355 lines
9.1 KiB
Elm
355 lines
9.1 KiB
Elm
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module Dict (empty,singleton,insert
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,lookup,findWithDefault
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,remove,member
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,foldl,foldr,map
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,union,intersect,diff
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,keys,values
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,toList,fromList
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) where
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import Maybe (isJust)
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data NColor = Red | Black
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data RBTree k v = RBNode NColor k v (RBTree k v) (RBTree k v) | RBEmpty
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empty = RBEmpty
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raise = console.log
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{-- Helpers for checking invariants
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-- Check that the tree has an equal number of black nodes on each path
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equal_pathLen t =
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let path_numBlacks t =
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case t of
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{ RBEmpty -> 1
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; RBNode col _ _ l r ->
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let { bl = path_numBlacks l ; br = path_numBlacks r } in
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if bl /= br || bl == 0-1 || br == 0-1
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then 0-1
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else bl + (if col == Red then 0 else 1)
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}
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in 0-1 /= path_numBlacks t
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rootBlack t =
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case t of
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{ RBEmpty -> True
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; RBNode Black _ _ _ _ -> True
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; _ -> False }
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redBlack_children t =
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case t of
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{ RBNode Red _ _ (RBNode Red _ _ _ _) _ -> False
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; RBNode Red _ _ _ (RBNode Red _ _ _ _) -> False
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; RBEmpty -> True
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; RBNode _ _ _ l r -> redBlack_children l && redBlack_children r
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}
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findExtreme f t =
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case t of
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{ RBEmpty -> Nothing
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; RBNode c k _ l r ->
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case findExtreme f (f (l,r)) of
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{ Nothing -> Just k
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; Just k' -> Just k' }
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}
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findminRbt t = findExtreme fst t
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findmaxRbt t = findExtreme snd t
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-- "Option LT than"
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-- Returns True if either xo or yo is Nothing
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-- Otherwise returns the result of comparing the values using f
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optionRelation f u xo yo =
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case (xo,yo) of
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{ (Nothing,_) -> u
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; (_,Nothing) -> u
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; (Just x, Just y) -> f x y }
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olt xo yo = optionRelation (< ) True xo yo
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olte xo yo = optionRelation (<=) True xo yo
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ordered t =
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case t of
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{ RBEmpty -> True
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; RBNode c k v l r ->
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let (lmax,rmin) = (findmaxRbt l, findminRbt r) in
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olte lmax (Just k) && olte (Just k) rmin && ordered l && ordered r
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}
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-- Check that there aren't any right red nodes in the tree *)
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leftLeaning t =
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case t of
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{ RBEmpty -> True
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; RBNode _ _ _ (RBNode Black _ _ _ _) (RBNode Red _ _ _ _) -> False
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; RBNode _ _ _ RBEmpty (RBNode Red _ _ _ _) -> False
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; RBNode _ _ _ l r -> (leftLeaning l) && (leftLeaning r)
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}
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invariants_hold t =
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ordered t && rootBlack t && redBlack_children t &&
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equal_pathLen t && leftLeaning t
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--** End invariant helpers *****
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--}
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min t =
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case t of
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{ RBNode _ k v RBEmpty _ -> (k,v)
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; RBNode _ _ _ l _ -> min l
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; RBEmpty -> raise "(min RBEmpty) is not defined"
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}
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{--
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max t =
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case t of
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{ RBNode _ k v _ RBEmpty -> (k,v)
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; RBNode _ _ _ _ r -> max r
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; RBEmpty -> raise "(max RBEmpty) is not defined"
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}
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--}
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lookup k t =
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case t of
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{ RBEmpty -> Nothing
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; RBNode _ k' v l r ->
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case compare k k' of
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{ LT -> lookup k l
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; EQ -> Just v
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; GT -> lookup k r }
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}
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findWithDefault base k t =
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case t of
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{ RBEmpty -> base
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; RBNode _ k' v l r ->
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case compare k k' of
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{ LT -> findWithDefault base k l
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; EQ -> v
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; GT -> findWithDefault base k r }
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}
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{--
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find k t =
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case t of
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{ RBEmpty -> raise "Key was not found in dictionary!"
