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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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aarne
265
src-3.0/GF/Speech/CFGToFiniteState.hs
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265
src-3.0/GF/Speech/CFGToFiniteState.hs
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----------------------------------------------------------------------
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-- |
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-- Module : CFGToFiniteState
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-- Maintainer : BB
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-- Stability : (stable)
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-- Portability : (portable)
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--
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-- > CVS $Date: 2005/11/10 16:43:44 $
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-- > CVS $Author: bringert $
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-- > CVS $Revision: 1.6 $
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--
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-- Approximates CFGs with finite state networks.
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-----------------------------------------------------------------------------
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module GF.Speech.CFGToFiniteState (cfgToFA, makeSimpleRegular,
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MFA(..), MFALabel, cfgToMFA,cfgToFA') where
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import Data.List
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import Data.Maybe
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import Data.Map (Map)
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import qualified Data.Map as Map
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import Data.Set (Set)
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import qualified Data.Set as Set
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import GF.Data.Utilities
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import GF.Formalism.CFG
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import GF.Formalism.Utilities (Symbol(..), mapSymbol, filterCats, symbol, NameProfile(..))
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import GF.Conversion.Types
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import GF.Infra.Ident (Ident)
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import GF.Infra.Option (Options)
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import GF.Compile.ShellState (StateGrammar)
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import GF.Speech.FiniteState
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import GF.Speech.Graph
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import GF.Speech.Relation
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import GF.Speech.TransformCFG
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data Recursivity = RightR | LeftR | NotR
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data MutRecSet = MutRecSet {
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mrCats :: Set Cat_,
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mrNonRecRules :: [CFRule_],
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mrRecRules :: [CFRule_],
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mrRec :: Recursivity
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}
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type MutRecSets = Map Cat_ MutRecSet
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--
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-- * Multiple DFA type
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--
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type MFALabel a = Symbol String a
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data MFA a = MFA String [(String,DFA (MFALabel a))]
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cfgToFA :: Options -> StateGrammar -> DFA Token
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cfgToFA opts s = minimize $ compileAutomaton start $ makeSimpleRegular opts s
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where start = getStartCatCF opts s
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makeSimpleRegular :: Options -> StateGrammar -> CFRules
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makeSimpleRegular opts s = makeRegular $ preprocess $ cfgToCFRules s
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where start = getStartCatCF opts s
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preprocess = topDownFilter start . bottomUpFilter
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. removeCycles
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--
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-- * Compile strongly regular grammars to NFAs
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--
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-- Convert a strongly regular grammar to a finite automaton.
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compileAutomaton :: Cat_ -- ^ Start category
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-> CFRules
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-> NFA Token
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compileAutomaton start g = make_fa (g,ns) s [Cat start] f fa
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where
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(fa,s,f) = newFA_
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ns = mutRecSets g $ mutRecCats False g
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-- | The make_fa algorithm from \"Regular approximation of CFLs: a grammatical view\",
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-- Mark-Jan Nederhof, Advances in Probabilistic and other Parsing Technologies, 2000.
