simpl -dsuppress-idinfo -dsuppress-coercions -dsuppress-type-applications -dsuppress-uniques -dsuppress-module-prefixes #-}
20-- {-# OPTIONS_GHC -ddump-simpl -dsuppress-idinfo -dsuppress-coercions -dsuppress-type-applications -dsuppress-uniques -dsuppress-module-prefixes #-}
23+Copyright: (c) 2017-2020 Kowainik
24+SPDX-License-Identifier: MPL-2.0
25+Maintainer: Kowainik <xrom.xkov@gmail.com>
21−{- | Internal API for 'TypeRepMap' and operations on it. The functions here do
27+Internal API for 'TypeRepMap' and operations on it. The functions here do
22not have any stability guarantees and can change between minor versions.
28not have any stability guarantees and can change between minor versions.
24If you need to use this module for purposes other than tests,
30If you need to use this module for purposes other than tests,
@@ -39,9 +45,9 @@ import Data.Kind (Type)
39import Data.Type.Equality ((:~:) (..), TestEquality (..))
45import Data.Type.Equality ((:~:) (..), TestEquality (..))
40import Data.List (intercalate, nubBy)
46import Data.List (intercalate, nubBy)
41import Data.Maybe (fromMaybe)
47import Data.Maybe (fromMaybe)
42−import Data.Primitive.Array (Array, MutableArray, indexArray, mapArray', readArray, sizeofArray,
48+import Data.Primitive.Array (Array, MutableArray, indexArray, mapArray', sizeofArray,
43 thawArray, unsafeFreezeArray, writeArray)
49 thawArray, unsafeFreezeArray, writeArray)
44−import Data.Primitive.PrimArray (PrimArray, indexPrimArray, sizeofPrimArray)
50+import Data.Primitive.PrimArray (writePrimArray, newPrimArray, unsafeFreezePrimArray, primArrayToList, MutablePrimArray, primArrayFromListN, PrimArray, indexPrimArray, sizeofPrimArray)
45import Data.Semigroup (Semigroup (..), All(..))
51import Data.Semigroup (Semigroup (..), All(..))
46import GHC.Base (Any, Int (..), Int#, (*#), (+#), (<#))
52import GHC.Base (Any, Int (..), Int#, (*#), (+#), (<#))
47import GHC.Exts (IsList (..), inline, sortWith)
53import GHC.Exts (IsList (..), inline, sortWith)
@@ -58,7 +64,6 @@ import Type.Reflection (SomeTypeRep (..), TypeRep, Typeable, typeRep, withTypeab
58import Type.Reflection.Unsafe (typeRepFingerprint)
64import Type.Reflection.Unsafe (typeRepFingerprint)
59import Unsafe.Coerce (unsafeCoerce)
65import Unsafe.Coerce (unsafeCoerce)
61−import qualified Data.Map.Strict as Map
62import qualified GHC.Exts as GHC (fromList, toList)
67import qualified GHC.Exts as GHC (fromList, toList)
@@ -164,33 +169,49 @@ prop> member @a (one (x :: f a)) == True
166one :: forall a f . Typeable a => f a -> TypeRepMap f
171one :: forall a f . Typeable a => f a -> TypeRepMap f
167−one x = insert x empty
172+one x = TypeRepMap (primArrayFromListN 1 [fa])
173+ (primArrayFromListN 1 [fb])
177+ (Fingerprint fa fb, v, k) = (calcFp @a, toAny x, unsafeCoerce $ typeRep @a)
168{-# INLINE one #-}
178{-# INLINE one #-}
172Insert a value into a 'TypeRepMap'.
182Insert a value into a 'TypeRepMap'.
183+TypeRepMap optimizes for fast reads rather than inserts, as a trade-off inserts are @O(n)@.
