diff --git a/HaLeX.cabal b/HaLeX.cabal
new file mode 100644
--- /dev/null
+++ b/HaLeX.cabal
@@ -0,0 +1,43 @@
+name:                HaLeX
+version:             1.1
+synopsis:            HaLeX enables modelling, manipulation and animation of regular languages
+description:         This library was developed in the context of a programming methodology course for
+                     undergraduate students, and as a consequence, it was defined mainly for educational purposes.
+                     Indeed, it provides a clear, efficient and concise way to define, to understand
+                     and to manipulate regular languages in Haskell. Furthermore, the construction
+                     of the complete library has been proposed as assignment projects to the students
+                     following the course.  HaLeX is now being used to support this course.
+category:            Data
+license:             PublicDomain
+license-file:        LICENSE
+author:              João Saraiva
+maintainer:          João Saraiva <jas@di.uminho.pt>
+homepage:            http://www.di.uminho.pt/~jas/Research/HaLeX/HaLeX.html
+
+tested-with:         GHC==6.8.2
+Cabal-Version:       >= 1.2
+build-type:          Simple
+data-files:          README, INSTALL, paper/HaLeX.ps, example/README, example/real_dfa.ps, example/real_ndfa.ps
+extra-source-files:  scripts/Make_Animation, scripts/faAnim.lefty, example/real, example/real_dfa.hs,
+                     example/real_ndfa.hs, example/GenMDfa.hs
+Library
+        build-depends:          base, mtl
+        extensions:             FlexibleContexts, FlexibleInstances, MultiParamTypeClasses
+
+        ghc-options:         -O2 -Wall -optl-Wl,-s
+        ghc-prof-options:    -prof -auto-all
+
+        hs-source-dirs:         HaLeX_lib
+        Exposed-modules:        Language.HaLex.RegExpAsDiGraph, Language.HaLex.Ndfa, Language.HaLex.Dfa2MDfa, Language.HaLex.Minimize,
+                                Language.HaLex.Examples.Real, Language.HaLex.Examples.Robot, Language.HaLex.RegExpParser,
+                                Language.HaLex.FaClasses, Language.HaLex.RegExp, Language.HaLex.Dfa, Language.HaLex.DfaMonad,
+                                Language.HaLex.Fa2RegExp, Language.HaLex.Parser, Language.HaLex.RegExp2Fa, Language.HaLex.FaAsDiGraph,
+                                Language.HaLex.FaOperations, Language.HaLex.Util, Language.HaLex.Equivalence
+
+Executable halex
+           executable:          halex
+           main-is:             halex.hs
+           hs-source-dirs:      HaLeX_tool, HaLeX_lib
+
+           ghc-options:         -O2 -Wall -optl-Wl,-s
+           ghc-prof-options:    -prof -auto-al
diff --git a/HaLeX_lib/Language/HaLex/Dfa.hs b/HaLeX_lib/Language/HaLex/Dfa.hs
new file mode 100644
--- /dev/null
+++ b/HaLeX_lib/Language/HaLex/Dfa.hs
@@ -0,0 +1,453 @@
+{-# LANGUAGE FlexibleContexts #-}
+-----------------------------------------------------------------------------
+-- |
+-- Module      :  Language.HaLex.Dfa
+-- Copyright   :  (c) Jooo Saraiva 2001,2002,2003,2004,2005
+-- License     :  LGPL
+--
+-- Maintainer  :  jas@di.uminho.pt
+-- Stability   :  provisional
+-- Portability :  portable
+--
+-- Deterministic Finite Automata in Haskell.
+--
+-- Code Included in the Lecture Notes on
+--      Language Processing (with a functional flavour).
+--
+-----------------------------------------------------------------------------
+
+module Language.HaLex.Dfa (
+              -- * Data type
+                Dfa (..)
+              -- * Acceptance
+              , dfaaccept
+              , dfawalk
+              -- * Transformation
+              , ttDfa2Dfa
+              , dfa2tdfa
+              -- * Transitions
+              , transitionsFromTo
+              , destinationsFrom
+              , transitionTableDfa
+              , reachedStatesFrom
+              -- * Printing
+              , beautifyDfa
+              , renameDfa
+              , showDfaDelta
+              , beautifyDfaWithSyncSt
+              , dfaIO
+              -- * Properties of 'Dfa'
+              , sizeDfa
+              , dfadeadstates
+              -- * Properties of States
+              , isStDead
+              , isStSync
+              , numberOutgoingArrows
+              , numberIncomingArrows
+           ) where
+
+import Data.List
+
+import Language.HaLex.Util
+
+-----------------------------------------------------------------------------
+-- * Data type with the acceptance function
+
+-- | The type of Deterministic Finite Automata parameterized with
+--   the type @st@ of states and @sy@ of symbols.
+
+data Dfa st sy = Dfa [sy]              -- Vocabulary
+                     [st]              -- Finite set of states
+                     st                -- The start state
+                     [st]              -- The set of final states
+                     (st -> sy -> st)  -- Transition Function
+
+
+-----------------------------------------------------------------------------
+-- * Acceptance
+
+
+-- | Execute the transition function of a 'Dfa' on an initial state
+--   and list of input symbol. Return the final state when all input
+--   symbols have been consumed.
+
+dfawalk :: (st -> sy -> st) -- ^ Transition function
+        -> st               -- ^ Initial state
+        -> [sy]             -- ^ Input symbols
+        -> st               -- ^ Final state
+dfawalk delta s [] = s
+dfawalk delta s (x:xs) = dfawalk delta (delta s x) xs
+
+
+-- | Test whether the given automaton accepts the given list of
+--   input symbols.
+
+dfaaccept' :: Eq st
+           => Dfa st sy  -- ^ Automaton
+           -> [sy]       -- ^ Input symbols
+           -> Bool
+dfaaccept' (Dfa v q s z delta) simb  = (dfawalk delta s simb) `elem` z
+
+
+-- | Test whether the given automaton accepts the given list of
+--   input symbols (expressed as a fold).
+
+dfaaccept :: Eq st
+           => Dfa st sy  -- ^ Automaton
+           -> [sy]       -- ^ Input symbols
+           -> Bool
+dfaaccept (Dfa v q s z delta) simb   = (foldl delta s simb) `elem` z
+
+
+
+-----------------------------------------------------------------------------
+-- * Printing
+
+-- | Print a 'Dfa' as a Haskell function.
+
+instance (Show st, Show sy) => Show (Dfa st sy) where
+      showsPrec p (Dfa v q s z delta) =
+                showString ("dfa = Dfa v q s z delta") .
+                showString ("\n  where \n\t v = ") .
+                showList v .
+                showString ("\n\t q = ") .
+                showList q .
+                showString ("\n\t s = ") .
+                shows s .
+                showString ("\n\t z = ") .
+                showList z .
+                showString ("\n\t -- delta :: st -> sy -> st \n") .
+                showDfaDelta q v delta
+
+-- | Helper function to show the transition function of a 'Dfa'.
+
+showDfaDelta :: (Show st, Show sy)
+             => [st] -> [sy] -> (st -> sy -> st) -> [Char] -> [Char]
+
+showDfaDelta q v d = foldr (.) (showChar '\n') f
+  where
+    f     = zipWith3 showF m n q'
+    (m,n) = unzip l
+    q'    = map (uncurry d) l
+    l     = [(a,b) | a <- q , b <- v]
+
+    showF st sy st' = showString("\t delta ") .
+                      shows st .
+                      showChar(' ') .
+                      shows sy .
+                      showString(" = ") .
+                      shows st' .
+                      showChar('\n')
+
+
+-- | Write a 'Dfa' to a Haskell module in a file.
+
+dfaIO :: (Show st , Show sy)
+      => (Dfa st sy)   -- ^ Automaton
+      -> String        -- ^ Haskell module name
+      -> IO ()
+dfaIO afd modulename =
+          writeFile (modulename ++ ".hs")
+                    ("module " ++ modulename ++ " where\n\nimport Dfa\n\n"
+                                 ++ (show afd))
+
+
+-----------------------------------------------------------------------------
+-- * Transitions
+
+
+-- | Compute the labels with the same (giving) origin and destination states
+
+transitionsFromTo :: Eq st
+                  => (st -> sy -> st)      -- ^ Transition function
+                  -> [sy]                  -- ^ Vocabulary
+                  -> st                    -- ^ Origin
+                  -> st                    -- ^ Destination
+                  -> [sy]                  -- ^ Labels
+transitionsFromTo delta vs o d = [ v
+                                 | v <- vs
+                                 , delta o v == d
+                                 ]
+
+
+-- | Compute the destination states giving the origin state
+
+destinationsFrom :: (st -> sy -> st)       -- ^ Tansition Function
+                 -> [sy]                   -- ^ Vocabulary
+                 -> st                     -- ^ Origin
+                 -> [st]                   -- ^ Destination States
+destinationsFrom delta vs o = [ delta o v | v <- vs ]
+
+
+-- | Compute the states that can be reached from a state
+--   according to a given transition function and vocabulary
+
+reachedStatesFrom :: (Eq [st], Ord st)
+                  => (st -> sy -> st)       -- ^ Transition function
+                  -> [sy]                   -- ^ Vocabulary
+                  -> st                     -- ^ Origin
+                  -> [st]                   -- ^ Reached states
+
+reachedStatesFrom d v origin = origin : qs
+  where qs      = limit stPath' (destinationsFrom d v origin)
+        stPath' = stPath d v
+
+
+stPath  :: Ord st => (st -> sy -> st) -> [sy] -> [st] -> [st]
+stPath d v sts = sort $ nub $
+                 (sts ++ (concat $ map (destinationsFrom d v) sts))
+
+
+
+-----------------------------------------------------------------------------
+-- * Transformation
+
+-- | Produce the transition table of a given 'Dfa'.
+--   Given a 'Dfa', it returns a list of triples of the form
+-- @
+--                 (Origin,Symbol,Destination)
+-- @
+-- defining all the transitions of the 'Dfa'.
+--
+
+transitionTableDfa :: (Ord st, Ord sy)
+                   => Dfa st sy          -- ^ Automaton
+                   -> [(st,sy,st)]       -- ^ Transition table
+transitionTableDfa (Dfa v q s z delta) = sort [ ( aq , av , delta aq av)
+                                              | aq <- q
+                                              , av <- v
+                                              ]
+
+
+-- | Reconstruct a 'Dfa' from a transition table.
+--   Given an automaton expressed by a transition table
+--   (ie a list of triples of the form
+-- @
+--                    (Origin,Symbol,Destination)
+-- @
+--   it constructs a 'Dfa'. The other elements of the
+--   input tuple are the vocabulary, a set of
+--   states, an initial state, and a set of
+--   final states.
+
+ttDfa2Dfa :: (Eq st, Eq sy)
+          => ([sy],[st],st,[st],[(st,sy,st)])  -- ^ Tuple-based Automaton
+          -> Dfa st sy                         -- ^ Automaton
+ttDfa2Dfa (vs,qs,s,z,ld) = Dfa vs qs s z d
+  where d st sy =  lookUptt st sy ld
+
+        lookUptt q v ((a,b,c) : [])                    = c
+        lookUptt q v ((a,b,c) : xs) | q == a && v == b = c
+                                    | otherwise        = lookUptt  q v xs
+
+
+--
+-- Beautify the Automata States
+--
+
+beautifyDfaWithSyncSt :: Eq st
+                      => Dfa [st] sy    -- ^ Original Automaton
+                      -> Dfa [Int] sy   -- ^ Beautified Automaton (states as integers)
+beautifyDfaWithSyncSt (Dfa v q s z delta) = (Dfa v q' s' z' delta')
+  where qaux = (giveNumber q 1) ++ [([],[])]
+        q'   = map snd qaux
+        s'   = lookupSt s qaux
+        z'   = getNewFinalSt z qaux
+        delta' st' sy' = lookupSt (delta (lookupNewSt st' qaux) sy') qaux
+
+lookupSt :: Eq st => st -> [(st,[Int])] -> [Int]
+lookupSt s (h:t) | fst h == s = snd h
+                 | otherwise  = lookupSt s t
+
+lookupNewSt :: [Int] -> [(st,[Int])] -> st
+lookupNewSt s (h:t) | snd h == s = fst h
+                    | otherwise  = lookupNewSt s t
+
+getNewFinalSt :: Eq st => [st] -> [(st,[Int])] -> [[Int]]
+getNewFinalSt [] qaux = []
+getNewFinalSt (h:t) qaux = (lookupSt h qaux) : getNewFinalSt t qaux
+
+giveNumber :: Eq st
+           => [[st]]
+           -> Int             -- ^ Initial number
+           -> [([st],[Int])]  -- ^ ??
+giveNumber []    i = []
+giveNumber (h:t) i | h == []   = giveNumber t i
+                   | otherwise = (h,[i]) : giveNumber t (i+1)
+
+
+-- | Type of Table-based Deterministic Finite Automata.
+--
+
+type TableDfa st = [(st, [st])]
+
+stsDfa      = map fst
+stsRHS      = map snd
+allstsTable = concat . stsRHS
+
+
+-- | Dfa to a Table-based Dfa
+--
+
+dfa2tdfa :: (Eq st, Ord sy)
+         => Dfa st sy              -- ^ Automaton
+         -> TableDfa st            -- ^ Transition table
+dfa2tdfa (Dfa v q s z delta) = limit (dfa2tdfaStep delta v') tbFstRow
+  where v'       = sort v
+        tbFstRow = consRows delta [s] v'
+
+-- | Add rows to a table-based Dfa, given a Dfa transition function
+--   and its vocabulary.
+dfa2tdfaStep :: Eq st
+             => (st -> sy -> st)  -- ^ Transition function
+             -> [sy]              -- ^ Vocabulary
+             -> TableDfa st       -- ^ Table-based Dfa
+             -> TableDfa st       -- ^ Table-based Dfa with additional rows.
+dfa2tdfaStep delta alfabet tb = tb `union` (consRows delta newSts alfabet)
+  where newSts = ((nub . allstsTable) tb) <-> (stsDfa tb)
+
+
+
+consRows :: (st -> sy -> st) -> [st] -> [sy] -> TableDfa st
+consRows delta []     alfabet = []
+consRows delta (q:qs) alfabet = (q , oneRow delta q alfabet) :
+                                (consRows delta qs alfabet)
+
+oneRow :: (st -> sy -> st) -> st -> [sy] -> [st]
+oneRow delta st alfabet = map (delta st) alfabet
+
+-- | Renames a 'Dfa'.
+-- It renames a DFA in such a way that the renaming of two isomorphic DFA
+-- returns the same DFA.
+-- It is the basis for the equivalence test for minimized DFA.
+--
+renameDfa :: (Ord st, Ord sy)
+          => Dfa st sy      -- ^ Automaton
+          -> Int            -- ^ Initial state ID
+          -> Dfa Int sy     -- ^ Renamed automaton
+renameDfa dfa@(Dfa v q s z delta) istid = Dfa v' q' s' z' delta'
+  where v'     = sort v
+        q'     = sort $ map snd newSts
+        tb     = dfa2tdfa dfa
+        s'     = istid
+        newSts = newStsOfTable tb s'
+        z'     = sort $ map snd (filter (\(a,b) -> a `elem` z) newSts)
+        delta' newSt sy = lookupNewSts delta newSt sy newSts
+
+--
+-- Giving new names to the Dfa states
+--
+
+newStsOfTable :: Eq st => TableDfa st -> Int -> [(st,Int)]
+newStsOfTable tb ini = newStsOfTableAux tb [(fst $ head tb,ini)]
+
+newStsOfTableAux :: Eq a => [(b,[a])] -> [(a,Int)] -> [(a,Int)]
+newStsOfTableAux []           newSt = newSt
+newStsOfTableAux ((st,sts):t) newSt = newSt''
+    where newSt' = procrhsSts sts newSt
+          newSt'' =  newStsOfTableAux t newSt'
+
+procrhsSts :: Eq a => [a] -> [(a,Int)] -> [(a,Int)]
+procrhsSts []       newSt = newSt
+procrhsSts (st:sts) newSt
+     | st `elem` (map fst newSt) = procrhsSts sts newSt
+     | otherwise = newSt'
+        where newSt' = procrhsSts sts ((st,( snd $ head newSt) + 1) : newSt)
+
+lookupNewSts delta newSt sy newSts = getNewSt newOldSt newSts
+  where newOldSt = delta (getOldSt newSt newSts) sy
+
+getNewSt oldSt newSts = snd $ head (filter (\(a,b) -> a == oldSt) newSts)
+getOldSt newSt newSts = fst $ head (filter (\(a,b) -> b == newSt) newSts)
+
+
+
+-- | Beautify a 'Dfa' by assigning (natural) numbers to states.
+
+beautifyDfa :: (Ord st, Ord sy) => Dfa st sy -> Dfa Int sy
+beautifyDfa dfa = renameDfa dfa 1
+
+
+
+
+-----------------------------------------------------------------------------
+-- * Properties of 'Dfa'
+
+-- | Compute the dead states of a 'Dfa'
+--
+
+dfadeadstates :: Ord st
+              => Dfa st sy      -- ^ Automaton
+              -> [st]           -- ^ Dead states
+dfadeadstates (Dfa v qs s z d) = filter (isStDead d v z) qs
+
+
+-- | Compute the size of a deterministic finite automaton.
+--   The size of an automaton is the number of its states.
+
+sizeDfa :: Dfa st sy -> Int
+sizeDfa (Dfa _ q _ _ _) = length q
+
+
+
+-----------------------------------------------------------------------------
+-- * Properties of States
+
+
+-- | Checks whether a state is dead or not.
+--
+--   One state is dead when it is not possible to reach a final state from it.
+--   (probably we should consider that it has to be reachable from the
+--    initial state, as well)
+
+isStDead :: Ord st
+         => (st -> sy -> st)        -- ^ Transition Function
+         -> [sy]                    -- ^ Vocabulary
+         -> [st]                    -- ^ Set of Final States
+         -> st                      -- ^ State
+         -> Bool
+
+isStDead d v z st = reachedStatesFrom d v st `intersect` z == []
+
+
+-- | Checks whether a state is a sync state or not
+--
+--   A sync state is a state that has transitions to itself for all
+--   symbols of the vocabulary
+
+
+isStSync :: Eq st
+         => (st -> sy -> st)        -- ^ Transition Function
+         -> [sy]                    -- ^ Vocabulary
+         -> [st]                    -- ^ Set of Final States
+         -> st                      -- ^ State
+         -> Bool
+isStSync d vs z st = and qs
+  where qs = [ st == dfawalk d st [v]
+             | v <- vs
+             ]
+
+-- | Compute the number of incoming arrows for a given state
+--
+
+numberIncomingArrows :: Eq st
+                     => (st -> sy -> st)       -- ^ Transition Function
+                     -> [sy]                   -- ^ Vocabulary
+                     -> [st]                   -- ^ Set of States
+                     -> st                     -- ^ Destination
+                     -> Int                    -- ^ Number of Arrows
+numberIncomingArrows d vs qs dest = length  [ q
+                                            | v <- vs
+                                            , q <- qs
+                                            , d q v == dest
+                                            ]
+
+-- | Compute the number of outgoing arrows for a given state
+
+
+numberOutgoingArrows :: (st -> sy -> st)       -- ^ Transition Function
+                     -> [sy]                   -- ^ Vocabulary
+                     -> st                     -- ^ Origin
+                     -> Int                    -- ^ Number of Arrows
+
+numberOutgoingArrows d v o = length $ destinationsFrom d v o
diff --git a/HaLeX_lib/Language/HaLex/Dfa2MDfa.hs b/HaLeX_lib/Language/HaLex/Dfa2MDfa.hs
new file mode 100644
--- /dev/null
+++ b/HaLeX_lib/Language/HaLex/Dfa2MDfa.hs
@@ -0,0 +1,135 @@
+--
+-- From DFA into Monadic DFA in Haskell
+--
+-- Code Included in the Lecture Notes on
+--
+--      Language Processing (with a functional flavour)
+--
+--
+-- copyright João Saraiva
+--           Department of Computer Science,
+--           University of Minho,
+--           Braga, Portugal
+--           jas@di.uminho.pt
+--           2001
+--
+
+module Language.HaLex.Dfa2MDfa where
+
+import Data.List
+import Language.HaLex.Dfa
+import Language.HaLex.Ndfa
+import Language.HaLex.FaOperations
+import Language.HaLex.RegExp
+import Language.HaLex.RegExp2Fa
+--import Language.HaLex.RegExpParser
+import Language.HaLex.Minimize
+
+showAsAccumDfa  (Dfa v q s z delta) =
+                showString ("dfa = Dfa v q s z delta") .
+                showString ("\n  where \n\t v = ") .
+                showList v .
+                showString ("\n\t q = ") .
+                showList q .
+                showString ("\n\t s = ") .
+                shows s    .
+                showString ("\n\t z = ") .
+                showList z .
+                showString ("\n\t -- delta :: st -> sy -> m st \n") .
+                showDfaMDelta q v delta .
+                showString ("\n\n") .
+                showString ("accum :: a -> State [a] () \n") .
+                showString ("accum x = modify (\\ s -> s++[x])")
+
+showDfaMDelta :: (Show st, Show sy) => [st] -> [sy] -> (st -> sy -> st) -> [Char] -> [Char]
+
+showDfaMDelta q v d = foldr (.) (showChar '\n') f
+  where
+    f     = zipWith3 showF m n q'
+    (m,n) = unzip l
+    q'    = map (uncurry d) l
+    l     = [(a,b) | a <- q , b <- v]
+
+    showF st sy st' = showString("\t delta ") .
+                      shows st .
+                      showChar(' ') .
+                      shows sy .
+                      showString(" = do { accum ") .
+                      shows sy .
+                      showString (" ; return ") .
+                      shows st' .
+                      showString(" }") .
+                      showChar('\n')
+
+
+
+dfa2MIO :: (Show st , Show sy) => (Dfa st sy) -> IO ()
+dfa2MIO afd = writeFile "GenMDfa.hs"
+                        ("module GenMDfa where\n\n" ++
+                         "import Language.HaLex.DfaMonad\n\n" ++
+                         "import MonadState\n\n" ++
+                          (showAsAccumDfa afd ""))
+
+
+re2MHaskellMod re m b = "module GenMDfa where\n\n" ++
+                        "import Language.HaLex.DfaMonad\n\n" ++
+                         "import MonadState\n\n" ++
+                        ((re2MDfa re m b) "")
+
+re2MDfa :: (Show sy,Ord sy)
+        => RegExp sy
+        -> Bool       -- Minimized?