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make_fa :: (CFRules,MutRecSets) -> State -> [Symbol Cat_ Token] -> State
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-> NFA Token -> NFA Token
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make_fa c@(g,ns) q0 alpha q1 fa =
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case alpha of
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[] -> newTransition q0 q1 Nothing fa
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[Tok t] -> newTransition q0 q1 (Just t) fa
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[Cat a] -> case Map.lookup a ns of
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-- a is recursive
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Just n@(MutRecSet { mrCats = ni, mrNonRecRules = nrs, mrRecRules = rs} ) ->
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case mrRec n of
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RightR ->
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-- the set Ni is right-recursive or cyclic
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let new = [(getState c, xs, q1) | CFRule c xs _ <- nrs]
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++ [(getState c, xs, getState d) | CFRule c ss _ <- rs,
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let (xs,Cat d) = (init ss,last ss)]
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in make_fas new $ newTransition q0 (getState a) Nothing fa'
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LeftR ->
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-- the set Ni is left-recursive
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let new = [(q0, xs, getState c) | CFRule c xs _ <- nrs]
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++ [(getState d, xs, getState c) | CFRule c (Cat d:xs) _ <- rs]
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in make_fas new $ newTransition (getState a) q1 Nothing fa'
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where
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(fa',stateMap) = addStatesForCats ni fa
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getState x = Map.findWithDefault
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(error $ "CFGToFiniteState: No state for " ++ x)
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x stateMap
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-- a is not recursive
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Nothing -> let rs = catRules g a
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in foldl' (\f (CFRule _ b _) -> make_fa_ q0 b q1 f) fa rs
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(x:beta) -> let (fa',q) = newState () fa
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in make_fa_ q beta q1 $ make_fa_ q0 [x] q fa'
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where
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make_fa_ = make_fa c
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make_fas xs fa = foldl' (\f' (s1,xs,s2) -> make_fa_ s1 xs s2 f') fa xs
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--
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-- * Compile a strongly regular grammar to a DFA with sub-automata
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--
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cfgToMFA :: Options -> StateGrammar -> MFA Token
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cfgToMFA opts s = buildMFA start $ makeSimpleRegular opts s
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where start = getStartCatCF opts s
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-- | Build a DFA by building and expanding an MFA
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cfgToFA' :: Options -> StateGrammar -> DFA Token
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cfgToFA' opts s = mfaToDFA $ cfgToMFA opts s
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buildMFA :: Cat_ -- ^ Start category
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-> CFRules -> MFA Token
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buildMFA start g = sortSubLats $ removeUnusedSubLats mfa
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where fas = compileAutomata g
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mfa = MFA start [(c, minimize fa) | (c,fa) <- fas]
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mfaStartDFA :: MFA a -> DFA (MFALabel a)
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mfaStartDFA (MFA start subs) =
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fromMaybe (error $ "Bad start MFA: " ++ start) $ lookup start subs
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mfaToDFA :: Ord a => MFA a -> DFA a
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mfaToDFA mfa@(MFA _ subs) = minimize $ expand $ dfa2nfa $ mfaStartDFA mfa
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where
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subs' = Map.fromList [(c, dfa2nfa n) | (c,n) <- subs]
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getSub l = fromJust $ Map.lookup l subs'
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expand (FA (Graph c ns es) s f)
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= foldl' expandEdge (FA (Graph c ns []) s f) es
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expandEdge fa (f,t,x) =
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case x of
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Nothing -> newTransition f t Nothing fa
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Just (Tok s) -> newTransition f t (Just s) fa
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Just (Cat l) -> insertNFA fa (f,t) (expand $ getSub l)
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removeUnusedSubLats :: MFA a -> MFA a
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removeUnusedSubLats mfa@(MFA start subs) = MFA start [(c,s) | (c,s) <- subs, isUsed c]
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where
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usedMap = subLatUseMap mfa
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used = growUsedSet (Set.singleton start)
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isUsed c = c `Set.member` used
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growUsedSet = fix (\s -> foldl Set.union s $ mapMaybe (flip Map.lookup usedMap) $ Set.toList s)
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subLatUseMap :: MFA a -> Map String (Set String)
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subLatUseMap (MFA _ subs) = Map.fromList [(c,usedSubLats n) | (c,n) <- subs]
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usedSubLats :: DFA (MFALabel a) -> Set String
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usedSubLats fa = Set.fromList [s | (_,_,Cat s) <- transitions fa]
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revMultiMap :: (Ord a, Ord b) => Map a (Set b) -> Map b (Set a)
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revMultiMap m = Map.fromListWith Set.union [ (y,Set.singleton x) | (x,s) <- Map.toList m, y <- Set.toList s]
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-- | Sort sub-networks topologically.
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sortSubLats :: MFA a -> MFA a
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sortSubLats mfa@(MFA main subs) = MFA main (reverse $ sortLats usedByMap subs)
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where
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usedByMap = revMultiMap (subLatUseMap mfa)
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sortLats _ [] = []
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sortLats ub ls = xs ++ sortLats ub' ys
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where (xs,ys) = partition ((==0) . indeg) ls
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ub' = Map.map (Set.\\ Set.fromList (map fst xs)) ub
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indeg (c,_) = maybe 0 Set.size $ Map.lookup c ub
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-- | Convert a strongly regular grammar to a number of finite automata,
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-- one for each non-terminal.
