@@ -1,48 +1,69 @@
1−{-# LANGUAGE AllowAmbiguousTypes #-}
2−{-# LANGUAGE BangPatterns #-}
3−{-# LANGUAGE DataKinds #-}
4−{-# LANGUAGE GADTs #-}
5−{-# LANGUAGE InstanceSigs #-}
6−{-# LANGUAGE KindSignatures #-}
7−{-# LANGUAGE MagicHash #-}
8−{-# LANGUAGE PolyKinds #-}
9−{-# LANGUAGE Rank2Types #-}
10−{-# LANGUAGE TypeFamilies #-}
11−{-# LANGUAGE TypeInType #-}
12−{-# LANGUAGE ViewPatterns #-}
1+{-# OPTIONS_GHC -Wno-missing-export-lists #-}
2+
3+{-# LANGUAGE AllowAmbiguousTypes #-}
4+{-# LANGUAGE BangPatterns #-}
5+{-# LANGUAGE CPP #-}
6+{-# LANGUAGE DataKinds #-}
7+{-# LANGUAGE GADTs #-}
8+{-# LANGUAGE InstanceSigs #-}
9+{-# LANGUAGE MagicHash #-}
10+{-# LANGUAGE PolyKinds #-}
11+{-# LANGUAGE Rank2Types #-}
12+{-# LANGUAGE TypeFamilies #-}
13+{-# LANGUAGE TypeInType #-}
14+{-# LANGUAGE ViewPatterns #-}
15+
16+#if __GLASGOW_HASKELL__ >= 806
17+{-# LANGUAGE QuantifiedConstraints #-}
18+#endif
1319
1420-- {-# OPTIONS_GHC -ddump-simpl -dsuppress-idinfo -dsuppress-coercions -dsuppress-type-applications -dsuppress-uniques -dsuppress-module-prefixes #-}
1521
16−-- | Internal API for 'TypeRepMap' and operations on it. The functions here do
17−-- not have any stability guarantees and can change between minor versions.
18−--
19−-- If you need to use this module for purposes other than tests,
20−-- create an issue.
21−--
22+{- |
23+Copyright: (c) 2017-2020 Kowainik
24+SPDX-License-Identifier: MPL-2.0
25+Maintainer: Kowainik <xrom.xkov@gmail.com>
26+
27+Internal API for 'TypeRepMap' and operations on it. The functions here do
28+not have any stability guarantees and can change between minor versions.
29+
30+If you need to use this module for purposes other than tests,
31+create an issue.
32+-}
33+
34+#include "MachDeps.h"
35+
2236module Data.TypeRepMap.Internal where
2337
2438import Prelude hiding (lookup)
2539
40+import Control.DeepSeq
2641import Control.Monad.ST (ST, runST)
2742import Control.Monad.Zip (mzip)
28−import Control.DeepSeq
2943import Data.Function (on)
3044import Data.Kind (Type)
45+import Data.Type.Equality ((:~:) (..), TestEquality (..))
3146import Data.List (intercalate, nubBy)
32−import Data.Primitive.Array (Array, MutableArray, indexArray, mapArray', readArray, sizeofArray,
47+import Data.Maybe (fromMaybe)
48+import Data.Primitive.Array (Array, MutableArray, indexArray, mapArray', sizeofArray,
3349 thawArray, unsafeFreezeArray, writeArray)
34−import Data.Primitive.PrimArray (PrimArray, indexPrimArray, sizeofPrimArray)
35−import Data.Semigroup (Semigroup (..))
50+import Data.Primitive.PrimArray (writePrimArray, newPrimArray, unsafeFreezePrimArray, primArrayToList, MutablePrimArray, primArrayFromListN, PrimArray, indexPrimArray, sizeofPrimArray)
51+import Data.Semigroup (Semigroup (..), All(..))
3652import GHC.Base (Any, Int (..), Int#, (*#), (+#), (<#))
3753import GHC.Exts (IsList (..), inline, sortWith)
3854import GHC.Fingerprint (Fingerprint (..))
55+#if WORD_SIZE_IN_BITS >= 64
3956import GHC.Prim (eqWord#, ltWord#)
57+#else
58+import GHC.IntWord64 (eqWord64#, ltWord64#)
59+#define eqWord eqWord64
60+#define ltWord ltWord64
61+#endif
4062import GHC.Word (Word64 (..))