+        -> Bool       -- Beautified?   (states as numbers)
+        -> String -> String
+re2MDfa re m b
+  | m     && b     = showAsAccumDfa ((beautifyDfa . minimizeDfa . ndfa2dfa . regExp2Ndfa) re)
+  | m     && not b = showAsAccumDfa ((minimizeDfa . ndfa2dfa . regExp2Ndfa) re)
+  | not m && b     = showAsAccumDfa ((beautifyDfa . ndfa2dfa . regExp2Ndfa) re)
+  | not m && not b = showAsAccumDfa ((ndfa2dfa . regExp2Ndfa) re)
+
+{- Uses parser
+re2MDfaIO :: [Char] -> IO ()
+re2MDfaIO er      = dfa2MIO dfa
+  where abst_er = f (parseRegExp er)
+        dfa     = (beautifyDfa . minimizeDfa . ndfa2dfa . regExp2Ndfa) abst_er
+
+re2MDfaIO' :: [Char] -> IO ()
+re2MDfaIO' er     = dfa2MIO dfa
+  where abst_er = f (parseRegExp er)
+        dfa     = (beautifyDfa . ndfa2dfa . regExp2Ndfa) abst_er
+
+re2MDfaIO'' :: [Char] -> IO ()
+re2MDfaIO'' er    = dfa2MIO dfa
+  where abst_er = f (parseRegExp er)
+        dfa     = (ndfa2dfa . regExp2Ndfa) abst_er
+-}
+
+
+f (Just p ) = p
+f _         = Epsilon
+
+
+
+
+
+
+dfa_int = Dfa ['+','-','0','1']
+              [1,2,3,4]
+              1
+              [3]
+              delta
+  where delta 1 '+' = 2
+        delta 1 '-' = 2
+        delta 1 '0' = 3
+        delta 1 '1' = 3
+        delta 2 '0' = 3
+        delta 2 '1' = 3
+        delta 3 '0' = 3
+        delta 3 '1' = 3
+        delta _  _  = 4
+
+
+
+
+
+
diff --git a/HaLeX_lib/Language/HaLex/DfaMonad.lhs b/HaLeX_lib/Language/HaLex/DfaMonad.lhs
new file mode 100644
--- /dev/null
+++ b/HaLeX_lib/Language/HaLex/DfaMonad.lhs
@@ -0,0 +1,631 @@
+
+
+\documentclass{article}
+\usepackage{alltt}
+
+
+\newenvironment{code}
+{\begin{alltt}}
+{\end{alltt}}
+
+
+\title{Deterministic Finite Automaton with Effects}
+
+\author{Jo\~ao Saraiva}
+
+\date{\today}
+
+\begin{document}
+
+\maketitle
+
+
+
+
+\begin{code}
+module Language.HaLex.DfaMonad where
+
+import Data.Char
+import Data.List
+import Language.HaLex.Ndfa
+import Control.Monad
+import Control.Monad.State
+
+import System.IO.Unsafe
+import Data.IORef
+
+--
+-- Generic Functions to Implement a Recognizer based on Finite State Machines
+-- (Deterministic Finite Automata)
+--
+
+data Dfa m st sy  = Dfa [sy]                -- Vocabulary
+                        [st]                -- Finite set of states
+                        st                  -- The start state
+                        [st]                -- The set of final states
+                        (st -> sy -> m st)  -- Monadic Transition Function
+\end{code}
+
+
+The function \texttt{dfawalk} recurses over a list. As a consequence,
+we can re-write that function using the pre.defined Monadic fold
+function \texttt{foldM}..
+
+\begin{code}
+dfawalk :: Monad m => (st -> sy -> m st) -> st -> [sy] -> m st
+dfawalk delta s = foldM delta s
+\end{code}
+
+
+\begin{code}
+dfaaccept' :: (Monad m , Eq st) => Dfa m st sy -> [sy] -> m Bool
+dfaaccept' (Dfa _ _ s z delta) sent =
+  do st <- foldM delta s sent
+     return (st `elem` z)
+
+dfaaccept :: (Monad m, Eq st) => Dfa m st sy -> [sy] -> m Bool
+dfaaccept (Dfa _ _ s z delta) sent =
+  do { st <- dfawalk delta s sent
+     ; return (st `elem` z)
+     }
+\end{code}
+
+
+
+\begin{code}
+
+runDfa :: Eq st => Dfa (State s) st sy -> [sy] -> s -> (Bool,s)
+runDfa dfa str initSt = runState (dfaaccept dfa str) initSt
+
+\end{code}
+
+
+\begin{code}
+
+showDfa :: (Monad m, Show st, Show sy) => Dfa m st sy -> m String
+showDfa (Dfa v q s z delta) =
+  do let a = showString ("dfa = Dfa v q s z delta") .
+             showString ("\n  where \n\t v = ") .
+             showList v .
+             showString ("\n\t q = ") .
+             showList q .
+             showString ("\n\t s = ") .
+             shows s .
+             showString ("\n\t z = ") .
+             showList z .
+             showString ("\n\t -- delta :: st -> sy -> st \n")
+     b <- showDfaDelta q v delta
+     return ((a . b) "" )
+
+showDfaDelta :: (Monad m, Show st, Show sy) => [st] -> [sy] -> (st -> sy -> m st) ->
+                                               m ([Char] -> [Char])
+showDfaDelta q v d =
+  do let l     = [(a,b) | a <- q , b <- v]
+     let (m,n) = unzip l
+     q'        <- mapM (uncurry d) l
+     let f     = zipWith3 showF m n q'
+     return (foldr (.) (showChar '\n') f)
+  where
+    showF st sy st' = showString("\t delta ") .
+                      shows st .
+                      showChar(' ') .
+                      shows sy .
+                      showString(" = return ") .
+                      shows st' .
+                      showChar('\n')
+\end{code}
+
+
+\begin{code}
+
+showInDot :: (Monad m , Eq st , Show st , Show sy)
+          => Dfa m  st sy             -- The Monadic Deterministic Finite Automaton
+          -> Bool                     -- Result's Type: True -> Show Dead States
+                                      --                 False -> Don't Show Dead States
+          -> m [Char]                 -- The Dot string
+showInDot dfa@(Dfa v q s z delta) t =
+   do dsts <- deadstates dfa
+      let a = showString ("digraph fa {\n") .
+              showString ("rankdir = LR ;\n") .
+              showString ("orientation=land;\n") .
+              (showInitialState s) . showChar '\n' .
+              showString (showElemsListPerLine (showFinalStates' z)) .
+              showString ("node [shape=circle , color=black];\n")
+      b <- showArrows dfa dsts t
+      return ((a (concat b)) ++ "}\n")
+
+
+showElemsListPerLine :: [String] -> String
+showElemsListPerLine []    = ""
+showElemsListPerLine (h:t) = ((showString h) "\n") ++ (showElemsListPerLine t)
+
+showInitialState s = showString("\"") . shows s .  showChar('\"') .
+                     showString (" [shape=circle , color=green];\n")
+
+-- showFinalStates' :: Show a => [a] -> [String]
+showFinalStates' z = [ "\"" ++ (show f) ++ "\""
+                       ++ " [shape=doublecircle , color=red];" | f <- z ]
+
+showArrows :: (Monad m, Eq st , Show st, Show sy)
+           => Dfa m st sy -> [st] -> Bool -> m [[Char]]
+showArrows (Dfa v qs s z delta) dsts t  =
+   do let qs' = if t then qs else qs <-> dsts
+      xpto [ mapM (buildLine q delta dsts t) v | q <- qs'  ]
+
+buildLine :: (Monad m , Eq st , Show st, Show sy)
+          => st -> (st -> sy -> m st) -> [st] -> Bool -> sy -> m [Char]
+buildLine q delta dsts t v =
+  do let a = showChar('\"') . shows q . showChar('\"') . showString (" -> \"")
+     q' <-  delta q v
+     let line = if ( (not t) && q' `elem` dsts ) then ""
+                else ((a . shows q' . showString ("\" [label = \"") . shows v .
+                      showString("\"];\n") ) "")
+     return line
+
+
+(<->) :: Eq a => [a] -> [a] -> [a]
+l1 <-> l2 = [ x | x <- l1 , not (x `elem` l2) ]
+
+
+
+xpto :: Monad m => [m [a]] -> m [a]
+xpto [] = return []
+xpto (x:xs) = do rx <- x
+                 rxs <- xpto xs
+                 return (rx++rxs)
+\end{code}
+
+
+
+\begin{code}
+
+deadstates :: (Monad m , Eq st) => Dfa m st sy -> m [st]
+deadstates (Dfa v qs s z d) = deadstates' qs v d
+
+deadstates' :: (Monad m, Eq st) => [st] -> [sy] -> (st -> sy -> m st) -> m [st]
+deadstates' [] _ _ = return []
+deadstates' (q:qs) v delta =
+  do rq <- isStDead q (mapM (delta q) v)
+     rqs <- deadstates' qs v delta
+     return (if rq then q : rqs else rqs)
+
+--
+-- A state a is dead whenever a final state can not be reached from a.
+-- (this function checks for synv states only: states that for every symbol
+--
+
+isStDead  :: (Monad m, Eq st) => st -> m [st] -> m Bool
+isStDead = isSyncState
+
+--
+-- We've implemented a simpler function only: isSyncState
+-- A non initial, non final state A is said to be a sync state
+-- iff for every vocabulary symbol the automaton moves to A.
+--
+
+isSyncState :: (Monad m, Eq st) => st -> m [st] -> m Bool
+isSyncState st msts = do sts <- msts
+                         return (and (isin' st sts))
+  where isin' e []     = [True]
+        isin' e (x:xs) = (e==x) : isin' e xs
+
+\end{code}
+
+
+
+\section{Maybe Monad based Automata}
+
+\begin{code}
+
+robot :: Dfa Maybe [Char] [Char]
+robot = Dfa ["esquerda","direita","largar","pegar"]
+            ["C0 sem pepita","C0 com pepita","C1 sem pepita","C1 com pepita"]
+            "C0 sem pepita"
+            ["C0 sem pepita"]
+            delta
+  where
+    delta "C0 sem pepita" "direita"  = -- do putStrLn "Vou para C1 sem pepita"
+                                          return "C1 sem pepita"
+    delta "C0 sem pepita" _          = return "C0 sem pepita"
+
+    delta "C0 com pepita" "largar"   = return "C0 sem pepita"
+    delta "C0 com pepita" "direita"  = return "C1 com pepita"
+    delta "C0 com pepita" _          = return "C0 com pepita"
+
+    delta "C1 sem pepita" "esquerda" = return "C0 sem pepita"
+    delta "C1 sem pepita" "pegar"    = return "C1 com pepita"
+    delta "C1 sem pepita" _          = return "C1 sem pepita"
+
+    delta "C1 com pepita" "esquerda" = -- do putStrLn "Vou para C0 com pepita"
+                                          return "C0 com pepita"
+    delta "C1 com pepita" "largar"   = return "C1 sem pepita"
+    delta "C1 com pepita" _          = return "C1 com pepita"
+
+
+moves = ["direita","pegar","esquerda","largar"]
+moves2 = ["esquerda","pegar","direita","pegar","esquerda","largar"]
+moves3 = ["esquerda","pegar","direita"]
+moves4 = moves2 ++ moves ++ moves3
+
+acc = dfaaccept robot moves4
+
+{-
+exShow = do d <- showInDot robot True
+            writeFile "xxx" d
+-}
+
+\end{code}
+
+
+\begin{verbatim}
+Dfa> dfaaccept ex "aba"
+Just True
+\end{verbatim}
+
+
+\section{IO Monad based Automata}
+
+
+\begin{code}
+varGlob = unsafePerformIO $ newIORef ""
+
+ex2 :: Dfa IO Char Char
+ex2 = Dfa ['a','b']
+         ['A','B','C','D']
+         'A'
+         ['C']
+         delta
+  where
+    delta 'A' 'a' = do  v <- readIORef varGlob
+                        writeIORef varGlob ('A':v)
+                        putStrLn ('A':v)
+                        return 'A'
+    delta 'A' 'b' = do  putStrLn "b"
+                        return 'B'
+    delta 'B' 'a' = return 'C'
+    delta _ _ = return 'D'
+\end{code}
+
+\begin{verbatim}
+Dfa>  dfaaccept ex2 "aba"
+A
+b
+True
+\end{verbatim}
+
+
+\section{State Monad Based Automata}
+
+
+The State Monad
+
+\begin{code}
+
+
+{-
+data State s v = State (s -> (v,s))
+
+instance Show (State s v) where
+  show = showState
+
+apply :: State s v -> s -> (v,s)
+apply (State f) s = f s
+
+
+instance Monad (State s) where
+  return x        = State f
+                      where f s = (x,s)
+  p >>= q         = State f
+                      where f s = let
+                                     (x,s') = apply p s
+                                  in apply (q x) s'
+
+runState :: State s v -> s -> (v,s)
+runState (State f) s0 = let (v,s) = f s0 in (v,s)
+-}
+
+\end{code}
+
+
+One Example
+
+\begin{code}
+
+-- er: a* b a
+-- Conta o numero de ocorrência dos caracter a
+
+ex3 :: Dfa (State Integer) Char Char
+ex3 = Dfa ['a','b']
+         ['A','B','C']
+         'A'
+         ['C']
+         delta
+  where
+    delta 'A' 'a' = do countA
+		       return 'A'
+    delta 'A' 'b' = return 'B'
+    delta 'B' 'a' = do countA
+                       return 'C'
+
+    countA = State f
+      where f s = ((),s+1)
+
+runAccept dfa str = runState (dfaaccept dfa str) 0
+
+
+\end{code}
+
+
+
+
+\begin{code}
+
+-- er: a* b a
+-- Accumulates in the State the occurrences of caracter a
+
+ex4 :: Dfa (State [Char]) Char Char
+ex4 = Dfa ['a','b']
+          ['A','B','C']
+          'A'
+          ['C']
+          delta
+  where
+    delta 'A' 'a' = do modify (\ s -> 'a':s)
+		       return 'A'
+    delta 'A' 'b' = return 'B'
+    delta 'B' 'a' = do modify (\ s -> 'a':s)
+                       return 'C'
+
+
+runAccept_ex4 dfa str = runState (dfaaccept dfa str) ""
+
+
+\end{code}
+
+
+
+\subsection{Computes Tracing Information}
+
+It computes the visited states (nodes).
+
+\begin{code}
+
+ex5 :: Dfa (State [Char]) Char Char
+ex5 = Dfa ['a','b']
+          ['A','B','C']
+          'A'
+          ['C']
+          delta
+  where
+    delta 'A' 'a' = do { accum 'A' ; return 'A' }
+    delta 'A' 'b' = do { accum 'B' ; return 'B' }
+    delta 'B' 'a' = do { accum 'C' ; return 'C' }
+
+    accum x = modify (\ s -> x:s)
+
+runAccept_ex5 str = runState (dfaaccept ex5 str) ""
+\end{code}
+
+
+
+
+
+\subsection{The language of Integer Numbers}
+
+
+
+\begin{code}
+
+-- er: ('+'|'-')?d+
+-- Accumulates in the State the occurrences of characters '-' and 'd'
+
+ex_int :: Dfa (State [Char]) Integer Char
+ex_int = Dfa ['+','-','d']
+             [1,2,3]
+             1
+             [3]
+             delta
+  where
+    delta 1 '+' = return 2
+    delta 1 '-' = do accumM
+                     return 2
+    delta 1 'd' = do accumD
+                     return 3
+    delta 2 'd' = do accumD
+                     return 3
+    delta 3 'd' = do accumD
+                     return 3
+
+    accumM = State f
+      where f s = (s,'-':s)
+
+    accumD = State f
+      where f s = (s,'d':s)
+
+
+runAccept_int str = runState (dfaaccept ex_int str) ""
+\end{code}
+
+
+
+
+The language of Integer Numbers Follow by " "
+
+
+
+\begin{code}
+
+-- er: ('+'|'-')?d+
+-- Accumulates in the State the occurrences of characters '-' and 'd'
+
+ex6 :: Dfa (State ([Char],Int)) Integer Char
+ex6 = Dfa ['+','-','1','2',' ']
+          [1,2,3,4,5]
+          1
+          [4]
+          delta
+  where
+    delta 1 '+' = return 2
+    delta 1 '-' = do { accum '-' ; return 2 }
+    delta 1 '1' = do accum '1'
+                     return 3
+    delta 1 '2' = do accum '2'
+                     return 3
+    delta 2 '1' = do accum '1'
+                     return 3
+    delta 2 '2' = do accum '2'
+                     return 3
+    delta 3 '1' = do accum '1'
+                     return 3
+    delta 3 '2' = do accum '2'
+                     return 3
+    delta 3 ' ' = do convert
+                     return 4
+
+    delta _ _ = return 5                      -- To complete the DFA
+
+    accum x = State f
+      where f s = ((),((fst s)++[x],snd s))
+
+    convert = State f
+      where f s = ((),(fst s,(read (fst s))::Int))
+
+
+runAccept_ex6 str = runState (dfaaccept ex6 str) ("",0::Int)
+
+
+\end{code}
+
+\begin{verbatim}
+Dfa> runAccept_ex6 "-12 "
+(True,("-12",-12))
+\end{verbatim}
+
+\section{A Text Editor Interpreter}
+
+
+\begin{code}
+type Instr = [Code]
+
+data Code = Open   String
+          | Locate Int
+          | Insert String
+          | Delete [Int]
+          | Save
+          | End
+          deriving Show
+\end{code}
+
+
+
+\begin{code}
+te :: Dfa (State ([Char],[Code])) Integer Char
+te = Dfa ['A','x','1','0',' ']
+         [1,2,3,4,9,10,20]
+         1
+         [3,4]
+         delta
+  where
+    delta 1 'A' = do init
+                     return 2
+    delta 2 x | isLower x  = do accum x
+                                return 3
+              | otherwise  = return 20
+    delta 3 'R' = do open
+                     return 4
+    delta 3 x | isLower x || isDigit x  = do accum x
+                                             return 3
+              | otherwise = return 20
+    delta 4 'A' = do init
+                     return 2
+
+    delta 4 'P' = do init
+                     return 9
+    delta 9 x | isDigit x = do accum x
+                               return 10
+    delta 10 x | isDigit x = do accum x
+                                return 10
+    delta 10 'R' = do locate
+                      return 4
+
+    delta _ _ = return 20
+
+
+    accum x = State f
+      where f s = ((),((fst s)++[x],snd s))
+
+    init = State f
+      where f s = ((),("",snd s))
+
+    open = State f
+      where f s = ((),(fst s,(snd s) ++ [Open (fst s)]))
+
+    locate = State f
+      where f s = ((),(fst s,(snd s) ++ [Locate (read (fst s))]))
+
+
+runAccept_te str = runState (dfaaccept te str) ("",[])
+
+\end{code}
+
+
+\begin{verbatim}
+Dfa> runAccept_te "Aficheiro10RP12R"
+(True,("12",[Open "ficheiro10",Locate 12]))
+\end{verbatim}
+
+
+
+\section{Protocol}
+
+"000((0|1)(0|1)(0|1)(001(0|1)(0|1)(0|1))*)111"
+
+\begin{code}
+pr :: Dfa (State ([Char],[Int])) Integer Char
+pr = Dfa ['1','0']
+         [1,2,3,4,5,6,7,8,9,10,11,12,13]
+         1
+         [12]
+         delta
+  where
+    delta 1  '0' = return 2
+    delta 2  '0' = return 3
+    delta 3  '0' = return 4
+    delta 4  '0' = do { accum '0' ; return 5 }
+    delta 4  '1' = do { accum '1' ; return 5 }
+    delta 5  '0' = do { accum '0' ; return 6 }
+    delta 5  '1' = do { accum '1' ; return 6 }
+    delta 6  '0' = do { accum '0' ; accumList ; return 7 }
+    delta 6  '1' = do { accum '1' ; accumList ; return 7 }
+    delta 7  '0' = return 8
+    delta 7  '1' = return 9
+    delta 8  '0' = return 10
+    delta 9  '1' = return 11
+    delta 10 '1' = do { init ; return 4 }
+    delta 11 '1' = do { init ; return 12 }
+
+    delta _ _ = return 13
+
+
+    accum x = modify (\ s -> ((fst s)++[x],snd s))
+    init        = modify (\ s -> ("",snd s))
+    accumList   = modify (\ s -> (fst s,snd s ++ [converte (fst s)]))
+
+
+converte :: [Char] -> Int
+converte []       = 0
+converte ('0':xs) = converte xs
+converte ('1':xs) = expo 2 (length xs) + converte xs
+
+expo v e | e > 0     = v * (expo v (e-1))
+         | otherwise = 1
+
+runAccept_pr :: [Char] -> (Bool,([Char],[Int]))
+runAccept_pr str = runState (dfaaccept pr str) ("",[])
+
+-- runAccept_gv = writeFile "xx.dot" (fst (runState (showDfaDiGraph  pr) ("",[])))
+
+
+\end{code}
+
+\end{document}
diff --git a/HaLeX_lib/Language/HaLex/Equivalence.hs b/HaLeX_lib/Language/HaLex/Equivalence.hs
new file mode 100644
--- /dev/null
+++ b/HaLeX_lib/Language/HaLex/Equivalence.hs
@@ -0,0 +1,89 @@
+
+-----------------------------------------------------------------------------
+-- |
+-- Module      :  Language.HaLex.RegExp
+-- Copyright   :  (c) João Saraiva 2001,2002,2003,2004,2005
+-- License     :  LGPL
+-- 
+-- Maintainer  :  jas@di.uminho.pt
+-- Stability   :  provisional
+-- Portability :  portable
+--
+-- Equivalence of Regular Expressions 
+-- 
+-- Code Included in the Lecture Notes on 
+--          Language Processing (with a functional flavour).   
+--
+-----------------------------------------------------------------------------
+
+
+module Language.HaLex.Equivalence ( 
+                     equivDfa
+                   , equivNdfa 
+                   , equivRE
+                   , equivREs
+                   ) where
+
+import Language.HaLex.RegExp
+import Language.HaLex.RegExp2Fa
+import Language.HaLex.Dfa
+import Language.HaLex.Ndfa
+import Language.HaLex.FaOperations
+import Language.HaLex.Minimize
+
+
+
+-- | Test whether two 'Dfa' are quivalent or not.
+
+equivDfa :: (Ord st, Ord sy) 
+         => Dfa st sy         -- ^ Deterministic Automaton
+         -> Dfa st sy         -- ^ Deterministic Automaton
+         -> Bool              -- ^ Equivalent?
+
+equivDfa dfa1 dfa2 = tdfa_1 == tdfa_2
+ where canonicalDfa1 = beautifyDfa $ minimizeDfa dfa1
+       canonicalDfa2 = beautifyDfa $ minimizeDfa dfa2
+       tdfa_1        = dfa2tdfa canonicalDfa1
+       tdfa_2        = dfa2tdfa canonicalDfa2
+
+
+-- | Test whether two 'Ndfa' are quivalent or not.
+
+equivNdfa :: (Ord st, Ord sy) 
+          => Ndfa st sy        -- ^ Non-Deterministic Automaton
+          -> Ndfa st sy        -- ^ Non-Deterministic Automaton
+          -> Bool              -- ^ Equivalent?
+
+equivNdfa ndfa1 ndfa2 = equivDfa (ndfa2dfa ndfa1) (ndfa2dfa ndfa2)
+
+
+-- | Test whether two 'RegExp' are quivalent or not.
+
+equivRE :: Ord sy 
+        => RegExp sy           -- ^ Regular Expression
+        -> RegExp sy           -- ^ Regular Expression
+        -> Bool                -- ^ Equivalent?
+
+equivRE re1 re2 = equivNdfa (regExp2Ndfa re1) (regExp2Ndfa re2)
+
+
+-- | Test whether a list of 'RegExp' are quivalent or not.
+
+equivREs :: Ord sy 
+         => [RegExp sy]        -- ^ List of Regular Expressions
+         -> Bool               -- ^ Equivalent?
