HaLeX (empty) → 1.1
raw patch · 34 files changed
+36018/−0 lines, 34 filesdep +basedep +mtlsetup-changed
Dependencies added: base, mtl
Files
- HaLeX.cabal +43/−0
- HaLeX_lib/Language/HaLex/Dfa.hs +453/−0
- HaLeX_lib/Language/HaLex/Dfa2MDfa.hs +135/−0
- HaLeX_lib/Language/HaLex/DfaMonad.lhs +631/−0
- HaLeX_lib/Language/HaLex/Equivalence.hs +89/−0
- HaLeX_lib/Language/HaLex/Examples/Real.lhs +257/−0
- HaLeX_lib/Language/HaLex/Examples/Robot.lhs +124/−0
- HaLeX_lib/Language/HaLex/Fa2RegExp.hs +115/−0
- HaLeX_lib/Language/HaLex/FaAsDiGraph.hs +176/−0
- HaLeX_lib/Language/HaLex/FaClasses.hs +85/−0
- HaLeX_lib/Language/HaLex/FaOperations.hs +246/−0
- HaLeX_lib/Language/HaLex/Minimize.hs +207/−0
- HaLeX_lib/Language/HaLex/Ndfa.hs +360/−0
- HaLeX_lib/Language/HaLex/Parser.hs +69/−0
- HaLeX_lib/Language/HaLex/RegExp.hs +264/−0
- HaLeX_lib/Language/HaLex/RegExp2Fa.hs +122/−0
- HaLeX_lib/Language/HaLex/RegExpAsDiGraph.hs +87/−0
- HaLeX_lib/Language/HaLex/RegExpParser.hs +74/−0
- HaLeX_lib/Language/HaLex/Util.hs +59/−0
- HaLeX_tool/halex.hs +155/−0
- INSTALL +34/−0
- LICENSE +5/−0
- README +222/−0
- Setup.hs +5/−0
- example/GenMDfa.hs +96/−0
- example/README +51/−0
- example/real +1/−0
- example/real_dfa.hs +88/−0
- example/real_dfa.ps +350/−0
- example/real_ndfa.hs +142/−0
- example/real_ndfa.ps +3615/−0
- paper/HaLeX.ps +27370/−0
- scripts/Make_Animation +6/−0
- scripts/faAnim.lefty +282/−0
+ HaLeX.cabal view
@@ -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
+ HaLeX_lib/Language/HaLex/Dfa.hs view
@@ -0,0 +1,453 @@+{-# LANGUAGE FlexibleContexts #-}+-----------------------------------------------------------------------------+-- |+-- Module : Language.HaLex.Dfa+-- Copyright : (c) Jooo 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
+ HaLeX_lib/Language/HaLex/Dfa2MDfa.hs view
@@ -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++++++
+ HaLeX_lib/Language/HaLex/DfaMonad.lhs view
@@ -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}
+ HaLeX_lib/Language/HaLex/Equivalence.hs view
@@ -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++++++++++++
+ HaLeX_lib/Language/HaLex/Examples/Real.lhs view
@@ -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}+++
+ HaLeX_lib/Language/HaLex/Examples/Robot.lhs view
@@ -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}
+ HaLeX_lib/Language/HaLex/Fa2RegExp.hs view
@@ -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)++
+ HaLeX_lib/Language/HaLex/FaAsDiGraph.hs view
@@ -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++
+ HaLeX_lib/Language/HaLex/FaClasses.hs view
@@ -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++
+ HaLeX_lib/Language/HaLex/FaOperations.hs view
@@ -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' _ _ = []
+ HaLeX_lib/Language/HaLex/Minimize.hs view
@@ -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+++
+ HaLeX_lib/Language/HaLex/Ndfa.hs view
@@ -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
+ HaLeX_lib/Language/HaLex/Parser.hs view
@@ -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 ]++++
+ HaLeX_lib/Language/HaLex/RegExp.hs view
@@ -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+ ) ++-----------------------------------------------------------------------------++
+ HaLeX_lib/Language/HaLex/RegExp2Fa.hs view
@@ -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++
+ HaLeX_lib/Language/HaLex/RegExpAsDiGraph.hs view
@@ -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++++++++
+ HaLeX_lib/Language/HaLex/RegExpParser.hs view
@@ -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 ()
+ HaLeX_lib/Language/HaLex/Util.hs view
@@ -0,0 +1,59 @@+-----------------------------------------------------------------------------+-- |+-- Module : Language.HaLex.Edfa+-- Copyright : (c) Jooo 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
+ HaLeX_tool/halex.hs view
@@ -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)+
+ INSTALL view
@@ -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.