4163import Type.Reflection (SomeTypeRep (..), TypeRep, Typeable, typeRep, withTypeable)
4264import Type.Reflection.Unsafe (typeRepFingerprint)
4365import Unsafe.Coerce (unsafeCoerce)
4466
45−import qualified Data.Map.Strict as Map
4667import qualified GHC.Exts as GHC (fromList, toList)
4768
4869{- |
@@ -97,6 +118,31 @@ instance Monoid (TypeRepMap f) where
97118 {-# INLINE mempty #-}
98119 {-# INLINE mappend #-}
99120
121+#if __GLASGOW_HASKELL__ >= 806
122+instance (forall a. Typeable a => Eq (f a)) => Eq (TypeRepMap f) where
123+ tm1 == tm2 = size tm1 == size tm2 && go 0
124+ where
125+ go :: Int -> Bool
126+ go i
127+ | i == size tm1 = True
128+ | otherwise = case testEquality tr1i tr2i of
129+ Nothing -> False
130+ Just Refl -> repEq tr1i (fromAny tv1i) (fromAny tv2i) && go (i + 1)
131+ where
132+ tr1i :: TypeRep x
133+ tr1i = anyToTypeRep $ indexArray (trKeys tm1) i
134+
135+ tr2i :: TypeRep y
136+ tr2i = anyToTypeRep $ indexArray (trKeys tm2) i
137+
138+ tv1i, tv2i :: Any
139+ tv1i = indexArray (trAnys tm1) i
140+ tv2i = indexArray (trAnys tm2) i
141+
142+ repEq :: TypeRep x -> f x -> f x -> Bool
143+ repEq tr = withTypeable tr (==)
144+#endif
145+
100146-- | Returns the list of 'Fingerprint's from 'TypeRepMap'.
101147toFingerprints :: TypeRepMap f -> [Fingerprint]
102148toFingerprints TypeRepMap{..} =
@@ -123,33 +169,49 @@ prop> member @a (one (x :: f a)) == True
123169
124170-}
125171one :: forall a f . Typeable a => f a -> TypeRepMap f
126−one x = insert x empty
172+one x = TypeRepMap (primArrayFromListN 1 [fa])
173+ (primArrayFromListN 1 [fb])
174+ (pure @Array v)
175+ (pure @Array k)
176+ where
177+ (Fingerprint fa fb, v, k) = (calcFp @a, toAny x, unsafeCoerce $ typeRep @a)
127178{-# INLINE one #-}
128179
129180{- |
130181
131182Insert a value into a 'TypeRepMap'.
183+TypeRepMap optimizes for fast reads rather than inserts, as a trade-off inserts are @O(n)@.
132184
133185prop> size (insert v tm) >= size tm
134186prop> member @a (insert (x :: f a) tm) == True
135187
136188-}
137189insert :: forall a f . Typeable a => f a -> TypeRepMap f -> TypeRepMap f
138−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)}
139195 where
140− tripleX :: (Fingerprint, Any, Any)
141− tripleX@(fpX, _, _) = (calcFp @a, toAny x, unsafeCoerce $ typeRep @a)
142−
143− addX :: [(Fingerprint, Any, Any)] -> [(Fingerprint, Any, Any)]
144− addX l = tripleX : deleteByFst fpX l
196+ changeAnyArr :: Int -> Array Any -> Array Any
197+ changeAnyArr i trAs = runST $ do
198+ let n = sizeofArray trAs
199+ mutArr <- thawArray trAs 0 n
200+ writeArray mutArr i $ toAny x
201+ unsafeFreezeArray mutArr
145202{-# INLINE insert #-}
146203
147204-- Extract the kind of a type. We use it to work around lack of syntax for
148205-- inferred type variables (which are not subject to type applications).
149206type KindOf (a :: k) = k
150207
208+type ArgKindOf (f :: k -> l) = k
209+
151210{- | Delete a value from a 'TypeRepMap'.
152211
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.
214+
153215prop> size (delete @a tm) <= size tm
154216prop> member @a (delete @a tm) == False
155217
@@ -162,30 +224,60 @@ False
162224True
163225-}
164226delete :: forall a (f :: KindOf a -> Type) . Typeable a => TypeRepMap f -> TypeRepMap f
165−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
166234{-# INLINE delete #-}
167235
236+deleteFirst :: (a -> Bool) -> [a] -> [a]
237+deleteFirst _ [] = []
238+deleteFirst p (x : xs) = if p x then xs else x : deleteFirst p xs
239+
168240{- |
169−Update a value at a specific key with the result of the provided function. When
170−the key is not a member of the map, the original map is returned.
