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+
+% (c) The AQUA Project, Glasgow University, 1994-1998
+%
+\section[FiniteMap]{An implementation of finite maps}
+
+``Finite maps'' are the heart of the compiler's
+lookup-tables/environments and its implementation of sets.  Important
+stuff!
+
+This code is derived from that in the paper:
+\begin{display}
+	S Adams
+	"Efficient sets: a balancing act"
+	Journal of functional programming 3(4) Oct 1993, pp553-562
+\end{display}
+
+The code is SPECIALIZEd to various highly-desirable types (e.g., Id)
+near the end.
+
+\begin{code}
+
+module FiniteMap (
+	FiniteMap,		-- abstract type
+
+	emptyFM, unitFM, listToFM,
+
+	addToFM,
+	addToFM_C,
+	addListToFM,
+	addListToFM_C,
+	delFromFM,
+	delListFromFM,
+
+	plusFM,
+	plusFM_C,
+	minusFM,
+	foldFM,
+
+	intersectFM,
+	intersectFM_C,
+	mapFM, filterFM, 
+
+	sizeFM, isEmptyFM, elemFM, lookupFM, lookupWithDefaultFM,
+
+	fmToList, keysFM, eltsFM
+
+	, bagToFM
+
+    ) where
+
+#include "HsVersions.h"
+#define IF_NOT_GHC(a) {--}
+
+#if defined(DEBUG_FINITEMAPS)/* NB NB NB */
+#define OUTPUTABLE_key , Outputable key
+#else
+#define OUTPUTABLE_key {--}
+#endif
+
+import Maybes
+import Bag	  ( Bag, foldrBag )
+import Util
+import Outputable
+
+import GLAEXTS
+
+#if ! OMIT_NATIVE_CODEGEN
+#  define IF_NCG(a) a
+#else
+#  define IF_NCG(a) {--}
+#endif
+
+
+-- SIGH: but we use unboxed "sizes"...
+#if __GLASGOW_HASKELL__
+#define IF_GHC(a,b) a
+#else /* not GHC */
+#define IF_GHC(a,b) b
+#endif /* not GHC */
+\end{code}
+
+
+%************************************************************************
+%*									*
+\subsection{The signature of the module}
+%*									*
+%************************************************************************
+
+\begin{code}
+--	BUILDING
+emptyFM		:: FiniteMap key elt
+unitFM		:: key -> elt -> FiniteMap key elt
+listToFM	:: (Ord key OUTPUTABLE_key) => [(key,elt)] -> FiniteMap key elt
+			-- In the case of duplicates, the last is taken
+bagToFM		:: (Ord key OUTPUTABLE_key) => Bag (key,elt) -> FiniteMap key elt
+			-- In the case of duplicates, who knows which is taken
+
+--	ADDING AND DELETING
+		   -- Throws away any previous binding
+		   -- In the list case, the items are added starting with the
+		   -- first one in the list
+addToFM		:: (Ord key OUTPUTABLE_key) => FiniteMap key elt -> key -> elt  -> FiniteMap key elt
+addListToFM	:: (Ord key OUTPUTABLE_key) => FiniteMap key elt -> [(key,elt)] -> FiniteMap key elt
+
+		   -- Combines with previous binding
+		   -- The combining fn goes (old -> new -> new)
+addToFM_C	:: (Ord key OUTPUTABLE_key) => (elt -> elt -> elt)
+			   -> FiniteMap key elt -> key -> elt
+			   -> FiniteMap key elt
+addListToFM_C	:: (Ord key OUTPUTABLE_key) => (elt -> elt -> elt)
+			   -> FiniteMap key elt -> [(key,elt)]
+			   -> FiniteMap key elt
+
+		   -- Deletion doesn't complain if you try to delete something
+		   -- which isn't there
+delFromFM	:: (Ord key OUTPUTABLE_key) => FiniteMap key elt -> key   -> FiniteMap key elt
+delListFromFM	:: (Ord key OUTPUTABLE_key) => FiniteMap key elt -> [key] -> FiniteMap key elt
+
+--	COMBINING