+ LICENSE view
@@ -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"
+ README view
@@ -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.++
+ Setup.hs view
@@ -0,0 +1,5 @@+#!/usr/bin/runhaskell++import Distribution.Simple++main = defaultMainWithHooks defaultUserHooks
+ example/GenMDfa.hs view
@@ -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])
+ example/README view
@@ -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).
+ example/real view
@@ -0,0 +1,1 @@+('+'|'-')?(0|1|2|3|4|5|6|7|8|9)*('.'?(0|1|2|3|4|5|6|7|8|9)+)
+ example/real_dfa.hs view
@@ -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++
+ example/real_dfa.ps view
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+ example/real_ndfa.hs view
@@ -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 _ _ = []+
+ example/real_ndfa.ps view
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(Epsilon) 42 14.00 -0.50 alignedtext+end grestore++% 77+gsave 10 dict begin+5427 234 20 20 ellipse_path+stroke+gsave 10 dict begin+5427 235 moveto (77) 14 14.00 -0.50 alignedtext+end grestore+end grestore++% 78+gsave 10 dict begin+5552 238 20 20 ellipse_path+stroke+gsave 10 dict begin+5552 239 moveto (78) 14 14.00 -0.50 alignedtext+end grestore+end grestore++% 77 -> 78+newpath 5447 235 moveto+5467 236 5499 237 5523 237 curveto+stroke+newpath 5522 235 moveto+5532 237 lineto+5522 240 lineto+closepath+fill+gsave 10 dict begin+5494 247 moveto ('7') 16 14.00 -0.50 alignedtext+end grestore++% 85+gsave 10 dict begin+5878 238 20 20 ellipse_path+stroke+gsave 10 dict begin+5878 239 moveto (85) 14 14.00 -0.50 alignedtext+end grestore+end grestore++% 78 -> 85+newpath 5572 238 moveto+5628 238 5784 238 5850 238 curveto+stroke+newpath 5848 236 moveto+5858 238 lineto+5848 241 lineto+closepath+fill+gsave 10 dict begin+5677 285 moveto (Epsilon) 42 14.00 -0.50 alignedtext+end grestore++% 80+gsave 10 dict begin+5494 182 20 20 ellipse_path+stroke+gsave 10 dict begin+5494 183 moveto (80) 14 14.00 -0.50 alignedtext+end grestore+end grestore++% 81+gsave 10 dict begin+5610 182 20 20 ellipse_path+stroke+gsave 10 dict begin+5610 183 moveto (81) 14 14.00 -0.50 alignedtext+end grestore+end grestore++% 80 -> 81+newpath 5514 182 moveto+5532 182 5560 182 5581 182 curveto+stroke+newpath 5580 180 moveto+5590 182 lineto+5580 185 lineto+closepath+fill+gsave 10 dict begin+5552 191 moveto ('8') 16 14.00 -0.50 alignedtext+end grestore++% 84+gsave 10 dict begin+5744 182 20 20 ellipse_path+stroke+gsave 10 dict begin+5744 183 moveto (84) 14 14.00 -0.50 alignedtext+end grestore+end grestore++% 81 -> 84+newpath 5630 182 moveto+5652 182 5689 182 5715 182 curveto+stroke+newpath 5714 180 moveto+5724 182 lineto+5714 185 lineto+closepath+fill+gsave 10 dict begin+5677 191 moveto (Epsilon) 42 14.00 -0.50 alignedtext+end grestore++% 82+gsave 10 dict begin+5494 124 20 20 ellipse_path+stroke+gsave 10 dict begin+5494 125 moveto (82) 14 14.00 -0.50 alignedtext+end grestore+end grestore++% 83+gsave 10 dict begin+5610 124 20 20 ellipse_path+stroke+gsave 10 