241+Update a value at a specific key with the result of the provided function.
242+When the key is not a member of the map, the original map is returned.
171243
172244>>> trmap = fromList @(TypeRepMap Identity) [WrapTypeable $ Identity "a"]
173245>>> lookup @String $ adjust (fmap (++ "ww")) trmap
174246Just (Identity "aww")
175247-}
176248adjust :: forall a f . Typeable a => (f a -> f a) -> TypeRepMap f -> TypeRepMap f
177−adjust fun tr = case cachedBinarySearch (typeFp @a) (fingerprintAs tr) (fingerprintBs tr) of
178− Nothing -> tr
179− Just i -> tr {trAnys = changeAnyArr i (trAnys tr)}
249+adjust fun = alter (fmap fun)
250+{-# INLINE adjust #-}
251+
252+{- |
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.
255+
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")
262+-}
263+alter :: forall a f . Typeable a => (Maybe (f a) -> Maybe (f a)) -> TypeRepMap f -> TypeRepMap f
264+alter fun tr = case cachedBinarySearch (typeFp @a) (fingerprintAs tr) (fingerprintBs tr) of
265+ Nothing ->
266+ case (fun Nothing) of
267+ Nothing -> tr
268+ Just v -> insert v tr
269+ Just i ->
270+ case fun (Just . fromAny $ indexArray (trAnys tr) i) of
271+ Nothing -> delete @a tr
272+ Just v -> tr{trAnys = replaceAnyAt i (toAny v) (trAnys tr)}
180273 where
181− changeAnyArr :: Int -> Array Any -> Array Any
182− changeAnyArr i trAs = runST $ do
274+ replaceAnyAt :: Int -> Any -> Array Any -> Array Any
275+ replaceAnyAt i v trAs = runST $ do
183276 let n = sizeofArray trAs
184277 mutArr <- thawArray trAs 0 n
185− a <- toAny . fun . fromAny <$> readArray mutArr i
186− writeArray mutArr i a
278+ writeArray mutArr i v
187279 unsafeFreezeArray mutArr
188−{-# INLINE adjust #-}
280+{-# INLINE alter #-}
189281
190282{- | Map over the elements of a 'TypeRepMap'.
191283
@@ -219,30 +311,89 @@ hoistWithKey f (TypeRepMap as bs ans ks) = TypeRepMap as bs newAns ks
219311 withTr t = withTypeable t f
220312{-# INLINE hoistWithKey #-}
221313
222−-- | The union of two 'TypeRepMap's using a combining function.
223−unionWith :: (forall x. f x -> f x -> f x) -> TypeRepMap f -> TypeRepMap f -> TypeRepMap f
224−unionWith f m1 m2 = fromTriples
225− $ toTripleList
226− $ Map.unionWith combine
227− (fromTripleList $ toTriples m1)
228− (fromTripleList $ toTriples m2)
314+-- | The union of two 'TypeRepMap's using a combining function for conflicting entries. @O(n + m)@
315+unionWith :: forall f. (forall x. Typeable x => f x -> f x -> f x) -> TypeRepMap f -> TypeRepMap f -> TypeRepMap f
316+unionWith f ma mb = do
317+ fromSortedTriples $ mergeMaps (toSortedTriples ma) (toSortedTriples mb)
229318 where
230− combine :: (Any, Any) -> (Any, Any) -> (Any, Any)
231− combine (av, ak) (bv, _) = (toAny $ f (fromAny av) (fromAny bv), ak)
232−
233− fromTripleList :: Ord a => [(a, b, c)] -> Map.Map a (b, c)
234− fromTripleList = Map.fromList . map (\(a, b, c) -> (a, (b, c)))
235−
236− toTripleList :: Map.Map a (b, c) -> [(a, b, c)]
237− toTripleList = map (\(a, (b, c)) -> (a, b, c)) . Map.toList
319+ f' :: forall x. TypeRep x -> f x -> f x -> f x
320+ f' tr = withTypeable tr f
321+
322+ combine :: (Fingerprint, Any, Any) -> (Fingerprint, Any, Any) -> (Fingerprint, Any, Any)
323+ combine (fp, av, ak) (_, bv, _) = (fp, toAny $ f' (fromAny ak) (fromAny av) (fromAny bv), ak)
324+
325+ -- Merges two typrepmaps into a sorted, dedup'd list of triples.
