GF/src is now for 2.9, and the new sources are in src-3.0 - keep it this way until the release of GF 3

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diff --git a/src-3.0/GF/Formalism/Utilities.hs b/src-3.0/GF/Formalism/Utilities.hs
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+----------------------------------------------------------------------
+-- |
+-- Maintainer  : PL
+-- Stability   : (stable)
+-- Portability : (portable)
+--
+-- > CVS $Date: 2005/05/13 12:40:19 $ 
+-- > CVS $Author: peb $
+-- > CVS $Revision: 1.6 $
+--
+-- Basic type declarations and functions for grammar formalisms
+-----------------------------------------------------------------------------
+
+
+module GF.Formalism.Utilities where
+
+import Control.Monad
+import Data.Array
+import Data.List (groupBy)
+
+import GF.Data.SortedList
+import GF.Data.Assoc
+import GF.Data.Utilities (sameLength, foldMerge, splitBy)
+
+import GF.Infra.PrintClass
+
+------------------------------------------------------------
+-- * symbols
+
+data Symbol c t = Cat c | Tok t
+		  deriving (Eq, Ord, Show)
+
+symbol :: (c -> a) -> (t -> a) -> Symbol c t -> a
+symbol fc ft (Cat cat) = fc cat
+symbol fc ft (Tok tok) = ft tok
+
+mapSymbol :: (c -> d) -> (t -> u) -> Symbol c t -> Symbol d u
+mapSymbol fc ft = symbol (Cat . fc) (Tok . ft)
+
+filterCats :: [Symbol c t] -> [c]
+filterCats syms = [ cat | Cat cat <- syms ]
+
+filterToks :: [Symbol c t] -> [t]
+filterToks syms = [ tok | Tok tok <- syms ]
+
+------------------------------------------------------------
+-- * edges
+
+data Edge s = Edge Int Int s
+	      deriving (Eq, Ord, Show)
+
+instance Functor Edge where
+    fmap f (Edge i j s) = Edge i j (f s)
+
+
+------------------------------------------------------------
+-- * representaions of input tokens
+
+data Input t = MkInput { inputEdges  :: [Edge t],
+			 inputBounds :: (Int, Int),
+			 inputFrom   :: Array Int (Assoc t [Int]),
+			 inputTo     :: Array Int (Assoc t [Int]),
+			 inputToken  :: Assoc t [(Int, Int)]
+		       }
+
+makeInput :: Ord t => [Edge t] -> Input t
+input     :: Ord t =>  [t]     -> Input t
+inputMany :: Ord t => [[t]]    -> Input t
+
+instance Show t => Show (Input t) where
+    show input = "makeInput " ++ show (inputEdges input)
+
+----------
+
+makeInput inEdges  | null inEdges = input []
+		   | otherwise    = MkInput inEdges inBounds inFrom inTo inToken
+    where inBounds = foldr1 minmax [ (i, j) | Edge i j _ <- inEdges ]
+	      where minmax (a, b) (a', b') = (min a a', max b b')
+	  inFrom   = fmap (accumAssoc id) $ accumArray (<++>) [] inBounds $
+		     [ (i, [(tok, j)]) | Edge i j tok <- inEdges ]
+	  inTo     = fmap (accumAssoc id) $ accumArray (<++>) [] inBounds
+		     [ (j, [(tok, i)]) | Edge i j tok <- inEdges ]
+	  inToken  = accumAssoc id [ (tok, (i, j)) | Edge i j tok <- inEdges ]
+
+input toks         = MkInput inEdges inBounds inFrom inTo inToken
+    where inEdges  = zipWith3 Edge [0..] [1..] toks
+	  inBounds = (0, length toks)
+	  inFrom   = listArray inBounds $
+		     [ listAssoc [(tok, [j])] | (tok, j) <- zip toks [1..] ] ++ [ listAssoc [] ]
+	  inTo     = listArray inBounds $
+		     [ listAssoc [] ] ++ [ listAssoc [(tok, [i])] | (tok, i) <- zip toks [0..] ]