+		   -- Bindings in right argument shadow those in the left
+plusFM		:: (Ord key OUTPUTABLE_key) => FiniteMap key elt -> FiniteMap key elt
+			   -> FiniteMap key elt
+
+		   -- Combines bindings for the same thing with the given function
+plusFM_C	:: (Ord key OUTPUTABLE_key) => (elt -> elt -> elt)
+			   -> FiniteMap key elt -> FiniteMap key elt -> FiniteMap key elt
+
+minusFM		:: (Ord key OUTPUTABLE_key) => FiniteMap key elt -> FiniteMap key elt -> FiniteMap key elt
+		   -- (minusFM a1 a2) deletes from a1 any bindings which are bound in a2
+
+intersectFM	:: (Ord key OUTPUTABLE_key) => FiniteMap key elt -> FiniteMap key elt -> FiniteMap key elt
+intersectFM_C	:: (Ord key OUTPUTABLE_key) => (elt1 -> elt2 -> elt3)
+			   -> FiniteMap key elt1 -> FiniteMap key elt2 -> FiniteMap key elt3
+
+--	MAPPING, FOLDING, FILTERING
+foldFM		:: (key -> elt -> a -> a) -> a -> FiniteMap key elt -> a
+mapFM		:: (key -> elt1 -> elt2) -> FiniteMap key elt1 -> FiniteMap key elt2
+filterFM	:: (Ord key OUTPUTABLE_key) => (key -> elt -> Bool)
+			   -> FiniteMap key elt -> FiniteMap key elt
+
+
+--	INTERROGATING
+sizeFM		:: FiniteMap key elt -> Int
+isEmptyFM	:: FiniteMap key elt -> Bool
+
+elemFM		:: (Ord key OUTPUTABLE_key) => key -> FiniteMap key elt -> Bool
+lookupFM	:: (Ord key OUTPUTABLE_key) => FiniteMap key elt -> key -> Maybe elt
+lookupWithDefaultFM
+		:: (Ord key OUTPUTABLE_key) => FiniteMap key elt -> elt -> key -> elt
+		-- lookupWithDefaultFM supplies a "default" elt
+		-- to return for an unmapped key
+
+--	LISTIFYING
+fmToList	:: FiniteMap key elt -> [(key,elt)]
+keysFM		:: FiniteMap key elt -> [key]
+eltsFM		:: FiniteMap key elt -> [elt]
+\end{code}
+
+%************************************************************************
+%*									*
+\subsection{The @FiniteMap@ data type, and building of same}
+%*									*
+%************************************************************************
+
+Invariants about @FiniteMap@:
+\begin{enumerate}
+\item
+all keys in a FiniteMap are distinct
+\item
+all keys in left  subtree are $<$ key in Branch and
+all keys in right subtree are $>$ key in Branch
+\item
+size field of a Branch gives number of Branch nodes in the tree
+\item
+size of left subtree is differs from size of right subtree by a
+factor of at most \tr{sIZE_RATIO}
+\end{enumerate}
+
+\begin{code}
+data FiniteMap key elt
+  = EmptyFM
+  | Branch key elt	    	-- Key and elt stored here
+    IF_GHC(Int#,Int{-STRICT-})	-- Size >= 1
+    (FiniteMap key elt)	    	-- Children
+    (FiniteMap key elt)
+\end{code}
+
+\begin{code}
+emptyFM = EmptyFM
+{-
+emptyFM
+  = Branch bottom bottom IF_GHC(0#,0) bottom bottom
+  where
+    bottom = panic "emptyFM"
+-}
+
+--  #define EmptyFM (Branch _ _ IF_GHC(0#,0) _ _)
+
+unitFM key elt = Branch key elt IF_GHC(1#,1) emptyFM emptyFM
+
+listToFM = addListToFM emptyFM
+
+bagToFM = foldrBag (\(k,v) fm -> addToFM fm k v) emptyFM
+\end{code}
+
+%************************************************************************
+%*									*
+\subsection{Adding to and deleting from @FiniteMaps@}
+%*									*
+%************************************************************************