326+ -- Using 'toSortedTriples' allows us to assume the triples are sorted by fingerprint,
327+ -- Given O(n) performance from 'toSortedTriples', and given that we can merge-sort in
328+ -- O(n + m) time, then can '.fromSortedTriples' back into cachedBinarySearch order in O(n + m)
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
334+ -- Merge
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
339+ -- fingerprints
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
238347{-# INLINE unionWith #-}
239348
240−-- | 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
241350-- duplicate keys are encountered, i.e. @'union' == 'unionWith' const@.
242351union :: TypeRepMap f -> TypeRepMap f -> TypeRepMap f
243352union = unionWith const
244353{-# INLINE union #-}
245354
355+-- | The 'intersection' of two 'TypeRepMap's using a combining function
356+--
357+-- @O(n + m)@
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)
361+ where
362+ f' :: forall x. TypeRep x -> f x -> f x -> f x
363+ f' tr = withTypeable tr f
364+
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)
367+
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.
371+ mergeMaps _ [] = []
372+ mergeMaps [] _ = []
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
378+ -- fingerprints
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 #-}
387+
388+-- | The intersection of two 'TypeRepMap's.
389+-- It keeps all values from the first map whose keys are present in the second.
390+--
391+-- @O(n + m)@
392+intersection :: TypeRepMap f -> TypeRepMap f -> TypeRepMap f
393+intersection = intersectionWith const
394+{-# INLINE intersection #-}
395+
396+
246397{- | Check if a value of the given type is present in a 'TypeRepMap'.
247398
248399>>> member @Char $ one (Identity 'a')
@@ -278,9 +429,22 @@ size = sizeofPrimArray . fingerprintAs
278429
279430-- | Return the list of 'SomeTypeRep' from the keys.
280431keys :: TypeRepMap f -> [SomeTypeRep]
281−keys TypeRepMap{..} = SomeTypeRep . anyToTypeRep <$> toList trKeys
432+keys = keysWith SomeTypeRep
282433{-# INLINE keys #-}
283434
435+-- | Return the list of keys by wrapping them with a user-provided function.
436+keysWith :: (forall (a :: ArgKindOf f). TypeRep a -> r) -> TypeRepMap f -> [r]
437+keysWith f TypeRepMap{..} = f . anyToTypeRep <$> toList trKeys
438+{-# INLINE keysWith #-}
439+
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
443+ where
444+ withTypeRep :: TypeRep a -> f a -> r
445+ withTypeRep tr an = withTypeable tr $ f an
446+ toF (_, an, k) = withTypeRep (unsafeCoerce k) (fromAny an)
447+
284448-- | Binary searched based on this article
285449-- http://bannalia.blogspot.com/2015/06/cache-friendly-binary-search.html
286450-- with modification for our two-vector search case.
@@ -324,8 +488,20 @@ typeFp = typeRepFingerprint $ typeRep @a
324488toTriples :: TypeRepMap f -> [(Fingerprint, Any, Any)]
325489toTriples tm = zip3 (toFingerprints tm) (GHC.toList $ trAnys tm) (GHC.toList $ trKeys tm)
326490
327−deleteByFst :: Eq a => a -> [(a, b, c)] -> [(a, b, c)]
328−deleteByFst x = filter ((/= x) . fst3)
491+-- | Efficiently get sorted triples from a map in O(n) time
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
499+ where
500+ trip i = ( Fingerprint (indexPrimArray (fingerprintAs tm) i) (indexPrimArray (fingerprintBs tm) i)
501+ , indexArray (trAnys tm) i
502+ , indexArray (trKeys tm) i)
503+ ordering :: [ Int ]
504+ ordering = generateOrderMapping (size tm)
329505
330506nubByFst :: (Eq a) => [(a, b, c)] -> [(a, b, c)]
331507nubByFst = nubBy ((==) `on` fst3)
@@ -372,19 +548,19 @@ instance IsList (TypeRepMap f) where
372548 k (WrapTypeable (_ :: f a)) = unsafeCoerce $ typeRep @a
373549
374550 toList :: TypeRepMap f -> [WrapTypeable f]
375− toList = map toWrapTypeable . toTriples
376− where