+	  inToken  = accumAssoc id [ (tok, (i, j)) | Edge i j tok <- inEdges ]
+
+inputMany toks     = MkInput inEdges inBounds inFrom inTo inToken
+    where inEdges  = [ Edge i j t | (i, j, ts) <- zip3 [0..] [1..] toks, t <- ts ]
+	  inBounds = (0, length toks)
+	  inFrom   = listArray inBounds $
+		     [ listAssoc [ (t, [j]) | t <- nubsort ts ] | (ts, j) <- zip toks [1..] ]
+		     ++ [ listAssoc [] ]
+	  inTo     = listArray inBounds $
+		     [ listAssoc [] ] ++ 
+		     [ listAssoc [ (t, [i]) | t <- nubsort ts ] | (ts, i) <- zip toks [0..] ]
+	  inToken  = accumAssoc id [ (tok, (i, j)) | Edge i j tok <- inEdges ]
+
+
+------------------------------------------------------------
+-- * representations of syntactical analyses
+
+-- ** charts as finite maps over edges
+
+-- | The values of the chart, a list of key-daughters pairs,
+-- has unique keys. In essence, it is a map from 'n' to daughters.
+-- The daughters should be a set (not necessarily sorted) of rhs's.
+type SyntaxChart n e = Assoc e [SyntaxNode n [e]]
+
+data SyntaxNode n e = SMeta
+                    | SNode n [e]
+                    | SString String
+                    | SInt    Integer
+                    | SFloat  Double
+                    deriving (Eq,Ord)
+
+groupSyntaxNodes :: Ord n => [SyntaxNode n e] -> [SyntaxNode n [e]]
+groupSyntaxNodes []                =  []
+groupSyntaxNodes (SNode n0 es0:xs) = (SNode n0 (es0:ess)) : groupSyntaxNodes xs'
+  where 
+    (ess,xs') = span xs
+
+    span []       = ([],[])
+    span xs@(SNode n es:xs')
+      | n0 == n   = let (ess,xs) = span xs' in (es:ess,xs)
+      | otherwise = ([],xs)
+groupSyntaxNodes (SString s:xs) = (SString s) : groupSyntaxNodes xs
+groupSyntaxNodes (SInt    n:xs) = (SInt    n) : groupSyntaxNodes xs
+groupSyntaxNodes (SFloat  f:xs) = (SFloat  f) : groupSyntaxNodes xs
+
+-- better(?) representation of forests:
+-- data Forest n = F (SMap n (SList [Forest n])) Bool
+-- ==
+-- type Forest n = GeneralTrie n (SList [Forest n]) Bool
+-- (the Bool == isMeta)
+
+-- ** syntax forests
+
+data SyntaxForest n = FMeta 
+		    | FNode n [[SyntaxForest n]]
+                      -- ^ The outer list should be a set (not necessarily sorted)
+		      -- of possible alternatives. Ie. the outer list 
+		      -- is a disjunctive node, and the inner lists 
+		      -- are (conjunctive) concatenative nodes
+		    | FString String
+		    | FInt    Integer
+		    | FFloat  Double
+		      deriving (Eq, Ord, Show)
+
+instance Functor SyntaxForest where
+    fmap f (FNode n forests) = FNode (f n) $ map (map (fmap f)) forests
+    fmap _ (FString s) = FString s
+    fmap _ (FInt    n) = FInt    n
+    fmap _ (FFloat  f) = FFloat  f
+    fmap _ (FMeta)     = FMeta
+
+forestName :: SyntaxForest n -> Maybe n
+forestName (FNode n _) = Just n
+forestName _           = Nothing
+
+unifyManyForests :: (Monad m, Eq n) => [SyntaxForest n] -> m (SyntaxForest n)
+unifyManyForests = foldM unifyForests FMeta
+
+-- | two forests can be unified, if either is 'FMeta', or both have the same parent, 
+-- and all children can be unified
+unifyForests :: (Monad m, Eq n) => SyntaxForest n -> SyntaxForest n -> m (SyntaxForest n)