174prop> size (insert v tm) >= size tm
185prop> size (insert v tm) >= size tm
175prop> member @a (insert (x :: f a) tm) == True
186prop> member @a (insert (x :: f a) tm) == True
178insert :: forall a f . Typeable a => f a -> TypeRepMap f -> TypeRepMap f
189insert :: forall a f . Typeable a => f a -> TypeRepMap f -> TypeRepMap f
179−insert x = fromTriples . addX . toTriples
190+insert x m
191+ | size m == 0 = one x
192+ | otherwise = case cachedBinarySearch (typeFp @a) (fingerprintAs m) (fingerprintBs m) of
193+ Nothing -> union m $ one x
194+ Just i -> m {trAnys = changeAnyArr i (trAnys m)}
181− tripleX :: (Fingerprint, Any, Any)
196+ changeAnyArr :: Int -> Array Any -> Array Any
182− tripleX@(fpX, _, _) = (calcFp @a, toAny x, unsafeCoerce $ typeRep @a)
197+ changeAnyArr i trAs = runST $ do
183−
198+ let n = sizeofArray trAs
184− addX :: [(Fingerprint, Any, Any)] -> [(Fingerprint, Any, Any)]
199+ mutArr <- thawArray trAs 0 n
185− addX l = tripleX : deleteByFst fpX l
200+ writeArray mutArr i $ toAny x
201+ unsafeFreezeArray mutArr
186{-# INLINE insert #-}
202{-# INLINE insert #-}
188-- Extract the kind of a type. We use it to work around lack of syntax for
204-- Extract the kind of a type. We use it to work around lack of syntax for
189-- inferred type variables (which are not subject to type applications).
205-- inferred type variables (which are not subject to type applications).
190type KindOf (a :: k) = k
206type KindOf (a :: k) = k
208+type ArgKindOf (f :: k -> l) = k
192{- | Delete a value from a 'TypeRepMap'.
210{- | Delete a value from a 'TypeRepMap'.
212+TypeRepMap optimizes for fast reads rather than modifications, as a trade-off deletes are
213+@O(n)@, with an @O(log(n))@ optimization for when the element is already missing.
194prop> size (delete @a tm) <= size tm
215prop> size (delete @a tm) <= size tm
195prop> member @a (delete @a tm) == False
216prop> member @a (delete @a tm) == False
@@ -203,30 +224,60 @@ False
205delete :: forall a (f :: KindOf a -> Type) . Typeable a => TypeRepMap f -> TypeRepMap f
226delete :: forall a (f :: KindOf a -> Type) . Typeable a => TypeRepMap f -> TypeRepMap f
206−delete = fromTriples . deleteByFst (typeFp @a) . toTriples
227+delete m
228+ -- Lookups are fast, so check if we even have the element first.
229+ | not (member @a m) = m
230+ -- We know we have the element, If the map has exactly one element, we can return the empty map
231+ | size m == 1 = empty
232+ -- Otherwise, filter out the element in linear time.
233+ | otherwise = fromSortedTriples . deleteFirst ((== typeFp @a) . fst3) . toSortedTriples $ m
207{-# INLINE delete #-}
234{-# INLINE delete #-}
236+deleteFirst :: (a -> Bool) -> [a] -> [a]
237+deleteFirst _ [] = []
238+deleteFirst p (x : xs) = if p x then xs else x : deleteFirst p xs
210−Update a value at a specific key with the result of the provided function. When
241+Update a value at a specific key with the result of the provided function.
211−the key is not a member of the map, the original map is returned.
242+When the key is not a member of the map, the original map is returned.
213>>> trmap = fromList @(TypeRepMap Identity) [WrapTypeable $ Identity "a"]
244>>> trmap = fromList @(TypeRepMap Identity) [WrapTypeable $ Identity "a"]
214>>> lookup @String $ adjust (fmap (++ "ww")) trmap
245>>> lookup @String $ adjust (fmap (++ "ww")) trmap
215Just (Identity "aww")
246Just (Identity "aww")
217adjust :: forall a f . Typeable a => (f a -> f a) -> TypeRepMap f -> TypeRepMap f
248adjust :: forall a f . Typeable a => (f a -> f a) -> TypeRepMap f -> TypeRepMap f
249+adjust fun = alter (fmap fun)
250+{-# INLINE adjust #-}
253+Updates a value at a specific key, whether or not it exists.
254+This can be used to insert, delete, or update a value of a given type in the map.