dict begin+5610 125 moveto (83) 14 14.00 -0.50 alignedtext+end grestore+end grestore++% 82 -> 83+newpath 5514 124 moveto+5532 124 5560 124 5581 124 curveto+stroke+newpath 5580 122 moveto+5590 124 lineto+5580 127 lineto+closepath+fill+gsave 10 dict begin+5552 133 moveto ('9') 16 14.00 -0.50 alignedtext+end grestore++% 83 -> 84+newpath 5629 131 moveto+5649 138 5680 150 5706 162 curveto+5710 164 5714 166 5717 168 curveto+stroke+newpath 5718 166 moveto+5726 172 lineto+5716 170 lineto+closepath+fill+gsave 10 dict begin+5677 171 moveto (Epsilon) 42 14.00 -0.50 alignedtext+end grestore++% 95+gsave 10 dict begin+7218 557 20 20 ellipse_path+stroke+gsave 10 dict begin+7218 558 moveto (95) 14 14.00 -0.50 alignedtext+end grestore+end grestore++% 96+gsave 10 dict begin+7429 557 20 20 ellipse_path+stroke+gsave 10 dict begin+7429 558 moveto (96) 14 14.00 -0.50 alignedtext+end grestore+end grestore++% 95 -> 96+newpath 7238 557 moveto+7275 557 7357 557 7400 557 curveto+stroke+newpath 7399 555 moveto+7409 557 lineto+7399 560 lineto+closepath+fill+gsave 10 dict begin+7285 566 moveto ('0') 16 14.00 -0.50 alignedtext+end grestore++% 131+gsave 10 dict begin+9805 523 24 24 ellipse_path+stroke+gsave 10 dict begin+9805 524 moveto (131) 21 14.00 -0.50 alignedtext+end grestore+end grestore++% 96 -> 131+newpath 7449 557 moveto+7477 558 7529 558 7573 558 curveto+7573 558 7573 558 9661 558 curveto+9701 558 9744 546 9773 535 curveto+stroke+newpath 9772 533 moveto+9782 532 lineto+9773 538 lineto+closepath+fill+gsave 10 dict begin+8581 567 moveto (Epsilon) 42 14.00 -0.50 alignedtext+end grestore++% 98+gsave 10 dict begin+7357 503 20 20 ellipse_path+stroke+gsave 10 dict begin+7357 504 moveto (98) 14 14.00 -0.50 alignedtext+end grestore+end grestore++% 99+gsave 10 dict begin+7573 506 20 20 ellipse_path+stroke+gsave 10 dict begin+7573 507 moveto (99) 14 14.00 -0.50 alignedtext+end grestore+end grestore++% 98 -> 99+newpath 7377 503 moveto+7415 504 7500 505 7544 506 curveto+stroke+newpath 7543 504 moveto+7553 506 lineto+7543 509 lineto+closepath+fill+gsave 10 dict begin+7429 514 moveto ('1') 16 14.00 -0.50 alignedtext+end grestore++% 130+gsave 10 dict begin+9661 506 24 24 ellipse_path+stroke+gsave 10 dict begin+9661 507 moveto (130) 21 14.00 -0.50 alignedtext+end grestore+end grestore++% 99 -> 130+newpath 7593 506 moveto+7621 506 7673 506 7717 506 curveto+7717 506 7717 506 9517 506 curveto+9555 506 9598 506 9627 506 curveto+stroke+newpath 9626 504 moveto+9636 506 lineto+9626 509 lineto+closepath+fill+gsave 10 dict begin+8581 515 moveto (Epsilon) 42 14.00 -0.50 alignedtext+end grestore++% 101+gsave 10 dict begin+7573 444 24 24 ellipse_path+stroke+gsave 10 dict begin+7573 445 moveto (101) 21 14.00 -0.50 alignedtext+end grestore+end grestore++% 102+gsave 10 dict begin+7717 454 24 24 ellipse_path+stroke+gsave 10 dict begin+7717 455 moveto (102) 21 14.00 -0.50 alignedtext+end grestore+end grestore++% 101 -> 102+newpath 7598 446 moveto+7621 448 7657 450 7683 452 curveto+stroke+newpath 7682 450 moveto+7692 452 