+
+\begin{code}
+addToFM fm key elt = addToFM_C (\ old new -> new) fm key elt
+
+addToFM_C combiner EmptyFM key elt = unitFM key elt
+addToFM_C combiner (Branch key elt size fm_l fm_r) new_key new_elt
+  = case compare new_key key of
+	LT -> mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r
+	GT -> mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt)
+	EQ -> Branch new_key (combiner elt new_elt) size fm_l fm_r
+
+addListToFM fm key_elt_pairs = addListToFM_C (\ old new -> new) fm key_elt_pairs
+
+addListToFM_C combiner fm key_elt_pairs
+  = foldl' add fm key_elt_pairs	-- foldl adds from the left
+  where
+    add fmap (key,elt) = addToFM_C combiner fmap key elt
+\end{code}
+
+\begin{code}
+delFromFM EmptyFM del_key = emptyFM
+delFromFM (Branch key elt size fm_l fm_r) del_key
+  = case compare del_key key of
+	GT -> mkBalBranch key elt fm_l (delFromFM fm_r del_key)
+	LT -> mkBalBranch key elt (delFromFM fm_l del_key) fm_r
+	EQ -> glueBal fm_l fm_r
+
+delListFromFM fm keys = foldl' delFromFM fm keys
+\end{code}
+
+%************************************************************************
+%*									*
+\subsection{Combining @FiniteMaps@}
+%*									*
+%************************************************************************
+
+\begin{code}
+plusFM_C combiner EmptyFM fm2 = fm2
+plusFM_C combiner fm1 EmptyFM = fm1
+plusFM_C combiner fm1 (Branch split_key elt2 _ left right)
+  = mkVBalBranch split_key new_elt
+		 (plusFM_C combiner lts left)
+		 (plusFM_C combiner gts right)
+  where
+    lts     = splitLT fm1 split_key
+    gts     = splitGT fm1 split_key
+    new_elt = case lookupFM fm1 split_key of
+		Nothing   -> elt2
+		Just elt1 -> combiner elt1 elt2
+
+-- It's worth doing plusFM specially, because we don't need
+-- to do the lookup in fm1.
+-- FM2 over-rides FM1.
+
+plusFM EmptyFM fm2 = fm2
+plusFM fm1 EmptyFM = fm1
+plusFM fm1 (Branch split_key elt1 _ left right)
+  = mkVBalBranch split_key elt1 (plusFM lts left) (plusFM gts right)
+  where
+    lts     = splitLT fm1 split_key
+    gts     = splitGT fm1 split_key
+
+minusFM EmptyFM fm2 = emptyFM
+minusFM fm1 EmptyFM = fm1
+minusFM fm1 (Branch split_key elt _ left right)
+  = glueVBal (minusFM lts left) (minusFM gts right)
+	-- The two can be way different, so we need glueVBal
+  where
+    lts = splitLT fm1 split_key		-- NB gt and lt, so the equal ones
+    gts = splitGT fm1 split_key		-- are not in either.
+
+intersectFM fm1 fm2 = intersectFM_C (\ left right -> right) fm1 fm2
+
+intersectFM_C combiner fm1 EmptyFM = emptyFM
+intersectFM_C combiner EmptyFM fm2 = emptyFM
+intersectFM_C combiner fm1 (Branch split_key elt2 _ left right)
+
+  | maybeToBool maybe_elt1	-- split_elt *is* in intersection
+  = mkVBalBranch split_key (combiner elt1 elt2) (intersectFM_C combiner lts left)
+						(intersectFM_C combiner gts right)
+
+  | otherwise			-- split_elt is *not* in intersection
+  = glueVBal (intersectFM_C combiner lts left) (intersectFM_C combiner gts right)
+
+  where
+    lts = splitLT fm1 split_key		-- NB gt and lt, so the equal ones
+    gts = splitGT fm1 split_key		-- are not in either.