256+>>> func = (\case Nothing -> Just (Identity "new"); Just (Identity s) -> Just (Identity (reverse s)))
257+>>> lookup @String $ alter func empty
258+Just (Identity "new")
259+>>> trmap = fromList @(TypeRepMap Identity) [WrapTypeable $ Identity "helllo"]
260+>>> lookup @String $ alter func trmap
261+>>> Just (Identity "olleh")
263+alter :: forall a f . Typeable a => (Maybe (f a) -> Maybe (f a)) -> TypeRepMap f -> TypeRepMap f
218−adjust fun tr = case cachedBinarySearch (typeFp @a) (fingerprintAs tr) (fingerprintBs tr) of
264+alter fun tr = case cachedBinarySearch (typeFp @a) (fingerprintAs tr) (fingerprintBs tr) of
219− Nothing -> tr
265+ Nothing ->
266+ case (fun Nothing) of
268+ Just v -> insert v tr
270+ case fun (Just . fromAny $ indexArray (trAnys tr) i) of
271+ Nothing -> delete @a tr
220− Just i -> tr {trAnys = changeAnyArr i (trAnys tr)}
272+ Just v -> tr{trAnys = replaceAnyAt i (toAny v) (trAnys tr)}
222− changeAnyArr :: Int -> Array Any -> Array Any
274+ replaceAnyAt :: Int -> Any -> Array Any -> Array Any
223− changeAnyArr i trAs = runST $ do
275+ replaceAnyAt i v trAs = runST $ do
224 let n = sizeofArray trAs
276 let n = sizeofArray trAs
225 mutArr <- thawArray trAs 0 n
277 mutArr <- thawArray trAs 0 n
226− a <- toAny . fun . fromAny <$> readArray mutArr i
227− writeArray mutArr i a
278+ writeArray mutArr i v
228 unsafeFreezeArray mutArr
279 unsafeFreezeArray mutArr
229−{-# INLINE adjust #-}
280+{-# INLINE alter #-}
231{- | Map over the elements of a 'TypeRepMap'.
282{- | Map over the elements of a 'TypeRepMap'.
@@ -260,33 +311,89 @@ hoistWithKey f (TypeRepMap as bs ans ks) = TypeRepMap as bs newAns ks
260 withTr t = withTypeable t f
311 withTr t = withTypeable t f
261{-# INLINE hoistWithKey #-}
312{-# INLINE hoistWithKey #-}
263−-- | The union of two 'TypeRepMap's using a combining function.
314+-- | The union of two 'TypeRepMap's using a combining function for conflicting entries. @O(n + m)@
264unionWith :: forall f. (forall x. Typeable x => f x -> f x -> f x) -> TypeRepMap f -> TypeRepMap f -> TypeRepMap f
315unionWith :: forall f. (forall x. Typeable x => f x -> f x -> f x) -> TypeRepMap f -> TypeRepMap f -> TypeRepMap f
265−unionWith f m1 m2 = fromTriples
316+unionWith f ma mb = do
266− $ toTripleList
317+ fromSortedTriples $ mergeMaps (toSortedTriples ma) (toSortedTriples mb)
267− $ Map.unionWith combine
268− (fromTripleList $ toTriples m1)
269− (fromTripleList $ toTriples m2)
271 f' :: forall x. TypeRep x -> f x -> f x -> f x
319 f' :: forall x. TypeRep x -> f x -> f x -> f x
272 f' tr = withTypeable tr f
320 f' tr = withTypeable tr f
274− combine :: (Any, Any) -> (Any, Any) -> (Any, Any)
322+ combine :: (Fingerprint, Any, Any) -> (Fingerprint, Any, Any) -> (Fingerprint, Any, Any)
275− combine (av, ak) (bv, _) = (toAny $ f' (fromAny ak) (fromAny av) (fromAny bv), ak)
323+ combine (fp, av, ak) (_, bv, _) = (fp, toAny $ f' (fromAny ak) (fromAny av) (fromAny bv), ak)
277− fromTripleList :: Ord a => [(a, b, c)] -> Map.Map a (b, c)
325+ -- Merges two typrepmaps into a sorted, dedup'd list of triples.
278− fromTripleList = Map.fromList . map (\(a, b, c) -> (a, (b, c)))
326+ -- Using 'toSortedTriples' allows us to assume the triples are sorted by fingerprint,
279−
327+ -- Given O(n) performance from 'toSortedTriples', and given that we can merge-sort in
280− toTripleList :: Map.Map a (b, c) -> [(a, b, c)]
328+ -- O(n + m) time, then can '.fromSortedTriples' back into cachedBinarySearch order in O(n + m)
281− toTripleList = map (\(a, (b, c)) -> (a, b, c)) . Map.toList
329+ -- that gives a total of O(n + m).