lineto+7682 455 lineto+closepath+fill+gsave 10 dict begin+7645 460 moveto ('2') 16 14.00 -0.50 alignedtext+end grestore++% 129+gsave 10 dict begin+9517 454 24 24 ellipse_path+stroke+gsave 10 dict begin+9517 455 moveto (129) 21 14.00 -0.50 alignedtext+end grestore+end grestore++% 102 -> 129+newpath 7742 454 moveto+7770 454 7819 454 7861 454 curveto+7861 454 7861 454 9373 454 curveto+9411 454 9454 454 9483 454 curveto+stroke+newpath 9482 452 moveto+9492 454 lineto+9482 457 lineto+closepath+fill+gsave 10 dict begin+8581 463 moveto (Epsilon) 42 14.00 -0.50 alignedtext+end grestore++% 104+gsave 10 dict begin+7645 394 24 24 ellipse_path+stroke+gsave 10 dict begin+7645 395 moveto (104) 21 14.00 -0.50 alignedtext+end grestore+end grestore++% 105+gsave 10 dict begin+7861 402 24 24 ellipse_path+stroke+gsave 10 dict begin+7861 403 moveto (105) 21 14.00 -0.50 alignedtext+end grestore+end grestore++% 104 -> 105+newpath 7670 395 moveto+7709 396 7784 399 7827 401 curveto+stroke+newpath 7826 399 moveto+7836 401 lineto+7826 404 lineto+closepath+fill+gsave 10 dict begin+7717 407 moveto ('3') 16 14.00 -0.50 alignedtext+end grestore++% 128+gsave 10 dict begin+9373 402 24 24 ellipse_path+stroke+gsave 10 dict begin+9373 403 moveto (128) 21 14.00 -0.50 alignedtext+end grestore+end grestore++% 105 -> 128+newpath 7886 402 moveto+7914 402 7963 402 8005 402 curveto+8005 402 8005 402 9229 402 curveto+9267 402 9310 402 9339 402 curveto+stroke+newpath 9338 400 moveto+9348 402 lineto+9338 405 lineto+closepath+fill+gsave 10 dict begin+8581 411 moveto (Epsilon) 42 14.00 -0.50 alignedtext+end grestore++% 107+gsave 10 dict begin+7861 336 24 24 ellipse_path+stroke+gsave 10 dict begin+7861 337 moveto (107) 21 14.00 -0.50 alignedtext+end grestore+end grestore++% 108+gsave 10 dict begin+8005 350 24 24 ellipse_path+stroke+gsave 10 dict begin+8005 351 moveto (108) 21 14.00 -0.50 alignedtext+end grestore+end grestore++% 107 -> 108+newpath 7885 338 moveto+7909 341 7945 344 7972 347 curveto+stroke+newpath 7971 344 moveto+7981 348 lineto+7971 349 lineto+closepath+fill+gsave 10 dict begin+7933 355 moveto ('4') 16 14.00 -0.50 alignedtext+end grestore++% 127+gsave 10 dict begin+9229 350 24 24 ellipse_path+stroke+gsave 10 dict begin+9229 351 moveto (127) 21 14.00 -0.50 alignedtext+end grestore+end grestore++% 108 -> 127+newpath 8030 350 moveto+8058 350 8107 350 8149 350 curveto+8149 350 8149 350 9085 350 curveto+9123 350 9166 350 9195 350 curveto+stroke+newpath 9194 348 moveto+9204 350 lineto+9194 353 lineto+closepath+fill+gsave 10 dict begin+8581 359 moveto (Epsilon) 42 14.00 -0.50 alignedtext+end grestore++% 110+gsave 10 dict begin+7933 290 24 24 ellipse_path+stroke+gsave 10 dict begin+7933 291 moveto (110) 21 14.00 -0.50 alignedtext+end grestore+end grestore++% 111+gsave 10 dict begin+8149 298 24 24 ellipse_path+stroke+gsave 10 dict begin+8149 299 moveto (111) 21 14.00 -0.50 alignedtext+end grestore+end grestore++% 110 -> 111+newpath 7958 291 moveto+7997 292 8072 295 8115 297 curveto+stroke+newpath 8114 295 moveto+8124 