+
+    maybe_elt1 = lookupFM fm1 split_key
+    Just elt1  = maybe_elt1
+\end{code}
+
+%************************************************************************
+%*									*
+\subsection{Mapping, folding, and filtering with @FiniteMaps@}
+%*									*
+%************************************************************************
+
+\begin{code}
+foldFM k z EmptyFM = z
+foldFM k z (Branch key elt _ fm_l fm_r)
+  = foldFM k (k key elt (foldFM k z fm_r)) fm_l
+
+mapFM f EmptyFM = emptyFM
+mapFM f (Branch key elt size fm_l fm_r)
+  = Branch key (f key elt) size (mapFM f fm_l) (mapFM f fm_r)
+
+filterFM p EmptyFM = emptyFM
+filterFM p (Branch key elt _ fm_l fm_r)
+  | p key elt		-- Keep the item
+  = mkVBalBranch key elt (filterFM p fm_l) (filterFM p fm_r)
+
+  | otherwise		-- Drop the item
+  = glueVBal (filterFM p fm_l) (filterFM p fm_r)
+\end{code}
+
+%************************************************************************
+%*									*
+\subsection{Interrogating @FiniteMaps@}
+%*									*
+%************************************************************************
+
+\begin{code}
+--{-# INLINE sizeFM #-}
+sizeFM EmptyFM		     = 0
+sizeFM (Branch _ _ size _ _) = IF_GHC(I# size, size)
+
+isEmptyFM fm = sizeFM fm == 0
+
+lookupFM EmptyFM key = Nothing
+lookupFM (Branch key elt _ fm_l fm_r) key_to_find
+  = case compare key_to_find key of
+	LT -> lookupFM fm_l key_to_find
+	GT -> lookupFM fm_r key_to_find
+	EQ -> Just elt
+
+key `elemFM` fm
+  = case (lookupFM fm key) of { Nothing -> False; Just elt -> True }
+
+lookupWithDefaultFM fm deflt key
+  = case (lookupFM fm key) of { Nothing -> deflt; Just elt -> elt }
+\end{code}
+
+%************************************************************************
+%*									*
+\subsection{Listifying @FiniteMaps@}
+%*									*
+%************************************************************************
+
+\begin{code}
+fmToList fm = foldFM (\ key elt rest -> (key,elt) : rest) [] fm
+keysFM fm   = foldFM (\ key elt rest -> key : rest)       [] fm
+eltsFM fm   = foldFM (\ key elt rest -> elt : rest)       [] fm
+\end{code}
+
+
+%************************************************************************
+%*									*
+\subsection{The implementation of balancing}
+%*									*
+%************************************************************************
+
+%************************************************************************
+%*									*
+\subsubsection{Basic construction of a @FiniteMap@}
+%*									*
+%************************************************************************
+
+@mkBranch@ simply gets the size component right.  This is the ONLY
+(non-trivial) place the Branch object is built, so the ASSERTion
+recursively checks consistency.  (The trivial use of Branch is in
+@unitFM@.)
+
+\begin{code}
+sIZE_RATIO :: Int
+sIZE_RATIO = 5
+
+mkBranch :: (Ord key OUTPUTABLE_key) 		-- Used for the assertion checking only
+	 => Int
+	 -> key -> elt
+	 -> FiniteMap key elt -> FiniteMap key elt
+	 -> FiniteMap key elt
+
+mkBranch which key elt fm_l fm_r
+  = --ASSERT( left_ok && right_ok && balance_ok )
+#if defined(DEBUG_FINITEMAPS)
+    if not ( left_ok && right_ok && balance_ok ) then
+	pprPanic ("mkBranch:"++show which) (vcat [ppr [left_ok, right_ok, balance_ok],
+				       ppr key,
+				       ppr fm_l,
+				       ppr fm_r])
+    else
+#endif
+    let
+	result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r
+    in
+--    if sizeFM result <= 8 then
+	result
+--    else
+--	pprTrace ("mkBranch:"++(show which)) (ppr result) (
+--	result
+--	)
+  where
+    left_ok  = case fm_l of
+		EmptyFM		         -> True
+		Branch left_key _ _ _ _  -> let
+						biggest_left_key = fst (findMax fm_l)
+					    in
+					    biggest_left_key < key
+    right_ok = case fm_r of
+		EmptyFM		         -> True
+		Branch right_key _ _ _ _ -> let
+						smallest_right_key = fst (findMin fm_r)
+					    in
+					    key < smallest_right_key
+    balance_ok = True -- sigh
+{- LATER:
+    balance_ok
+      = -- Both subtrees have one or no elements...