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; RBNode _ k' v l r ->
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case compare k k' of
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{ LT -> find k l
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; EQ -> v
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; GT -> find k r }
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}
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--}
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-- Does t contain k?
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member k t = isJust $ lookup k t
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rotateLeft t =
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case t of
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{ RBNode cy ky vy a (RBNode cz kz vz b c) -> RBNode cy kz vz (RBNode Red ky vy a b) c
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; _ -> raise "rotateLeft of a node without enough children" }
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-- rotateRight -- the reverse, and
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-- makes Y have Z's color, and makes Z Red.
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rotateRight t =
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case t of
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{ RBNode cz kz vz (RBNode cy ky vy a b) c -> RBNode cz ky vy a (RBNode Red kz vz b c)
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; _ -> raise "rotateRight of a node without enough children" }
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rotateLeftIfNeeded t =
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case t of
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{ RBNode _ _ _ _ (RBNode Red _ _ _ _) -> rotateLeft t
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; _ -> t }
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rotateRightIfNeeded t =
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case t of
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{ RBNode _ _ _ (RBNode Red _ _ (RBNode Red _ _ _ _) _) _ -> rotateRight t
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; _ -> t }
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otherColor c = case c of { Red -> Black ; Black -> Red }
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color_flip t =
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case t of
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{ RBNode c1 bk bv (RBNode c2 ak av la ra) (RBNode c3 ck cv lc rc) ->
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RBNode (otherColor c1) bk bv
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(RBNode (otherColor c2) ak av la ra)
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(RBNode (otherColor c3) ck cv lc rc)
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; _ -> raise "color_flip called on a RBEmpty or RBNode with a RBEmpty child" }
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color_flipIfNeeded t =
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case t of
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{ RBNode _ _ _ (RBNode Red _ _ _ _) (RBNode Red _ _ _ _) -> color_flip t
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; _ -> t }
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fixUp t = color_flipIfNeeded (rotateRightIfNeeded (rotateLeftIfNeeded t))
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ensureBlackRoot t =
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case t of
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{ RBNode Red k v l r -> RBNode Black k v l r
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; _ -> t }
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-- Invariant: t is a valid left-leaning rb tree *)
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insert k v t =
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let ins t =
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case t of
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{ RBEmpty -> RBNode Red k v RBEmpty RBEmpty
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; RBNode c k' v' l r ->
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let h = case compare k k' of
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{ LT -> RBNode c k' v' (ins l) r
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; EQ -> RBNode c k' v l r -- replace
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; GT -> RBNode c k' v' l (ins r) }
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in fixUp h }
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in ensureBlackRoot (ins t)
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{--
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if not (invariants_hold t) then
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raise "invariants broken before insert"
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else (let new_t = ensureBlackRoot (ins t) in
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if not (invariants_hold new_t) then
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raise "invariants broken after insert"
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else new_t)
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--}
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singleton k v = insert k v RBEmpty
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isRed t =
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case t of
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{ RBNode Red _ _ _ _ -> True
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; _ -> False }
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isRedLeft t =
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case t of
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{ RBNode _ _ _ (RBNode Red _ _ _ _) _ -> True
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; _ -> False }
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isRedLeftLeft t =
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case t of
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{ RBNode _ _ _ (RBNode _ _ _ (RBNode Red _ _ _ _) _) _ -> True
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; _ -> False }
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isRedRight t =
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case t of
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{ RBNode _ _ _ _ (RBNode Red _ _ _ _) -> True
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; _ -> False }
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isRedRightLeft t =
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case t of
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{ RBNode _ _ _ _ (RBNode _ _ _ (RBNode Red _ _ _ _) _) -> True
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; _ -> False }
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moveRedLeft t =
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let t' = color_flip t in
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case t' of
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{ RBNode c k v l r ->
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case r of
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{ RBNode _ _ _ (RBNode Red _ _ _ _) _ ->
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color_flip (rotateLeft (RBNode c k v l (rotateRight r)))