377− toWrapTypeable :: (Fingerprint, Any, Any) -> WrapTypeable f
378− toWrapTypeable (_, an, k) = withTypeable (unsafeCoerce k) $ fromAny an
551+ toList = toListWith WrapTypeable
379552
380553calcFp :: forall a . Typeable a => Fingerprint
381554calcFp = typeRepFingerprint $ typeRep @a
382555
383556fromTriples :: [(Fingerprint, Any, Any)] -> TypeRepMap f
384−fromTriples kvs = TypeRepMap (GHC.fromList fpAs) (GHC.fromList fpBs) (GHC.fromList ans) (GHC.fromList ks)
557+fromTriples = fromSortedTriples . sortWith fst3 . nubByFst
558+
559+fromSortedTriples :: [(Fingerprint, Any, Any)] -> TypeRepMap f
560+fromSortedTriples kvs = TypeRepMap (GHC.fromList fpAs) (GHC.fromList fpBs) (GHC.fromList ans) (GHC.fromList ks)
385561 where
386562 (fpAs, fpBs) = unzip $ map (\(Fingerprint a b) -> (a, b)) fps
387− (fps, ans, ks) = unzip3 $ fromSortedList $ sortWith fst3 $ nubByFst kvs
563+ (fps, ans, ks) = unzip3 $ fromSortedList kvs
388564
389565----------------------------------------------------------------------------
390566-- Tree-like conversion
@@ -410,3 +586,85 @@ fromSortedList l = runST $ do
410586 newFirst <- loop (2 * i + 1) first
411587 writeArray result i (indexArray origin newFirst)
412588 loop (2 * i + 2) (newFirst + 1)
589+
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]
593+--
594+-- >>> generateOrderMapping 6
595+-- [3,1,4,0,5,2]
596+--
597+-- >>> generateOrderMapping 8
598+-- [7,3,1,4,0,5,2,6]
599+generateOrderMapping :: Int -> [Int]
600+generateOrderMapping len = runST $ do
601+ orderMappingArr <- newPrimArray len
602+ _ <- loop orderMappingArr 0 0
603+ primArrayToList <$> unsafeFreezePrimArray orderMappingArr
604+ where
605+ loop :: MutablePrimArray s Int -> Int -> Int -> ST s Int
606+ loop result i first =
607+ if i >= len
608+ then pure first
609+ else do
610+ newFirst <- loop result (2 * i + 1) first
611+ writePrimArray result newFirst i
612+ loop result (2 * i + 2) (newFirst + 1)
613+
614+----------------------------------------------------------------------------
615+-- Helper functions.
616+----------------------------------------------------------------------------
617+
618+-- | Check that invariant of the structure holds.
619+-- The structure maintains the following invariant.
620+-- For each element @A@ at index @i@:
621+--
622+-- 1. if there is an element @B@ at index @2*i+1@,
623+-- then @B < A@.
624+--
625+-- 2. if there is an element @C@ at index @2*i+2@,
626+-- then @A < C@.
627+--
628+invariantCheck :: TypeRepMap f -> Bool
629+invariantCheck TypeRepMap{..} = getAll (check 0)
630+ where
631+ lastMay [] = Nothing
632+ lastMay [x] = Just x
633+ lastMay (_:xs) = lastMay xs
634+ sz = sizeofPrimArray fingerprintAs
635+ check i | i >= sz = All True
636+ | otherwise =
637+ let left = i*2+1
638+ right = i*2+2
639+ -- maximum value in the left branch
640+ leftMax =
641+ fmap (\j -> (indexPrimArray fingerprintAs j, indexPrimArray fingerprintBs j))
642+ $ lastMay
643+ $ takeWhile (<sz)
644+ $ iterate (\j -> j*2+2) left
645+ -- minimum value in the right branch
646+ rightMin =
647+ fmap (\j -> (indexPrimArray fingerprintAs j, indexPrimArray fingerprintBs j))
648+ $ lastMay
649+ $ takeWhile (<sz)
650+ $ iterate (\j -> j*2+1) right
651+ in mconcat
652+ [ All $
653+ if left < sz
654+ then
655+ case indexPrimArray fingerprintAs i `compare` indexPrimArray fingerprintAs left of
656+ LT -> False
657+ EQ -> indexPrimArray fingerprintBs i >= indexPrimArray fingerprintBs left
658+ GT -> True
659+ else True
660+ , All $
661+ if right < sz
662+ then
663+ case indexPrimArray fingerprintAs i `compare` indexPrimArray fingerprintAs right of
664+ LT -> True
665+ EQ -> indexPrimArray fingerprintBs i <= indexPrimArray fingerprintBs right
666+ GT -> False
667+ else True
668+ , All $ fromMaybe True $ (<=) <$> leftMax <*> rightMin
669+ , check (i+1)
670+ ]