+	(left_size + right_size <= 1)
+-- NO	      || left_size == 0  -- ???
+-- NO	      || right_size == 0 -- ???
+    	-- ... or the number of elements in a subtree does not exceed
+	-- sIZE_RATIO times the number of elements in the other subtree
+      || (left_size  * sIZE_RATIO >= right_size &&
+    	  right_size * sIZE_RATIO >= left_size)
+-}
+
+    left_size  = sizeFM fm_l
+    right_size = sizeFM fm_r
+
+#ifdef __GLASGOW_HASKELL__
+    unbox :: Int -> Int#
+    unbox (I# size) = size
+#else
+    unbox :: Int -> Int
+    unbox x = x
+#endif
+\end{code}
+
+%************************************************************************
+%*									*
+\subsubsection{{\em Balanced} construction of a @FiniteMap@}
+%*									*
+%************************************************************************
+
+@mkBalBranch@ rebalances, assuming that the subtrees aren't too far
+out of whack.
+
+\begin{code}
+mkBalBranch :: (Ord key OUTPUTABLE_key)
+	    => key -> elt
+	    -> FiniteMap key elt -> FiniteMap key elt
+	    -> FiniteMap key elt
+
+mkBalBranch key elt fm_L fm_R
+
+  | size_l + size_r < 2
+  = mkBranch 1{-which-} key elt fm_L fm_R
+
+  | size_r > sIZE_RATIO * size_l	-- Right tree too big
+  = case fm_R of
+	Branch _ _ _ fm_rl fm_rr
+		| sizeFM fm_rl < 2 * sizeFM fm_rr -> single_L fm_L fm_R
+		| otherwise	   	          -> double_L fm_L fm_R
+	-- Other case impossible
+
+  | size_l > sIZE_RATIO * size_r	-- Left tree too big
+  = case fm_L of
+	Branch _ _ _ fm_ll fm_lr
+		| sizeFM fm_lr < 2 * sizeFM fm_ll -> single_R fm_L fm_R
+		| otherwise		          -> double_R fm_L fm_R
+	-- Other case impossible
+
+  | otherwise				-- No imbalance
+  = mkBranch 2{-which-} key elt fm_L fm_R
+
+  where
+    size_l   = sizeFM fm_L
+    size_r   = sizeFM fm_R
+
+    single_L fm_l (Branch key_r elt_r _ fm_rl fm_rr)
+	= mkBranch 3{-which-} key_r elt_r (mkBranch 4{-which-} key elt fm_l fm_rl) fm_rr
+
+    double_L fm_l (Branch key_r elt_r _ (Branch key_rl elt_rl _ fm_rll fm_rlr) fm_rr)
+	= mkBranch 5{-which-} key_rl elt_rl (mkBranch 6{-which-} key   elt   fm_l   fm_rll)
+				 (mkBranch 7{-which-} key_r elt_r fm_rlr fm_rr)
+
+    single_R (Branch key_l elt_l _ fm_ll fm_lr) fm_r
+	= mkBranch 8{-which-} key_l elt_l fm_ll (mkBranch 9{-which-} key elt fm_lr fm_r)
+
+    double_R (Branch key_l elt_l _ fm_ll (Branch key_lr elt_lr _ fm_lrl fm_lrr)) fm_r
+	= mkBranch 10{-which-} key_lr elt_lr (mkBranch 11{-which-} key_l elt_l fm_ll  fm_lrl)
+				 (mkBranch 12{-which-} key   elt   fm_lrr fm_r)
+\end{code}
+
+
+\begin{code}
+mkVBalBranch :: (Ord key OUTPUTABLE_key)
+	     => key -> elt
+	     -> FiniteMap key elt -> FiniteMap key elt
+	     -> FiniteMap key elt
+
+-- Assert: in any call to (mkVBalBranch_C comb key elt l r),
+--	   (a) all keys in l are < all keys in r
+--	   (b) all keys in l are < key
+--	   (c) all keys in r are > key
+
+mkVBalBranch key elt EmptyFM fm_r = addToFM fm_r key elt
+mkVBalBranch key elt fm_l EmptyFM = addToFM fm_l key elt
+
+mkVBalBranch key elt fm_l@(Branch key_l elt_l _ fm_ll fm_lr)
+		     fm_r@(Branch key_r elt_r _ fm_rl fm_rr)
+  | sIZE_RATIO * size_l < size_r
+  = mkBalBranch key_r elt_r (mkVBalBranch key elt fm_l fm_rl) fm_rr
+
+  | sIZE_RATIO * size_r < size_l
+  = mkBalBranch key_l elt_l fm_ll (mkVBalBranch key elt fm_lr fm_r)
+
+  | otherwise
+  = mkBranch 13{-which-} key elt fm_l fm_r
+
+  where
+    size_l = sizeFM fm_l
+    size_r = sizeFM fm_r
+\end{code}
+
+%************************************************************************
+%*									*
+\subsubsection{Gluing two trees together}
+%*									*
+%************************************************************************
+
+@glueBal@ assumes its two arguments aren't too far out of whack, just
+like @mkBalBranch@.  But: all keys in first arg are $<$ all keys in
+second.