+unifyForests FMeta  forest = return forest
+unifyForests forest FMeta  = return forest
+unifyForests (FNode name1 children1) (FNode name2 children2)
+    | name1 == name2 && not (null children) = return $ FNode name1 children
+    where children = [ forests | forests1 <- children1, forests2 <- children2,
+		       sameLength forests1 forests2,
+		       forests <- zipWithM unifyForests forests1 forests2 ]
+unifyForests (FString s1) (FString s2)
+    | s1 == s2  = return $ FString s1
+unifyForests (FInt n1) (FInt n2)
+    | n1 == n2  = return $ FInt n1
+unifyForests (FFloat f1) (FFloat f2)
+    | f1 == f2  = return $ FFloat f1
+unifyForests _ _ = fail "forest unification failure"
+
+{- måste tänka mer på detta:
+compactForests :: Ord n => [SyntaxForest n] -> SList (SyntaxForest n)
+compactForests = map joinForests . groupBy eqNames . sortForests
+    where eqNames f g    = forestName f == forestName g
+	  sortForests    = foldMerge mergeForests [] . map return 
+	  mergeForests [] gs = gs
+	  mergeForests fs [] = fs
+	  mergeForests fs@(f:fs') gs@(g:gs') 
+	      = case forestName f `compare` forestName g of
+		  LT ->     f : mergeForests fs' gs
+		  GT ->     g : mergeForests fs  gs'
+		  EQ -> f : g : mergeForests fs' gs'
+	  joinForests fs = case forestName (head fs) of
+			     Nothing   -> FMeta
+			     Just name -> FNode name $
+					  compactDaughters $
+					  concat [ fss | FNode _ fss <- fs ]
+	  compactDaughters fss = case head fss of
+				   []  -> [[]]
+				   [_] -> map return $ compactForests $ concat fss
+				   _   -> nubsort fss
+-}
+
+-- ** syntax trees
+
+data SyntaxTree n = TMeta
+                  | TNode n [SyntaxTree n]
+                  | TString  String
+                  | TInt     Integer
+                  | TFloat   Double
+		  deriving (Eq, Ord, Show)
+
+instance Functor SyntaxTree where
+    fmap f (TNode n trees) = TNode (f n) $ map (fmap f) trees
+    fmap _ (TString s)     = TString s
+    fmap _ (TInt    n)     = TInt    n
+    fmap _ (TFloat  f)     = TFloat  f
+    fmap _ (TMeta)         = TMeta 
+
+treeName :: SyntaxTree n -> Maybe n
+treeName (TNode n _) = Just n
+treeName (TMeta)     = Nothing
+
+unifyManyTrees :: (Monad m, Eq n) => [SyntaxTree n] -> m (SyntaxTree n)
+unifyManyTrees = foldM unifyTrees TMeta
+
+-- | two trees can be unified, if either is 'TMeta', 
+-- or both have the same parent, and their children can be unified
+unifyTrees :: (Monad m, Eq n) => SyntaxTree n -> SyntaxTree n -> m (SyntaxTree n)
+unifyTrees TMeta tree = return tree
+unifyTrees tree TMeta = return tree
+unifyTrees (TNode name1 children1) (TNode name2 children2)
+    | name1 == name2 && sameLength children1 children2 
+	= liftM (TNode name1) $ zipWithM unifyTrees children1 children2 
+unifyTrees (TString s1) (TString s2)
+    | s1 == s2 = return (TString s1)
+unifyTrees (TInt n1) (TInt n2)
+    | n1 == n2 = return (TInt n1)
+unifyTrees (TFloat f1) (TFloat f2)
+    | f1 == f2 = return (TFloat f1)
+unifyTrees _ _ = fail "tree unification failure"
+
+-- ** conversions between representations
+
+chart2forests :: (Ord n, Ord e) => 
+		 SyntaxChart n e  -- ^ The complete chart
+	      -> (e -> Bool)      -- ^ When is an edge 'FMeta'?