297 lineto+8114 300 lineto+closepath+fill+gsave 10 dict begin+8005 303 moveto ('5') 16 14.00 -0.50 alignedtext+end grestore++% 126+gsave 10 dict begin+9085 298 24 24 ellipse_path+stroke+gsave 10 dict begin+9085 299 moveto (126) 21 14.00 -0.50 alignedtext+end grestore+end grestore++% 111 -> 126+newpath 8174 298 moveto+8202 298 8251 298 8293 298 curveto+8293 298 8293 298 8941 298 curveto+8979 298 9022 298 9051 298 curveto+stroke+newpath 9050 296 moveto+9060 298 lineto+9050 301 lineto+closepath+fill+gsave 10 dict begin+8581 307 moveto (Epsilon) 42 14.00 -0.50 alignedtext+end grestore++% 113+gsave 10 dict begin+8149 232 24 24 ellipse_path+stroke+gsave 10 dict begin+8149 233 moveto (113) 21 14.00 -0.50 alignedtext+end grestore+end grestore++% 114+gsave 10 dict begin+8293 246 24 24 ellipse_path+stroke+gsave 10 dict begin+8293 247 moveto (114) 21 14.00 -0.50 alignedtext+end grestore+end grestore++% 113 -> 114+newpath 8173 234 moveto+8197 237 8233 240 8260 243 curveto+stroke+newpath 8259 240 moveto+8269 244 lineto+8259 245 lineto+closepath+fill+gsave 10 dict begin+8221 251 moveto ('6') 16 14.00 -0.50 alignedtext+end grestore++% 125+gsave 10 dict begin+8941 246 24 24 ellipse_path+stroke+gsave 10 dict begin+8941 247 moveto (125) 21 14.00 -0.50 alignedtext+end grestore+end grestore++% 114 -> 125+newpath 8318 246 moveto+8346 246 8395 246 8437 246 curveto+8437 246 8437 246 8797 246 curveto+8835 246 8878 246 8907 246 curveto+stroke+newpath 8906 244 moveto+8916 246 lineto+8906 249 lineto+closepath+fill+gsave 10 dict begin+8581 255 moveto (Epsilon) 42 14.00 -0.50 alignedtext+end grestore++% 116+gsave 10 dict begin+8221 186 24 24 ellipse_path+stroke+gsave 10 dict begin+8221 187 moveto (116) 21 14.00 -0.50 alignedtext+end grestore+end grestore++% 117+gsave 10 dict begin+8437 194 24 24 ellipse_path+stroke+gsave 10 dict begin+8437 195 moveto (117) 21 14.00 -0.50 alignedtext+end grestore+end grestore++% 116 -> 117+newpath 8246 187 moveto+8285 188 8360 191 8403 193 curveto+stroke+newpath 8402 191 moveto+8412 193 lineto+8402 196 lineto+closepath+fill+gsave 10 dict begin+8293 199 moveto ('7') 16 14.00 -0.50 alignedtext+end grestore++% 124+gsave 10 dict begin+8797 194 24 24 ellipse_path+stroke+gsave 10 dict begin+8797 195 moveto (124) 21 14.00 -0.50 alignedtext+end grestore+end grestore++% 117 -> 124+newpath 8462 194 moveto+8524 194 8690 194 8763 194 curveto+stroke+newpath 8762 192 moveto+8772 194 lineto+8762 197 lineto+closepath+fill+gsave 10 dict begin+8581 230 moveto (Epsilon) 42 14.00 -0.50 alignedtext+end grestore++% 119+gsave 10 dict begin+8365 136 24 24 ellipse_path+stroke+gsave 10 dict begin+8365 137 moveto (119) 21 14.00 -0.50 alignedtext+end grestore+end grestore++% 120+gsave 10 dict begin+8509 136 24 24 ellipse_path+stroke+gsave 10 dict begin+8509 137 moveto (120) 21 14.00 -0.50 alignedtext+end grestore+end grestore++% 119 -> 120+newpath 8390 136 moveto+8413 136 8449 136 8475 136 curveto+stroke+newpath 8474 134 moveto+8484 136 lineto+8474 139 lineto+closepath+fill+gsave 10 dict