Name constructors so that they are less likely to collide with something.

This commit is contained in:
evancz 2012-10-10 15:05:23 -07:00
parent 2fcf29ca8f
commit 7822f02666

View file

@ -5,11 +5,11 @@ import Data.Maybe (isJust)
data NColor = Red | Black
data RBTree k v = Node NColor k v (RBTree k v) (RBTree k v) | Empty
data RBTree k v = RBNode NColor k v (RBTree k v) (RBTree k v) | RBEmpty
raise = console.log
empty = Empty
empty = RBEmpty
-- Helpers for checking invariants
@ -17,8 +17,8 @@ empty = Empty
equal_pathLen t =
let path_numBlacks t =
case t of
{ Empty -> 1
; Node col _ _ l r ->
{ RBEmpty -> 1
; RBNode col _ _ l r ->
let { bl = path_numBlacks l ; br = path_numBlacks r } in
if bl /= br || bl == 0-1 || br == 0-1
then 0-1
@ -28,22 +28,22 @@ equal_pathLen t =
rootBlack t =
case t of
{ Empty -> True
; Node Black _ _ _ _ -> True
{ RBEmpty -> True
; RBNode Black _ _ _ _ -> True
; _ -> False }
redBlack_children t =
case t of
{ Node Red _ _ (Node Red _ _ _ _) _ -> False
; Node Red _ _ _ (Node Red _ _ _ _) -> False
; Empty -> True
; Node _ _ _ l r -> redBlack_children l && redBlack_children r
{ RBNode Red _ _ (RBNode Red _ _ _ _) _ -> False
; RBNode Red _ _ _ (RBNode Red _ _ _ _) -> False
; RBEmpty -> True
; RBNode _ _ _ l r -> redBlack_children l && redBlack_children r
}
findExtreme f t =
case t of
{ Empty -> Nothing
; Node c k _ l r ->
{ RBEmpty -> Nothing
; RBNode c k _ l r ->
case findExtreme f (f (l,r)) of
{ Nothing -> Just k
; Just k' -> Just k' }
@ -67,8 +67,8 @@ olte xo yo = optionRelation (<=) True xo yo
ordered t =
case t of
{ Empty -> True
; Node c k v l r ->
{ RBEmpty -> True
; RBNode c k v l r ->
let (lmax,rmin) = (findmaxRbt l, findminRbt r) in
olte lmax (Just k) && olte (Just k) rmin && ordered l && ordered r
}
@ -76,10 +76,10 @@ ordered t =
-- Check that there aren't any right red nodes in the tree *)
leftLeaning t =
case t of
{ Empty -> True
; Node _ _ _ (Node Black _ _ _ _) (Node Red _ _ _ _) -> False
; Node _ _ _ Empty (Node Red _ _ _ _) -> False
; Node _ _ _ l r -> (leftLeaning l) && (leftLeaning r)
{ RBEmpty -> True
; RBNode _ _ _ (RBNode Black _ _ _ _) (RBNode Red _ _ _ _) -> False
; RBNode _ _ _ RBEmpty (RBNode Red _ _ _ _) -> False
; RBNode _ _ _ l r -> (leftLeaning l) && (leftLeaning r)
}
invariants_hold t =
@ -91,22 +91,22 @@ invariants_hold t =
min t =
case t of
{ Node _ k v Empty _ -> (k,v)
; Node _ _ _ l _ -> min l
; Empty -> console.log "(min Empty) is not defined"
{ RBNode _ k v RBEmpty _ -> (k,v)
; RBNode _ _ _ l _ -> min l
; RBEmpty -> console.log "(min RBEmpty) is not defined"
}
max t =
case t of
{ Node _ k v _ Empty -> (k,v)
; Node _ _ _ _ r -> max r
; Empty -> console.log "(max Empty) is not defined"
{ RBNode _ k v _ RBEmpty -> (k,v)
; RBNode _ _ _ _ r -> max r
; RBEmpty -> console.log "(max RBEmpty) is not defined"
}
lookup k t =
case t of
{ Empty -> Nothing
; Node _ k' v l r ->
{ RBEmpty -> Nothing
; RBNode _ k' v l r ->
case compare k k' of
{ LT -> lookup k l
; EQ -> Just v
@ -118,39 +118,39 @@ member k t = isJust $ lookup k t
rotateLeft t =
case t of
{ Node cy ky vy a (Node cz kz vz b c) -> Node cy kz vz (Node Red ky vy a b) c
{ RBNode cy ky vy a (RBNode cz kz vz b c) -> RBNode cy kz vz (RBNode Red ky vy a b) c
; _ -> raise "rotateLeft of a node without enough children" }
-- rotateRight -- the reverse, and
-- makes Y have Z's color, and makes Z Red.
