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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) where
import Data.List
import Data.Maybe (catMaybes,fromJust)
import Data.Map (Map)
import qualified Data.Map as Map
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 = 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 :: (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
determinize :: Ord a => NFA a -> DFA a
determinize (FA g s f) = let (ns,es) = h [start] [] []
final = filter (not . null . (f `intersect`)) ns
fa = FA (Graph undefined [(n,()) | n <- ns] es) start final
in numberStates fa
where out = outgoing g
start = closure out [s]
isDFAFinal n = not (null (f `intersect` n))
-- Get the new DFA states and edges produced by a set of DFA states.
new ns = unzip [ (s, (n,s,c)) | n <- ns, (c,s) <- reachable out n]
h currentStates oldStates oldEdges
| null currentStates = (oldStates,oldEdges)
| otherwise = h newStates' allOldStates (newEdges++oldEdges)
where (newStates,newEdges) = new currentStates
allOldStates = currentStates ++ oldStates
newStates' = nub newStates \\ allOldStates
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 = zip (map fst (nodes g)) ns
newName n = lookup' n newNodes
s' = newName s
fs' = map newName fs
-- | Get all the nodes reachable from a set of nodes by only empty edges.
closure :: Eq n => Outgoing n a (Maybe b) -> [n] -> [n]
closure out = fix closure_
where closure_ r = r `union` [y | x <- r, (_,y,Nothing) <- getOutgoing out x]
-- | Get a map which maps labels to a sort list of all nodes reachable
-- from a given 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) -> [n] -> [(b,[n])]
reachable out ns = Map.toList $ Map.map (sort . closure out) $ Map.fromListWith union [(c,[y]) | n <- ns, (_,y,Just c) <- getOutgoing out n]
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 . toGraphviz
prFAGraphviz_ :: (Eq n,Show n,Show a, Show b) => FA n a b -> String
prFAGraphviz_ = Dot.prGraphviz . toGraphviz . mapStates show . mapTransitions show
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)]
|