+
+\begin{code}
+glueBal :: (Ord key OUTPUTABLE_key)
+	=> FiniteMap key elt -> FiniteMap key elt
+	-> FiniteMap key elt
+
+glueBal EmptyFM fm2 = fm2
+glueBal fm1 EmptyFM = fm1
+glueBal fm1 fm2
+	-- The case analysis here (absent in Adams' program) is really to deal
+	-- with the case where fm2 is a singleton. Then deleting the minimum means
+	-- we pass an empty tree to mkBalBranch, which breaks its invariant.
+  | sizeFM fm2 > sizeFM fm1
+  = mkBalBranch mid_key2 mid_elt2 fm1 (deleteMin fm2)
+
+  | otherwise
+  = mkBalBranch mid_key1 mid_elt1 (deleteMax fm1) fm2
+  where
+    (mid_key1, mid_elt1) = findMax fm1
+    (mid_key2, mid_elt2) = findMin fm2
+\end{code}
+
+@glueVBal@ copes with arguments which can be of any size.
+But: all keys in first arg are $<$ all keys in second.
+
+\begin{code}
+glueVBal :: (Ord key OUTPUTABLE_key)
+	 => FiniteMap key elt -> FiniteMap key elt
+	 -> FiniteMap key elt
+
+glueVBal EmptyFM fm2 = fm2
+glueVBal fm1 EmptyFM = fm1
+glueVBal fm_l@(Branch key_l elt_l _ fm_ll fm_lr)
+	 fm_r@(Branch key_r elt_r _ fm_rl fm_rr)
+  | sIZE_RATIO * size_l < size_r
+  = mkBalBranch key_r elt_r (glueVBal fm_l fm_rl) fm_rr
+
+  | sIZE_RATIO * size_r < size_l
+  = mkBalBranch key_l elt_l fm_ll (glueVBal fm_lr fm_r)
+
+  | otherwise		-- We now need the same two cases as in glueBal above.