begin+8437 145 moveto ('8') 16 14.00 -0.50 alignedtext+end grestore++% 123+gsave 10 dict begin+8653 136 24 24 ellipse_path+stroke+gsave 10 dict begin+8653 137 moveto (123) 21 14.00 -0.50 alignedtext+end grestore+end grestore++% 120 -> 123+newpath 8534 136 moveto+8557 136 8593 136 8619 136 curveto+stroke+newpath 8618 134 moveto+8628 136 lineto+8618 139 lineto+closepath+fill+gsave 10 dict begin+8581 145 moveto (Epsilon) 42 14.00 -0.50 alignedtext+end grestore++% 121+gsave 10 dict begin+8365 70 24 24 ellipse_path+stroke+gsave 10 dict begin+8365 71 moveto (121) 21 14.00 -0.50 alignedtext+end grestore+end grestore++% 122+gsave 10 dict begin+8509 70 24 24 ellipse_path+stroke+gsave 10 dict begin+8509 71 moveto (122) 21 14.00 -0.50 alignedtext+end grestore+end grestore++% 121 -> 122+newpath 8390 70 moveto+8413 70 8449 70 8475 70 curveto+stroke+newpath 8474 68 moveto+8484 70 lineto+8474 73 lineto+closepath+fill+gsave 10 dict begin+8437 79 moveto ('9') 16 14.00 -0.50 alignedtext+end grestore++% 122 -> 123+newpath 8531 80 moveto+8552 90 8583 104 8610 116 curveto+8614 118 8618 119 8622 121 curveto+stroke+newpath 8623 119 moveto+8631 125 lineto+8621 123 lineto+closepath+fill+gsave 10 dict begin+8581 125 moveto (Epsilon) 42 14.00 -0.50 alignedtext+end grestore++% 2 -> 3+newpath 172 614 moveto+178 617 185 621 192 624 curveto+215 634 242 643 262 650 curveto+stroke+newpath 260 647 moveto+269 652 lineto+259 652 lineto+closepath+fill+gsave 10 dict begin+221 653 moveto (Epsilon) 42 14.00 -0.50 alignedtext+end grestore++% 2 -> 5+newpath 174 606 moveto+196 605 234 605 259 604 curveto+stroke+newpath 258 602 moveto+268 604 lineto+258 607 lineto+closepath+fill+gsave 10 dict begin+221 613 moveto (Epsilon) 42 14.00 -0.50 alignedtext+end grestore++% 9+gsave 10 dict begin+672 576 18 18 ellipse_path+stroke+gsave 10 dict begin+672 577 moveto (9) 7 14.00 -0.50 alignedtext+end grestore+end grestore++% 8 -> 9+newpath 239 552 moveto+262 552 303 552 338 552 curveto+338 552 338 552 542 552 curveto+579 552 621 562 647 569 curveto+stroke+newpath 646 566 moveto+655 571 lineto+645 571 lineto+closepath+fill+gsave 10 dict begin+401 561 moveto (Epsilon) 42 14.00 -0.50 alignedtext+end grestore++% 7 -> 9+newpath 560 600 moveto+582 595 620 587 646 582 curveto+stroke+newpath 644 580 moveto+654 580 lineto+645 585 lineto+closepath+fill+gsave 10 dict begin+607 604 moveto (Epsilon) 42 14.00 -0.50 alignedtext+end grestore++% 10+gsave 10 dict begin+804 576 20 20 ellipse_path+stroke+gsave 10 dict begin+804 577 moveto (10) 14 14.00 -0.50 alignedtext+end grestore+end grestore++% 9 -> 10+newpath 690 576 moveto+711 576 749 576 775 576 curveto+stroke+newpath 774 574 moveto+784 576 lineto+774 579 lineto+closepath+fill+gsave 10 dict begin+737 585 moveto (Epsilon) 42 14.00 -0.50 alignedtext+end grestore++% 11+gsave 10 dict begin+938 705 20 20 ellipse_path+stroke+gsave 10 dict begin+938 706 moveto (11) 14 14.00 -0.50 alignedtext+end grestore+end grestore++% 10 -> 11+newpath 819 590 moveto+842 612 891 659 918 686 curveto+stroke+newpath 