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|
----------------------------------------------------------------------
-- |
-- Module : FiniteState
-- Maintainer : BB
-- Stability : (stable)
-- Portability : (portable)
--
-- > CVS $Date: 2005/11/10 16:43:44 $
-- > CVS $Author: bringert $
-- > CVS $Revision: 1.16 $
--
-- A simple finite state network module.
-----------------------------------------------------------------------------
module GF.Speech.FiniteState (FA, State, NFA, DFA,
startState, finalStates,
states, transitions,
newFA,
addFinalState,
newState, newStates,
newTransition,
mapStates, mapTransitions,
oneFinalState,
moveLabelsToNodes, minimize,
dfa2nfa,
prFAGraphviz, faToGraphviz) where
import Data.List
import Data.Maybe
import Data.Map (Map)
import qualified Data.Map as Map
import Data.Set (Set)
import qualified Data.Set as Set
import GF.Data.Utilities
import GF.Speech.Graph
import qualified GF.Visualization.Graphviz as Dot
type State = Int
data FA n a b = FA !(Graph n a b) !n ![n]
type NFA a = FA State () (Maybe a)
type DFA a = FA State () a
startState :: FA n a b -> n
startState (FA _ s _) = s
finalStates :: FA n a b -> [n]
finalStates (FA _ _ ss) = ss
states :: FA n a b -> [(n,a)]
states (FA g _ _) = nodes g
transitions :: FA n a b -> [(n,n,b)]
transitions (FA g _ _) = edges g
newFA :: Enum n => a -- ^ Start node label
-> FA n a b
newFA l = FA g s []
where (g,s) = newNode l (newGraph [toEnum 0..])
addFinalState :: n -> FA n a b -> FA n a b
addFinalState f (FA g s ss) = FA g s (f:ss)
newState :: a -> FA n a b -> (FA n a b, n)
newState x (FA g s ss) = (FA g' s ss, n)
where (g',n) = newNode x g
newStates :: [a] -> FA n a b -> (FA n a b, [(n,a)])
newStates xs (FA g s ss) = (FA g' s ss, ns)
where (g',ns) = newNodes xs g
newTransition :: n -> n -> b -> FA n a b -> FA n a b
newTransition f t l = onGraph (newEdge (f,t,l))
mapStates :: (a -> c) -> FA n a b -> FA n c b
mapStates f = onGraph (nmap f)
mapTransitions :: (b -> c) -> FA n a b -> FA n a c
mapTransitions f = onGraph (emap f)
minimize :: Ord a => NFA a -> DFA a
minimize = determinize . reverseNFA . dfa2nfa . determinize . reverseNFA
onGraph :: (Graph n a b -> Graph n c d) -> FA n a b -> FA n c d
onGraph f (FA g s ss) = FA (f g) s ss
-- | Make the finite automaton have a single final state
-- by adding a new final state and adding an edge
-- from the old final states to the new state.
oneFinalState :: a -- ^ Label to give the new node
-> b -- ^ Label to give the new edges
-> FA n a b -- ^ The old network
-> FA n a b -- ^ The new network
oneFinalState nl el fa =
let (FA g s fs,nf) = newState nl fa
es = [ (f,nf,el) | f <- fs ]
in FA (newEdges es g) s [nf]
-- | Transform a standard finite automaton with labelled edges
-- to one where the labels are on the nodes instead. This can add
-- up to one extra node per edge.
moveLabelsToNodes :: (Ord n,Eq a) => FA n () (Maybe a) -> FA n (Maybe a) ()
moveLabelsToNodes = removeTrivialEmptyNodes . onGraph f
where f gr@(Graph c _ _) = Graph c' ns (concat ess)
where is = incomingToList $ incoming gr
(c',is') = mapAccumL fixIncoming c is
(ns,ess) = unzip (concat is')
-- | Remove nodes which are not start or final, and have
-- exactly one incoming or exactly one outgoing edge.