+
+equivREs re = or (map (equivRE reFst) (tail re))
+  where reFst = head re
+
+
+
+
+
+
+
+
+
+
+
+
diff --git a/HaLeX_lib/Language/HaLex/Examples/Real.lhs b/HaLeX_lib/Language/HaLex/Examples/Real.lhs
new file mode 100644
--- /dev/null
+++ b/HaLeX_lib/Language/HaLex/Examples/Real.lhs
@@ -0,0 +1,257 @@
+
+\documentclass{article}
+\usepackage{a4wide}
+\usepackage{graphics}
+\usepackage{graphicx}
+\usepackage{color}
+\usepackage{alltt}
+
+\usepackage[dvips]{epsfig}
+\usepackage{epic}
+\usepackage{eepic}
+
+
+\def\Ipe#1{\def\IPEfile{#1}\input{#1}}
+
+\newenvironment{code}
+{\begin{alltt}}
+{\end{alltt}}
+
+
+\title{\sf Finite Automata in Haskell: \\
+An Exercise with the Language of Real Numbers}
+
+\author{Jo\~ao Saraiva}
+
+\date{\today}
+
+\begin{document}
+
+\maketitle
+
+
+\section{Deterministic Finite Automaton}
+
+\begin{figure}[htb!]
+{\hrule\bigskip}
+\begin{center}
+\Ipe{FIGURES/Real.ipe}
+\end{center}
+\caption{Deterministic Finite Automaton for the Language of the
+Real Numbers.}
+{\bigskip\hrule}
+\end{figure}
+
+
+\begin{code}
+module Language.HaLex.Examples.Real where
+
+import Data.List
+import Language.HaLex.RegExp
+import Language.HaLex.Dfa
+import Language.HaLex.Ndfa
+import Language.HaLex.RegExp2Fa
+import Language.HaLex.FaOperations
+
+import Language.HaLex.FaAsDiGraph
+
+import Language.HaLex.Minimize
+import Language.HaLex.RegExpAsDiGraph
+--import RegExpParser
+
+import Language.HaLex.Fa2RegExp
+
+import qualified Language.HaLex.FaClasses as Fa
+
+
+
+
+
+sinal'' = (Literal '-') `Or` (Literal '+') `Or` Epsilon
+
+d = Literal 'd'
+
+
+re_int = sinal'' `Then` d `Then` (Star d)
+
+
+intdfa = (beautifyDfa . ndfa2dfa . regExp2Ndfa) re_int
+
+
+d' = (Literal '0') `Or`  (Literal '1') `Or`  (Literal '2') `Or`
+     (Literal '3') `Or`  (Literal '4') `Or`  (Literal '5') `Or`
+     (Literal '6') `Or`  (Literal '7') `Or`  (Literal '8') `Or`
+     (Literal '9')
+
+
+re_real = sinal'' `Then` (Star d')
+                  `Then` ((Literal '.') `Or` Epsilon)
+                  `Then` d' `Then` (Star d')
+
+re_real' = sinal'' `Then` (Star d)
+                  `Then` ((Literal '.') `Or` Epsilon)
+                  `Then` d `Then` (Star d)
+
+
+
+
+cre_real = "('+'|'-')?d*('.')?d+"
+
+
+realdfa' = (beautifyDfa . ndfa2dfa . regExp2Ndfa) re_real
+
+realdfa'' = (beautifyDfa . minimizeDfa . ndfa2dfa . regExp2Ndfa) re_real'
+
+realdfa''' = (beautifyDfa . stdMinimizeDfa . ndfa2dfa . regExp2Ndfa) re_real'
+
+
+
+realdfa'''' = beautifyDfa . minimizeNdfa . regExp2Ndfa $ re_real'
+
+genGraph fa = tographvizIO fa "exp"
+
+
+realdfa = Dfa ['+','-','.','0','1','2','3','4','5','6','7','8','9']
+              ['A','B','C','D','E','F']
+              'A'
+              ['C','E']
+              delta_realdfa
+
+delta_realdfa :: Char -> Char -> Char
+delta_realdfa 'A' '+' = 'B'
+delta_realdfa 'A' '-' = 'B'
+delta_realdfa 'A' '0' = 'C'
+delta_realdfa 'A' '1' = 'C'
+delta_realdfa 'A' '2' = 'C'
+delta_realdfa 'A' '3' = 'C'
+delta_realdfa 'A' '4' = 'C'
+delta_realdfa 'A' '.' = 'D'
+delta_realdfa 'B' '0' = 'C'
+delta_realdfa 'B' '1' = 'C'
+delta_realdfa 'B' '2' = 'C'
+delta_realdfa 'B' '3' = 'C'
+delta_realdfa 'B' '4' = 'C'
+delta_realdfa 'B' '.' = 'D'
+delta_realdfa 'C' '0' = 'C'
+delta_realdfa 'C' '1' = 'C'
+delta_realdfa 'C' '2' = 'C'
+delta_realdfa 'C' '3' = 'C'
+delta_realdfa 'C' '4' = 'C'
+delta_realdfa 'C' '.' = 'D'
+delta_realdfa 'D' '0' = 'E'
+delta_realdfa 'D' '1' = 'E'
+delta_realdfa 'D' '2' = 'E'
+delta_realdfa 'D' '3' = 'E'
+delta_realdfa 'D' '4' = 'E'
+delta_realdfa 'E' '0' = 'E'
+delta_realdfa 'E' '1' = 'E'
+delta_realdfa 'E' '2' = 'E'
+delta_realdfa 'E' '3' = 'E'
+delta_realdfa 'E' '4' = 'E'
+delta_realdfa _ _     = 'F'
+
+
+isreal :: String -> Bool
+isreal = Fa.accept realdfa
+
+\end{code}
+
+
+
+\section{Non-deterministic Finite Automaton}
+
+\begin{figure}[htb!]
+{\hrule\bigskip}
+\begin{center}
+\Ipe{FIGURES/RealNdfa.ipe}
+\end{center}
+\caption{Non-deterministic Finite Automaton for the Language of the
+Real Numbers.}
+{\bigskip\hrule}
+\end{figure}
+
+
+\begin{code}
+
+realndfa = Ndfa ['+','-','.','0','1','2','3','4','5','6','7','8','9']
+                ['A','B','C','D','E']
+                ['A','C']
+                ['C','E']
+                deltaNdfa
+
+deltaNdfa 'A' (Just '+') = ['B']
+deltaNdfa 'A' (Just '-') = ['B']
+deltaNdfa 'A' Nothing    = ['B']
+
+deltaNdfa 'B' (Just '0') = ['C']
+deltaNdfa 'B' (Just '1') = ['C']
+deltaNdfa 'B' (Just '2') = ['C']
+deltaNdfa 'B' (Just '3') = ['C']
+deltaNdfa 'B' (Just '4') = ['C']
+deltaNdfa 'B' (Just '5') = ['C']
+deltaNdfa 'B' (Just '6') = ['C']
+deltaNdfa 'B' (Just '7') = ['C']
+deltaNdfa 'B' (Just '8') = ['C']
+deltaNdfa 'B' (Just '9') = ['C']
+--deltaNdfa 'B' Nothing = ['C']
+deltaNdfa 'B' (Just '.') = ['D']
+
+deltaNdfa 'C' (Just '.') = ['D']
+deltaNdfa 'C' Nothing    = ['B']
+
+deltaNdfa 'D' (Just '0') = ['E']
+deltaNdfa 'D' (Just '1') = ['E']
+deltaNdfa 'D' (Just '2') = ['E']
+deltaNdfa 'D' (Just '3') = ['E']
+deltaNdfa 'D' (Just '4') = ['E']
+deltaNdfa 'D' (Just '5') = ['E']
+deltaNdfa 'D' (Just '6') = ['E']
+deltaNdfa 'D' (Just '7') = ['E']
+deltaNdfa 'D' (Just '8') = ['E']
+deltaNdfa 'D' (Just '9') = ['E']
+
+deltaNdfa 'E' (Just '0') = ['E']
+deltaNdfa 'E' (Just '1') = ['E']
+deltaNdfa 'E' (Just '2') = ['E']
+deltaNdfa 'E' (Just '3') = ['E']
+deltaNdfa 'E' (Just '4') = ['E']
+deltaNdfa 'E' (Just '5') = ['E']
+deltaNdfa 'E' (Just '6') = ['E']
+deltaNdfa 'E' (Just '7') = ['E']
+deltaNdfa 'E' (Just '8') = ['E']
+deltaNdfa 'E' (Just '9') = ['E']
+
+deltaNdfa _ _ = []
+
+-- isrealNdfa :: Fa (Ndfa Char Char) Char => String -> Bool
+isrealNdfa = Fa.accept realndfa
+
+\end{code}
+
+
+
+Running hugs we have:
+
+
+\begin{verbatim}
+Real> isrealNdfa "-1.1"
+True
+Real> isrealNdfa "+12."
+False
+Real> isreal "-1.1"
+True
+Real> isreal "+12."
+False
+
+
+Real> isrealNdfa "122.122"
+True
+(1029 reductions, 1818 cells)
+\end{verbatim}
+
+
+
+\end{document}
+
+
+
diff --git a/HaLeX_lib/Language/HaLex/Examples/Robot.lhs b/HaLeX_lib/Language/HaLex/Examples/Robot.lhs
new file mode 100644
--- /dev/null
+++ b/HaLeX_lib/Language/HaLex/Examples/Robot.lhs
@@ -0,0 +1,124 @@
+
+
+
+\begin{code}
+
+
+module Language.HaLex.Examples.Robot where
+
+import Language.HaLex.Dfa
+import Language.HaLex.FaAsDiGraph
+import qualified Language.HaLex.DfaMonad as DfaMonad
+
+
+\end{code}
+
+
+\begin{code}
+
+
+-- ex :: Dfa IO [Char] [Char]
+ex = Dfa ["esquerda","direita","largar","pegar"]
+         ["C0 sem pepita","C0 com pepita","C1 sem pepita","C1 com pepita"]
+         "C0 sem pepita"
+         ["C0 sem pepita"]
+         delta
+  where 
+    delta "C0 sem pepita" "direita"  = "C1 sem pepita" 
+    delta "C0 sem pepita" _          = "C0 sem pepita" 
+
+    delta "C0 com pepita" "largar"   = "C0 sem pepita" 
+    delta "C0 com pepita" "direita"  = "C1 com pepita" 
+    delta "C0 com pepita" _          = "C0 com pepita" 
+
+    delta "C1 sem pepita" "esquerda" = "C0 sem pepita" 
+    delta "C1 sem pepita" "pegar"    = "C1 com pepita" 
+    delta "C1 sem pepita" _          = "C1 sem pepita"
+
+    delta "C1 com pepita" "esquerda" = "C0 com pepita" 
+    delta "C1 com pepita" "largar"   = "C1 sem pepita" 
+    delta "C1 com pepita" _          = "C1 com pepita"     
+
+moves = ["direita","pegar","esquerda","largar"]
+moves2 = ["esquerda","pegar","direita","pegar","esquerda","largar"]
+moves3 = ["esquerda","pegar","direita"]
+moves4 = moves2 ++ moves
+
+g = dfa2graphviz2file ex "xxx"
+
+\end{code}
+
+
+
+
+
+\begin{code}
+
+robotM :: DfaMonad.Dfa Maybe [Char] [Char]
+robotM = DfaMonad.Dfa ["esquerda","direita","largar","pegar"]
+             ["C0 sem pepita","C0 com pepita","C1 sem pepita","C1 com pepita"]
+             "C0 sem pepita"
+             ["C0 sem pepita"]
+             delta
+  where 
+    delta "C0 sem pepita" "direita"  = return "C1 sem pepita" 
+    delta "C0 sem pepita" _          = return "C0 sem pepita" 
+
+    delta "C0 com pepita" "largar"   = return "C0 sem pepita" 
+    delta "C0 com pepita" "direita"  = return "C1 com pepita" 
+    delta "C0 com pepita" _          = return "C0 com pepita" 
+
+    delta "C1 sem pepita" "esquerda" = return "C0 sem pepita" 
+    delta "C1 sem pepita" "pegar"    = return "C1 com pepita" 
+    delta "C1 sem pepita" _          = return "C1 sem pepita"
+
+    delta "C1 com pepita" "esquerda" = return "C0 com pepita" 
+    delta "C1 com pepita" "largar"   = return "C1 sem pepita" 
+    delta "C1 com pepita" _          = return "C1 com pepita"     
+
+
+
+acc = DfaMonad.dfaaccept robotM moves4
+
+\end{code}
+
+
+
+
+
+
+\begin{code}
+
+robotM2 :: DfaMonad.Dfa IO [Char] [Char]
+robotM2 = DfaMonad.Dfa ["esquerda","direita","largar","pegar"]
+                       ["C0 sem pepita","C0 com pepita","C1 sem pepita","C1 com pepita"]
+                       "C0 sem pepita"
+                       ["C0 sem pepita"]
+                       delta
+  where 
+    delta "C0 sem pepita" "direita"  = do putStrLn "Vou para C1 sem pepita"
+                                          return "C1 sem pepita" 
+    delta "C0 sem pepita" _          = return "C0 sem pepita" 
+
+    delta "C0 com pepita" "largar"   = return "C0 sem pepita" 
+    delta "C0 com pepita" "direita"  = return "C1 com pepita" 
+    delta "C0 com pepita" _          = return "C0 com pepita" 
+
+    delta "C1 sem pepita" "esquerda" = return "C0 sem pepita" 
+    delta "C1 sem pepita" "pegar"    = return "C1 com pepita" 
+    delta "C1 sem pepita" _          = return "C1 sem pepita"
+
+    delta "C1 com pepita" "esquerda" = do putStrLn "Vou para C0 com pepita"
+                                          return "C0 com pepita" 
+    delta "C1 com pepita" "largar"   = return "C1 sem pepita" 
+    delta "C1 com pepita" _          = return "C1 com pepita"     
+
+
+
+acc2 = DfaMonad.dfaaccept robotM2 moves4
+
+
+exShow = do d <- DfaMonad.showInDot robotM2 True
+            writeFile "xxx" d
+
+\end{code}
diff --git a/HaLeX_lib/Language/HaLex/Fa2RegExp.hs b/HaLeX_lib/Language/HaLex/Fa2RegExp.hs
new file mode 100644
--- /dev/null
+++ b/HaLeX_lib/Language/HaLex/Fa2RegExp.hs
@@ -0,0 +1,115 @@
+-----------------------------------------------------------------------------
+-- |
+-- Module      :  Language.HaLex.Fa2RegExp
+-- Copyright   :  (c) João Saraiva 2001,2002,2003,2004,2005
+-- License     :  LGPL
+--
+-- Maintainer  :  jas@di.uminho.pt
+-- Stability   :  provisional
+-- Portability :  portable
+--
+-- From Finite Automata into Regular Expressions
+--
+-- Code Included in the Lecture Notes on
+--        Language Processing (with a functional flavour).
+--
+-----------------------------------------------------------------------------
+
+module Language.HaLex.Fa2RegExp ( dfa2RegExp
+                                , regExpFromTo
+                                , ndfaregExpFromTo
+                                ) where
+
+
+import Data.List
+import Language.HaLex.Util
+import Language.HaLex.RegExp
+import Language.HaLex.Dfa
+import Language.HaLex.Ndfa
+
+
+-- | Compute a regular expression that defines the transitions from an
+--   origin to a destination in a 'Dfa'.
+
+regExpFromTo :: Eq st
+             => (st -> sy -> st)       -- ^ Transition Function
+             -> [sy]                   -- ^ Vocabulary
+             -> st                     -- ^ Origin State
+             -> st                     -- ^ Destination State
+             -> RegExp sy              -- ^ Regular Expression
+
+regExpFromTo delta v o d = let sys = transitionsFromTo delta v o d
+                           in  toRegExp sys
+
+toRegExp :: [sy] -> RegExp sy
+toRegExp []     = Empty
+toRegExp (x:xs) = toRegExp2 (x:xs)
+
+toRegExp2 []     = Epsilon
+toRegExp2 [x]    = Literal x
+toRegExp2 (x:xs) = Or (Literal x) (toRegExp2 xs)
+
+
+-- | Compute a regular expression that defines the transitions from an
+--   origin to a destination in a 'Ndfa'.
+
+ndfaregExpFromTo :: Eq st
+                 => (st -> Maybe sy -> [st])   -- ^ Transition Function
+                 -> [sy]                       -- ^ Vocabulary
+                 -> st                         -- ^ Origin State
+                 -> st                         -- ^ Destination State
+                 -> RegExp sy                  -- ^ Regular Expression
+
+ndfaregExpFromTo delta v o d = let sys = ndfaTransitionsFromTo delta v o d
+                               in  toRegExp' sys
+
+toRegExp' :: [Maybe sy] -> RegExp sy
+toRegExp' []     = Empty
+toRegExp' (x:xs) = toRegExp2' (x:xs)
+
+toRegExp2' []     = Epsilon
+toRegExp2' [x]    = case x of
+                      Nothing    -> Epsilon
+                      (Just x )  -> Literal x
+toRegExp2' (x:xs) = case x of
+                      Nothing    -> Or Epsilon (toRegExp2' xs)
+                      (Just x )  -> Or (Literal x) (toRegExp2' xs)
+
+
+
+regular :: Num st
+        => (st -> sy -> st)
+        -> [sy]
+        -> st
+        -> st
+        -> st
+        -> RegExp sy
+
+regular d v i j 0
+      |  i==j      =  (regExpFromTo d v i j) `Or` Epsilon
+      | otherwise  =  regExpFromTo d v i j              -- force to Int !!
+regular d v i j k  =  Or (Then (Then (regular d v i k (k-1))
+                                  (Star (regular d v k k (k-1))  )  )
+                         (regular d v k j (k-1))) (regular d v i j (k-1))
+
+
+-- | Compute a regular expression from a 'Dfa'.
+
+dfa2RegExp :: Eq sy
+           => Dfa Int sy            -- ^ Deterministic Automaton
+           -> RegExp sy             -- ^ Equivalent Regular Expression
+dfa2RegExp dfa@(Dfa v q s z delta) =
+          limit simplifyRegExp (applyD delta v s z (sizeDfa dfa))
+
+applyD :: Num st
+       => (st -> sy -> st)
+       -> [sy]
+       -> st
+       -> [st]
+       -> st
+       -> RegExp sy
+
+applyD d v _ []     _   = Epsilon
+applyD d v i (z:zs) k   = (regular d v i z k) `Or` (applyD d v i zs k)
+
+
diff --git a/HaLeX_lib/Language/HaLex/FaAsDiGraph.hs b/HaLeX_lib/Language/HaLex/FaAsDiGraph.hs
new file mode 100644
--- /dev/null
+++ b/HaLeX_lib/Language/HaLex/FaAsDiGraph.hs
@@ -0,0 +1,176 @@
+-----------------------------------------------------------------------------
+-- |
+-- Module      :  Language.HaLex.FaAsDiGraph
+-- Copyright   :  (c) João Saraiva 2001,2002,2003,2004,2005
+-- License     :  LGPL
+-- 
+-- Maintainer  :  jas@di.uminho.pt
+-- Stability   :  provisional
+-- Portability :  portable
+--
+-- Finite Automata as Directed Graphs in GraphViz. 
+-- Code Included in the Lecture Notes on 
+--             Language Processing (with a functional flavour).   
+--
+-----------------------------------------------------------------------------
+
+module Language.HaLex.FaAsDiGraph ( 
+                      ndfa2graphviz
+                    , ndfa2graphviz2file
+                    , dfa2graphviz 
+                    , dfa2graphviz2file
+                    , tographviz
+                    , tographvizIO
+                    , dfa2DiGraphWithNoSyncSt
+                    , dfaDiGraphWithNoSyncStIO
+                    , genOneArrow
+                    ) where
+
+import Language.HaLex.RegExp
+import Language.HaLex.RegExp2Fa
+import Language.HaLex.Ndfa
+import Language.HaLex.Dfa
+import Language.HaLex.FaOperations
+import Language.HaLex.Minimize 
+
+
+-- | Print a 'Ndfa' in GraphViz
+ndfa2graphviz ndfa name = tographviz ndfa name "circle" "LR" show 
+
+-- | Print a 'Ndfa' in GraphViz in a file
+ndfa2graphviz2file ndfa name = writeFile (name++".dot") (ndfa2graphviz ndfa  name) 
+
+
+-- | Print a 'Dfa' in GraphViz
+dfa2graphviz dfa name = tographviz (dfa2ndfa dfa) name "circle" "LR" show 
+
+-- | Print a 'Dfa' in GraphViz in a file
+dfa2graphviz2file dfa name = writeFile (name++".dot") (dfa2graphviz dfa  name) 
+
+
+
+-- | Print a 'Ndfa' in GraphViz
+
+tographviz :: (Eq sy, Show sy, Ord st , Show st) 
+        => Ndfa st sy            -- ^ Automaton
+        -> [Char]                -- ^ Graph's name
+        -> [Char]                -- ^ Node's shape
+        -> [Char]                -- ^ Orientation
+        -> (st -> [Char])        -- ^ Show function to print the state ids
+        -> [Char]
+tographviz ndfa@(Ndfa v q s z delta) name shape orientation showState = 
+  "digraph " ++ name ++ " {\n " 
+             ++ "rankdir = " ++ orientation ++ " ;\n " 
+             ++ (showElemsListPerLine (showStates q)) ++ "\n " 
+             ++ (showElemsListPerLine (showInitialStates s)) ++ "\n " 
+             ++ (showElemsListPerLine (showFinalStates' z))
+             ++ (showElemsListPerLine (showNdfaArrows'' ndfa)) 
+             ++ "node [shape=none, lavel=initialState, style = invis];\n"
+             ++ (createInitialArrows (mirroredInitialStates s) s)
+             ++ "\n}"
+  where 
+    showElemsListPerLine :: [String] -> String
+    showElemsListPerLine []    = ""
+    showElemsListPerLine (h:t) = ((showString h) "\n ") ++ 
+                                 (showElemsListPerLine t) 
+
+    showStates qs = [(showState q) ++ 
+                     " [shape=" ++ shape ++" , label=" ++ (showState q) ++ " ,color=black];" 
+                    | q <- qs , not (ndfaIsStDead delta v z q ) ]
+ 
+    showInitialStates ss = map showInitialState ss
+
+    showInitialState  s = (showState s) 
+                          ++ " [shape=" ++ shape ++ " , label= " ++ (showState s) 
+                          ++ ", color=green];\n " 
+
+--    showFinalStates' :: Show a => [a] -> [String]
+    showFinalStates' zs = [ (showState z) 
+                          ++ " [shape=double" ++ shape ++" , color=red];" | z <- zs ]
+
+--     showNdfaArrows' :: (Eq sy,  Show sy) => Ndfa st sy -> [String]
+    showNdfaArrows' ndfa
+       = map (\ (o,l,d) -> genOneArrow (showState o) (show l) (showState d)) 
+             ((groupMoves . transitionTableNdfa) ndfa)
+
+--     showNdfaArrows'' :: (Ord st, Eq sy, Show st, Show sy) => Ndfa st sy -> [String]
+    showNdfaArrows'' ndfa@(Ndfa v q s z delta)
+         = map (\ (o,l,d) -> if (ndfaIsStDead delta v z o) || (ndfaIsStDead delta v z d) then ""
+                             else genOneArrow (showState o) (showListMaybe l) (showState d)) 
+                                  ((groupMoves . transitionTableNdfa) ndfa)
+
+
+-- Creating the incoming arrows for the initial states
+-- (for each state we create an invisible node and a arrow connecting to the initial one)
+
+    mirroredInitialStates = map (\state -> "_newState" ++ (show state)) 
+    createInitialArrows [] []         = " "
+    createInitialArrows (x:xs) (y:ys) = x ++ " -> " ++ (showState y) ++ 
+                                        "[color = green];\n" ++ 
+                                        createInitialArrows xs ys
+
+
+showListMaybe []     = ""
+showListMaybe (x:xs) = case x of
+                       Just a -> (show a) ++ if (showListMaybe xs == "") then ""
+                                   else ("," ++ showListMaybe xs)
+                       Nothing -> "Epsilon" ++ if (showListMaybe xs == "") then ""
+                                   else ("," ++ showListMaybe xs)
+
+--
+-- Given the Transition Table of a Ndfa it groups the transtions with
+-- the same origin and destination into a single transtion, whose transtion
+-- is the list of labels of the original transtions.