+	      -> [e]              -- ^ The starting edges
+	      -> SList (SyntaxForest n) -- ^ The result has unique keys, ie. all 'n' are joined together.
+					-- In essence, the result is a map from 'n' to forest daughters
+
+-- simplest implementation
+
+chart2forests chart isMeta = concatMap (edge2forests [])
+    where edge2forests edges edge
+              | isMeta edge       = [FMeta]
+              | edge `elem` edges = []
+              | otherwise         = map (item2forest (edge:edges)) $ chart ? edge
+          item2forest edges (SMeta)               = FMeta
+          item2forest edges (SNode name children) = 
+                                    FNode name $ children >>= mapM (edge2forests edges)
+          item2forest edges (SString s)           = FString s
+          item2forest edges (SInt    n)           = FInt    n
+          item2forest edges (SFloat  f)           = FFloat  f
+
+{- -before AR inserted peb's patch 8/7/2007, this was:
+
+chart2forests chart isMeta  = concatMap edge2forests
+    where edge2forests edge = if isMeta edge then [FMeta]
+			      else map item2forest $ chart ? edge
+	  item2forest (SMeta)               = FMeta
+	  item2forest (SNode name children) = FNode name $ children >>= mapM edge2forests
+	  item2forest (SString s)           = FString s
+	  item2forest (SInt    n)           = FInt    n
+	  item2forest (SFloat  f)           = FFloat  f
+	  
+-}
+
+{-
+-- more intelligent(?) implementation,
+-- requiring that charts and forests are sorted maps and sorted sets
+chart2forests chart isMeta = es2fs
+    where e2fs  e  = if isMeta e then [FMeta] else map i2f $ chart ? e
+	  es2fs es = if null metas then fs else FMeta : fs
+	      where (metas, nonMetas) = splitBy isMeta es
+		    fs = map i2f $ unionMap (<++>) $ map (chart ?) nonMetas
+	  i2f (name, children) = FNode name $ 
+				 case head children of
+				   []  -> [[]]
+				   [_] -> map return $ es2fs $ concat children
+				   _   -> children >>= mapM e2fs
+-}
+
+
+forest2trees :: SyntaxForest n -> SList (SyntaxTree n)
+forest2trees (FNode n forests) = map (TNode n) $ forests >>= mapM forest2trees
+forest2trees (FString s) = [TString s]
+forest2trees (FInt    n) = [TInt    n]
+forest2trees (FFloat  f) = [TFloat  f]
+forest2trees (FMeta)     = [TMeta]
+
+----------------------------------------------------------------------
+-- * profiles
+
+-- | Pairing a rule name with a profile
+data NameProfile a = Name a [Profile (SyntaxForest a)]
+		     deriving (Eq, Ord, Show)
+
+name2fun :: NameProfile a -> a
+name2fun (Name fun _) = fun
+
+-- | A profile is a simple representation of a function on a number of arguments.
+-- We only use lists of profiles
+data Profile a = Unify [Int] -- ^ The Int's are the argument positions.
