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|
----------------------------------------------------------------------
-- |
-- Module : FiniteState
-- Maintainer : BB
-- Stability : (stable)
-- Portability : (portable)
--
-- > CVS $Date: 2005/09/12 22:32:24 $
-- > CVS $Author: bringert $
-- > CVS $Revision: 1.6 $
--
-- A simple finite state network module.
-----------------------------------------------------------------------------
module GF.Speech.FiniteState (FA, State,
startState, finalStates,
states, transitions,
newFA,
addFinalState,
newState, newTransition,
mapStates, mapTransitions,
moveLabelsToNodes, minimize,
prGraphGraphviz) where
import Data.List
import Data.Maybe (fromJust)
import Debug.Trace
data FA a b = FA (Graph a b) State [State]
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 _ _) = nodes g
transitions :: FA a b -> [(State,State,b)]
transitions (FA g _ _) = edges g
newFA :: a -- ^ Start node label
-> FA a b
newFA l = FA g s []
where (g,s) = newNode l newGraph
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) = newNode x g
newTransition :: Node -> Node -> b -> FA a b -> FA a b
newTransition f t l = onGraph (newEdge f t l)
mapStates :: (a -> c) -> FA a b -> FA c b
mapStates f = onGraph (nmap f)
mapTransitions :: (b -> c) -> FA a b -> FA a c
mapTransitions f = onGraph (emap f)
asGraph :: FA a b -> Graph a b
asGraph (FA g _ _) = g
minimize :: FA () (Maybe a) -> FA () (Maybe a)
minimize = onGraph mimimizeGr1
-- | 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_
prGraphGraphviz :: FA String String -> String
prGraphGraphviz (FA (Graph _ ns es) _ _) =
"digraph {\n" ++ unlines (map prNode ns)
++ "\n"
++ unlines (map prEdge es)
++ "\n}\n"
where prNode (n,l) = show n ++ " [label = " ++ show l ++ "]"
prEdge (f,t,l) = show f ++ " -> " ++ show t ++ " [label = " ++ show l ++ "]"
--
-- * Graphs
--
type Node = Int
data Graph a b = Graph Node [(Node,a)] [(Node,Node,b)]
deriving (Eq,Show)
onGraph :: (Graph a b -> Graph c d) -> FA a b -> FA c d
onGraph f (FA g s ss) = FA (f g) s ss
-- graphToFA :: State -> [State] -> Graph a b -> FA a b
-- graphToFA s fs (Graph _ ss ts) = buildFA s fs ss ts
newGraph :: Graph a b
newGraph = Graph 0 [] []
nodes :: Graph a b -> [(Node,a)]
nodes (Graph _ ns _) = ns
edges :: Graph a b -> [(Node,Node,b)]
edges (Graph _ _ es) = es
nmap :: (a -> c) -> Graph a b -> Graph c b
nmap f (Graph c ns es) = Graph c [(n,f l) | (n,l) <- ns] es
emap :: (b -> c) -> Graph a b -> Graph a c
emap f (Graph c ns es) = Graph c ns [(x,y,f l) | (x,y,l) <- es]
newNode :: a -> Graph a b -> (Graph a b,State)
newNode l (Graph c ns es) = (Graph s ((s,l):ns) es, s)
where s = c+1
newEdge :: State -> State -> b -> Graph a b -> Graph a b
newEdge f t l (Graph c ns es) = Graph c ns ((f,t,l):es)
incoming :: Graph a b -> [(Node,a,[(Node,Node,b)])]
incoming (Graph _ ns es) = snd $ mapAccumL f (sortBy compareDest es) (sortBy compareFst ns)
where destIs d (_,t,_) = t == d
compareDest (_,t1,_) (_,t2,_) = compare t1 t2
compareFst p1 p2 = compare (fst p1) (fst p2)
f es' (n,l) = let (nes,es'') = span (destIs n) es' in (es'',(n,l,nes))
moveLabelsToNodes_ :: Eq a => Graph () (Maybe a) -> Graph (Maybe a) ()
moveLabelsToNodes_ gr@(Graph c _ _) = mimimizeGr2 $ Graph c' (zip ns ls) (concat ess)
where is = incoming gr
(c',is') = mapAccumL fixIncoming c is
(ns,ls,ess) = unzip3 (concat is')
fixIncoming :: Eq a => Node -> (Node,(),[(Node,Node,Maybe a)]) -> (Node,[(Node,Maybe a,[(Node,Node,())])])
fixIncoming next c@(n,(),es) = (next', (n,Nothing,es'):newContexts)
where ls = nub $ map getLabel es
next' = next + length ls
newNodes = zip [next..next'-1] 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 = [ (x, l, to x l) | (x,l) <- newNodes ]
getLabel :: (Node,Node,b) -> b
getLabel (_,_,l) = l
mimimizeGr1 :: Graph () (Maybe a) -> Graph () (Maybe a)
mimimizeGr1 = removeEmptyLoops1
removeEmptyLoops1 :: Graph () (Maybe a) -> Graph () (Maybe a)
removeEmptyLoops1 (Graph c ns es) = Graph c ns (filter (not . isEmptyLoop) es)
where isEmptyLoop (f,t,Nothing) | f == t = True
isEmptyLoop _ = False
mimimizeGr2 :: Graph (Maybe a) () -> Graph (Maybe a) ()
mimimizeGr2 = id
removeDuplicateEdges :: Ord b => Graph a b -> Graph a b
removeDuplicateEdges (Graph c ns es) = Graph c ns (sortNub es)
--
-- * Utilities
--
sortNub :: Ord a => [a] -> [a]
sortNub = map head . group . sort
|