+--
+
+groupMoves []           = []
+groupMoves ((o,l,d):rs) = res
+  where (l',rs') = groupMoves' (o,l,d) ((o,l,d):rs)
+        res      = (o,l',d) : groupMoves rs'
+
+
+groupMoves' :: (Eq st, Eq sy) => (st,Maybe sy,st) -> [(st,Maybe sy,st)] 
+            -> ([Maybe sy],[(st,Maybe sy,st)])
+groupMoves' _ []  = ([],[])
+groupMoves' (o,l,d) ((o',l',d'):rs) 
+             | o==o' && d==d' = (new_label,rs')
+             | otherwise      = (l'', (o',l',d') : rs')
+       where (l'',rs') = groupMoves' (o,l,d) rs 
+             new_label = if l'' == [] then [l'] 
+                                      else l' : l''
+
+
+showNdfaArrows :: (Ord st,Show st,Show sy) => Ndfa st sy -> [String]
+showNdfaArrows (Ndfa vs qs s z delta) = [ genOneArrow (show q) (show v) (show r) 
+                                        | q <- qs , v <- vs 
+                                        , r <- delta q (Just v)
+                                        , not (ndfaIsStDead delta vs z r )
+                                        , not (ndfaIsStDead delta vs z q )
+                                        ] ++ 
+                                        [ genOneArrow (show q) "Epsilon" (show r)
+                                        | q <- qs
+                                        , r <- delta q Nothing
+                                        , not (ndfaIsStDead delta vs z r )
+                                        , not (ndfaIsStDead delta vs z q )
+                                        ]
+
+genOneArrow orin label dest = orin  
+                              ++ " -> " ++ dest 
+                              ++ " [label = " ++ (show label) ++ "];"
+
+
+
+tographvizIO ndfa name shape orientation showState = 
+   writeFile (name++".dot") (tographviz ndfa name shape orientation showState)
+
+
+dfa2DiGraphWithNoSyncSt dfa name = dfa2graphviz dfa name
+
+dfa2DiGraphIO dfa name fn = writeFile (fn++".gph") (dfa2graphviz dfa  name ) 
+
+dfaDiGraphWithNoSyncStIO dfa name fn = writeFile fn (dfa2graphviz dfa  name) 
+
+-- dfa2DiGraphIO'' :: (Show sy, Ord sy , Eq st) => Dfa st sy -> [Char] -> IO ()
+dfa2DiGraphIO'' dfa name = dfa2DiGraphIO (beautifyDfa dfa) name name
+
+
diff --git a/HaLeX_lib/Language/HaLex/FaClasses.hs b/HaLeX_lib/Language/HaLex/FaClasses.hs
new file mode 100644
--- /dev/null
+++ b/HaLeX_lib/Language/HaLex/FaClasses.hs
@@ -0,0 +1,85 @@
+{-# LANGUAGE FlexibleInstances, MultiParamTypeClasses #-}
+-----------------------------------------------------------------------------
+-- |
+-- Module      :  Language.HaLex.Dfa
+-- Copyright   :  (c) João Saraiva 2001,2002,2003,2004,2005
+-- License     :  LGPL
+--
+-- Maintainer  :  jas@di.uminho.pt
+-- Stability   :  provisional
+-- Portability :  portable
+--
+-- The Class of Finite Automaton in Haskell
+--
+-- Code Included in the Lecture Notes on
+--      Language Processing (with a functional flavour).
+--
+-----------------------------------------------------------------------------
+
+module Language.HaLex.FaClasses where
+
+import Language.HaLex.Dfa
+import Language.HaLex.Ndfa
+import Language.HaLex.FaOperations
+import Language.HaLex.Equivalence
+import Language.HaLex.Minimize
+import Language.HaLex.FaAsDiGraph
+
+
+-- | Class of Finite automaton
+
+class Fa fa st sy where
+  accept     :: fa st sy -> [sy] -> Bool
+  sizeFa     :: fa st sy -> Int
+  equiv      :: fa st sy -> fa st sy -> Bool
+  minimize   :: fa st sy -> Dfa [[st]] sy
+  reverseFa  :: fa st sy -> Ndfa st sy
+  deadstates :: fa st sy -> [st]
+  toHaskell' :: fa st sy -> String -> IO ()
+  toGraph    :: fa st sy -> String -> String
+  toGraphIO  :: fa st sy -> String -> IO()
+
+
+  unionFa    :: fa st sy -> fa st sy -> Ndfa st sy
+  concatFa   :: fa st sy -> fa st sy -> Ndfa st sy
+  starFa     :: fa st sy -> Ndfa st sy
+  plusFa     :: fa st sy -> Ndfa st sy
+
+
+-- | Instance of class 'Fa' for a 'Dfa'
+
+instance (Show st , Show sy , Ord st , Ord sy) => Fa Dfa st sy where
+  accept     = dfaaccept
+  sizeFa     = sizeDfa
+  equiv      = equivDfa
+  minimize   = minimizeDfa
+  reverseFa  = reverseDfa
+  deadstates = dfadeadstates
+  toHaskell' = toHaskell
+  toGraph    = dfa2graphviz
+  toGraphIO  = dfa2graphviz2file
+
+  unionFa    = unionDfa
+  starFa     = starDfa
+  concatFa   = concatDfa
+  plusFa     = plusDfa
+
+-- | Instance of class 'Fa' for a 'Ndfa'
+
+instance (Show st , Show sy , Ord st , Ord sy) => Fa Ndfa st sy where
+  accept     = ndfaaccept
+  sizeFa     = sizeNdfa
+  equiv      = equivNdfa
+  minimize   = minimizeNdfa
+  reverseFa  = reverseNdfa
+  deadstates = ndfadeadstates
+  toHaskell' = toHaskell
+  toGraph    = ndfa2graphviz
+  toGraphIO  = ndfa2graphviz2file
+
+  unionFa    = unionNdfa
+  starFa     = starNdfa
+  concatFa   = concatNdfa
+  plusFa     = plusNdfa
+
+
diff --git a/HaLeX_lib/Language/HaLex/FaOperations.hs b/HaLeX_lib/Language/HaLex/FaOperations.hs
new file mode 100644
--- /dev/null
+++ b/HaLeX_lib/Language/HaLex/FaOperations.hs
@@ -0,0 +1,246 @@
+--
+-- Functions manipulating Finite Automata (DFA and NDFA)
+--
+--
+-- Code Included in the Lecture Notes on
+--
+--      Language Processing (with a functional flavour)
+--
+--
+-- copyright João Saraiva
+--           Department of Computer Science,
+--           University of Minho,
+--           Braga, Portugal
+--           jas@di.uminho.pt
+--           2001
+--
+
+
+
+
+
+module Language.HaLex.FaOperations (
+                      ndfa2dfa
+                    , dfa2ndfa
+                    , ndfa2ct
+                    , CT
+                    , lookupCT
+                    , stsDfa
+                    , concatNdfa
+                    , unionNdfa
+                    , starNdfa
+                    , plusNdfa
+                    , expNdfa
+                    , unionDfa
+                    , concatDfa
+                    , starDfa
+                    , plusDfa
+                    ) where
+
+import Data.List
+import Language.HaLex.Util
+import Language.HaLex.Dfa
+import Language.HaLex.Ndfa
+
+
+
+--
+-- Making a DFA from a NDFA
+--
+
+type StDfa st = [st]
+
+type CT st = [( StDfa st, [StDfa st])]
+
+stsDfa   = map fst
+stsRHS   = map snd
+allstsCT = concat . stsRHS
+
+
+ndfa2ct :: Ord st => Ndfa st sy -> CT st
+ndfa2ct (Ndfa v q s z delta) = limit (ndfa2dfaStep delta v) ttFstRow
+  where  ttFstRow = consRows delta [epsilon_closure delta s] v
+
+
+ndfa2dfaStep :: Ord st => (st -> (Maybe sy) -> [st]) -> [sy] -> CT st -> CT st
+ndfa2dfaStep delta alfabet ct = nub (ct `union` consRows delta newSts alfabet)
+  where newSts =  ((nub . allstsCT) ct) <-> (stsDfa ct)
+
+
+consRows :: Ord st => (st -> (Maybe sy) -> [st]) -> [StDfa st] -> [sy] -> CT st
+consRows delta []     alfabet = []
+consRows delta (q:qs) alfabet = (q , oneRow delta q alfabet) :
+                                (consRows delta qs alfabet)
+
+
+oneRow :: Ord st => (st -> (Maybe sy) -> [st]) -> (StDfa st) -> [sy] -> [StDfa st]
+oneRow delta sts alfabet = map (\ v -> sort (ndfawalk delta sts [v])) alfabet
+
+ndfa2dfa :: (Ord st,Eq sy) => Ndfa st sy -> Dfa [st] sy
+ndfa2dfa ndfa@(Ndfa v q s z delta)  = (Dfa v' q' s' z' delta')
+  where  tt = ndfa2ct ndfa
+         v' = v
+         q' = stsDfa tt
+         s' = fst (head tt)
+         z' = finalStatesDfa q' z
+         delta' st sy = lookupCT st sy tt v
+
+finalStatesDfa :: Eq st => [StDfa st] -> [st] -> [StDfa st]
+finalStatesDfa []     z = []
+finalStatesDfa (q:qs) z | (q `intersect` z /= []) = q : finalStatesDfa qs z
+                        | otherwise               = finalStatesDfa qs z
+
+-- lookupCT :: (Eq st, Eq sy) => [st] -> sy -> CT st -> [sy] -> StDfa st
+lookupCT st sy []     v  = []
+lookupCT st sy (q:qs) v  | (fst q == st) = (snd q) !! col
+                         | otherwise     = lookupCT st sy qs v
+   where (Just col) = elemIndex sy v
+
+
+--
+-- Making a NDFA from a DFA
+--
+
+dfa2ndfa :: Dfa st sy -> Ndfa st sy
+dfa2ndfa (Dfa v q s z delta) = (Ndfa v q [s] z delta')
+  where delta' q (Just a) = [delta q a]
+        delta' q Nothing  = []
+
+
+--
+-- Concatenation of Ndfa's
+--
+
+concatNdfa :: (Eq a, Eq b) => Ndfa b a -> Ndfa b a -> Ndfa b a
+concatNdfa (Ndfa vp qp sp zp dp) (Ndfa vq qq sq zq dq) = Ndfa v' q' s' z' d'
+  where v' = vp `union` vq
+        q' = qp `union` qq
+        s' = sp
+        z' = zq
+        d' q | q `elem` zp = dp' q
+             | q `elem` qp = dp  q
+             | otherwise   = dq  q
+         where dp' q Nothing = (dp q Nothing) `union` sq
+               dp' q sy      = dp q sy
+
+--
+-- Union Ndfa
+--
+
+unionNdfa :: (Eq a, Eq b) => Ndfa b a -> Ndfa b a -> Ndfa b a
+unionNdfa (Ndfa vp qp sp zp dp) (Ndfa vq qq sq zq dq) = Ndfa v' q' s' z' d'
+  where v' = vp `union` vq
+        q' = qp `union` qq
+        s' = sp `union` sq
+        z' = zp `union` zq
+        d' q | q `elem` qp = dp q
+             | q `elem` qq = dq q
+
+--
+-- Star Ndfa
+--
+
+starNdfa :: Eq st => Ndfa st sy -> Ndfa st sy
+starNdfa (Ndfa v qs s z d) = Ndfa v qs s z d'
+  where d' q | q `elem` s = ds' q
+             | q `elem` z = dz' q
+             | otherwise  = d q
+          where ds' q Nothing  = z `union` (d q Nothing)
+                ds' q sy       = d q sy
+
+                dz' q Nothing  = s `union` (d q Nothing)
+                dz' q sy       = d q sy
+
+--
+-- Plus Ndfa
+--
+
+plusNdfa :: Eq st => Ndfa st sy -> Ndfa st sy
+plusNdfa (Ndfa v qs s z d) = Ndfa v qs s z d'
+  where d' q | q `elem` z = dz' q
+             | otherwise  = d q
+          where dz' q Nothing  = s `union` (d q Nothing)
+                dz' q sy       = d q sy
+
+--
+-- Exponenciation
+--
+
+expNdfa :: (Eq st,Eq sy) => Ndfa st sy -> Int -> Ndfa Int sy
+expNdfa ndfa n = expNdfa' (renameNdfa ndfa 1) n
+
+expNdfa' :: Eq sy => Ndfa Int sy -> Int -> Ndfa Int sy
+expNdfa'  ndfa 1 = ndfa
+expNdfa'  ndfa i = concatNdfa ndfa (expNdfa' ndfa (i-1))
+
+--
+-- Concatenation of Dfa's
+--
+
+concatDfa :: (Eq a, Eq b) => Dfa b a -> Dfa b a -> Ndfa b a
+concatDfa (Dfa vp qp sp zp dp) (Dfa vq qq sq zq dq) = Ndfa v' q' s' z' d'
+  where v' = vp `union` vq
+        s' = [sp]
+        z' = zq
+        q' = qp `union` qq
+        d' q | q `elem` zp = dz' q
+             | q `elem` qp = dp' q
+             | q `elem` qq = dq' q
+         where dz' q  Nothing = [sq]
+               dz' q (Just y) | y `elem` vp = [dp q y]
+                              | otherwise   = []
+
+               dp' q Nothing  = []
+               dp' q (Just y) | y `elem` vp = [dp q y]
+                              | otherwise   = []
+
+               dq' q Nothing  = []
+               dq' q (Just y) | y `elem` vq = [dq q y]
+                              | otherwise   = []
+
+--
+-- Union of Dfa's
+--
+
+unionDfa :: (Eq a, Eq b) => Dfa b a -> Dfa b a -> Ndfa b a
+unionDfa (Dfa vp qp sp zp dp) (Dfa vq qq sq zq dq) = Ndfa v' q' s' z' d'
+  where v' = vp `union` vq
+        q' = qp `union` qq
+        s' = [sp,sq]
+        z' = zp ++ zq
+        d' _ Nothing                 = []
+        d' q (Just sy) | q `elem` qp && sy `elem` vp = [dp q sy]
+                       | q `elem` qq && sy `elem` vq = [dq q sy]
+                       | otherwise   = []
+
+--
+-- Star Dfa
+--
+
+starDfa :: Eq st => Dfa st sy -> Ndfa st sy
+starDfa (Dfa v q s z d) = Ndfa v q [s] z d'
+  where d' q | q == s     = ds' q
+             | q `elem` z = dz' q
+             | otherwise  = dd' q
+          where ds' q Nothing  = z
+                ds' q (Just y) = [d q y]
+
+                dz' q Nothing  = [s]
+                dz' q (Just y) = [d q y]
+
+                dd' q (Just y) = [d q y]
+                dd' _ _        = []
+
+--
+-- Plus Dfa
+--
+
+plusDfa :: Eq st => Dfa st sy -> Ndfa st sy
+plusDfa (Dfa v q s z d) = Ndfa v q [s] z d'
+  where d' q | q `elem` z = dz' q
+             | otherwise  = dd' q
+          where dz' q Nothing  = [s]
+                dz' q (Just y) = [d q y]
+
+                dd' q (Just y) = [d q y]
+                dd' _ _ = []
diff --git a/HaLeX_lib/Language/HaLex/Minimize.hs b/HaLeX_lib/Language/HaLex/Minimize.hs
new file mode 100644
--- /dev/null
+++ b/HaLeX_lib/Language/HaLex/Minimize.hs
@@ -0,0 +1,207 @@
+
+-----------------------------------------------------------------------------
+-- |
+-- Module      :  Language.HaLex.Minimize
+-- Copyright   :  (c) João Saraiva 2001,2002,2003,2004,2005
+-- License     :  LGPL
+--
+-- Maintainer  :  jas@di.uminho.pt
+-- Stability   :  provisional
+-- Portability :  portable
+--
+-- Minimization of the States of a Deterministica Finite Automata
+--
+-- Code Included in the Lecture Notes on
+--      Language Processing (with a functional flavour).
+--
+-----------------------------------------------------------------------------
+
+module Language.HaLex.Minimize (
+                -- * Minimization
+                  minimizeDfa
+                , stdMinimizeDfa
+                , minimizeExp
+                , minimizeNdfa
+                -- * Reversing Automata
+                , reverseDfa
+                , reverseDfaAsDfa
+                , reverseNdfa
+                ) where
+
+import Data.List
+import Language.HaLex.Util
+import Language.HaLex.Dfa
+import Language.HaLex.Ndfa
+import Language.HaLex.FaOperations
+
+
+-----------------------------------------------------------------------------
+-- * Minimization
+
+
+-- | Minimize the number of states of a given 'Dfa'.
+--   This function uses Brzozowski's algorithm
+
+minimizeDfa :: (Eq sy, Ord st)
+            => Dfa st sy              -- ^ Original 'Dfa'
+            -> Dfa [[st]] sy          -- ^ Equivalent Minimized 'Dfa'
+
+minimizeDfa = ndfa2dfa . reverseDfa . ndfa2dfa . reverseDfa
+
+
+-- | Minimize the number of states of a given 'Ndfa'.
+--   This function uses Brzozowski's algorithm
+
+minimizeNdfa :: (Eq sy, Ord st)
+             => Ndfa st sy            -- ^ Original 'Ndfa'
+             -> Dfa [[st]] sy         -- ^ Equivalent Minimized 'Dfa'
+
+minimizeNdfa =  ndfa2dfa . reverseDfa . ndfa2dfa . reverseNdfa
+
+
+-- | Minimize the number of states of a given 'Dfa'.
+--
+-- This minimization algorithm is described in
+--   \"An Introduction to Formal Languages and Automata\", Peter Linz, 3rd Ed.
+--   Jones and Bartlett Publishers
+--
+
+stdMinimizeDfa :: (Ord st, Ord sy)
+               => Dfa st sy                  -- ^ Original 'Dfa'
+               -> Dfa [st] sy                -- ^ Equivalent Minimized 'Dfa'
+stdMinimizeDfa dfa = ttDfa2Dfa  (vs,und,bl ss ,z',list)
+  where a = removeinaccessible dfa
+        Dfa vs qs ss zs ds = a
+        dist = distinguishable a
+        und  = undistinguishable a dist
+        tt = [ (q,v,z) | q <- qs , v <- vs , z <- [ds q v] ]
+        list = nub [ (bl x , y , bl z ) | (x,y,z) <- tt , bl x /= [] , bl z/= [] ]
+        z' = nub (filter (/=[]) (map bl zs))
+
+        bl x = concat ([] : (filter (x `elem`) und))
+
+
+undistinguishable :: Eq st => Dfa st sy -> [(st,st)] -> [[st]]
+undistinguishable (Dfa _ qs _ _ _) dist =
+        eraseintersect [ i : [j | j <- qs , ne(i,j) , ne (j,i), j/= i ] | i <- qs ]
+  where ne p = not (p `elem` dist)
+
+
+eraseintersect :: Eq a => [[a]] -> [[a]]
+eraseintersect []     = []
+eraseintersect (x:xs) | (concat . map (x `intersect`)) xs == []  = x : eraseintersect xs
+                      | otherwise                                = eraseintersect xs
+
+
+distinguishable :: Eq st => Dfa st sy -> [(st,st)]
+distinguishable (Dfa vs qs _ zs delta) = limit (\x -> nub (x ++ nthdist qs x)) (fstdist qs)
+  where fstdist []     = []
+        fstdist (x:xs) = [(x,a) | a <- xs , (x `elem` zs) /= (a `elem` zs) ] ++ fstdist xs
+
+        nthdist []     _    = []
+        nthdist (a:as) dist = [ (a,b) | b <- qs , x <- vs , move2Disting (a,b) x dist ]
+                              ++ nthdist as dist
+
+        move2Disting (a,b) x dist = (delta a x , delta b x) `elem` dist
+
+
+removeinaccessible dfa@(Dfa v s i f d) = Dfa v states i (f `intersect` states) d
+  where states = nub (i:(flowdown [i] (transitionTableDfa dfa)))
+        flowdown zz ss = limit (\ x -> nub(x ++ nextlevel ss x)) (nextlevel ss zz)
+        nextlevel ss zz = (nub . concat) [ next z ss | z <- zz ]
+        next z = concat . map (\(a,_,c) -> if a == z then [c] else [])
+
+removeinaccessible' a = ndfa2dfa . dfa2ndfa $ a
+
+
+
+
+-- | Minimize the number of states of a given 'Dfa'.
+--
+--   (a third algorithm)
+
+minimizeExp :: Ord st
+            => Dfa st sy                      -- ^ Original 'Dfa'
+            -> Dfa [st] sy                    -- ^ Equivalent Minimized 'Dfa'
+
+minimizeExp (Dfa t lst si lsf d) = Dfa t l (head (filter (\x->elem si x) l))
+                                        (filter (\x->intersect x lsf /= []) l) ndelta
+                                where (a,b)=partition f lst
+			              f x = elem x lsf
+				      l = (minaux lst d t) [a,b]
+				      ndelta st s | elem st l = rfind (d (head st) s) l
+					          | otherwise = []
+
+rfind :: Eq a => a -> [[a]] -> [a]
+rfind _ []=[]
+rfind x (h:t)| elem x h  = h
+             | otherwise = rfind x t
+
+minaux :: (Ord a) => [a] -> (a -> b -> a) -> [b] -> [[a]] -> [[a]]
+minaux lst d simb p | p == p' = p
+                    | otherwise = minaux lst d simb p'
+		    where p' =concatMap (partes lst d simb p []) p
+
+partes :: Eq a => [a] -> (a -> b -> a) -> [b] -> [[a]] -> [a] -> [a] -> [[a]]
+partes _ _ _ _ _ []  =[]
+partes _ _ _ _ ac [h] | elem h ac = []
+                      | otherwise = [[h]]
+partes lst d simb p ac (h:hs) |(elem h ac) = partes lst d simb p ac hs
+                              |otherwise = ([h]++r):(partes lst d simb p  (ac++r) hs)
+			      where r = raux hs
+			            raux []=[]
+		                    raux (x:xs) | (comparaDelta lst d simb p h x) = x:(raux xs)
+			                        | otherwise = raux xs
+
+
+mesmoGrupo :: Eq a => [a] -> [[a]] -> a -> a -> Bool
+mesmoGrupo lst [] s t = (elem s lst) == (elem t lst)
+mesmoGrupo lst (h:t) x y | ((elem x h) && (elem y h)) = True
+                         | otherwise = mesmoGrupo lst t x y
+
+comparaDelta :: Eq a => [a] -> (a -> b -> a) -> [b] -> [[a]] -> a -> a -> Bool
+comparaDelta lst d simb p s t= and (map (comparaDeltaSimb lst d p s t) simb)
+
+
+
+comparaDeltaSimb :: Eq a => [a] -> (a -> b -> a) -> [[a]] -> a -> a -> b -> Bool
+comparaDeltaSimb lst d p s t v = mesmoGrupo lst p s' t'
+                                 where s' = d s v
+				       t' = d t v
+
+
+-----------------------------------------------------------------------------
+-- * Reversing Automata
+
+
+
+-- | Reverse a 'Dfa'
+
+reverseDfa :: Eq st
+           => Dfa st sy               -- ^ Original 'Dfa'
+           -> Ndfa st sy              -- ^ Resulting 'Ndfa'
+
+reverseDfa (Dfa v qs s z delta) = Ndfa v qs z [s] delta'
+  where delta' st (Just sy) = [ q | q <- qs
+                                  , delta q sy == st ]
+        delta' st Nothing   = []
+
+
+-- | Reverse a 'Ndfa'
+
+reverseNdfa :: Eq st
+            => Ndfa st sy             -- ^ Original 'Ndfa'
+            -> Ndfa st sy             -- ^ Resulting 'Ndfa'
+reverseNdfa (Ndfa v qs s z delta) = Ndfa v qs z s delta'
+  where delta' st sy = [ q | q <- qs
+                           , st `elem` delta q sy  ]
+
+-- | Reverse a 'Dfa' into a 'Dfa'. It uses a 'Ndfa' as an intermediate representation.