+  = glueBal fm_l fm_r
+  where
+    size_l = sizeFM fm_l
+    size_r = sizeFM fm_r
+\end{code}
+
+%************************************************************************
+%*									*
+\subsection{Local utilities}
+%*									*
+%************************************************************************
+
+\begin{code}
+splitLT, splitGT :: (Ord key OUTPUTABLE_key) => FiniteMap key elt -> key -> FiniteMap key elt
+
+-- splitLT fm split_key  =  fm restricted to keys <  split_key
+-- splitGT fm split_key  =  fm restricted to keys >  split_key
+
+splitLT EmptyFM split_key = emptyFM
+splitLT (Branch key elt _ fm_l fm_r) split_key
+  = case compare split_key key of
+	LT -> splitLT fm_l split_key
+	GT -> mkVBalBranch key elt fm_l (splitLT fm_r split_key)
+	EQ -> fm_l
+
+splitGT EmptyFM split_key = emptyFM
+splitGT (Branch key elt _ fm_l fm_r) split_key
+  = case compare split_key key of
+	GT -> splitGT fm_r split_key
+	LT -> mkVBalBranch key elt (splitGT fm_l split_key) fm_r
+	EQ -> fm_r
+
+findMin :: FiniteMap key elt -> (key,elt)
+findMin (Branch key elt _ EmptyFM _) = (key,elt)
+findMin (Branch key elt _ fm_l    _) = findMin fm_l
+
+deleteMin :: (Ord key OUTPUTABLE_key) => FiniteMap key elt -> FiniteMap key elt
+deleteMin (Branch key elt _ EmptyFM fm_r) = fm_r
+deleteMin (Branch key elt _ fm_l    fm_r) = mkBalBranch key elt (deleteMin fm_l) fm_r
+
+findMax :: FiniteMap key elt -> (key,elt)
+findMax (Branch key elt _ _ EmptyFM) = (key,elt)
+findMax (Branch key elt _ _    fm_r) = findMax fm_r
+
+deleteMax :: (Ord key OUTPUTABLE_key) => FiniteMap key elt -> FiniteMap key elt
+deleteMax (Branch key elt _ fm_l EmptyFM) = fm_l
+deleteMax (Branch key elt _ fm_l    fm_r) = mkBalBranch key elt fm_l (deleteMax fm_r)
+\end{code}
+
+%************************************************************************
+%*									*
+\subsection{Output-ery}
+%*									*
+%************************************************************************
+
+\begin{code}
+#if defined(DEBUG_FINITEMAPS)
+
+instance (Outputable key) => Outputable (FiniteMap key elt) where
+    ppr fm = pprX fm
+
+pprX EmptyFM = char '!'
+pprX (Branch key elt sz fm_l fm_r)
+ = parens (hcat [pprX fm_l, space,
+		      ppr key, space, int (IF_GHC(I# sz, sz)), space,
+		      pprX fm_r])
+#else
+-- and when not debugging the package itself...
+instance (Outputable key, Outputable elt) => Outputable (FiniteMap key elt) where
+    ppr fm = ppr (fmToList fm)
+#endif
+
+#if 0
+instance (Eq key, Eq elt) => Eq (FiniteMap key elt) where
+  fm_1 == fm_2 = (sizeFM   fm_1 == sizeFM   fm_2) &&   -- quick test
+		 (fmToList fm_1 == fmToList fm_2)
+
+{- NO: not clear what The Right Thing to do is:
+instance (Ord key, Ord elt) => Ord (FiniteMap key elt) where
+  fm_1 <= fm_2 = (sizeFM   fm_1 <= sizeFM   fm_2) &&   -- quick test
+		 (fmToList fm_1 <= fmToList fm_2)
+-}
+#endif
+\end{code}
+
+%************************************************************************
+%*									*
+\subsection{Efficiency pragmas for GHC}
+%*									*
+%************************************************************************
+
+When the FiniteMap module is used in GHC, we specialise it for
+\tr{Uniques}, for dastardly efficiency reasons.
