module FST.Deterministic (
determinize
) where
import FST.Automaton
import Data.List (sort, nub)
newtype SubSet = SubSet [StateTy]
type SubSets = [SubSet]
type Done = SubSets
type UnDone = SubSets
type SubTransitions a = [(SubSet, [(a, SubSet)])]
instance Eq (SubSet) where
SubSet xs == SubSet ys = xs == ys
sub :: [StateTy] -> SubSet
sub sts = SubSet $ sort $ nub sts
containsFinal :: Automaton a -> SubSet -> Bool
containsFinal automaton (SubSet xs) = any (isFinal automaton) xs
determinize :: Ord a => Automaton a -> Automaton a
determinize automaton = let inS = sub $ initials automaton
in det automaton ([],[inS]) []
det :: Ord a => Automaton a -> (Done,UnDone) ->
SubTransitions a -> Automaton a
det auto (done,[]) trans = rename (reverse trans)
(alphabet auto) [sub (initials auto)]
(filter (containsFinal auto) done)
(firstState auto)
det auto (done,subset:undone) trans
| elemSS done subset = det auto (done,undone) trans
| otherwise = let (subs,nTrans) = getTransitions auto subset trans
nsubs = filter (not.(elemSS (subset:done))) subs
in det auto (subset:done,undone++nsubs) nTrans
where elemSS subs sub = elem sub subs
getTransitions :: Ord a => Automaton a -> SubSet ->
SubTransitions a -> (SubSets, SubTransitions a)
getTransitions auto subset@(SubSet xs) trans
= let tr = groupBySymbols (concat $ map (transitionList auto) xs) []
in (map snd tr, (subset,tr):trans)
groupBySymbols :: Eq a => [(a,StateTy)] -> [(a,[StateTy])] -> [(a,SubSet)]
groupBySymbols [] tr = map (\(a,xs) -> (a,sub xs)) tr
groupBySymbols ((a,s):xs) tr = groupBySymbols xs (ins (a,s) tr)
where ins (a1,s1) [] = [(a1,[s1])]
ins (a1,s1) ((b,ys):zs)
| a1 == b = (b,s1:ys):zs
| otherwise = (b,ys): ins (a,s) zs