+
+reverseDfaAsDfa :: (Ord st , Eq sy)
+                => Dfa st sy          -- ^ Orginal 'Dfa'
+                -> Dfa [st] sy        -- ^ Resulting 'Dfa'
+reverseDfaAsDfa = ndfa2dfa . reverseDfa
+
+
+
diff --git a/HaLeX_lib/Language/HaLex/Ndfa.hs b/HaLeX_lib/Language/HaLex/Ndfa.hs
new file mode 100644
--- /dev/null
+++ b/HaLeX_lib/Language/HaLex/Ndfa.hs
@@ -0,0 +1,360 @@
+-----------------------------------------------------------------------------
+-- |
+-- Module      :  Language.HaLex.Ndfa
+-- Copyright   :  (c) João Saraiva 2001,2002,2003,2004,2005
+-- License     :  LGPL
+--
+-- Maintainer  :  jas@di.uminho.pt
+-- Stability   :  provisional
+-- Portability :  portable
+--
+-- Non-Deterministic Finite Automata in Haskell.
+--
+-- Code Included in the Lecture Notes on
+--           Language Processing (with a functional flavour).
+--
+-----------------------------------------------------------------------------
+
+
+module Language.HaLex.Ndfa (
+             -- * Data type
+               Ndfa (..)
+             -- * Acceptance
+             , ndfaaccept
+             , ndfawalk
+             , epsilon_closure
+             -- * Transformation
+             , ttNdfa2Ndfa
+             -- * Transitions
+             , ndfaTransitionsFromTo
+             , ndfadestinationsFrom
+             , transitionTableNdfa
+             , ndfareachedStatesFrom
+             -- * Printing
+             , toHaskell
+             , renameNdfa
+             , showNdfaDelta
+             -- * Properties of 'Ndfa'
+             , sizeNdfa
+             , ndfadeadstates
+             -- * Properties of States
+             , ndfaIsStDead
+             , ndfanumberIncomingArrows
+             , ndfanumberOutgoingArrows
+             ) where
+
+import Data.List
+import Language.HaLex.Util
+import Language.HaLex.Dfa
+
+-----------------------------------------------------------------------------
+-- * Data type
+
+-- | Type of Non-Deterministic Finite Automata. Parameterized with
+--   the type @st@ of states and @sy@ of symbols.
+
+data Ndfa st sy = Ndfa [sy]                     -- Vocabulary
+                       [st]                     -- Finite set of states
+                       [st]                     -- The set of start state
+                       [st]                     -- The set of final states
+                       (st -> Maybe sy -> [st]) -- Transition function
+
+-----------------------------------------------------------------------------
+-- * Acceptance
+
+-- | Test whether the given automaton accepts the given list of
+--   input symbols.
+
+ndfaaccept :: Ord st
+           => Ndfa st sy    -- ^ Automaton
+           -> [sy]          -- ^ Input symbols
+           -> Bool
+
+ndfaaccept (Ndfa _ _ s z delta) symbs =
+       (ndfawalk delta (epsilon_closure delta s) symbs) `intersect` z /= []
+
+
+-- | Execute the transition function of a 'Ndfa' on an initial state
+--   and list of input symbol. Return the final state when all input
+--   symbols have been consumed.
+
+ndfawalk :: Ord st
+         => (st -> Maybe sy -> [st])   -- ^ Transition function
+         -> [st]                       -- ^ Initial states
+         -> [sy]                       -- ^ Input symbols
+         -> [st]                       -- ^ Reached states
+
+ndfawalk delta sts []     = sts
+ndfawalk delta sts (x:xs) =
+        ndfawalk delta (epsilon_closure delta (delta' delta sts (Just x))) xs
+
+
+-- | Apply the transition function to a list of states.
+delta' :: Eq st
+       => (st -> (Maybe sy) -> [st])   -- ^ Transition function
+       -> [st]                         -- ^ Current states
+       -> (Maybe sy)                   -- ^ Symbol to consume
+       -> [st]                         -- ^ Reached states
+
+delta' delta []       sy = []
+delta' delta (st:sts) sy = (delta st sy) `union` (delta' delta sts sy)
+
+
+-- | Compute the eplison closure of a 'Ndfa'.
+epsilon_closure :: Ord st
+                => (st -> Maybe sy -> [st]) -- ^ Transition function
+                -> [st]                     -- ^ Current states
+                -> [st]                     -- ^ Reached states
+epsilon_closure delta = limit f
+  where f sts = sort (sts `union` (delta' delta sts Nothing))
+
+
+-----------------------------------------------------------------------------
+-- * Printing
+
+
+-- | Print a 'Ndfa' as a Haskell function.
+instance (Eq st , Show st, Show sy) => Show (Ndfa st sy) where
+      showsPrec p (Ndfa v q s z delta) =
+                showString("ndfa = Ndfa v q s z delta") .
+                showString ("\n  where \n\t v = ") .
+                showList v .
+                showString ("\n\t q = ") .
+                showList q .
+                showString ("\n\t s = ") .
+                shows s .
+                showString ("\n\t z = ") .
+                showList z .
+                showString ("\n\t -- delta :: st -> sy -> st \n") .
+                (showNdfaDelta q v delta) .
+                showString ("\t delta _ _ = []\n")
+
+-- | Helper function to show the transition function of a 'Ndfa'.
+showNdfaDelta q v d = foldr (.) (showChar '\n') f
+  where f     = zipWith3 showF m n q'
+        (m,n) = unzip l'
+        q'    = map (uncurry d) l'
+        l'    = filter ((/= []) . (uncurry d)) l
+        l     = [(a, c) | a <- q
+                        , b <- v
+                        , c <- [(Just b)]
+                        ]  ++ [ (a,Nothing) | a <- q ]
+
+        showF st sy st' = showString("\t delta ") .
+                          shows st .
+                          showString(" (") .
+                          shows sy .
+                          showString(") = ") .
+                          shows st' .
+                          showChar('\n')
+
+-- | Produce the transition table of a given finite automaton.
+toHaskell :: Show fa
+          => fa        -- ^ Automaton
+          -> [Char]    -- ^ Haskell module or file name
+          -> IO ()
+toHaskell fa modulename =  writeFile (modulename ++ ".hs")
+                                ("module " ++ modulename ++ " where\n\n" ++
+                                "import Language.HaLex.Dfa\n\n" ++
+                                "import Language.HaLex.Ndfa\n\n" ++
+                                (show fa))
+
+
+
+-----------------------------------------------------------------------------
+-- * Transitions
+
+
+-- | Compute the labels with the same (giving) origin and destination
+
+ndfaTransitionsFromTo :: Eq st
+                      => (st -> Maybe sy -> [st]) -> [sy] -> st -> st -> [Maybe sy]
+ndfaTransitionsFromTo delta vs o d = [ v
+                                     | v <- vs'
+                                     , d `elem` delta o v
+                                     ]
+  where vs' = map Just vs ++ [Nothing]
+
+
+-- | Compute the destination states giving the origin state
+
+ndfadestinationsFrom :: Ord st
+                     => (st -> Maybe sy -> [st])      -- ^ Transition Function
+                     -> [sy]                          -- ^ Vocabulary
+                     -> st                            -- ^ Origin
+                     -> [st]                          -- ^ Destination States
+ndfadestinationsFrom delta vs o = concat (o'' : [ ndfawalk delta o' [v] | v <- vs ])
+  where o'  = epsilon_closure delta [o]
+        o'' = delete o o'
+
+-- | Compute the states that can be reached from a given state
+--   according to a given transition function and vocabulary
+
+
+ndfareachedStatesFrom :: Ord st
+                      => (st -> Maybe sy -> [st])     -- ^ Transition Function
+                      -> [sy]                         -- ^ Vocabulary
+                      -> st                           -- ^ Origin
+                      -> [st]                         -- ^ Reached States
+ndfareachedStatesFrom d v origin = nub $ origin : qs
+  where qs      = limit stPath' (ndfadestinationsFrom d v origin)
+        stPath' = stPath d v
+
+
+stPath  :: Ord st => (st -> Maybe sy -> [st]) -> [sy] -> [st] -> [st]
+stPath d v sts = sort $ nub $ (concat $ map (ndfadestinationsFrom d v) sts) ++ sts
+
+
+-----------------------------------------------------------------------------
+-- * Transformation
+
+
+-- | Produce the transition table of a given 'Ndfa'.
+--
+-- Given a 'Ndfa' it returns a list of triples of the form
+-- @
+--                 (Origin,Symbol,Destination)
+-- @
+-- defining all the transitions of the 'Ndfa'.
+--
+
+transitionTableNdfa :: Ndfa st sy            -- ^ Automaton
+                    -> [(st,Maybe sy,st)]    -- ^ Transition table
+transitionTableNdfa (Ndfa vs qs s z delta) = [ (q,Just v,r)
+                                             | q <- qs , v <- vs
+                                             , r <- delta q (Just v)
+                                             ] ++
+                                             [ (q,Nothing,r)
+                                             | q <- qs
+                                             , r <- delta q Nothing
+                                             ]
+
+
+-- | Reconstruct a 'Ndfa' from a transition table.
+--   Given a 'Ndfa' expressed by a transition table
+--   (ie a list of triples of the form
+-- @
+--                    (Origin,Maybe Symbol,Destination)
+-- @
+--   it constructs a 'Ndfa'. The other elements of the
+--   input tuple are the vocabulary, a set of
+--   states, and the sets of  initial and final states
+--
+ttNdfa2Ndfa :: (Eq st, Eq sy)
+            => ([sy],[st],[st],[st],[(st,Maybe sy,st)])   -- ^ Tuple-based 'Ndfa'
+            -> Ndfa st sy                                 -- ^ Automaton
+ttNdfa2Ndfa (vs,qs,s,z,tt) = Ndfa vs qs s z d
+  where d st sy =  lookupTT st sy tt
+
+        lookupTT st sy ((a,b,c) : []) | st == a && sy == b  = [c]
+                                      | otherwise           = []
+        lookupTT st sy ((a,b,c) : xs) | st == a && sy == b  = c : lookupTT st sy xs
+                                      | otherwise           = lookupTT st sy xs
+
+
+
+
+
+
+-- | Renames a 'Ndfa'.
+
+renameNdfa :: Eq st
+           => Ndfa st sy                -- ^ Automaton
+           -> Int                       -- ^ Initial integer number
+           -> Ndfa Int sy               -- ^ Renamed Automaton
+renameNdfa (Ndfa v q s z d) istid = (Ndfa v q' s' z' d')
+  where newSts   = zipWith (\ a b -> (a,b)) q [istid .. ]
+        q'       = old2new newSts q
+        s'       = old2new newSts s
+        z'       = old2new newSts z
+        d' st sy = old2new newSts (d (lookupSnd newSts st) sy)
+
+
+old2new :: Eq st => [(st,Int)] -> [st] -> [Int]
+old2new nsts sts = map (lookupFst nsts) sts
+
+lookupFst :: Eq st => [(st,Int)] -> st -> Int
+lookupFst nsts ost = snd $ head (filter (\ (a,b) -> a == ost) nsts)
+
+
+lookupSnd :: [(st,Int)] -> Int -> st
+lookupSnd nsts nst = fst $ head (filter (\ (a,b) -> b == nst) nsts)
+
+
+-----------------------------------------------------------------------------
+-- * Properties of 'Ndfa'
+
+
+-- | Compute the dead states of a 'Ndfa'
+--
+
+ndfadeadstates :: Ord st
+               => Ndfa st sy        -- ^ Automaton
+               -> [st]              -- ^ Dead States
+ndfadeadstates (Ndfa v qs s z d) = filter (ndfaIsStDead d v z) qs
+
+
+-- | The size of an automaton is the number of its states.
+
+sizeNdfa :: Ndfa st sy        -- ^ Automaton
+         -> Int               -- ^ Size
+sizeNdfa (Ndfa _ q _ _ _) = length q
+
+
+
+
+-----------------------------------------------------------------------------
+-- * Properties of States
+
+
+-- | Checks whether a 'Ndfa' state is dead or not.
+
+
+ndfaIsStDead :: Ord st
+             => (st -> Maybe sy -> [st])        -- ^ Transition Function
+             -> [sy]                            -- ^ Vocabulary
+             -> [st]                            -- ^ Set of Final States
+             -> st                              -- ^ State
+             -> Bool
+ndfaIsStDead d v z st = ndfareachedStatesFrom d v st `intersect` z == []
+
+-- | Checks whether a 'Ndfa' state is a sync state or not
+--
+
+
+isSyncState :: Ord st => st -> [sy] -> [st] -> (st -> Maybe sy -> [st]) -> Bool
+isSyncState st vs z d = (not (st `elem` z)) && (and qs)
+  where qs = [ [st] == (d st (Just v))
+               && (([st] == d st Nothing) || ([] == d st Nothing))
+             | v <- vs
+             ]
+
+
+-- | Compute the number of incoming arrows for a given state
+--
+
+ndfanumberIncomingArrows :: Eq st
+                         => (st -> Maybe sy -> [st])   -- ^ Transition Function
+                         -> [sy]                       -- ^ Vocabulary
+                         -> [st]                       -- ^ Set of States
+                         -> st                         -- ^ Destination
+                         -> Int                        -- ^ Number of Arrows
+ndfanumberIncomingArrows d vs qs dest =
+        length  [ q
+                | v <- vs
+                , q <- qs
+                , (dest `elem` d q (Just v)) || (dest `elem` d q Nothing)
+                ]
+
+
+
+-- | Compute the number of outgoing arrows for a given state
+
+
+ndfanumberOutgoingArrows :: Ord st
+                         => (st -> Maybe sy -> [st])   -- ^ Transition Function
+                         -> [sy]                       -- ^ Vocabulary
+                         -> st                         -- ^ Origin
+                         -> Int                        -- ^ Number of Arrows
+
+ndfanumberOutgoingArrows d v o = length $ ndfadestinationsFrom d v o
diff --git a/HaLeX_lib/Language/HaLex/Parser.hs b/HaLeX_lib/Language/HaLex/Parser.hs
new file mode 100644
--- /dev/null
+++ b/HaLeX_lib/Language/HaLex/Parser.hs
@@ -0,0 +1,69 @@
+--
+-- Parser Combinators Library
+--        (Utrecht University style) 
+--
+-- Code Included in the Lecture Notes on
+-- 
+--      Language Processing (with a functional flavour)             
+--
+--
+-- copyright João Saraiva
+--           Department of Computer Science,
+--           University of Minho, 
+--           Braga, Portugal
+--           jas@di.uminho.pt
+--           2001
+--
+
+module Language.HaLex.Parser where
+
+infixl 3 <|> ; infixl 4 <*>
+
+
+--
+-- The type of a (sub) Parser Function
+--
+
+type Parser s r = [s] -> [(r,[s])]
+
+
+--
+-- Elementary Parser Combinators
+--
+
+symbol :: Eq a => a -> Parser a a 
+symbol _ []                 = []
+symbol s (x:xs) | x == s    = [(s,xs)]
+                | otherwise = []
+
+satisfy :: (s -> Bool) -> Parser s s
+satisfy p []                 = []
+satisfy p (x:xs) | p x       = [(x,xs)]
+                 | otherwise = []
+
+token :: Eq s => [s] -> Parser s [s]
+token k xs | k == take n xs = [(k,drop n xs)]
+           | otherwise       = []
+ where n = length k
+
+succeed :: a -> Parser s a
+succeed r xs = [(r,xs)]
+
+--
+-- Basic Parser Combinators
+--
+
+(<|>) :: Parser s a -> Parser s a -> Parser s a
+(p <|> q) xs = p xs ++ q xs
+
+
+(p <*> q) xs = [ ( f z , zs )
+               | ( f   , ys ) <- p xs
+               , (   z , zs ) <- q ys 
+               ]
+
+(f <$> p) xs = [(f y, ys) | (y,ys) <- p xs ]
+
+
+
+
diff --git a/HaLeX_lib/Language/HaLex/RegExp.hs b/HaLeX_lib/Language/HaLex/RegExp.hs
new file mode 100644
--- /dev/null
+++ b/HaLeX_lib/Language/HaLex/RegExp.hs
@@ -0,0 +1,264 @@
+-----------------------------------------------------------------------------
+-- |
+-- Module      :  Language.HaLex.RegExp
+-- Copyright   :  (c) João Saraiva 2001,2002,2003,2004,2005
+-- License     :  LGPL
+-- 
+-- Maintainer  :  jas@di.uminho.pt
+-- Stability   :  provisional
+-- Portability :  portable
+--
+-- Regular Expressions in Haskell. 
+-- 
+-- Code Included in the Lecture Notes on 
+--          Language Processing (with a functional flavour).   
+--
+-----------------------------------------------------------------------------
+
+module Language.HaLex.RegExp ( 
+              -- * Data type with recursion pattern
+                RegExp (..)
+              , cataRegExp
+              -- * Matching
+              , matchesRE
+              , matches'
+              -- * Size
+              , sizeRegExp
+              -- * Printing
+              , showRE
+              -- * Simplification
+              , simplifyRegExp
+              -- * Normalization
+              , extREtoRE
+              ) where
+
+-----------------------------------------------------------------------------
+-- * Data type with recursion pattern
+
+-- | Type of regular expressions.
+data RegExp sy  = Empty                              -- ^ Empty Language
+                | Epsilon                            -- ^ Empty String
+                | Literal   sy                       -- ^ Literals
+                | Or        (RegExp sy) (RegExp sy)  -- ^ Disjuncion
+                | Then      (RegExp sy) (RegExp sy)  -- ^ Sequence
+                | Star      (RegExp sy)              -- ^ Repetition, possibly zero time
+                | OneOrMore (RegExp sy)              -- ^ One or more times (extended RegExp)
+                | Optional  (RegExp sy)              -- ^ Optional (extended RegExp)
+   deriving (Read, Eq)
+   
+-- | Catamorphism induced by the 'RegExp' inductive data type
+
+cataRegExp :: ( re 
+              , re
+              , re -> re -> re
+              , re -> re
+              , sy -> re
+              , re -> re -> re
+              , re -> re
+              , re -> re
+              ) -> RegExp sy -> re
+
+cataRegExp (empty,epsilon,or,star,lit,th,one,opt) = cata
+ where cata Empty          = empty 
+       cata Epsilon        = epsilon
+       cata (Or er1 er2)   = or (cata er1) (cata er2)
+       cata (Star er)      = star (cata er)
+       cata (Literal a)    = lit a
+       cata (Then er1 er2) = th (cata er1) (cata er2)
+       cata (OneOrMore er) = one (cata er)
+       cata (Optional er)  = opt (cata er)
+
+-----------------------------------------------------------------------------
+-- * Matching
+
+-- | Test whether a match can be found for the given regular expression
+--   in the given sequence of characters. The regular expression is
+--   assumed not to contain 'OneOrMore' or 'Optional'. See also @matches'@.
+
+matchesRE :: Eq sy 
+          => RegExp sy         -- ^ (canonical) Regular Expression
+          -> [sy]              -- ^ Input Symbols
+          -> Bool
+matchesRE Empty inp          = False
+matchesRE Epsilon inp        = inp == []
+matchesRE (Literal l) inp    = ([l] == inp)
+matchesRE (Or re1 re2) inp   = matchesRE re1 inp || matchesRE re2 inp 
+matchesRE (Then re1 re2) inp = or [ matchesRE re1 s1 && matchesRE re2 s2 
+                                  | (s1,s2) <- splits inp]
+matchesRE (Star re) inp      = matchesRE Epsilon inp ||
+                               or [ matchesRE re s1 && matchesRE (Star re) s2 
+                                  | (s1,s2) <- frontSplits inp ]
+
+-- | Test whether a match can be found for the given regular expression
+--   in the given sequence of characters. The regular expression is
+--   allowed to contain 'OneOrMore' or 'Optional'.
+
+matches' :: Eq sy 
+         => RegExp sy          -- ^ Regular Expression 
+         -> [sy]               -- ^ Input Symbols
+         -> Bool
+matches' = matchesRE . extREtoRE
+
+-- | Produce a list of all possible ways of splitting the input list
+--   into two parts. For instance, 
+-- @ 
+--   splits "foo" 
+--     = [(\"\","foo"),("f","oo"),("fo","o"),("foo",\"\")] 
+-- @
+
+splits :: [a]                -- ^ Input List
+       -> [ ([a],[a]) ]      -- ^ Splited List
+splits s = [ splitAt n s | n <- [ 0 .. length s ] ]
+
+
+-- | Produce a list of all possible ways of splitting the input list
+--   into two parts where the first part is non-empy. For instance, 
+-- @ 
+--   splits "foo" 
+--     = [("f","oo"),("fo","o"),("foo",\"\")]
+-- @
+
+frontSplits :: [a] -> [ ([a],[a]) ]
+frontSplits s = [ splitAt n s | n <- [ 1 .. length s ] ]
+
+
+-----------------------------------------------------------------------------
+-- * Size
+
+-- | Compute the size of a regular expression.
+--   We define the size of a regular expression as the number of occurrences 
+--   of symbols of the alfabeth
+
+sizeRegExp :: RegExp sy      -- ^ Regular Expression
+           -> Int            -- ^ Size
+sizeRegExp = cataRegExp (0,0,(+),id,\x -> 1,(+),id,id)
+
+
+-----------------------------------------------------------------------------
+-- * Printing
+
+-- | Print regular expression to String as a catamorphism.
+--   A straightforward (catamorphic) show function.
+--
+--   (it produces too many brackets, making it difficult to read or 
+--    understand the expression)
+
+showRE :: Show sy 
+       => RegExp sy        -- ^ Regular Expression
+       -> [Char]           -- ^ String-based Regular Expression
+showRE = cataRegExp  ("{}"
+                     , "@"
+                     , \ l r -> "(" ++ l ++ "|" ++ r ++ ")"
+                     , \ er  -> "(" ++ er ++ ")*"
+                     , show 
+                     , \ l r -> "(" ++ l ++ r ++ ")"
+                     , \ er  -> "(" ++ er ++ ")+"
+                     , \ er  -> "(" ++ er ++ ")?"