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; _ -> t' }
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; _ -> t' }
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moveRedRight t =
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let t' = color_flip t in
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if isRedLeftLeft t' then color_flip (rotateRight t') else t'
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moveRedLeftIfNeeded t =
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if not (isRedLeft t) && not (isRedLeftLeft t)
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then moveRedLeft t
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else t
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moveRedRightIfNeeded t =
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if not (isRedRight t) && not (isRedRightLeft t)
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then moveRedRight t
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else t
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deleteMin t =
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let del t =
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case t of
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{ RBNode _ _ _ RBEmpty _ -> RBEmpty
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; _ -> let t' = moveRedLeftIfNeeded t in
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case t' of
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{ RBNode c k v l r -> fixUp (RBNode c k v (del l) r)
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; RBEmpty -> RBEmpty }
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}
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in ensureBlackRoot (del t)
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{--
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deleteMax t =
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let del t =
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let t' = if isRedLeft t then rotateRight t else t in
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case t' of
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{ RBNode _ _ _ _ RBEmpty -> RBEmpty
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; _ -> let t'' = moveRedRightIfNeeded t' in
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case t'' of
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{ RBNode c k v l r -> fixUp (RBNode c k v l (del r))
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; RBEmpty -> RBEmpty } }
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in ensureBlackRoot (del t)
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--}
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remove k t =
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let eq_and_noRightNode t = case t of { RBNode _ k' _ _ RBEmpty -> k == k' ; _ -> False } in
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let eq t = case t of { RBNode _ k' _ _ _ -> k == k' ; _ -> False } in
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let delLT t = let t' = moveRedLeftIfNeeded t in
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case t' of
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{ RBNode c k' v l r -> fixUp (RBNode c k' v (del l) r)
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; RBEmpty -> raise "delLT on RBEmpty" }
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in
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let delEQ t = case t of -- Replace with successor
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{ RBNode c _ _ l r ->
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let (k',v') = min r in
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fixUp (RBNode c k' v' l (deleteMin r))
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; RBEmpty -> raise "delEQ called on a RBEmpty" }
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in
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let delGT t = case t of
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{ RBNode c k' v l r -> fixUp (RBNode c k' v l (del r))
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; RBEmpty -> raise "delGT called on a RBEmpty" }
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in
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let del t = case t of
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{ RBEmpty -> RBEmpty
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; RBNode _ k' _ _ _ ->
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if k < k' then delLT t
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else (let t' = if isRedLeft t then rotateRight t else t in
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if eq_and_noRightNode t' then RBEmpty
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else (let t = moveRedRightIfNeeded t in
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if eq t then delEQ t else delGT t)) }
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in ensureBlackRoot (del t)
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{--
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if not (invariants_hold t) then
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raise "invariants broken before remove"
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else (let t' = ensureBlackRoot (del t) in
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if invariants_hold t' then t' else
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raise "invariants broken after remove")
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--}
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map f t =
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case t of
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{ RBEmpty -> RBEmpty
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; RBNode c k v l r -> RBNode c k (f v) (map f l) (map f r)
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}
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foldl f acc t =
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case t of
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{ RBEmpty -> acc
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; RBNode _ k v l r -> foldl f (f k v (foldl f acc l)) r
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}
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foldr f acc t =
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case t of
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{ RBEmpty -> acc
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; RBNode _ k v l r -> foldr f (f k v (foldr f acc r)) l
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}
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union t1 t2 = foldl insert t2 t1
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intersect t1 t2 = foldl (\k v t -> if k `member` t2 then insert k v t else t) empty t1
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diff t1 t2 = foldl (\k _ t -> remove k t) t1 t2
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keys t = foldl (\k _ acc -> k : acc) [] t
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values t = foldl (\_ -> (:)) [] t
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toList t = foldl (\k v acc -> (k,v) : acc) [] t
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fromList assocs = List.foldl (uncurry insert) empty assocs
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