```{-
**************************************************************
* Filename      : Deterministic.hs                           *
* Author        : Markus Forsberg                            *
*                 d97forma@dtek.chalmers.se                  *
* Lines         : 78                                         *
**************************************************************
-}

module FST.Deterministic ( determinize  -- Makes an automaton deterministic and usefulS.
) where

import FST.Automaton

import Data.List (sort, nub)

{- *************************************
* Types for subsets.                *
*************************************
-}

newtype SubSet  = SubSet [State] -- a subset is an ordered set
-- without duplication.
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 :: [State] -> SubSet
sub sts = SubSet \$ sort \$ nub sts

containsFinal :: Automaton a -> SubSet -> Bool
containsFinal automaton (SubSet xs) = or \$ map (isFinal automaton) xs

{- ************************************************
* Construct a deterministic, usefulS automaton. *
************************************************
-}

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,State)] -> [(a,[State])] -> [(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
```