+                     )
+
+-- | Pretty print of regular expressions.
+
+instance Show sy => Show (RegExp sy) where
+          showsPrec _ Empty             = showString "{}"
+ 	  showsPrec _ Epsilon           = showChar '@'
+ 	  showsPrec _ (Literal c)       = showsPrec 0 c
+{-                | isSymbol c            = showChar '\''
+                                        . showChar c
+                                        . showChar '\''
+                | otherwise             = showChar c
+-}
+   	  showsPrec n (Star e)          = showsPrec 10 e . showChar '*'
+ 	  showsPrec n (OneOrMore e)     = showParen (n == 4)
+                                        $ showsPrec 10 e
+                                        . showChar '+'
+ 	  showsPrec _ (Optional e)      = showsPrec 10 e
+                                        . showChar '?'
+ 	  showsPrec n (e1 `Or` e2)      = showParen (n /= 0 && n /= 4)
+                                        $ showsPrec 4 e1
+                                        . showChar '|'
+                                        . showsPrec 4 e2
+	  showsPrec n (e1 `Then` e2)    = showParen (n /= 0 && n /= 6)
+                                        $ showsPrec 6 e1
+                                        . showChar ' '
+                                        . showsPrec 6 e2
+ 
+isSymbol x = x `elem` "|? "
+
+-----------------------------------------------------------------------------
+-- * Simplification
+
+-- | Simplify regular expressions according to the algebra of regular expressions.
+
+simplifyRegExp :: Eq sy => RegExp sy -> RegExp sy
+simplifyRegExp Empty        = Empty
+simplifyRegExp Epsilon      = Epsilon
+simplifyRegExp (Literal x)  = Literal x
+
+simplifyRegExp (Star x)     = case x' of                                -- Algebraic Rules:
+                               Epsilon      -> Epsilon                  -- @*       = @
+  		               Empty        -> Epsilon                  -- {}*      = @
+                               Or Epsilon a -> Star (simplifyRegExp a)  -- (a | @)* = a*
+                               Or a Epsilon -> Star (simplifyRegExp a)  -- (@ | a)* = a*
+                               _            -> Star x'
+  where x' = simplifyRegExp x 
+
+
+simplifyRegExp (Then x y)  | x' == Empty    = Empty                     -- {} p = {}
+                           | y' == Empty    = Empty                     -- p {} = {}
+                           | x' == Epsilon  = y'                        -- @ p  = p
+                           | y' == Epsilon  = x'                        -- p @  = p
+                           | y' == Star x'  = OneOrMore x'              -- p p* = p+
+                           | x' == Star y'  = OneOrMore y'              -- p* p = p+
+                           | otherwise      = Then x' y'
+  where x' =  simplifyRegExp x
+        y' =  simplifyRegExp y
+
+
+simplifyRegExp a@(Or x y)  
+      | x' == y'                       = x'                             -- p  | p  = p
+      | x' == Empty                    = y'                             -- {} | p  = p 
+      | y' == Empty                    = x'                             -- p  | {} = p
+--    | x == (Star a) && y == Epsilon  = simplifyRegExp x       
+      | otherwise                      = f x' y'                        -- Or x' y'
+  where x' = simplifyRegExp x 
+        y' = simplifyRegExp y
+
+        f Epsilon (OneOrMore p) = Star p                                -- (@ | p+) = p*
+        f Epsilon re            = Optional re                           -- p | @    = p? 
+        f (OneOrMore p) Epsilon = Star p                                -- (p+ | @) = p*
+        f re Epsilon            = Optional re                           -- @ | p    = p? 
+        f re1 re2               = Or re1 re2
+
+
+simplifyRegExp (OneOrMore x) = case x' of
+                                Empty        -> Empty                   -- {}+      = {}
+                                Epsilon      -> Epsilon                 -- @+       = @
+                                Or p Epsilon -> Star p                  -- (p | @)+ = p*
+                                Or Epsilon p -> Star p                  -- (@ | p)+ = p*
+                                _            -> OneOrMore x'
+  where  x' = simplifyRegExp x
+
+simplifyRegExp (Optional x) = Optional (simplifyRegExp x)
+
+
+-----------------------------------------------------------------------------
+-- * Normalization
+
+-- | Rewrite extended regular expressions to
+--   plain regular expression. This means that the 'OneOrMore' 
+--   and 'Optional' constructors are normalized away.
+
+extREtoRE :: RegExp sy -> RegExp sy
+extREtoRE  = cataRegExp ( Empty
+                        , Epsilon 
+                        , \ l r -> Or l r
+                        , \ er  -> Star er
+                        , \ a   -> Literal a 
+                        , \ l r -> Then l r 
+                        , \ er  -> Then er (Star er)
+                        , \ er  -> Or Epsilon er
+                        ) 
+
+-----------------------------------------------------------------------------
+
+
diff --git a/HaLeX_lib/Language/HaLex/RegExp2Fa.hs b/HaLeX_lib/Language/HaLex/RegExp2Fa.hs
new file mode 100644
--- /dev/null
+++ b/HaLeX_lib/Language/HaLex/RegExp2Fa.hs
@@ -0,0 +1,122 @@
+-----------------------------------------------------------------------------
+-- |
+-- Module      :  Language.HaLex.RegExp2Fa
+-- Copyright   :  (c) João Saraiva 2001,2002,2003,2004,2005
+-- License     :  LGPL
+--
+-- Maintainer  :  jas@di.uminho.pt
+-- Stability   :  provisional
+-- Portability :  portable
+--
+-- From Regular Expressions into Non-Deterministic and Deterministic Finite Automata
+--
+-- Code Included in the Lecture Notes on
+--         Language Processing (with a functional flavour).
+--
+-----------------------------------------------------------------------------
+
+module Language.HaLex.RegExp2Fa (
+                   regExp2Ndfa
+                 , regExp2Dfa
+                 , regExp2Ndfa'
+                 ) where
+
+import Data.List
+import Language.HaLex.RegExp
+import Language.HaLex.Dfa
+import Language.HaLex.Ndfa
+import Language.HaLex.FaOperations
+
+
+-- |  Compute a 'Ndfa' from a 'RegExp'.
+
+regExp2Ndfa :: Eq sy
+            => RegExp sy     -- ^ Regular expression
+            -> Ndfa Int sy   -- ^ Automaton
+regExp2Ndfa er = fst (regExp2Ndfa' er 1)
+
+
+
+-- |  Compute a 'Ndfa' from a 'RegExp'.
+--    Auxiliar function threading the context: the first available int to
+--    name the states
+
+regExp2Ndfa' :: Eq sy => RegExp sy -> Int -> (Ndfa Int sy , Int)
+
+
+regExp2Ndfa' Empty n = ( Ndfa [] [sa,za] [sa] [za] delta , n+2 )
+  where sa = n
+        za = n+1
+        delta _ _ = []
+
+
+regExp2Ndfa' Epsilon n = ( Ndfa [] [sa] [sa] [sa] delta , n+1 )
+  where sa = n
+        delta _ _ = []
+
+regExp2Ndfa' (Literal a) n = ( Ndfa [a] [sa,za] [sa] [za] delta , n+2)
+  where sa = n
+        za = n+1
+        delta q (Just v) | q == sa && (v == a) = [za]
+        delta _ _ = []
+
+regExp2Ndfa' (Then p q) n = ( Ndfa v' q' s' z' delta' , nq)
+  where (Ndfa vp qp sp zp dp , np) = regExp2Ndfa' p n
+        (Ndfa vq qq sq zq dq , nq) = regExp2Ndfa' q np
+        v' = vp `union` vq
+        q' = qp `union` qq
+        s' = sp
+        z' = zq
+        delta' q | q `elem` qp = if q `elem` zp then dp' q
+                                                else dp  q
+                 | otherwise   = dq q
+         where dp' q Nothing = (dp q Nothing) `union` sq
+               dp' q (Just aa) = dp q (Just aa)
+
+regExp2Ndfa' (Or p q) n = ( Ndfa v' q' s' z' delta' , nq+1 )
+  where (Ndfa vp qp sp zp dp , np) = regExp2Ndfa' p (n + 1)
+        (Ndfa vq qq sq zq dq , nq) = regExp2Ndfa' q np
+        v' = vp `union` vq
+        s' = [n]
+        z' = [nq]
+        q' = s' `union` qp `union` qq `union` z'
+        delta' q | q `elem` s' = dd q
+                 | q `elem` zp = ddp' q
+                 | q `elem` zq = ddq' q
+                 | q `elem` qp = dp q
+                 | q `elem` qq = dq q
+                 | otherwise   = dd'' q
+         where dd q  Nothing = sp `union` sq
+               dd _ _        = []
+
+               ddp' q Nothing = z' `union` (dp q Nothing)
+               ddp' _ _       = []
+
+               ddq' q Nothing = z' `union` (dq q Nothing)
+               ddq' _ _       = []
+
+               dd'' _ _ = []
+
+regExp2Ndfa' (Star p) n = ( Ndfa v' q' s' z' delta' , np+1 )
+  where (Ndfa vp qp sp zp dp , np) = regExp2Ndfa' p (n + 1)
+        v' = vp
+        s' = [n]
+        z' = [np]
+        q' = s'  `union` qp `union` z'
+        delta' q | q `elem` s' = dd q
+                 | q `elem` zp = dd' q
+                 | otherwise   = dp q
+          where dd q Nothing = sp `union` z'
+                dd _ _ = []
+
+                dd' q Nothing = sp `union` z'
+                dd' _ _ = []
+
+-- | Compute a 'Dfa' from a 'RegExp'.
+--   (via the intermediate 'Ndfa')
+regExp2Dfa :: Eq sy
+           => RegExp sy       -- ^ Regular expression
+           -> Dfa [Int] sy    -- ^ Automaton
+regExp2Dfa = ndfa2dfa . regExp2Ndfa
+
+
diff --git a/HaLeX_lib/Language/HaLex/RegExpAsDiGraph.hs b/HaLeX_lib/Language/HaLex/RegExpAsDiGraph.hs
new file mode 100644
--- /dev/null
+++ b/HaLeX_lib/Language/HaLex/RegExpAsDiGraph.hs
@@ -0,0 +1,87 @@
+-----------------------------------------------------------------------------
+-- |
+-- Module      :  Language.HaLex.RegExpAsDiGraph
+-- Copyright   :  (c) João Saraiva 2001,2002,2003,2004,2005
+-- License     :  LGPL
+-- 
+-- Maintainer  :  jas@di.uminho.pt
+-- Stability   :  provisional
+-- Portability :  portable
+--
+-- Regular Expressions as Directed Graphs (in GraphViz)
+--
+-- Code Included in the Lecture Notes on 
+--      Language Processing (with a functional flavour).   
+--
+-----------------------------------------------------------------------------
+
+module Language.HaLex.RegExpAsDiGraph ( 
+                         re2graphviz
+                       ) where
+
+import Language.HaLex.RegExp
+import Language.HaLex.RegExp2Fa
+--import Language.HaLex.RegExpParser
+import Language.HaLex.Dfa
+import Language.HaLex.Ndfa
+import Language.HaLex.FaOperations
+import Language.HaLex.Minimize
+import Language.HaLex.FaAsDiGraph
+
+-- | Print a 'RegExp' in GraphViz-dot (as a string) 
+re2graphviz :: (Ord sy, Show sy)
+            => RegExp sy  -- ^ Regular Expression (Abstract)
+            -> [Char]     -- ^ Graph's Name
+            -> Bool       -- ^ True: Deterministic ; False: Non-Deterministic
+            -> Bool       -- ^ Minimized?
+            -> Bool       -- ^ Beautified?   (states as numbers)
+            -> Bool       -- ^ Dead States?
+            -> [Char]     -- ^ dot sentence
+
+re2graphviz re n d m b s 
+  | not d                        = re2DiGraphNdfa re n
+  | d && not m          && s     = re2DiGraph    re n
+  | d && not m && b     && not s = re2DiGraph'   re n
+  | d && m     && b     && s     = re2DiGraph''' re n
+  | d && m     && b     && not s = re2DiGraph''  re n
+  | otherwise                    = re2DiGraph''' re n
+
+
+
+re2DiGraph :: (Show sy, Ord sy) 
+           => RegExp sy               -- ^ Regular Expression
+           -> [Char]                  -- ^ Module Name
+           -> [Char]                  -- ^ Dot Graph
+re2DiGraph re name = dfa2graphviz dfa name 
+  where dfa = (ndfa2dfa . regExp2Ndfa) re
+
+re2DiGraph' re name = dfa2graphviz dfa name 
+  where dfa = (beautifyDfa .ndfa2dfa . regExp2Ndfa) re
+
+re2DiGraph'' re name = dfa2graphviz dfa name 
+  where dfa = (beautifyDfa . minimizeDfa . ndfa2dfa . regExp2Ndfa) re
+
+
+re2DiGraph''' re name = dfa2DiGraphWithNoSyncSt dfa name 
+  where dfa = (beautifyDfaWithSyncSt . minimizeDfa . ndfa2dfa . regExp2Ndfa) re
+
+re2DiGraphNdfa re name = ndfa2graphviz ndfa name
+  where ndfa = regExp2Ndfa re  
+
+
+re2DiGraphIO :: (Show sy, Ord sy) => RegExp sy -> [Char] -> IO ()
+re2DiGraphIO er name = dfa2graphviz2file dfa name 
+  where dfa = (beautifyDfa . ndfa2dfa . regExp2Ndfa) er
+
+
+absRe2DiGraph_File er name = 
+        dfaDiGraphWithNoSyncStIO dfa name (name++".dot") 
+  where dfa = (beautifyDfaWithSyncSt . minimizeDfa . ndfa2dfa . regExp2Ndfa) er
+
+
+
+
+
+
+
+
diff --git a/HaLeX_lib/Language/HaLex/RegExpParser.hs b/HaLeX_lib/Language/HaLex/RegExpParser.hs
new file mode 100644
--- /dev/null
+++ b/HaLeX_lib/Language/HaLex/RegExpParser.hs
@@ -0,0 +1,74 @@
+
+-----------------------------------------------------------------------------
+-- |
+-- Module      :  Language.HaLex.Dfa
+-- Copyright   :  (c) João Saraiva 2001,2002,2003,2004,2005
+-- License     :  LGPL
+--
+-- Maintainer  :  jas@di.uminho.pt
+-- Stability   :  provisional
+-- Portability :  portable
+--
+-- Parsing (through parsing combinators) concrete regular Expressions
+--                (in the Unix like notation)
+--
+-- Code Included in the Lecture Notes on
+--      Language Processing (with a functional flavour).
+--
+-----------------------------------------------------------------------------
+
+
+module Language.HaLex.RegExpParser ( parseRegExp
+                                   ) where
+
+import Data.Char
+import Language.HaLex.Parser
+import Language.HaLex.RegExp
+
+
+-- | Parser for regular expressions
+
+parseRegExp :: [Char]                -- ^ Input symbols
+            -> Maybe (RegExp Char)   -- ^ Regular expression
+parseRegExp re = res
+  where parsed_re = expr re
+        res | parsed_re == [] = Nothing
+            | otherwise       = Just (fst (head parsed_re))
+
+expr :: Parser Char (RegExp Char)
+expr =  f  <$> termThen <*> symbol '|' <*> expr
+    <|> id <$> termThen
+    <|> succeed Epsilon
+  where f l _ r = Or l r
+
+termThen :: Parser Char (RegExp Char)
+termThen =  f  <$> term <*> termThen
+        <|> id <$> term
+  where f l r   = Then l r
+
+term :: Parser Char (RegExp Char)
+term =  f  <$> factor <*> symbol '?'
+    <|> g  <$> factor <*> symbol '*'
+    <|> h  <$> factor <*> symbol '+'
+    <|> id <$> factor
+  where
+     f e _ = Or   e Epsilon
+     g e _ = Star e
+     h e _ = Then e (Star e)
+
+factor :: Parser Char (RegExp  Char)
+factor =  f <$> letterOrDigit
+      <|> g <$> symbol '\'' <*> satisfy (\ x -> True) <*> symbol '\''
+      <|> h <$> symbol '(' <*> expr <*> symbol ')'
+  where
+     f a     = Literal a
+     g _ e _ = Literal e
+     h _ e _ = e
+
+letterOrDigit :: Parser Char Char
+letterOrDigit = satisfy (\x -> isDigit x || isAlpha x)
+
+-- Not used yet
+spaces :: Parser Char ()
+spaces = (\ _ _ -> ()) <$> symbol ' ' <*> spaces
+      <|> succeed ()
diff --git a/HaLeX_lib/Language/HaLex/Util.hs b/HaLeX_lib/Language/HaLex/Util.hs
new file mode 100644
--- /dev/null
+++ b/HaLeX_lib/Language/HaLex/Util.hs
@@ -0,0 +1,59 @@
+-----------------------------------------------------------------------------
+-- |
+-- Module      :  Language.HaLex.Edfa
+-- Copyright   :  (c) Jooo Saraiva 2001,2002,2003,2004,2005
+-- License     :  LGPL
+--
+-- Maintainer  :  jas@di.uminho.pt
+-- Stability   :  provisional
+-- Portability :  portable
+--
+-- HaLeX Utility Functions
+--
+-- Code Included in the Lecture Notes on
+--      Language Processing (with a functional flavour).
+--
+-----------------------------------------------------------------------------
+
+module Language.HaLex.Util (
+             (<->)
+           , limit
+           , permutations
+           ) where
+
+import Data.List
+
+
+-- | List Function: l1 - l2.
+--   Unlike List.(\\), this function removes duplicates as well.
+(<->) :: Eq a => [a] -> [a] -> [a]
+l1 <-> l2 = [ x | x <- l1 , not (x `elem` l2) ]
+
+-- | Apply a function repeatedly, until a fix point is reached, i.e. until
+--   the result of the function is the same as the argument.
+limit :: Eq a => (a -> a) -> a -> a
+limit f s | s == next = s
+          | otherwise = limit f next
+            where next = f s
+
+
+-- | Compute the permutations of a given list. For instance,
+--
+--    permutations [1,2,3]
+--       = [[1,2,3],[2,1,3],[2,3,1],[1,3,2],[3,1,2],[3,2,1]]
+--
+permutations :: [a] -> [[a]]
+permutations []   = [[]]
+permutations (x:xs)   = insAllPosLst x x'
+  where x' = permutations xs
+
+insAllPosLst :: a -> [[a]] -> [[a]]
+insAllPosLst e l = concat $ map (insAllPos e) l
+
+insAllPos :: a -> [a] -> [[a]]
+insAllPos e l = [ insAtPos i e l
+                | i <- [1..length l + 1]
+                ]
+
+insAtPos 1 e l       = e : l
+insAtPos i e (x:xs)  = x : insAtPos (i-1) e xs
diff --git a/HaLeX_tool/halex.hs b/HaLeX_tool/halex.hs
new file mode 100644
--- /dev/null
+++ b/HaLeX_tool/halex.hs
@@ -0,0 +1,155 @@
+--
+-- The Main function of the halex tool
+--
+-- Code Included in the Lecture Notes on
+--
+--      Language Processing (with a functional flavour)
+--
+--
+-- copyright João Saraiva
+--           Department of Computer Science,
+--           University of Minho,
+--           Braga, Portugal
+--           jas@di.uminho.pt
+--           2001
+--
+
+
+
+module Main where
+
+import System.Console.GetOpt
+import System.Environment
+import System.IO
+import Data.List (partition)
+
+import Language.HaLex.RegExp
+import Language.HaLex.RegExpParser
+import Language.HaLex.RegExp2Fa
+import Language.HaLex.RegExpAsDiGraph
+import Language.HaLex.Equivalence
+
+import Language.HaLex.Dfa
+import Language.HaLex.Ndfa
+import Language.HaLex.Minimize
+import Language.HaLex.FaAsDiGraph
+import Language.HaLex.Parser
+
+import Language.HaLex.Dfa2MDfa
+
+options     :: [OptDescr String]
+options     =  [ Option ['N','n']
+                 ["NDFA"]
+                 (NoArg "N")
+                 "generate Non-Deterministic Finite Automaton"
+               , Option ['D','d']
+                 ["DFA"]
+                 (NoArg "D")
+                 "generate Deterministic Finite Automaton"
+               , Option ['M','m']
+                 ["MinDfa"]
+                 (NoArg "M")
+                 "generate Minimized Deterministic Finite Automaton"
+               , Option ['E','e']
+                 ["Dfa with Effects"]
+                 (NoArg "E")
+                 "generate Reactive Deterministic Finite Automaton"
+               ,  Option ['G','g']
+                 ["graph"]
+                 (NoArg "G")
+                 "generate GraphViz input file"
+               , Option ['S','s']
+                 ["Sync State"]
+                 (NoArg "S")
+                 "include a Synk State In the Graph Representation"
+               , Option ['R','r']
+                 ["regular expression"]
+                 (ReqArg ('r':) "string")
+                 "specify regular expression"
+               , Option ['o']
+                 ["output"]
+                 (ReqArg ('o':) "file")
+                 "specify output file"
+               , Option ['h','?']
+                 ["help"]
+                 (NoArg "h")
+                 "output a brief help message"
+               ]
+
+
+main :: IO ()
+main =
+  do args <- getArgs
+     let (o,n,errs) = getOpt Permute options args
+     let (re,opts')  = partition ((=='r') . head) o
+     let (fo,opts'') = partition ((=='o') . head) opts'
+     let output = map tail re ++ repeat ""
+     let opts = opts''
+     if (errs /= []) || ("h" `elem` opts)
+        then putStr $ usageInfo usageheader options
+        else if (re == [] && n == [])
+                then compileFromStdIn fo opts
+                else compileFromFile re n fo opts
+  where
+    usageheader = "HaLex: Regular Languages in Haskell\n\n" ++
+          "    Course project of Metodos de Programacao III (2001/2002)\n\n" ++
+                  "Usage: halex options [file] ...\n\nList of options:"
+
+
+type Options = [String]
+
+compileFromFile :: [String] -> [String] -> [String] -> Options -> IO ()
+compileFromFile re filei fileo opts
+   = do let absREs :: [Maybe (RegExp Char)]
+            absREs  = map (\x -> parseRegExp (tail x)) re
+        let absREs' = map (\ (Just x) -> x)  absREs
+        absREsFile <- mapM readRegExpFile filei
+        let absREsFile' = map (\ (Just x) -> x)  absREsFile
+
+        let absRE_all = absREs' ++ absREsFile'
+--                  putStrLn (show absRE_all)
+
+        if ((length absRE_all) == 1)
+           then compileRegExp (head absRE_all) fileo opts
+           else do let equiv = equivREs absRE_all
+                   putStrLn (if equiv
+                                then " The regular expressions are equivalent"
+                                else " The regular expressions are not equivalent")
+
+
+compileFromStdIn fileo opts
+  = do (Just s) <- readRegExpFileHandle stdin
+       compileRegExp s fileo opts
+
+compileRegExp re fileo opts
+  = do let fw = if (fileo == [])
+                then if ("E" `elem` opts)
+                     then writeFile "GenMDfa.hs"
+                     else putStrLn
+                else writeFile (tail (head fileo))
+       if ("G" `elem` opts)
+          then fw (re2graphviz re "HaLeX"
+                                  (("D" `elem` opts) || not ("N" `elem` opts))
+                                  ("M" `elem` opts) True ("S" `elem` opts))
+          else if ("N" `elem` opts)
+                 then do fw "import Ndfa"
+                         fw (show (regExp2Ndfa re))
+                 else if ("E" `elem` opts)
+                      then do putStrLn " Generating file: GenMDfa "
+                              fw (re2MHaskellMod re ("M" `elem` opts) True)
+                      else do fw "import Dfa"
+                              fw (show . beautifyDfa . minimizeDfa . regExp2Dfa $ re)
+
+
+readRegExpFile :: FilePath -> IO (Maybe (RegExp Char))
+readRegExpFile fp = do
+    fh <- openFile fp ReadMode
+    content <- hGetContents fh
+    --hClose fh
+    return (parseRegExp content)
+
+readRegExpFileHandle :: Handle  -> IO (Maybe (RegExp Char))
+readRegExpFileHandle fh = do
+    content <- hGetContents fh
+    return (parseRegExp content)
+
diff --git a/INSTALL b/INSTALL
new file mode 100644
--- /dev/null
+++ b/INSTALL
@@ -0,0 +1,34 @@
+
+  HaLeX: A Haskell Library to Model, 
+                              Manipulate and 
+                              Animate Regular Languages
+
+        http://www.di.uminho.pt/~jas/Research/HaLeX
+
+copyright João Saraiva
+          Department of Computer Science,
+          University of Minho, 
+          Braga, Portugal
+          jas@di.uminho.pt
+
+
+Version: 1.1 (January, 2005)
+
+
+- halex batch tool
+
+To install the halex batch tool just call the provided makefile. The
+halex tool is installed in the sub-directory bin.