330+ mergeMaps :: [(Fingerprint, Any, Any)] -> [(Fingerprint, Any, Any)] -> [(Fingerprint, Any, Any)]
331+ -- We've addressed all elements from both maps
332+ mergeMaps as [] = as
333+ mergeMaps [] bs = bs
335+ mergeMaps (a@(af, _, _) : as) (b@(bf, _, _) : bs) =
336+ case compare af bf of
337+ -- Fingerprints are equal, union the elements using our function
338+ -- If the incoming maps were de-duped, there shouldn't be any other equivalent
340+ EQ -> combine a b : mergeMaps as bs
341+ -- First fingerprint must not be in the second map or we would have seen it by now
342+ -- Add it to the result as-is
343+ LT -> a : mergeMaps as (b : bs)
344+ -- Second fingerprint must not be in the first map or we would have seen it by now
345+ -- Add it to the result as-is
346+ GT -> b : mergeMaps (a:as) bs
282{-# INLINE unionWith #-}
347{-# INLINE unionWith #-}
284−-- | The (left-biased) union of two 'TypeRepMap's. It prefers the first map when
349+-- | The (left-biased) union of two 'TypeRepMap's in @O(n + m)@. It prefers the first map when
285-- duplicate keys are encountered, i.e. @'union' == 'unionWith' const@.
350-- duplicate keys are encountered, i.e. @'union' == 'unionWith' const@.
286union :: TypeRepMap f -> TypeRepMap f -> TypeRepMap f
351union :: TypeRepMap f -> TypeRepMap f -> TypeRepMap f
287union = unionWith const
352union = unionWith const
288{-# INLINE union #-}
353{-# INLINE union #-}
355+-- | The 'intersection' of two 'TypeRepMap's using a combining function
358+intersectionWith :: forall f. (forall x. Typeable x => f x -> f x -> f x) -> TypeRepMap f -> TypeRepMap f -> TypeRepMap f
359+intersectionWith f ma mb =
360+ fromSortedTriples $ mergeMaps (toSortedTriples ma) (toSortedTriples mb)
362+ f' :: forall x. TypeRep x -> f x -> f x -> f x
363+ f' tr = withTypeable tr f
365+ combine :: (Fingerprint, Any, Any) -> (Fingerprint, Any, Any) -> (Fingerprint, Any, Any)
366+ combine (fp, av, ak) (_, bv, _) = (fp, toAny $ f' (fromAny ak) (fromAny av) (fromAny bv), ak)
368+ -- Merges two typrepmaps into a sorted, dedup'd list of triples.
369+ mergeMaps :: [(Fingerprint, Any, Any)] -> [(Fingerprint, Any, Any)] -> [(Fingerprint, Any, Any)]
370+ -- If either list is empty, the intersection must be finished.
373+ -- Merge the two maps considering one element at a time.
374+ mergeMaps (a@(af, _, _) : as) (b@(bf, _, _) : bs) =
375+ case compare af bf of
376+ -- Fingerprints are equal, union the elements using our function
377+ -- If the incoming maps were de-duped, there shouldn't be any other equivalent
379+ EQ -> combine a b : mergeMaps as bs
380+ -- First fingerprint must not be in the second map or we would have seen it by now
381+ -- Skip it an move on
382+ LT -> mergeMaps as (b : bs)
383+ -- Second fingerprint must not be in the first map or we would have seen it by now
384+ -- Skip it an move on
385+ GT -> mergeMaps (a:as) bs
386+{-# INLINE intersectionWith #-}
388+-- | The intersection of two 'TypeRepMap's.
389+-- It keeps all values from the first map whose keys are present in the second.
392+intersection :: TypeRepMap f -> TypeRepMap f -> TypeRepMap f
393+intersection = intersectionWith const
394+{-# INLINE intersection #-}
290{- | Check if a value of the given type is present in a 'TypeRepMap'.
397{- | Check if a value of the given type is present in a 'TypeRepMap'.
292>>> member @Char $ one (Identity 'a')
399>>> member @Char $ one (Identity 'a')
@@ -322,9 +429,22 @@ size = sizeofPrimArray . fingerprintAs
323-- | Return the list of 'SomeTypeRep' from the keys.
430-- | Return the list of 'SomeTypeRep' from the keys.