rotateRight t =
case t of
{ Node cz kz vz (Node cy ky vy a b) c -> Node cz ky vy a (Node Red kz vz b c)
{ RBNode cz kz vz (RBNode cy ky vy a b) c -> RBNode cz ky vy a (RBNode Red kz vz b c)
; _ -> raise "rotateRight of a node without enough children" }
rotateLeftIfNeeded t =
case t of
{ Node _ _ _ _ (Node Red _ _ _ _) -> rotateLeft t
{ RBNode _ _ _ _ (RBNode Red _ _ _ _) -> rotateLeft t
; _ -> t }
rotateRightIfNeeded t =
case t of
{ Node _ _ _ (Node Red _ _ (Node Red _ _ _ _) _) _ -> rotateRight t
{ RBNode _ _ _ (RBNode Red _ _ (RBNode Red _ _ _ _) _) _ -> rotateRight t
; _ -> t }
otherColor c = case c of { Red -> Black ; Black -> Red }
color_flip t =
case t of
{ Node c1 bk bv (Node c2 ak av la ra) (Node c3 ck cv lc rc) ->
Node (otherColor c1) bk bv
(Node (otherColor c2) ak av la ra)
(Node (otherColor c3) ck cv lc rc)
; _ -> raise "color_flip called on a Empty or Node with a Empty child" }
{ RBNode c1 bk bv (RBNode c2 ak av la ra) (RBNode c3 ck cv lc rc) ->
RBNode (otherColor c1) bk bv
(RBNode (otherColor c2) ak av la ra)
(RBNode (otherColor c3) ck cv lc rc)
; _ -> raise "color_flip called on a RBEmpty or RBNode with a RBEmpty child" }
color_flipIfNeeded t =
case t of
{ Node _ _ _ (Node Red _ _ _ _) (Node Red _ _ _ _) -> color_flip t
{ RBNode _ _ _ (RBNode Red _ _ _ _) (RBNode Red _ _ _ _) -> color_flip t
; _ -> t }
fixUp t = color_flipIfNeeded (rotateRightIfNeeded (rotateLeftIfNeeded t))
@ -158,19 +158,19 @@ fixUp t = color_flipIfNeeded (rotateRightIfNeeded (rotateLeftIfNeeded t))
ensureBlackRoot t =
case t of
{ Node Red k v l r -> Node Black k v l r
{ RBNode Red k v l r -> RBNode Black k v l r
; _ -> t }
-- Invariant: t is a valid left-leaning rb tree *)
insert k v t =
let ins t =
case t of
{ Empty -> Node Red k v Empty Empty
; Node c k' v' l r ->
{ RBEmpty -> RBNode Red k v RBEmpty RBEmpty
; RBNode c k' v' l r ->
let h = case compare k k' of
{ LT -> Node c k' v' (ins l) r
; EQ -> Node c k' v l r -- replace
; GT -> Node c k' v' l (ins r) }
{ LT -> RBNode c k' v' (ins l) r
; EQ -> RBNode c k' v l r -- replace
; GT -> RBNode c k' v' l (ins r) }
in fixUp h }
in if not (invariants_hold t) then
raise "invariants broken before insert"
@ -179,42 +179,42 @@ insert k v t =
raise "invariants broken after insert"
else new_t)
singleton k v = insert k v Empty
singleton k v = insert k v RBEmpty
isRed t =
case t of
{ Node Red _ _ _ _ -> True
{ RBNode Red _ _ _ _ -> True
; _ -> False }
isRedLeft t =
case t of
{ Node _ _ _ (Node Red _ _ _ _) _ -> True
{ RBNode _ _ _ (RBNode Red _ _ _ _) _ -> True
; _ -> False }
isRedLeftLeft t =
case t of
{ Node _ _ _ (Node _ _ _ (Node Red _ _ _ _) _) _ -> True
{ RBNode _ _ _ (RBNode _ _ _ (RBNode Red _ _ _ _) _) _ -> True
; _ -> False }
isRedRight t =
case t of
{ Node _ _ _ _ (Node Red _ _ _ _) -> True
{ RBNode _ _ _ _ (RBNode Red _ _ _ _) -> True
; _ -> False }
isRedRightLeft t =