removeTrivialEmptyNodes :: FA n (Maybe a) () -> FA n (Maybe a) ()
removeTrivialEmptyNodes = id -- FIXME: implement
fixIncoming :: (Ord n, Eq a) => [n] -> (Node n (),[Edge n (Maybe a)]) -> ([n],[(Node n (Maybe a),[Edge n ()])])
fixIncoming cs c@((n,()),es) = (cs'', ((n,Nothing),es'):newContexts)
where ls = nub $ map getLabel es
(cs',cs'') = splitAt (length ls) cs
newNodes = zip cs' ls
es' = [ (x,n,()) | x <- map fst newNodes ]
-- separate cyclic and non-cyclic edges
(cyc,ncyc) = partition (\ (f,_,_) -> f == n) es
-- keep all incoming non-cyclic edges with the right label
to (x,l) = [ (f,x,()) | (f,_,l') <- ncyc, l == l']
-- for each cyclic edge with the right label,
-- add an edge from each of the new nodes (including this one)
++ [ (y,x,()) | (f,_,l') <- cyc, l == l', (y,_) <- newNodes]
newContexts = [ (v, to v) | v <- newNodes ]
alphabet :: Eq b => Graph n a (Maybe b) -> [b]
alphabet = nub . catMaybes . map getLabel . edges
determinize :: Ord a => NFA a -> DFA a
determinize (FA g s f) = let (ns,es) = h (Set.singleton start) Set.empty Set.empty
(ns',es') = (Set.toList ns, Set.toList es)
final = filter isDFAFinal ns'
fa = FA (Graph undefined [(n,()) | n <- ns'] es') start final
in numberStates fa
where out = outgoing g
-- reach = nodesReachable out
start = closure out $ Set.singleton s
isDFAFinal n = not (Set.null (Set.fromList f `Set.intersection` n))
h currentStates oldStates es
| Set.null currentStates = (oldStates,es)
| otherwise = ((h $! uniqueNewStates) $! allOldStates) $! es'
where
allOldStates = oldStates `Set.union` currentStates
(newStates,es') = new (Set.toList currentStates) Set.empty es
uniqueNewStates = newStates Set.\\ allOldStates
-- Get the sets of states reachable from the given states
-- by consuming one symbol, and the associated edges.
new [] rs es = (rs,es)
new (n:ns) rs es = new ns rs' es'
where cs = reachable out n --reachable reach n
rs' = rs `Set.union` Set.fromList (map snd cs)
es' = es `Set.union` Set.fromList [(n,s,c) | (c,s) <- cs]
numberStates :: (Ord x,Enum y) => FA x a b -> FA y a b
numberStates (FA g s fs) = FA (renameNodes newName rest g) s' fs'
where (ns,rest) = splitAt (length (nodes g)) $ [toEnum 0 .. ]
newNodes = Map.fromList (zip (map fst (nodes g)) ns)
newName n = Map.findWithDefault (error "FiniteState.newName") n newNodes
s' = newName s
fs' = map newName fs
-- | Get all the nodes reachable from a list of nodes by only empty edges.
closure :: Ord n => Outgoing n a (Maybe b) -> Set n -> Set n
closure out x = closure_ x x
where closure_ acc check | Set.null check = acc
| otherwise = closure_ acc' check'
where
reach = Set.fromList [y | x <- Set.toList check,
(_,y,Nothing) <- getOutgoing out x]
acc' = acc `Set.union` reach
check' = reach Set.\\ acc
-- | Get a map of labels to sets of all nodes reachable
-- from a the set of nodes by one edge with the given
-- label and then any number of empty edges.
reachable :: (Ord n,Ord b) => Outgoing n a (Maybe b) -> Set n -> [(b,Set n)]
reachable out ns = Map.toList $ Map.map (closure out . Set.fromList) $ reachable1 out ns
reachable1 out ns = Map.fromListWith (++) [(c, [y]) | n <- Set.toList ns, (_,y,Just c) <- getOutgoing out n]
{-
-- Alternative implementation of reachable, seems to use too much memory.
type Reachable n b = Map n (Map b (Set n))
reachable :: (Ord n, Ord b) => Reachable n b -> Set n -> [(b,Set n)]
reachable r ns = Map.toList $ Map.unionsWith Set.union $ lookups (Set.toList ns) r
nodesReachable :: (Ord n, Ord b) => Outgoing n a (Maybe b) -> Reachable n b
nodesReachable out = Map.map (f . snd) out
where f = Map.map (closure out . Set.fromList) . edgesByLabel
edgesByLabel es = Map.fromListWith (++) [(c,[y]) | (_,y,Just c) <- es]
-}
reverseNFA :: NFA a -> NFA a
reverseNFA (FA g s fs) = FA g''' s' [s]
where g' = reverseGraph g
(g'',s') = newNode () g'
g''' = newEdges [(s',f,Nothing) | f <- fs] g''
dfa2nfa :: DFA a -> NFA a
dfa2nfa = mapTransitions Just
--
-- * Visualization
--
prFAGraphviz :: (Eq n,Show n) => FA n String String -> String
prFAGraphviz = Dot.prGraphviz . faToGraphviz ""
prFAGraphviz_ :: (Eq n,Show n,Show a, Show b) => FA n a b -> String
prFAGraphviz_ = Dot.prGraphviz . faToGraphviz "" . mapStates show . mapTransitions show
faToGraphviz :: (Eq n,Show n) => String -- ^ Graph ID
-> FA n String String -> Dot.Graph
faToGraphviz i (FA (Graph _ ns es) s f) = Dot.Graph Dot.Directed i [] (map mkNode ns) (map mkEdge es) []
where mkNode (n,l) = Dot.Node (show n) attrs
where attrs = [("label",l)]
++ if n == s then [("shape","box")] else []
++ if n `elem` f then [("style","bold")] else []
mkEdge (x,y,l) = Dot.Edge (show x) (show y) [("label",l)]
--
-- * Utilities
--
lookups :: Ord k => [k] -> Map k a -> [a]
lookups xs m = mapMaybe (flip Map.lookup m) xs
|