324keys :: TypeRepMap f -> [SomeTypeRep]
431keys :: TypeRepMap f -> [SomeTypeRep]
325−keys TypeRepMap{..} = SomeTypeRep . anyToTypeRep <$> toList trKeys
432+keys = keysWith SomeTypeRep
326{-# INLINE keys #-}
433{-# INLINE keys #-}
435+-- | Return the list of keys by wrapping them with a user-provided function.
436+keysWith :: (forall (a :: ArgKindOf f). TypeRep a -> r) -> TypeRepMap f -> [r]
437+keysWith f TypeRepMap{..} = f . anyToTypeRep <$> toList trKeys
438+{-# INLINE keysWith #-}
440+-- | Return the list of key-value pairs by wrapping them with a user-provided function.
441+toListWith :: forall f r. (forall (a :: ArgKindOf f). Typeable a => f a -> r) -> TypeRepMap f -> [r]
442+toListWith f = map toF . toTriples
444+ withTypeRep :: TypeRep a -> f a -> r
445+ withTypeRep tr an = withTypeable tr $ f an
446+ toF (_, an, k) = withTypeRep (unsafeCoerce k) (fromAny an)
328-- | Binary searched based on this article
448-- | Binary searched based on this article
329-- http://bannalia.blogspot.com/2015/06/cache-friendly-binary-search.html
449-- http://bannalia.blogspot.com/2015/06/cache-friendly-binary-search.html
330-- with modification for our two-vector search case.
450-- with modification for our two-vector search case.
@@ -368,8 +488,20 @@ typeFp = typeRepFingerprint $ typeRep @a
368toTriples :: TypeRepMap f -> [(Fingerprint, Any, Any)]
488toTriples :: TypeRepMap f -> [(Fingerprint, Any, Any)]
369toTriples tm = zip3 (toFingerprints tm) (GHC.toList $ trAnys tm) (GHC.toList $ trKeys tm)
489toTriples tm = zip3 (toFingerprints tm) (GHC.toList $ trAnys tm) (GHC.toList $ trKeys tm)
371−deleteByFst :: Eq a => a -> [(a, b, c)] -> [(a, b, c)]
491+-- | Efficiently get sorted triples from a map in O(n) time
372−deleteByFst x = filter ((/= x) . fst3)
492+--
493+-- We assume the incoming TypeRepMap is already sorted into 'cachedBinarySearch' order using fromSortedList.
494+-- Then we can construct the index mapping from the "cached" ordering into monotonically
495+-- increasing order using 'generateOrderMapping' with the length of the TRM. This takes @O(n).
496+-- We then pull those indexes from the source TRM to get the sorted triples in a total of @O(n).
497+toSortedTriples :: TypeRepMap f -> [(Fingerprint, Any, Any)]
498+toSortedTriples tm = trip <$> ordering
500+ trip i = ( Fingerprint (indexPrimArray (fingerprintAs tm) i) (indexPrimArray (fingerprintBs tm) i)
501+ , indexArray (trAnys tm) i
502+ , indexArray (trKeys tm) i)
504+ ordering = generateOrderMapping (size tm)
374nubByFst :: (Eq a) => [(a, b, c)] -> [(a, b, c)]
506nubByFst :: (Eq a) => [(a, b, c)] -> [(a, b, c)]
375nubByFst = nubBy ((==) `on` fst3)
507nubByFst = nubBy ((==) `on` fst3)
@@ -389,9 +521,6 @@ data WrapTypeable f where
389instance Show (WrapTypeable f) where
521instance Show (WrapTypeable f) where
390 show (WrapTypeable (_ :: f a)) = show $ calcFp @a
522 show (WrapTypeable (_ :: f a)) = show $ calcFp @a
392−wrapTypeable :: TypeRep a -> f a -> WrapTypeable f
393−wrapTypeable tr = withTypeable tr WrapTypeable
397prop> fromList . toList == 'id'
526prop> fromList . toList == 'id'
@@ -419,19 +548,19 @@ instance IsList (TypeRepMap f) where
419 k (WrapTypeable (_ :: f a)) = unsafeCoerce $ typeRep @a
548 k (WrapTypeable (_ :: f a)) = unsafeCoerce $ typeRep @a
421 toList :: TypeRepMap f -> [WrapTypeable f]
550 toList :: TypeRepMap f -> [WrapTypeable f]
422− toList = map toWrapTypeable . toTriples
551+ toList = toListWith WrapTypeable
424− toWrapTypeable :: (Fingerprint, Any, Any) -> WrapTypeable f
