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|
----------------------------------------------------------------------
-- |
-- Module : FiniteState
-- Maintainer : BB
-- Stability : (stable)
-- Portability : (portable)
--
-- > CVS $Date: 2005/09/12 15:46:44 $
-- > CVS $Author: bringert $
-- > CVS $Revision: 1.3 $
--
-- A simple finite state network module.
-----------------------------------------------------------------------------
module GF.Speech.FiniteState (FA, State,
startState, finalStates,
states, transitions,
newFA, addFinalState,
newState, newTransition, newTransitions,
moveLabelsToNodes, minimize, asGraph) where
import Data.Graph.Inductive
import Data.List (nub,partition)
import Data.Maybe (fromJust)
import Debug.Trace
data FA a b = FA (Gr a b) Node [Node]
type State = Node
startState :: FA a b -> State
startState (FA _ s _) = s
finalStates :: FA a b -> [State]
finalStates (FA _ _ ss) = ss
states :: FA a b -> [(State,a)]
states (FA g _ _) = labNodes g
transitions :: FA a b -> [(State,State,b)]
transitions (FA g _ _) = labEdges g
newFA :: a -- ^ Start node label
-> FA a b
newFA l = FA g' s []
where g = empty
s = freshNode g
g' = insNode (s,l) g
addFinalState :: Node -> FA a b -> FA a b
addFinalState f (FA g s ss) = FA g s (f:ss)
newState :: a -> FA a b -> (FA a b, State)
newState x (FA g s ss) = (FA g' s ss, n)
where (g',n) = addNode x g
newTransition :: Node -> Node -> b -> FA a b -> FA a b
newTransition f t l = onGraph (insEdge (f,t,l))
newTransitions :: [(Node,Node,b)] -> FA a b -> FA a b
newTransitions ts = onGraph (insEdges ts)
mapStates :: (a -> c) -> FA a b -> FA c b
mapStates f (FA g s ss) = FA (nmap f g) s ss
asGraph :: FA a b -> Gr a b
asGraph (FA g _ _) = g
minimize :: FA () (Maybe a) -> FA () (Maybe a)
minimize = onGraph mimimizeGr1
--
-- * Graph functions
--
onGraph :: (Gr a b -> Gr c d) -> FA a b -> FA c d
onGraph f (FA g s ss) = FA (f g) s ss
addNode :: DynGraph gr => a -> gr a b -> (gr a b, Node)
addNode x g = let s = freshNode g in (insNode (s,x) g, s)
freshNode :: Graph gr => gr a b -> Node
freshNode = succ . snd . nodeRange
-- | Get an infinte supply of new nodes.
freshNodes :: Graph gr => gr a b -> [Node]
freshNodes g = [snd (nodeRange g)+1..]
-- | 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 :: Eq a => FA () (Maybe a) -> FA (Maybe a) ()
moveLabelsToNodes = onGraph moveLabelsToNodes_
moveLabelsToNodes_ :: (DynGraph gr, Eq a) => gr () (Maybe a) -> gr (Maybe a) ()
moveLabelsToNodes_ g = gmap f g'
where g' = sameLabelIncoming g
f (to,n,(),fr) = (removeAdjLabels to, n, l, removeAdjLabels fr)
where l | not (allEqual ls)
= error $ "moveLabelsToNodes: not all incoming labels are equal"
| null ls = Nothing
| otherwise = head ls
ls = map snd $ lpre g' n
removeAdjLabels = map (\ (_,n) -> ((),n))
-- | Add the extra nodes needed to make sure that all edges to a node
-- have the same label.
sameLabelIncoming :: (DynGraph gr, Eq b) => gr () (Maybe b) -> gr () (Maybe b)
sameLabelIncoming gr = foldr fixIncoming gr (nodes gr)
fixIncoming :: (DynGraph gr, Eq b) => Node -> gr () (Maybe b) -> gr () (Maybe b)
fixIncoming n gr | allLabelsEqual to' = gr
| otherwise = addContexts newContexts $ delNode n gr
where (to,_,_,fr) = context gr n
-- move cyclic edges to the list of incoming edges
(cyc,fr') = partition (\ (_,t) -> t == n) fr
to' = to ++ cyc
-- make new nodes for each unique label
newNodes = zip (nub $ map fst to') (freshNodes gr)
-- for each cyclic edge, add an edge to the node for
-- that label (could be the current node).
fr'' = fr' ++ [ (l',fromJust (lookup l' newNodes)) | (l',f) <- to', f == n ]
-- keep all incoming non-cyclic edges with the right label.
to'' l = [ e | e@(l',f) <- to', l'==l, f /= n ]
newContexts = [ (to'' l,n',(),fr'') | (l,n') <- newNodes]
allLabelsEqual :: Eq b => Adj b -> Bool
allLabelsEqual = allEqual . map fst
edgeLabel :: LEdge b -> b
edgeLabel (_,_,l) = l
ledgeToEdge :: LEdge b -> Edge
ledgeToEdge (f,t,_) = (f,t)
addContexts :: DynGraph gr => [Context a b] -> gr a b -> gr a b
addContexts cs gr = foldr (&) gr cs
mimimizeGr1 :: DynGraph gr => gr () (Maybe a) -> gr () (Maybe a)
mimimizeGr1 = removeEmptyLoops
removeEmptyLoops :: DynGraph gr => gr () (Maybe a) -> gr () (Maybe a)
removeEmptyLoops = gmap (\ (i,n,(),o) -> (filter (r n) i,n,(),filter (r n) o))
where r n (Nothing,n') | n' == n = False
r _ _ = True
mimimizeGr2 :: DynGraph gr => gr (Maybe a) () -> gr (Maybe a) ()
mimimizeGr2 gr = gr
--
-- * Utilities
--
allEqual :: Eq a => [a] -> Bool
allEqual [] = True
allEqual (x:xs) = all (==x) xs
|