+
+The makefile uses the ghc compiler, but this tool can be compiled (or
+interpreted) using any Haskell compiler (or using hmake).
+
+- the animations
+
+To run the animations, the library includes a main module
+(MainAnim.hs) that imports the generated Haskell-based automata
+produced by halex. This module runs the (lefty) script that animates
+the acceptance function. 
+
+To install this module it is needed to update the path to the lefty
+script (lefty_tool) in  file animation.hs.
diff --git a/LICENSE b/LICENSE
new file mode 100644
--- /dev/null
+++ b/LICENSE
@@ -0,0 +1,5 @@
+From <http://www.di.uminho.pt/~jas/Research/HaLeX/HaLeX.html>:
+
+"6- Where to get the software
+
+The HaLeX system is public domain and it is available as a gzipped tar file at: HaLeX_1.1.tgz"
diff --git a/README b/README
new file mode 100644
--- /dev/null
+++ b/README
@@ -0,0 +1,222 @@
+
+  HaLeX: A Haskell Library to Model, 
+                              Manipulate and 
+                              Animate Regular Languages
+
+        http://www.di.uminho.pt/~jas/Research/HaLeX
+
+copyright João Saraiva
+          Department of Computer Science,
+          University of Minho, 
+          Braga, Portugal
+          jas@di.uminho.pt
+
+
+Version: 1.1 (January, 2005)
+
+
+1- What is HaleX
+----------------
+
+HaLeX is a library of datatypes and functions implemented in Haskell
+that allows us to model, manipulate and animate regular languages.
+
+This library was developed in the context of a programming methodology
+course for undergraduate students, and as a consequence, it was
+defined mainly for educational purposes.
+
+
+2- Features of the Library
+--------------------------
+
+The library provides the following features:
+
+  - The definition of deterministic finite automata, non-deterministic
+  finite automata, and regular expressions directly and
+  straightforwardly in Haskell.
+
+  - The definition of the acceptance functions for all those models.
+
+  - The transformation from regular expressions into non-deterministic
+  finite automata (NDFA) and from NDFA into deterministic finite
+  automata (DFA).
+
+  - The transformation from NDFA and DFA into regular expressions
+
+  - The minimization of the number of states of deterministic finite
+  automata.
+
+  - The equivalence of regular expressions and finite automata.
+
+  - The graphical representation of finite automata.
+
+  - The definition of reactive finite automata.
+
+  - The automatic animation of the acceptance function of finite automata.
+
+       The animations are produced in an external tool: the
+       high-quality graph visualization system GraphViz. Thus, to be
+       able to visualize and animate regular languages, you have to
+       install GraphViz tool.
+
+       The GraphViz system is public domain and it is available at:
+
+            http://www.research.att.com/sw/tools/graphviz/
+
+
+3- The HaLeX Library
+--------------------
+
+   The library consists of the following modules:
+
+   - RegExp.hs             -> Regular Expressions
+   - Dfa.hs                -> Deterministic Finite Automata (DFA)
+   - Ndfa.hs               -> Non Deterministic Finite Automata (NDFA)
+   - RegExp2Fa.hs          -> Converts Regular expressions into Finite Automata
+   - RegExpAsDiGraph.hs    -> Graphic Representation of Regular Expressions
+   - FaAsDiGraph.hs        -> Graphic Representation of Finite Automata
+                                (using GraphViz language/tools)
+   - FaOperations.hs       -> Operations on Finite Automata
+                                (ndfa2dfa , dfa2ndfa, unions , concats, etc)
+   - FaClasses.hs          -> Type Classes to overload operations
+   - Minimize.hs           -> Minimization of the number of states 
+   - Equivalence.hs        -> Equivalence of Regular Expressions/Automata
+   - ReactiveDfa.hs        -> Reactive Finite Automata
+   - Dfa2MDfa.hs           -> Produces a Reactive Dfa from a DFA
+   - RegExpParser.hs       -> Simple Parser for Concrete Regular Expressions
+                                (Unix like notation)
+   - Parser.hs             -> Basic Parser Combinators
+
+   - Main.hs               -> The Main Module of halex Tool (see next section)
+   - MainAnim.hs           -> The Main Fomule to run Animations
+
+   - faAnin.lefty          -> A script written in lefty (one of GraphViz tools)
+                              that animates the acceptance function
+
+
+4- Using HaLeX: The halex Tool
+------------------------------
+
+The HaLeX library includes a useful tool to manipulate and vizualize
+regular languages: the halex tool. This is a batch tool that can be
+used in Unix pipes. It accepts as input a regular expression and it
+produces Haskell or graphic representations (graphviz) based on finite
+automata.
+
+To install the halex tool, just compile the library modules using a
+Haskell compiler (see file INSTALL).
+
+
+4.1 The synopsis of halex is:
+----------------------------
+
+Usage: halex options [file] ...
+
+List of options:
+  -N, -n                --NDFA                       generate Non-Deterministic Finite Automaton
+  -D, -d                --DFA                        generate Deterministic Finite Automaton
+  -M, -m                --MinDfa                     generate Minimized Deterministic Finite Automaton
+  -E, -e                --Dfa with Effects           generate Reactive Deterministic Finite Automaton
+  -G, -g                --graph                      generate GraphViz input file
+  -S, -s                --Sync State                 include a Synk State In the Graph Representation
+  -R string, -r string  --regular expression=string  specify regular expression
+  -o file               --output=file                specify output file
+  -h, -?                --help                       output a brief help message
+
+
+4.2 Running halex: some Examples
+--------------------------------
+
+  - Generating a Haskell-based NDFA
+
+       halex -N -R"('+'|'-')?d*('.')?d+"
+
+
+  - Producing the postscript of the graphic representation of a NDFA
+
+       halex -N -G -R"('+'|'-')?d*('.')?d+" | dot -Tps
+
+
+  - DFA with minimal number of states, visualized with dotty (one of
+    GraphViz tools)
+
+       halex -D -M -G -R"('+'|'-')?d*('.')?d+" | dotty -
+
+
+  - Proving one law of the algebra of regular expressions
+
+       halex -R"a*" -R"(a+)?"
+
+
+4.2.1 Running one Animation
+--------------------------
+
+    - First, we have to configure the path in the makefile
+    Make_Animation (subdirectory scripts) that produces the executable
+    for the animation. Update the variable HaLeX_DIR with the location
+    of the HaLeX library oin your machine.
+
+    - The above makefile, uses the Haskell main module MainAnim.hs
+    (subdirectory src) which calls the GraphViz tool lefty with the
+    script that animates the finite automata (file faAnim.lefty in
+    subdirectory scripts). Edit that module and update the path of
+    lefty_tool constant function.
+
+
+    - After that we are able to produce and run the animations. For
+    example, we can produce the reactive finite automata as
+    follows
+
+          halex -E -M -R"('+'|'-')?d*('.')?d+"
+
+      which generates the automaton (in this case, the minimized
+      automaton, due to the use of the -M option) in the file
+      GenMDfa.hs.
+
+    - The Haskell module MainAnim is the main module to run the animations.
+      It imports the previouly generated GenMDfa and it produces the
+      animations.
+
+      Its main function accepts as argument the sentence to be
+      accepted/animated by the acceptance function and calls the lefty
+      tool.
+
+    - The lefty tool interprets the lefty script (faAnim.lefty), which
+      produces the animations. Lefty provides the text view of the
+      script. To start running the animation we have to call the
+      functions provided in the lefty script:
+
+            - fa.init()
+            - fa.main()
+
+      which initialize the lefty tool and the animation. Write these
+      functions in the top frame followed by return. At this moment, a
+      new window will be displayed that contains the graphic
+      representation of the input. The right button of the mouse
+      provides a set of operations to run the animation
+      (forwards/backwards, adjusting the speed, tracking the path,
+      etc)
+
+
+6- Lecture/Exercise Notes
+-------------------------
+
+I have started developing the HaLeX library in 2000 in the context of
+a third year course on programming methodology. This course has a
+working load of 24 hours of theoretical classes and another 24 hours
+of laboratory classes, running for 12 weeks (\ie, a semester). The
+theoretical classes introduce the basic concepts of regular
+expressions, finite automata and context-free languages. HaLeX is
+used to support such classes. In the laboratory (a two hour class per
+week) the students have to solve exercises using a computer. 
+
+I have defined eleven exercise sets (one per week), using literate
+Haskell, that the students have to complete. Each set of exercises
+defines a module of the \HaLeX\ library. Thus, at the end of the
+course the students have a complete documentation of all the exercises
+and topics covered in the course, and, also, of the HaLeX library.
+
+The Exercise Notes are (still in Portuguese...) avaliable at the HaLeX
+homepage.
+
+
diff --git a/Setup.hs b/Setup.hs
new file mode 100644
--- /dev/null
+++ b/Setup.hs
@@ -0,0 +1,5 @@
+#!/usr/bin/runhaskell
+
+import Distribution.Simple
+
+main = defaultMainWithHooks defaultUserHooks
diff --git a/example/GenMDfa.hs b/example/GenMDfa.hs
new file mode 100644
--- /dev/null
+++ b/example/GenMDfa.hs
@@ -0,0 +1,96 @@
+module GenMDfa where
+
+import DfaMonad
+
+import MonadState
+
+dfa = Dfa v q s z delta
+  where 
+	 v = "+-.0123456789"
+	 q = [1,2,3,4,5,6]
+	 s = 1
+	 z = [4,6]
+	 -- delta :: st -> sy -> m st 
+	 delta 1 '+' = do { accum '+' ; return 2 }
+	 delta 1 '-' = do { accum '-' ; return 2 }
+	 delta 1 '.' = do { accum '.' ; return 3 }
+	 delta 1 '0' = do { accum '0' ; return 4 }
+	 delta 1 '1' = do { accum '1' ; return 4 }
+	 delta 1 '2' = do { accum '2' ; return 4 }
+	 delta 1 '3' = do { accum '3' ; return 4 }
+	 delta 1 '4' = do { accum '4' ; return 4 }
+	 delta 1 '5' = do { accum '5' ; return 4 }
+	 delta 1 '6' = do { accum '6' ; return 4 }
+	 delta 1 '7' = do { accum '7' ; return 4 }
+	 delta 1 '8' = do { accum '8' ; return 4 }
+	 delta 1 '9' = do { accum '9' ; return 4 }
+	 delta 2 '+' = do { accum '+' ; return 5 }
+	 delta 2 '-' = do { accum '-' ; return 5 }
+	 delta 2 '.' = do { accum '.' ; return 3 }
+	 delta 2 '0' = do { accum '0' ; return 4 }
+	 delta 2 '1' = do { accum '1' ; return 4 }
+	 delta 2 '2' = do { accum '2' ; return 4 }
+	 delta 2 '3' = do { accum '3' ; return 4 }
+	 delta 2 '4' = do { accum '4' ; return 4 }
+	 delta 2 '5' = do { accum '5' ; return 4 }
+	 delta 2 '6' = do { accum '6' ; return 4 }
+	 delta 2 '7' = do { accum '7' ; return 4 }
+	 delta 2 '8' = do { accum '8' ; return 4 }
+	 delta 2 '9' = do { accum '9' ; return 4 }
+	 delta 3 '+' = do { accum '+' ; return 5 }
+	 delta 3 '-' = do { accum '-' ; return 5 }
+	 delta 3 '.' = do { accum '.' ; return 5 }
+	 delta 3 '0' = do { accum '0' ; return 6 }
+	 delta 3 '1' = do { accum '1' ; return 6 }
+	 delta 3 '2' = do { accum '2' ; return 6 }
+	 delta 3 '3' = do { accum '3' ; return 6 }
+	 delta 3 '4' = do { accum '4' ; return 6 }
+	 delta 3 '5' = do { accum '5' ; return 6 }
+	 delta 3 '6' = do { accum '6' ; return 6 }
+	 delta 3 '7' = do { accum '7' ; return 6 }
+	 delta 3 '8' = do { accum '8' ; return 6 }
+	 delta 3 '9' = do { accum '9' ; return 6 }
+	 delta 4 '+' = do { accum '+' ; return 5 }
+	 delta 4 '-' = do { accum '-' ; return 5 }
+	 delta 4 '.' = do { accum '.' ; return 3 }
+	 delta 4 '0' = do { accum '0' ; return 4 }
+	 delta 4 '1' = do { accum '1' ; return 4 }
+	 delta 4 '2' = do { accum '2' ; return 4 }
+	 delta 4 '3' = do { accum '3' ; return 4 }
+	 delta 4 '4' = do { accum '4' ; return 4 }
+	 delta 4 '5' = do { accum '5' ; return 4 }
+	 delta 4 '6' = do { accum '6' ; return 4 }
+	 delta 4 '7' = do { accum '7' ; return 4 }
+	 delta 4 '8' = do { accum '8' ; return 4 }
+	 delta 4 '9' = do { accum '9' ; return 4 }
+	 delta 5 '+' = do { accum '+' ; return 5 }
+	 delta 5 '-' = do { accum '-' ; return 5 }
+	 delta 5 '.' = do { accum '.' ; return 5 }
+	 delta 5 '0' = do { accum '0' ; return 5 }
+	 delta 5 '1' = do { accum '1' ; return 5 }
+	 delta 5 '2' = do { accum '2' ; return 5 }
+	 delta 5 '3' = do { accum '3' ; return 5 }
+	 delta 5 '4' = do { accum '4' ; return 5 }
+	 delta 5 '5' = do { accum '5' ; return 5 }
+	 delta 5 '6' = do { accum '6' ; return 5 }
+	 delta 5 '7' = do { accum '7' ; return 5 }
+	 delta 5 '8' = do { accum '8' ; return 5 }
+	 delta 5 '9' = do { accum '9' ; return 5 }
+	 delta 6 '+' = do { accum '+' ; return 5 }
+	 delta 6 '-' = do { accum '-' ; return 5 }
+	 delta 6 '.' = do { accum '.' ; return 5 }
+	 delta 6 '0' = do { accum '0' ; return 6 }
+	 delta 6 '1' = do { accum '1' ; return 6 }
+	 delta 6 '2' = do { accum '2' ; return 6 }
+	 delta 6 '3' = do { accum '3' ; return 6 }
+	 delta 6 '4' = do { accum '4' ; return 6 }
+	 delta 6 '5' = do { accum '5' ; return 6 }
+	 delta 6 '6' = do { accum '6' ; return 6 }
+	 delta 6 '7' = do { accum '7' ; return 6 }
+	 delta 6 '8' = do { accum '8' ; return 6 }
+	 delta 6 '9' = do { accum '9' ; return 6 }
+
+
+
+accum :: a -> State [a] () 
+accum x = modify (\ s -> s++[x])
diff --git a/example/README b/example/README
new file mode 100644
--- /dev/null
+++ b/example/README
@@ -0,0 +1,51 @@
+
+  HaLeX: A Haskell Library to Model, 
+                              Manipulate and 
+                              Animate Regular Languages
+
+        http://www.di.uminho.pt/~jas/Research/HaLeX
+
+copyright João Saraiva
+          Department of Computer Science,
+          University of Minho, 
+          Braga, Portugal
+          jas@di.uminho.pt
+
+
+Version: 1.0 (January, 2002)
+
+
+
+The example directory contain the following files:
+
+  - real         
+
+    the regular expression defining a notation for real numbers 
+
+  - real_dfa.hs
+
+    the result of:  ../bin/halex -D -M < real > real_dfa.hs
+ 
+  - real_ndfa.hs
+
+    the result of:  ../bin/halex -N < real > real_ndfa.hs
+
+  - real_dfa.ps
+
+    the result of:  ../bin/halex -G -M < real | dot -Tps > real_dfa.ps
+
+  - real_ndfa.ps
+
+    the result of:  ../bin/halex -G -N < real | dot -Tps -Gsize=30,30 > real_ndfa.ps
+
+  - GenMDfa.hs 
+
+    the result of:  ../bin/halex -M -E < real
+
+    (to produce an "animator" for the real regular expression, just
+     call the following makefile
+
+                make -f ../scripts/Make_Animation 
+
+     the program animation if produced. It accepts as input a sentence
+     (a real number) and produces the animation).
diff --git a/example/real b/example/real
new file mode 100644
--- /dev/null
+++ b/example/real
@@ -0,0 +1,1 @@
+('+'|'-')?(0|1|2|3|4|5|6|7|8|9)*('.'?(0|1|2|3|4|5|6|7|8|9)+)
diff --git a/example/real_dfa.hs b/example/real_dfa.hs
new file mode 100644
--- /dev/null
+++ b/example/real_dfa.hs
@@ -0,0 +1,88 @@
+import Dfa
+dfa = Dfa v q s z delta
+  where 
+	 v = "+-.0123456789"
+	 q = [1,2,3,4,5,6]
+	 s = 1
+	 z = [4,6]
+	 -- delta :: st -> sy -> st 
+	 delta 1 '+' = 2
+	 delta 1 '-' = 2
+	 delta 1 '.' = 3
+	 delta 1 '0' = 4
+	 delta 1 '1' = 4
+	 delta 1 '2' = 4
+	 delta 1 '3' = 4
+	 delta 1 '4' = 4
+	 delta 1 '5' = 4
+	 delta 1 '6' = 4
+	 delta 1 '7' = 4
+	 delta 1 '8' = 4
+	 delta 1 '9' = 4
+	 delta 2 '+' = 5
+	 delta 2 '-' = 5
+	 delta 2 '.' = 3
+	 delta 2 '0' = 4
+	 delta 2 '1' = 4
+	 delta 2 '2' = 4
+	 delta 2 '3' = 4
+	 delta 2 '4' = 4
+	 delta 2 '5' = 4
+	 delta 2 '6' = 4
+	 delta 2 '7' = 4
+	 delta 2 '8' = 4
+	 delta 2 '9' = 4
+	 delta 3 '+' = 5
+	 delta 3 '-' = 5
+	 delta 3 '.' = 5
+	 delta 3 '0' = 6
+	 delta 3 '1' = 6
+	 delta 3 '2' = 6
+	 delta 3 '3' = 6
+	 delta 3 '4' = 6
+	 delta 3 '5' = 6
+	 delta 3 '6' = 6
+	 delta 3 '7' = 6
+	 delta 3 '8' = 6
+	 delta 3 '9' = 6
+	 delta 4 '+' = 5
+	 delta 4 '-' = 5
+	 delta 4 '.' = 3
+	 delta 4 '0' = 4
+	 delta 4 '1' = 4
+	 delta 4 '2' = 4
+	 delta 4 '3' = 4
+	 delta 4 '4' = 4
+	 delta 4 '5' = 4
+	 delta 4 '6' = 4
+	 delta 4 '7' = 4
+	 delta 4 '8' = 4
+	 delta 4 '9' = 4
+	 delta 5 '+' = 5
+	 delta 5 '-' = 5
+	 delta 5 '.' = 5
+	 delta 5 '0' = 5
+	 delta 5 '1' = 5
+	 delta 5 '2' = 5
+	 delta 5 '3' = 5
+	 delta 5 '4' = 5
+	 delta 5 '5' = 5
+	 delta 5 '6' = 5
+	 delta 5 '7' = 5
+	 delta 5 '8' = 5
+	 delta 5 '9' = 5
+	 delta 6 '+' = 5
+	 delta 6 '-' = 5
+	 delta 6 '.' = 5
+	 delta 6 '0' = 6
+	 delta 6 '1' = 6
+	 delta 6 '2' = 6
+	 delta 6 '3' = 6
+	 delta 6 '4' = 6
+	 delta 6 '5' = 6
+	 delta 6 '6' = 6
+	 delta 6 '7' = 6
+	 delta 6 '8' = 6
+	 delta 6 '9' = 6
+
+
diff --git a/example/real_dfa.ps b/example/real_dfa.ps
new file mode 100644
--- /dev/null
+++ b/example/real_dfa.ps
@@ -0,0 +1,350 @@
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diff --git a/example/real_ndfa.hs b/example/real_ndfa.hs
new file mode 100644
--- /dev/null
+++ b/example/real_ndfa.hs
@@ -0,0 +1,142 @@
+import Ndfa
+ndfa = Ndfa v q s z delta
+  where 
+	 v = "+-0123456789."
