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|
----------------------------------------------------------------------
-- |
-- Module : FiniteState
-- Maintainer : BB
-- Stability : (stable)
-- Portability : (portable)
--
-- > CVS $Date: 2005/09/15 18:10:44 $
-- > CVS $Author: bringert $
-- > CVS $Revision: 1.11 $
--
-- A simple finite state network module.
-----------------------------------------------------------------------------
module GF.Speech.FiniteState (FA, State, NFA, DFA,
startState, finalStates,
states, transitions,
newFA,
addFinalState,
newState, newTransition,
mapStates, mapTransitions,
moveLabelsToNodes, minimize,
prFAGraphviz) where
import GF.Data.Utilities
import Data.List
import Data.Maybe (catMaybes,fromJust)
import GF.Data.Utilities
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
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 :: NFA a -> NFA a
minimize = onGraph id
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
-- | 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 = onGraph moveLabelsToNodes_
where moveLabelsToNodes_ gr@(Graph c _ _) = Graph c' ns (concat ess)
where is = incoming gr
(c',is') = mapAccumL fixIncoming c is
(ns,ess) = unzip (concat is')
fixIncoming :: (Eq 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
reachable :: (Eq b, Ord n) => Graph n a (Maybe b) -> n -> b -> [n]
reachable g s c = fix reachable_ [s]
where reachable_ r = r `union` [y | x <- r, es <- outf x, (_,y,l) <- es, maybe True (==c) l]
out = outgoing g
outf x = [ es | ((y,_),es) <- out, x == y ]
determinize :: Eq a => NFA a -> DFA a
determinize (FA g s f) = undefined
where sigma = alphabet g
--
-- * Visualization
--
prFAGraphviz :: (Eq n,Show n) => FA n String String -> String
prFAGraphviz = Dot.prGraphviz . toGraphviz
toGraphviz :: (Eq n,Show n) => FA n String String -> Dot.Graph
toGraphviz (FA (Graph _ ns es) s f) = Dot.Graph Dot.Directed [] (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)]
--
-- * Graphs
--
data Graph n a b = Graph [n] [Node n a] [Edge n b]
deriving (Eq,Show)
type Node n a = (n,a)
type Edge n b = (n,n,b)
newGraph :: [n] -> Graph n a b
newGraph ns = Graph ns [] []
nodes :: Graph n a b -> [Node n a]
nodes (Graph _ ns _) = ns
edges :: Graph n a b -> [Edge n b]
edges (Graph _ _ es) = es
nmap :: (a -> c) -> Graph n a b -> Graph n c b
nmap f (Graph c ns es) = Graph c [(n,f l) | (n,l) <- ns] es
emap :: (b -> c) -> Graph n a b -> Graph n a c
emap f (Graph c ns es) = Graph c ns [(x,y,f l) | (x,y,l) <- es]
newNode :: a -> Graph n a b -> (Graph n a b,n)
newNode l (Graph (c:cs) ns es) = (Graph cs ((c,l):ns) es, c)
newEdge :: n -> n -> b -> Graph n a b -> Graph n a b
newEdge f t l (Graph c ns es) = Graph c ns ((f,t,l):es)
incoming :: Ord n => Graph n a b -> [(Node n a,[Edge n b])]
incoming = groupEdgesBy getTo
outgoing :: Ord n => Graph n a b -> [(Node n a,[Edge n b])]
outgoing = groupEdgesBy getTo
groupEdgesBy :: (Ord n) => (Edge n b -> n) -> Graph n a b -> [(Node n a,[Edge n b])]
groupEdgesBy h (Graph _ ns es) =
snd $ mapAccumL f (sortBy (compareBy h) es) (sortBy (compareBy fst) ns)
where f es' v@(n,_) = let (nes,es'') = span ((==n) . h) es' in (es'',(v,nes))
getFrom :: Edge n b -> n
getFrom (f,_,_) = f
getTo :: Edge n b -> n
getTo (_,t,_) = t
getLabel :: Edge n b -> b
getLabel (_,_,l) = l
reverseGraph :: Graph n a b -> Graph n a b
reverseGraph (Graph c ns es) = Graph c ns [ (t,f,l) | (f,t,l) <- es ]
|