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-- The edges in the automata accept tokens, or name another automaton to use.
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compileAutomata :: CFRules
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-> [(Cat_,NFA (Symbol Cat_ Token))]
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-- ^ A map of non-terminals and their automata.
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compileAutomata g = [(c, makeOneFA c) | c <- allCats g]
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where
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mrs = mutRecSets g $ mutRecCats True g
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makeOneFA c = make_fa1 mr s [Cat c] f fa
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where (fa,s,f) = newFA_
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mr = fromJust (Map.lookup c mrs)
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-- | The make_fa algorithm from \"Regular approximation of CFLs: a grammatical view\",
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-- Mark-Jan Nederhof, Advances in Probabilistic and other Parsing Technologies, 2000,
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-- adapted to build a finite automaton for a single (mutually recursive) set only.
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-- Categories not in the set will result in category-labelled edges.
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make_fa1 :: MutRecSet -- ^ The set of (mutually recursive) categories for which
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-- we are building the automaton.
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-> State -- ^ State to come from
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-> [Symbol Cat_ Token] -- ^ Symbols to accept
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-> State -- ^ State to end up in
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-> NFA (Symbol Cat_ Token) -- ^ FA to add to.
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-> NFA (Symbol Cat_ Token)
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make_fa1 mr q0 alpha q1 fa =
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case alpha of
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[] -> newTransition q0 q1 Nothing fa
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[t@(Tok _)] -> newTransition q0 q1 (Just t) fa
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[c@(Cat a)] | not (a `Set.member` mrCats mr) -> newTransition q0 q1 (Just c) fa
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[Cat a] ->
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case mrRec mr of
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NotR -> -- the set is a non-recursive (always singleton) set of categories
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-- so the set of category rules is the set of rules for the whole set
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make_fas [(q0, b, q1) | CFRule _ b _ <- mrNonRecRules mr] fa
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RightR -> -- the set is right-recursive or cyclic
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let new = [(getState c, xs, q1) | CFRule c xs _ <- mrNonRecRules mr]
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++ [(getState c, xs, getState d) | CFRule c ss _ <- mrRecRules mr,
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let (xs,Cat d) = (init ss,last ss)]
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in make_fas new $ newTransition q0 (getState a) Nothing fa'
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LeftR -> -- the set is left-recursive
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let new = [(q0, xs, getState c) | CFRule c xs _ <- mrNonRecRules mr]
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++ [(getState d, xs, getState c) | CFRule c (Cat d:xs) _ <- mrRecRules mr]
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in make_fas new $ newTransition (getState a) q1 Nothing fa'
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where
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(fa',stateMap) = addStatesForCats (mrCats mr) fa
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getState x = Map.findWithDefault
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(error $ "CFGToFiniteState: No state for " ++ x)
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x stateMap
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(x:beta) -> let (fa',q) = newState () fa
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in make_fas [(q0,[x],q),(q,beta,q1)] fa'
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where
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make_fas xs fa = foldl' (\f' (s1,xs,s2) -> make_fa1 mr s1 xs s2 f') fa xs
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mutRecSets :: CFRules -> [Set Cat_] -> MutRecSets
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mutRecSets g = Map.fromList . concatMap mkMutRecSet
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where
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mkMutRecSet cs = [ (c,ms) | c <- csl ]
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where csl = Set.toList cs
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rs = catSetRules g cs
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(nrs,rrs) = partition (ruleIsNonRecursive cs) rs
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ms = MutRecSet {
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mrCats = cs,
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mrNonRecRules = nrs,
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mrRecRules = rrs,
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mrRec = rec
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}
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rec | null rrs = NotR
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| all (isRightLinear cs) rrs = RightR
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| otherwise = LeftR
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--
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-- * Utilities
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--
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-- | Add a state for the given NFA for each of the categories
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-- in the given set. Returns a map of categories to their
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-- corresponding states.
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addStatesForCats :: Set Cat_ -> NFA t -> (NFA t, Map Cat_ State)
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addStatesForCats cs fa = (fa', m)
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where (fa', ns) = newStates (replicate (Set.size cs) ()) fa
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m = Map.fromList (zip (Set.toList cs) (map fst ns))
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