+	 q = [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132]
+	 s = [1]
+	 z = [132]
+	 -- delta :: st -> sy -> st 
+	 delta 3 (Just '+') = [4]
+	 delta 5 (Just '-') = [6]
+	 delta 12 (Just '0') = [13]
+	 delta 15 (Just '1') = [16]
+	 delta 18 (Just '2') = [19]
+	 delta 21 (Just '3') = [22]
+	 delta 24 (Just '4') = [25]
+	 delta 27 (Just '5') = [28]
+	 delta 30 (Just '6') = [31]
+	 delta 33 (Just '7') = [34]
+	 delta 36 (Just '8') = [37]
+	 delta 38 (Just '9') = [39]
+	 delta 51 (Just '.') = [52]
+	 delta 56 (Just '0') = [57]
+	 delta 59 (Just '1') = [60]
+	 delta 62 (Just '2') = [63]
+	 delta 65 (Just '3') = [66]
+	 delta 68 (Just '4') = [69]
+	 delta 71 (Just '5') = [72]
+	 delta 74 (Just '6') = [75]
+	 delta 77 (Just '7') = [78]
+	 delta 80 (Just '8') = [81]
+	 delta 82 (Just '9') = [83]
+	 delta 95 (Just '0') = [96]
+	 delta 98 (Just '1') = [99]
+	 delta 101 (Just '2') = [102]
+	 delta 104 (Just '3') = [105]
+	 delta 107 (Just '4') = [108]
+	 delta 110 (Just '5') = [111]
+	 delta 113 (Just '6') = [114]
+	 delta 116 (Just '7') = [117]
+	 delta 119 (Just '8') = [120]
+	 delta 121 (Just '9') = [122]
+	 delta 1 (Nothing) = [2,8]
+	 delta 2 (Nothing) = [3,5]
+	 delta 4 (Nothing) = [7]
+	 delta 6 (Nothing) = [7]
+	 delta 7 (Nothing) = [9]
+	 delta 8 (Nothing) = [9]
+	 delta 9 (Nothing) = [10]
+	 delta 10 (Nothing) = [11,49]
+	 delta 11 (Nothing) = [12,14]
+	 delta 13 (Nothing) = [48]
+	 delta 14 (Nothing) = [15,17]
+	 delta 16 (Nothing) = [47]
+	 delta 17 (Nothing) = [18,20]
+	 delta 19 (Nothing) = [46]
+	 delta 20 (Nothing) = [21,23]
+	 delta 22 (Nothing) = [45]
+	 delta 23 (Nothing) = [24,26]
+	 delta 25 (Nothing) = [44]
+	 delta 26 (Nothing) = [27,29]
+	 delta 28 (Nothing) = [43]
+	 delta 29 (Nothing) = [30,32]
+	 delta 31 (Nothing) = [42]
+	 delta 32 (Nothing) = [33,35]
+	 delta 34 (Nothing) = [41]
+	 delta 35 (Nothing) = [36,38]
+	 delta 37 (Nothing) = [40]
+	 delta 39 (Nothing) = [40]
+	 delta 40 (Nothing) = [41]
+	 delta 41 (Nothing) = [42]
+	 delta 42 (Nothing) = [43]
+	 delta 43 (Nothing) = [44]
+	 delta 44 (Nothing) = [45]
+	 delta 45 (Nothing) = [46]
+	 delta 46 (Nothing) = [47]
+	 delta 47 (Nothing) = [48]
+	 delta 48 (Nothing) = [11,49]
+	 delta 49 (Nothing) = [50]
+	 delta 50 (Nothing) = [51,53]
+	 delta 52 (Nothing) = [54]
+	 delta 53 (Nothing) = [54]
+	 delta 54 (Nothing) = [55]
+	 delta 55 (Nothing) = [56,58]
+	 delta 57 (Nothing) = [92]
+	 delta 58 (Nothing) = [59,61]
+	 delta 60 (Nothing) = [91]
+	 delta 61 (Nothing) = [62,64]
+	 delta 63 (Nothing) = [90]
+	 delta 64 (Nothing) = [65,67]
+	 delta 66 (Nothing) = [89]
+	 delta 67 (Nothing) = [68,70]
+	 delta 69 (Nothing) = [88]
+	 delta 70 (Nothing) = [71,73]
+	 delta 72 (Nothing) = [87]
+	 delta 73 (Nothing) = [74,76]
+	 delta 75 (Nothing) = [86]
+	 delta 76 (Nothing) = [77,79]
+	 delta 78 (Nothing) = [85]
+	 delta 79 (Nothing) = [80,82]
+	 delta 81 (Nothing) = [84]
+	 delta 83 (Nothing) = [84]
+	 delta 84 (Nothing) = [85]
+	 delta 85 (Nothing) = [86]
+	 delta 86 (Nothing) = [87]
+	 delta 87 (Nothing) = [88]
+	 delta 88 (Nothing) = [89]
+	 delta 89 (Nothing) = [90]
+	 delta 90 (Nothing) = [91]
+	 delta 91 (Nothing) = [92]
+	 delta 92 (Nothing) = [93]
+	 delta 93 (Nothing) = [94,132]
+	 delta 94 (Nothing) = [95,97]
+	 delta 96 (Nothing) = [131]
+	 delta 97 (Nothing) = [98,100]
+	 delta 99 (Nothing) = [130]
+	 delta 100 (Nothing) = [101,103]
+	 delta 102 (Nothing) = [129]
+	 delta 103 (Nothing) = [104,106]
+	 delta 105 (Nothing) = [128]
+	 delta 106 (Nothing) = [107,109]
+	 delta 108 (Nothing) = [127]
+	 delta 109 (Nothing) = [110,112]
+	 delta 111 (Nothing) = [126]
+	 delta 112 (Nothing) = [113,115]
+	 delta 114 (Nothing) = [125]
+	 delta 115 (Nothing) = [116,118]
+	 delta 117 (Nothing) = [124]
+	 delta 118 (Nothing) = [119,121]
+	 delta 120 (Nothing) = [123]
+	 delta 122 (Nothing) = [123]
+	 delta 123 (Nothing) = [124]
+	 delta 124 (Nothing) = [125]
+	 delta 125 (Nothing) = [126]
+	 delta 126 (Nothing) = [127]
+	 delta 127 (Nothing) = [128]
+	 delta 128 (Nothing) = [129]
+	 delta 129 (Nothing) = [130]
+	 delta 130 (Nothing) = [131]
+	 delta 131 (Nothing) = [94,132]
+
+	 delta _ _ = []
+
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+showpage
+
+% stop using temporary dictionary
+end
+
+% restore original state
+origstate restore
+
+%%Trailer
+
+%%EndDocument
+ @endspecial Black Black 1638 4189 a @beginspecial 17
+@llx 418 @lly 248 @urx 506 @ury 2310 @rwi @clip @setspecial
+%%BeginDocument: TOOL/anim2.ps
+%!PS-Adobe-2.0 EPSF-2.0
+%%Title: /home/jas/Research/Papers/HaLeX/TOOL/anim2.ps
+%%Creator: XV Version 3.10a  Rev: 12/29/94 (PNG patch 1.2)  -  by John Bradley
+%%BoundingBox: 17 418 248 506
+%%Pages: 1
+%%DocumentFonts:
+%%EndComments
+%%EndProlog
+
+%%Page: 1 1
+
+% remember original state
+/origstate save def
+
+% build a temporary dictionary
+20 dict begin
+
+% define string to hold a scanline's worth of data
+/pix 1731 string def
+
+% define space for color conversions
+/grays 577 string def  % space for gray scale line
+/npixls 0 def
+/rgbindx 0 def
+
+% lower left corner
+17 418 translate
+
+% size of image (on paper, in 1/72inch coords)
+230.83200 87.62400 scale
+
+% define 'colorimage' if it isn't defined
+%   ('colortogray' and 'mergeprocs' come from xwd2ps
+%     via xgrab)
+/colorimage where   % do we know about 'colorimage'?
+  { pop }           % yes: pop off the 'dict' returned
+  {                 % no:  define one
+    /colortogray {  % define an RGB->I function
+      /rgbdata exch store    % call input 'rgbdata'
+      rgbdata length 3 idiv
+      /npixls exch store
+      /rgbindx 0 store
+      0 1 npixls 1 sub {
+        grays exch
+        rgbdata rgbindx       get 20 mul    % Red
+        rgbdata rgbindx 1 add get 32 mul    % Green
+        rgbdata rgbindx 2 add get 12 mul    % Blue
+        add add 64 idiv      % I = .5G + .31R + .18B
+        put
+        /rgbindx rgbindx 3 add store
+      } for
+      grays 0 npixls getinterval
+    } bind def
+
+    % Utility procedure for colorimage operator.
+    % This procedure takes two procedures off the
+    % stack and merges them into a single procedure.
+
+    /mergeprocs { % def
+      dup length
+      3 -1 roll
+      dup
+      length
+      dup
+      5 1 roll
+      3 -1 roll
+      add
+      array cvx
+      dup
+      3 -1 roll
+      0 exch
+      putinterval
+      dup
+      4 2 roll
+      putinterval
+    } bind def
+
+    /colorimage { % def
+      pop pop     % remove 'false 3' operands
+      {colortogray} mergeprocs
+      image
+    } bind def
+  } ifelse          % end of 'false' case
+
+
+
+577 219 8			% dimensions of data
+[577 0 0 -219 0 219]		% mapping matrix
+{currentfile pix readhexstring pop}
+false 3 colorimage
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+(literate)g Fr(Haskell)p Fy(,)f(that)i(the)f(studen)n(ts)h(ha)n(v)n(e)e
+(to)h(complete.)g(Eac)n(h)g(set)g(of)h(exercises)d(de-)150
+2564 y(\034nes)f(a)g(mo)r(dule)g(of)g(the)h Fq(HaL)l(eX)39
+b Fy(library)-7 b(.)25 b(Th)n(us,)h(at)g(the)g(end)g(of)h(the)f(course)
+f(the)h(studen)n(ts)h(ha)n(v)n(e)d(a)i(complete)150 2663
+y(do)r(cumen)n(tation)20 b(of)g(all)h(the)f(exercises)f(and)i(topics)f
+(co)n(v)n(ered)e(in)j(the)g(course,)e(and,)h(also,)g(of)g(the)h
+Fq(HaL)l(eX)33 b Fy(library)-7 b(.)275 2763 y(F)g(urthermore,)23
+b(during)i(the)g(semester)f(the)i(studen)n(ts)f(ha)n(v)n(e)e(to)i
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+b(The)150 2863 y(construction)34 b(of)h(parts)f(of)h(the)g
+Fq(HaL)l(eX)48 b Fy(library)33 b(has)i(b)r(een)g(prop)r(osed)f(as)g
+(suc)n(h)h(a)f(pro)5 b(ject.)34 b(F)-7 b(or)35 b(example,)150
+2962 y(in)g(the)g(last)g(instance)f(of)h(the)g(course)e(the)i(\034rst)g
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+(minimization)150 3062 y(and)f(the)h(visualization)e(of)h(a)g(DF)-9
+b(A,)35 b(while)f(the)h(second)e(one)h(w)n(as)f(the)i(de\034nition)f
+(of)h(a)e(concrete)h(notation)150 3162 y(for)f(regular)e(expressions,)h
+(the)h(implemen)n(tation)g(of)h(its)f(parser)f(\(through)g(parser)g
+(com)n(binators\),)g(and)h(the)150 3261 y(construction)27
+b(of)g(\(a)h(simpli\034ed)g(v)n(ersion)e(of)6 b(\))28
+b(the)g(halex)f(program.)150 3499 y Fs(6)112 b(Conclusion)150
+3670 y Fy(This)30 b(pap)r(er)g(summarizes)g(the)h(design)f(and)g
+(implemen)n(tation)g(of)h(the)g Fq(HaL)l(eX)43 b Fy(library)-7
+b(.)30 b(T)-7 b(w)n(o)29 b(examples)h(are)150 3769 y(presen)n(ted,)22
+b(namely)g(the)g(visualization/animation)e(of)j(a)f(language)e(of)i
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+(a)g(reactiv)n(e)g(\034nite)h(automata.)150 4040 y Fq(A)l(cknow)t(le)l
+(dgements:)46 b Fy(I)30 b(w)n(ould)f(lik)n(e)h(to)g(thank)f(the)i
+(studen)n(ts)f(who)f(follo)n(w)n(ed)g(the)i(course)d
+Fq(M\351to)l(dos)33 b(de)g(Pr)l(o-)150 4140 y(gr)l(ama\347\343o)d(III)
+39 b Fy(in)26 b(the)g(sc)n(holar)e(y)n(ears)g(2000/2001)d(and)26
+b(2001/2002)21 b(for)k(their)h(en)n(th)n(usiasm)f(and)h(co)r(op)r
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+(during)h(classes.)f(I)i(thank)f(Jos\351)g(Bacelar)f(Almeida)h(who)h
+(ga)n(v)n(e)d(helpful)150 4339 y(commen)n(ts)27 b(during)g(the)h(dev)n
+(elopmen)n(t)f(of)h Fq(HaL)l(eX)p Fy(.)150 4577 y Fs(References)p
+Black 150 4732 a Fx([Brz62])p Black 43 w(J.)34 b(A.)f(Brzozo)n(wski.)58
+b(Canonical)35 b(regular)e(expressions)h(and)f(minimal)e(state)j
+(graphs)f(for)h(de\034nite)e(ev)n(en)n(ts.)426 4824 y
+Fu(Mathematic)l(al)c(the)l(ory)i(of)d(A)n(utomata)p Fx(,)g
+(12:529\025561,)j(1962.)p Black 150 4908 a([GN99])p Black
+43 w(Emden)24 b(R.)h(Gransner)h(and)f(Stephen)f(C.)i(North.)34
+b(An)24 b(op)r(en)i(graph)f(visualization)i(system)e(and)g(its)h
+(applica-)426 4999 y(tions)g(to)g(soft)n(w)n(are)h(engineering.)36
+b Fu(Softwar)l(e)28 b(Pr)l(actic)l(e)h(and)f(Exp)l(erienc)l(e)p
+Fx(,)g(00\(S1\):1\02529,)g(1999.)p Black 150 5084 a([JS99])p
+Black 76 w(Johan)19 b(Jeuring)h(and)e(Doaitse)i(Swierstra.)k(A)n(dv)l
+(anced)17 b(Programming)i(Concepts)g(in)g(a)g(Course)h(on)f(Grammars)
+426 5175 y(and)25 b(P)n(arsing.)35 b(In)25 b(Matthias)i(F)-6
+b(elleisen,)26 b(Mic)n(hael)h(Han)n(us,)e(and)g(Simon)g(Thompson,)g
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+y(the)j(W)-6 b(orkshop)32 b(on)e(F)-6 b(unctional)32
+b(and)f(De)l(clar)l(ative)h(Pr)l(o)l(gr)l(amming)f(in)f(Educ)l(ation)p
+Fx(,)h(Rice)e(T)-6 b(ec)n(hnical)29 b(Rep)r(ort)426 5358
+y(99-346,)f(August)d(1999.)p Black 150 5442 a([Tho00])p
+Black 43 w(Simon)36 b(Thompson.)67 b(Regular)37 b(expressions)h(and)e
+(automata)h(using)g(hask)n(ell.)68 b(T)-6 b(ec)n(hnical)37
+b(Rep)r(ort)g(5-00,)426 5533 y(Computing)25 b(Lab)r(oratory)-6
+b(,)26 b(Univ)n(ersit)n(y)f(of)h(Ken)n(t,)f(Jan)n(uary)h(2000.)p
+Black Black eop
+%%Trailer
+end
+userdict /end-hook known{end-hook}if
+%%EOF
diff --git a/scripts/Make_Animation b/scripts/Make_Animation
new file mode 100644
--- /dev/null
+++ b/scripts/Make_Animation
@@ -0,0 +1,6 @@
+
+HaLeX_DIR = /home/jas/HaLeX
+HaLeX_SOURCE = $(HaLeX_DIR)/src
+
+animation:
+	ghc --make -I$(HaLeX_SOURCE) -i$(HaLeX_SOURCE) -package util -O2 $(HaLeX_SOURCE)/MainAnim.hs -o animation	
diff --git a/scripts/faAnim.lefty b/scripts/faAnim.lefty
new file mode 100644
--- /dev/null
+++ b/scripts/faAnim.lefty
@@ -0,0 +1,282 @@
+#  HaLeX: A Haskell Library to Model, 
+#                              Manipulate and 
+#                              Animate Regular Languages
+#
+#        http://www.di.uminho.pt/~jas/Research/HaLeX
+#
+# The script to animate the Reactive Finite Automata produced by HaLeX
+#
+# copyright João Saraiva
+#           Department of Computer Science,
+#           University of Minho, 
+#           Braga, Portugal
+#           jas@di.uminho.pt
+#
+# Version: 1.0 (January, 2002)
+#
+
+load('dotty.lefty');
+
+# filenames
+fa.graphfilename = 'fa.dot';
+fa.transfilename = 'fa.trans';
+
+# tracking the states/nodes
+fa.normalcolor    = 'black';
+fa.highlightcolor = 'light_grey';
+fa.currentcolor   = 'tan';
+
+
+fa.trackcur = 0;    # 0: No   1: Yes 
+
+
+# tracking the path
+fa.trackpath               = 0;   # 0: No   1: Yes
+fa.trackhighlightcolor     = 'red';
+fa.trackhighlightfontcolor = 'red';
+fa.trackhighlightfontsize  = '30';
+
+# tracking the input sentence
+fa.sentence = '';
+
+
+
+fa.protogt.graph.edgeattr.color = 'red';
+
+fa.sleep = 500000;
+fa.start = '1';
+
+
+fa.init = function () {
+  dotty.init ();
+  monitorfile = dotty.monitorfile;
+};
+
+fa.protogt = [
+  'layoutmode' = 'sync';
+  'actions' = copy (dotty.protogt.actions);
+];
+
+fa.protovt = [
+  'name' = 'FA';
+  'type' = 'normal'; 
+];
+
+fa.main = function () {
+  local gnvt , gt ;
+
+  gnvt = dotty.createviewandgraph(null,'file',fa.protogt,fa.protovt);
+  gt = gnvt.gt ;
+  gt.loadgraph (gt, fa.graphfilename,'file',fa.protogt.graph, 1);
+  fa.currstate = gt.graph.nodes[gt.graph.nodedict[fa.start]];   #   <-- Init Node
+  fa.loadtrans ('fa.trans');
+  fa.setcurrcolor(gt, fa.currstate);
+  fa.focuson (gt , fa.currstate);
+};
+
+fa.loadtrans = function (filename) {
+  local fd , i ;
+
+  if (~((fd = openio ('file',filename,'r')) >= 0)) {
+     echo ('cannot open transition file: ',filename);
+     return;
+  }
+  echo ('reading transition file');
+  i = 0;
+  while ((fa.trans[i] = readline (fd)))
+    i = i + 1;
+  closeio (fd);
+  fa.trani = 0 ;
+  fa.states[0] = fa.currstate ;
+  fa.currstate.count = 1 ;
+};
+
+fa.next = function (gt) {
+  local label , eid , edge , tran ;
+
+  if (~(label = fa.trans[fa.trani]))
+    return 0;
+  for (eid in fa.currstate.edges) {
+      edge = fa.currstate.edges[eid];
+      if (edge.attr.label == label & edge.tail == fa.currstate) {
+          tran = edge ;
+          break ;
+      }
+  }
+  if (tran) {
+     if (fa.trackpath)  fa.setedegecolor (gt ,  tran);
+
+     sleep(fa.sleep);                    
+     fa.trani = fa.trani + 1;
+     fa.setcolor (gt , fa.currstate);
+     fa.currstate = (fa.states[fa.trani] = tran.head) ;
+     if (fa.currstate.count)
+        fa.currstate.count = fa.currstate.count + 1;
+     else 
+        fa.currstate.count = 1;
+     fa.setcurrcolor (gt, fa.currstate);
+     fa.focuson (gt , fa.currstate);
+     sleep(fa.sleep); 
+  }
+  return 1;
+};
+
+fa.prev = function (gt) {
+  if (fa.trani == 0)
+     return 0;
+  sleep(fa.sleep); 
+  remove (fa.trani , fa.states);
+  fa.trani = fa.trani - 1;
+  fa.currstate.count = fa.currstate.count - 1;
+  fa.setcolor (gt , fa.currstate );
+  fa.currstate = fa.states[fa.trani];
+  fa.setcurrcolor (gt, fa.currstate);
+  fa.focuson (gt , fa.currstate);
+  return 1;
+};
+
+
+fa.setedegecolor = function (gt , edge) {
+   edge.attr.color = fa.trackhighlightcolor;
+   edge.attr.fontcolor = fa.trackhighlightfontcolor;
+   edge.attr.fontsize = fa.trackhighlightfontsize;
+   ge.undrawedge(gt , gt.views , edge);
+   remove('style',edge.attr);
+   gt.unpackedgeattr (gt, edge);
+   gt.drawedge (gt , gt.views , edge);
+};
+
+
+fa.setcolor = function (gt , node) {
+  if (node.count) {
+     node.attr.style = 'filled' ;
+     node.attr.color = fa.highlightcolor ;
+  } else {
+     gt.undrawnode (gt , gt.views , node);
+     remove ('style' , node.attr);
+     node.attr.color = fa.normalcolor ;
+  }
+  gt.unpacknodeattr (gt, node);
+  gt.drawnode (gt , gt.views , node);
+};
+
+fa.setcurrcolor = function (gt , node) {
+  node.attr.style = 'filled' ;
+  node.attr.color = fa.currentcolor ;
+  gt.unpacknodeattr (gt, node);
+  gt.drawnode (gt , gt.views , node);
+};
+
+fa.focuson = function (gt , node) {
+  gt.setviewcenter (gt.views , node.pos);
+};
+
+fa.protogt.actions.general['play fwd'] = function (gt , vt , data) {
+  while (fa.next(gt))
+    ;
+};
+
+fa.protogt.actions.general['play bwd'] = function (gt , vt , data) {
+  while (fa.prev(gt))
+    ;
+};
+
+fa.protogt.actions.general['track node'] = function (gt , vt , data) {
+  if (fa.trackcur)
+    fa.trackcur = 0;
+  else {
+    fa.trackcur = 1;
+    fa.focuson (gt , fa.currstate);
+  }
+};
+
+fa.protogt.actions.general['track path (y/n)'] = function (gt , vt , data) {
+  if (fa.trackpath) fa.trackpath = 0 ; 
+  else              fa.trackpath = 1 ;
+};
+
+fa.protogt.actions.general['inc sleep'] = function (gt , vt , data) {
+  fa.sleep = fa.sleep + 200000;
+};
+
+fa.protogt.actions.general['dec sleep'] = function (gt , vt , data) {
+  fa.sleep = fa.sleep - 200000;
+};
+
+
+
+fa.protovt.menus = [
+    'general' = [
+        0 = "undo";
+        1 = "paste";
+        2 = "do layout";
+        3 = "cancel layout";
+        4 = "redraw";
+        5 = "new graph";
+        6 = "load graph";
+        7 = "reload graph";
+        8 = "open view";
+        9 = "copy view";
+        10 = "clone view";
+        11 = "birdseye view";
+        12 = "close view";
+        13 = "play fwd";
+        14 = "play bwd";
+        15 = "inc sleep";
+        16 = "dec sleep";
+        17 = "zoom in";
+        18 = "zoom out";
+        19 = "find node";
+        20 = "track node";
+        21 = "track path (y/n)";
+        22 = "print graph";
+        23 = "text view";
+        24 = "quit";
+    ];
+    'node' = [
+        0 = "cut";
+        1 = "Cut";
+        2 = "copy";
+        3 = "Copy";
+        4 = "group";
+        5 = "Group";
+        6 = "delete";
+        7 = "Delete";
+        8 = "remove";
+        9 = "Remove";
+        10 = "set attr";
+        11 = "print attr";
+    ];
+    'edge' = [
+        0 = "cut";
+        1 = "Cut";
+        2 = "copy";
+        3 = "Copy";
+        4 = "group";
+        5 = "Group";
+        6 = "delete";
+        7 = "Delete";
+        8 = "set attr";
+        9 = "print attr";
+    ];
+];
+fa.protovt.uifuncs.rightdown = dotty.protovt.normal.uifuncs.rightdown;
+fa.protovt.uifuncs.keyup = dotty.protovt.normal.uifuncs.keyup;
+fa.protovt.uifuncs.redraw = dotty.protovt.normal.uifuncs.redraw;
+fa.protovt.uifuncs.closeview = dotty.protovt.normal.uifuncs.closeview;
+
+fa.protovt.uifuncs.leftup = function (data) {
+  local gt ;
+
+  gt = dotty.graphs[dotty.views[data.widget].gtid];
+  if (fa.next(gt) == 0)
+     echo ('at end of log');
+};
+
+fa.protovt.uifuncs.middleup = function (data) {
+  local gt ;
+
+  gt = dotty.graphs[dotty.views[data.widget].gtid];
+  if (fa.prev(gt) == 0)
+     echo ('at end of log');
+};