+			     -- 'Unify []' will become a metavariable,
+			     -- 'Unify [a,b]' means that the arguments are equal,
+	       | Constant a
+		 deriving (Eq, Ord, Show)
+
+instance Functor Profile where
+    fmap f (Constant a) = Constant (f a)
+    fmap f (Unify xs)   = Unify xs
+
+-- | a function name where the profile does not contain arguments 
+-- (i.e. denoting a constant, not a function)
+constantNameToForest :: NameProfile a -> SyntaxForest a
+constantNameToForest name@(Name fun profile) = FNode fun [map unConstant profile] 
+    where unConstant (Constant a) = a
+	  unConstant (Unify [])   = FMeta
+	  unConstant _ = error $ "constantNameToForest: the profile should not contain arguments"
+
+-- | profile application; we need some way of unifying a list of arguments
+applyProfile :: ([b] -> a) -> [Profile a] -> [b] -> [a]
+applyProfile unify profile args = map apply profile
+    where apply (Unify xs)  = unify $ map (args !!) xs
+	  apply (Constant a) = a
+
+-- | monadic profile application
+applyProfileM :: Monad m => ([b] -> m a) -> [Profile a] -> [b] -> m [a]
+applyProfileM unify profile args = mapM apply profile
+    where apply (Unify xs)  = unify $ map (args !!) xs
+	  apply (Constant a) = return a
+
+-- | profile composition: 
+-- 
+-- >   applyProfile u z (ps `composeProfiles` qs) args
+-- >      ==
+-- >   applyProfile u z ps (applyProfile u z qs args)
+--
+-- compare with function composition
+--
+-- >   (p . q) arg
+-- >      ==
+-- >   p (q arg)
+--
+-- Note that composing an 'Constant' with two or more arguments returns an error
+-- (since 'Unify' can only take arguments) -- this might change in the future, if there is a need.
+composeProfiles :: [Profile a] -> [Profile a] -> [Profile a]
+composeProfiles ps qs = map compose ps
+    where compose (Unify [x]) = qs !! x
+	  compose (Unify xs)  = Unify [ y | x <- xs, let Unify ys = qs !! x, y <- ys ]
+	  compose constant    = constant
+
+
+
+------------------------------------------------------------
+-- pretty-printing
+
+instance (Print c, Print t) => Print (Symbol c t) where
+    prt = symbol prt (simpleShow . prt)
+	where simpleShow str = "\"" ++ concatMap mkEsc str ++ "\""
+	      mkEsc '\\' = "\\\\"
+	      mkEsc '\"' = "\\\""
+	      mkEsc '\n' = "\\n"
+	      mkEsc '\t' = "\\t"
+	      mkEsc chr  = [chr]
+    prtList = prtSep " "
+
+instance Print t => Print (Input t) where
+    prt input = "input " ++ prt (inputEdges input)
+
+instance (Print s) => Print (Edge s) where
+    prt (Edge i j s) = "[" ++ show i ++ "-" ++ show j ++ ": " ++ prt s ++ "]"
+    prtList = prtSep ""
+
+instance (Print s) => Print (SyntaxTree s) where
+    prt (TNode s trees)
+	| null trees = prt s
+	| otherwise  = "(" ++ prt s ++ prtBefore " " trees ++ ")"
+    prt (TString  s) = show s
+    prt (TInt     n) = show n
+    prt (TFloat   f) = show f
+    prt (TMeta)      = "?"
+    prtList = prtAfter "\n"
+
+instance (Print s) => Print (SyntaxForest s) where
+    prt (FNode s []) = "(" ++ prt s ++ " - ERROR: null forests)"
+    prt (FNode s [[]]) = prt s
+    prt (FNode s [forests]) = "(" ++ prt s ++ prtBefore " " forests ++ ")"
+    prt (FNode s children) = "{" ++ prtSep " | " [ prt s ++ prtBefore " " forests | 
+						   forests <- children ] ++ "}"
+    prt (FString s) = show s
+    prt (FInt    n) = show n
+    prt (FFloat  f) = show f
+    prt (FMeta)     = "?"
+    prtList = prtAfter "\n"
+
+instance Print a => Print (Profile a) where
+    prt (Unify [])   = "?"
+    prt (Unify args) = prtSep "=" args
+    prt (Constant a) = prt a
+
+instance Print a => Print (NameProfile a) where
+    prt (Name fun profile) = prt fun ++ prt profile
+
+