425− toWrapTypeable (_, an, k) = wrapTypeable (unsafeCoerce k) (fromAny an)
427calcFp :: forall a . Typeable a => Fingerprint
553calcFp :: forall a . Typeable a => Fingerprint
428calcFp = typeRepFingerprint $ typeRep @a
554calcFp = typeRepFingerprint $ typeRep @a
430fromTriples :: [(Fingerprint, Any, Any)] -> TypeRepMap f
556fromTriples :: [(Fingerprint, Any, Any)] -> TypeRepMap f
557+fromTriples = fromSortedTriples . sortWith fst3 . nubByFst
559+fromSortedTriples :: [(Fingerprint, Any, Any)] -> TypeRepMap f
431−fromTriples kvs = TypeRepMap (GHC.fromList fpAs) (GHC.fromList fpBs) (GHC.fromList ans) (GHC.fromList ks)
560+fromSortedTriples kvs = TypeRepMap (GHC.fromList fpAs) (GHC.fromList fpBs) (GHC.fromList ans) (GHC.fromList ks)
433 (fpAs, fpBs) = unzip $ map (\(Fingerprint a b) -> (a, b)) fps
562 (fpAs, fpBs) = unzip $ map (\(Fingerprint a b) -> (a, b)) fps
434− (fps, ans, ks) = unzip3 $ fromSortedList $ sortWith fst3 $ nubByFst kvs
563+ (fps, ans, ks) = unzip3 $ fromSortedList kvs
436----------------------------------------------------------------------------
565----------------------------------------------------------------------------
437-- Tree-like conversion
566-- Tree-like conversion
@@ -458,18 +587,42 @@ fromSortedList l = runST $ do
458 writeArray result i (indexArray origin newFirst)
587 writeArray result i (indexArray origin newFirst)
459 loop (2 * i + 2) (newFirst + 1)
588 loop (2 * i + 2) (newFirst + 1)
590+-- Returns a list of indexes which represents the "sorted" order of an array generated by
591+-- fromSortedList of the provided length.
592+-- I.e. fmap (fromSortedList [1, 2, 3, 4, 5, 6] !!) (generateOrderMapping 6) == [1, 2, 3, 4, 5, 6]
594+-- >>> generateOrderMapping 6
597+-- >>> generateOrderMapping 8
599+generateOrderMapping :: Int -> [Int]
600+generateOrderMapping len = runST $ do
601+ orderMappingArr <- newPrimArray len
602+ _ <- loop orderMappingArr 0 0
603+ primArrayToList <$> unsafeFreezePrimArray orderMappingArr
605+ loop :: MutablePrimArray s Int -> Int -> Int -> ST s Int
606+ loop result i first =
610+ newFirst <- loop result (2 * i + 1) first
611+ writePrimArray result newFirst i
612+ loop result (2 * i + 2) (newFirst + 1)
461----------------------------------------------------------------------------
614----------------------------------------------------------------------------
462-- Helper functions.
615-- Helper functions.
463----------------------------------------------------------------------------
616----------------------------------------------------------------------------
465−-- | Check that invariant of the structure is hold.
618+-- | Check that invariant of the structure holds.
466-- The structure maintains the following invariant.
619-- The structure maintains the following invariant.
467-- For each element @A@ at index @i@:
620-- For each element @A@ at index @i@:
469−-- 1. if there is an element @B@ at index @2*i+1@,
622+-- 1. if there is an element @B@ at index @2*i+1@,
470-- then @B < A@.
623-- then @B < A@.
472−-- 2. if there is an element @C@ at index @2*i+2@,
625+-- 2. if there is an element @C@ at index @2*i+2@,
473-- then @A < C@.
626-- then @A < C@.
475invariantCheck :: TypeRepMap f -> Bool
628invariantCheck :: TypeRepMap f -> Bool
@@ -515,4 +668,3 @@ invariantCheck TypeRepMap{..} = getAll (check 0)
515 , All $ fromMaybe True $ (<=) <$> leftMax <*> rightMin
668 , All $ fromMaybe True $ (<=) <$> leftMax <*> rightMin
516 , check (i+1)
669 , check (i+1)