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106 lines
3.3 KiB
Haskell
106 lines
3.3 KiB
Haskell
module GF.Speech.FiniteState (FA, State,
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startState, finalStates,
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states, transitions,
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moveLabelsToNodes) where
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import Data.Graph.Inductive
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import Data.List (nub,partition)
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import Data.Maybe (fromJust)
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import Debug.Trace
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data FA a b = FA (Gr a b) Node [Node]
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type State = Node
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startState :: FA a b -> State
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startState (FA _ s _) = s
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finalStates :: FA a b -> [State]
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finalStates (FA _ _ ss) = ss
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states :: FA a b -> [(State,a)]
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states (FA g _ _) = labNodes g
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transitions :: FA a b -> [(State,State,b)]
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transitions (FA g _ _) = labEdges g
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onGraph :: (Gr a b -> Gr c d) -> FA a b -> FA c d
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onGraph f (FA g s ss) = FA (f g) s ss
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newState :: a -> FA a b -> (FA a b, State)
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newState x (FA g s ss) = (FA g' s ss, n)
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where (g',n) = addNode x g
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newEdge :: Node -> Node -> b -> FA a b -> FA a b
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newEdge f t l = onGraph (insEdge (f,t,l))
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addNode :: DynGraph gr => a -> gr a b -> (gr a b, Node)
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addNode x g = let s = freshNode g in (insNode (s,x) g, s)
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freshNode :: Graph gr => gr a b -> Node
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freshNode = succ . snd . nodeRange
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-- | Get an infinte supply of new nodes.
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freshNodes :: Graph gr => gr a b -> [Node]
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freshNodes g = [snd (nodeRange g)+1..]
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-- | Transform a standard finite automaton with labelled edges
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-- to one where the labels are on the nodes instead. This can add
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-- up to one extra node per edge.
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moveLabelsToNodes :: Eq a => FA () (Maybe a) -> FA (Maybe a) ()
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moveLabelsToNodes = onGraph moveLabelsToNodes_
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moveLabelsToNodes_ :: (DynGraph gr, Eq a) => gr () (Maybe a) -> gr (Maybe a) ()
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moveLabelsToNodes_ g = gmap f g'
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where g' = sameLabelIncoming g
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f (to,n,(),fr) = (removeAdjLabels to, n, l, removeAdjLabels fr)
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where l | not (allEqual ls)
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= error $ "moveLabelsToNodes: not all incoming labels are equal"
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| null ls = Nothing
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| otherwise = head ls
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ls = map snd $ lpre g' n
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removeAdjLabels = map (\ (_,n) -> ((),n))
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-- | Add the extra nodes needed to make sure that all edges to a node
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-- have the same label.
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sameLabelIncoming :: (DynGraph gr, Eq b) => gr () (Maybe b) -> gr () (Maybe b)
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sameLabelIncoming gr = foldr fixIncoming gr (nodes gr)
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fixIncoming :: (DynGraph gr, Eq b) => Node -> gr () (Maybe b) -> gr () (Maybe b)
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fixIncoming n gr | allLabelsEqual to' = gr
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| otherwise = addContexts newContexts $ delNode n gr
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where (to,_,_,fr) = context gr n
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-- move cyclic edges to the list of incoming edges
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(cyc,fr') = partition (\ (_,t) -> t == n) fr
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to' = to ++ cyc
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-- make new nodes for each unique label
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newNodes = zip (nub $ map fst to') (freshNodes gr)
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-- for each cyclic edge, add an edge to the node for
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-- that label (could be the current node).
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fr'' = fr' ++ [ (l',fromJust (lookup l' newNodes)) | (l',f) <- to', f == n ]
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-- keep all incoming non-cyclic edges with the right label.
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to'' l = [ e | e@(l',f) <- to', l'==l, f /= n ]
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newContexts = [ (to'' l,n',(),fr'') | (l,n') <- newNodes]
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allLabelsEqual :: Eq b => Adj b -> Bool
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allLabelsEqual = allEqual . map fst
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edgeLabel :: LEdge b -> b
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edgeLabel (_,_,l) = l
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ledgeToEdge :: LEdge b -> Edge
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ledgeToEdge (f,t,_) = (f,t)
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addContexts :: DynGraph gr => [Context a b] -> gr a b -> gr a b
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addContexts cs gr = foldr (&) gr cs
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--
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-- * Utilities
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--
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allEqual :: Eq a => [a] -> Bool
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allEqual [] = True
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allEqual (x:xs) = all (==x) xs
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