+
+\begin{code}
+#if 0
+
+#if __GLASGOW_HASKELL__
+
+{-# SPECIALIZE addListToFM
+		:: FiniteMap (FastString, FAST_STRING) elt -> [((FAST_STRING, FAST_STRING),elt)] -> FiniteMap (FAST_STRING, FAST_STRING) elt
+		 , FiniteMap RdrName elt -> [(RdrName,elt)] -> FiniteMap RdrName elt
+    IF_NCG(COMMA   FiniteMap Reg elt -> [(Reg COMMA elt)] -> FiniteMap Reg elt)
+    #-}
+{-# SPECIALIZE addListToFM_C
+		:: (elt -> elt -> elt) -> FiniteMap TyCon elt -> [(TyCon,elt)] -> FiniteMap TyCon elt
+		 , (elt -> elt -> elt) -> FiniteMap FastString elt -> [(FAST_STRING,elt)] -> FiniteMap FAST_STRING elt
+    IF_NCG(COMMA   (elt -> elt -> elt) -> FiniteMap Reg elt -> [(Reg COMMA elt)] -> FiniteMap Reg elt)
+    #-}
+{-# SPECIALIZE addToFM
+		:: FiniteMap CLabel elt -> CLabel -> elt  -> FiniteMap CLabel elt
+		 , FiniteMap FastString elt -> FAST_STRING -> elt  -> FiniteMap FAST_STRING elt
+		 , FiniteMap (FastString, FAST_STRING) elt -> (FAST_STRING, FAST_STRING) -> elt  -> FiniteMap (FAST_STRING, FAST_STRING) elt
+		 , FiniteMap RdrName elt -> RdrName -> elt  -> FiniteMap RdrName elt
+    IF_NCG(COMMA   FiniteMap Reg elt -> Reg -> elt  -> FiniteMap Reg elt)
+    #-}
+{-# SPECIALIZE addToFM_C
+		:: (elt -> elt -> elt) -> FiniteMap (RdrName, RdrName) elt -> (RdrName, RdrName) -> elt -> FiniteMap (RdrName, RdrName) elt
+		 , (elt -> elt -> elt) -> FiniteMap FastString elt -> FAST_STRING -> elt -> FiniteMap FAST_STRING elt
+    IF_NCG(COMMA   (elt -> elt -> elt) -> FiniteMap Reg elt -> Reg -> elt -> FiniteMap Reg elt)
+    #-}
+{-# SPECIALIZE bagToFM
+		:: Bag (FastString,elt) -> FiniteMap FAST_STRING elt
+    #-}
+{-# SPECIALIZE delListFromFM
+		:: FiniteMap RdrName elt -> [RdrName]   -> FiniteMap RdrName elt
+		 , FiniteMap FastString elt -> [FAST_STRING]   -> FiniteMap FAST_STRING elt
+    IF_NCG(COMMA   FiniteMap Reg elt -> [Reg]   -> FiniteMap Reg elt)
+    #-}
+{-# SPECIALIZE listToFM
+		:: [([Char],elt)] -> FiniteMap [Char] elt
+		 , [(FastString,elt)] -> FiniteMap FAST_STRING elt
+		 , [((FastString,FAST_STRING),elt)] -> FiniteMap (FAST_STRING, FAST_STRING) elt
+    IF_NCG(COMMA   [(Reg COMMA elt)] -> FiniteMap Reg elt)
+    #-}
+{-# SPECIALIZE lookupFM
+		:: FiniteMap CLabel elt -> CLabel -> Maybe elt
+		 , FiniteMap [Char] elt -> [Char] -> Maybe elt
+		 , FiniteMap FastString elt -> FAST_STRING -> Maybe elt
+		 , FiniteMap (FastString,FAST_STRING) elt -> (FAST_STRING,FAST_STRING) -> Maybe elt
+		 , FiniteMap RdrName elt -> RdrName -> Maybe elt
+		 , FiniteMap (RdrName,RdrName) elt -> (RdrName,RdrName) -> Maybe elt
+    IF_NCG(COMMA   FiniteMap Reg elt -> Reg -> Maybe elt)
+    #-}
+{-# SPECIALIZE lookupWithDefaultFM
+		:: FiniteMap FastString elt -> elt -> FAST_STRING -> elt
+    IF_NCG(COMMA   FiniteMap Reg elt -> elt -> Reg -> elt)
+    #-}
+{-# SPECIALIZE plusFM
+		:: FiniteMap RdrName elt -> FiniteMap RdrName elt -> FiniteMap RdrName elt
+		 , FiniteMap FastString elt -> FiniteMap FAST_STRING elt -> FiniteMap FAST_STRING elt
+    IF_NCG(COMMA   FiniteMap Reg elt -> FiniteMap Reg elt -> FiniteMap Reg elt)
+    #-}
+{-# SPECIALIZE plusFM_C
+		:: (elt -> elt -> elt) -> FiniteMap FastString elt -> FiniteMap FAST_STRING elt -> FiniteMap FAST_STRING elt
+    IF_NCG(COMMA   (elt -> elt -> elt) -> FiniteMap Reg elt -> FiniteMap Reg elt -> FiniteMap Reg elt)
+    #-}
+
+#endif /* compiling with ghc and have specialiser */
+
+#endif /* 0 */
+\end{code}