case t of
{ Node _ _ _ _ (Node _ _ _ (Node Red _ _ _ _) _) -> True
{ RBNode _ _ _ _ (RBNode _ _ _ (RBNode Red _ _ _ _) _) -> True
; _ -> False }
moveRedLeft t =
let t' = color_flip t in
case t' of
{ Node c k v l r ->
{ RBNode c k v l r ->
case r of
{ Node _ _ _ (Node Red _ _ _ _) _ ->
color_flip (rotateLeft (Node c k v l (rotateRight r)))
{ RBNode _ _ _ (RBNode Red _ _ _ _) _ ->
color_flip (rotateLeft (RBNode c k v l (rotateRight r)))
; _ -> t' }
; _ -> t' }
@ -235,11 +235,11 @@ moveRedRightIfNeeded t =
deleteMin t =
let del t =
case t of
{ Node _ _ _ Empty _ -> Empty
{ RBNode _ _ _ RBEmpty _ -> RBEmpty
; _ -> let t' = moveRedLeftIfNeeded t in
case t' of
{ Node c k v l r -> fixUp (Node c k v (del l) r)
; Empty -> Empty }
{ RBNode c k v l r -> fixUp (RBNode c k v (del l) r)
; RBEmpty -> RBEmpty }
}
in ensureBlackRoot (del t)
@ -247,39 +247,39 @@ deleteMax t =
let del t =
let t' = if isRedLeft t then rotateRight t else t in
case t' of
{ Node _ _ _ _ Empty -> Empty
{ RBNode _ _ _ _ RBEmpty -> RBEmpty
; _ -> let t'' = moveRedRightIfNeeded t' in
case t'' of
{ Node c k v l r -> fixUp (Node c k v l (del r))
; Empty -> Empty } }
{ RBNode c k v l r -> fixUp (RBNode c k v l (del r))
; RBEmpty -> RBEmpty } }
in ensureBlackRoot (del t)
remove k t =
let {
eq_and_noRightNode t = case t of { Node _ k' _ _ Empty -> k == k' ; _ -> False }
; eq t = case t of { Node _ k' _ _ _ -> k == k' ; _ -> False }
eq_and_noRightNode t = case t of { RBNode _ k' _ _ RBEmpty -> k == k' ; _ -> False }
; eq t = case t of { RBNode _ k' _ _ _ -> k == k' ; _ -> False }
; delLT t =
let t' = moveRedLeftIfNeeded t in
case t' of
{ Node c k' v l r -> fixUp (Node c k' v (del l) r)
; Empty -> raise "delLT on Empty" }
{ RBNode c k' v l r -> fixUp (RBNode c k' v (del l) r)
; RBEmpty -> raise "delLT on RBEmpty" }
; delEQ t =
case t of -- Replace with successor
{ Node c _ _ l r ->
{ RBNode c _ _ l r ->
let (k',v') = min r in
fixUp (Node c k' v' l (deleteMin r))
; Empty -> raise "delEQ called on a Empty" }
fixUp (RBNode c k' v' l (deleteMin r))
; RBEmpty -> raise "delEQ called on a RBEmpty" }
; delGT t =
case t of
{ Node c k' v l r -> fixUp (Node c k' v l (del r))
; Empty -> raise "delGT called on a Empty" }
{ RBNode c k' v l r -> fixUp (RBNode c k' v l (del r))
; RBEmpty -> raise "delGT called on a RBEmpty" }
; del t =
case t of
{ Empty -> Empty
; Node _ k' _ _ _ ->
{ RBEmpty -> RBEmpty
; RBNode _ k' _ _ _ ->
if k < k' then delLT t
else (let t' = if isRedLeft t then rotateRight t else t in
if eq_and_noRightNode t' then Empty
if eq_and_noRightNode t' then RBEmpty
else (let t = moveRedRightIfNeeded t in
if eq t then delEQ t else delGT t)) }
}
@ -291,9 +291,6 @@ remove k t =
fold f acc t =
case t of
{ Empty -> acc
; Node _ k v l r -> fold f (f k v (fold f acc l)) r
{ RBEmpty -> acc
; RBNode _ k v l r -> fold f (f k v (fold f acc l)) r
}
{--
--}