918 682 moveto+923 691 lineto+914 686 lineto+closepath+fill+gsave 10 dict begin+871 675 moveto (Epsilon) 42 14.00 -0.50 alignedtext+end grestore++% 49+gsave 10 dict begin+3618 583 20 20 ellipse_path+stroke+gsave 10 dict begin+3618 584 moveto (49) 14 14.00 -0.50 alignedtext+end grestore+end grestore++% 10 -> 49+newpath 823 571 moveto+849 564 897 553 938 553 curveto+938 553 938 553 3484 553 curveto+3522 553 3564 564 3591 573 curveto+stroke+newpath 3591 570 moveto+3599 576 lineto+3589 575 lineto+closepath+fill+gsave 10 dict begin+2211 562 moveto (Epsilon) 42 14.00 -0.50 alignedtext+end grestore++% 11 -> 12+newpath 939 725 moveto+942 762 950 844 976 908 curveto+996 955 1032 1001 1054 1028 curveto+stroke+newpath 1054 1024 moveto+1058 1033 lineto+1050 1027 lineto+closepath+fill+gsave 10 dict begin+1005 1009 moveto (Epsilon) 42 14.00 -0.50 alignedtext+end grestore++% 14+gsave 10 dict begin+1072 967 20 20 ellipse_path+stroke+gsave 10 dict begin+1072 968 moveto (14) 14 14.00 -0.50 alignedtext+end grestore+end grestore++% 11 -> 14+newpath 947 723 moveto+970 769 1032 890 1059 942 curveto+stroke+newpath 1060 939 moveto+1063 949 lineto+1056 942 lineto+closepath+fill+gsave 10 dict begin+1005 897 moveto (Epsilon) 42 14.00 -0.50 alignedtext+end grestore++% 50+gsave 10 dict begin+3752 583 20 20 ellipse_path+stroke+gsave 10 dict begin+3752 584 moveto (50) 14 14.00 -0.50 alignedtext+end grestore+end grestore++% 49 -> 50+newpath 3638 583 moveto+3660 583 3697 583 3723 583 curveto+stroke+newpath 3722 581 moveto+3732 583 lineto+3722 586 lineto+closepath+fill+gsave 10 dict begin+3685 592 moveto (Epsilon) 42 14.00 -0.50 alignedtext+end grestore++% 14 -> 15+newpath 1090 976 moveto+1096 980 1103 983 1110 987 curveto+1159 1011 1217 1039 1249 1054 curveto+stroke+newpath 1247 1050 moveto+1255 1057 lineto+1245 1055 lineto+closepath+fill+gsave 10 dict begin+1139 1023 moveto (Epsilon) 42 14.00 -0.50 alignedtext+end grestore++% 17+gsave 10 dict begin+1206 967 20 20 ellipse_path+stroke+gsave 10 dict begin+1206 968 moveto (17) 14 14.00 -0.50 alignedtext+end grestore+end grestore++% 14 -> 17+newpath 1092 967 moveto+1114 967 1151 967 1177 967 curveto+stroke+newpath 1176 965 moveto+1186 967 lineto+1176 970 lineto+closepath+fill+gsave 10 dict begin+1139 976 moveto (Epsilon) 42 14.00 -0.50 alignedtext+end grestore++% 48 -> 11+newpath 954 682 moveto+976 653 1021 604 1072 605 curveto+1072 605 1072 605 3350 605 curveto+3392 604 3439 615 3465 622 curveto+stroke+newpath 957 682 moveto+949 688 lineto+953 679 lineto+closepath+fill+gsave 10 dict begin+2211 614 moveto (Epsilon) 42 14.00 -0.50 alignedtext+end grestore++% 48 -> 49+newpath 3503 622 moveto+3525 614 3564 601 3591 592 curveto+stroke+newpath 3589 590 moveto+3599 589 lineto+3591 595 lineto+closepath+fill+gsave 10 dict begin+3551 622 moveto (Epsilon) 42 14.00 -0.50 alignedtext+end grestore++% 17 -> 18+newpath 1225 975 moveto+1231 977 1238 980 1244 983 curveto+1268 992 1294 1001 1314 1008 curveto+stroke+newpath 1312 1005 moveto+1321 1010 lineto+1311 1010 lineto+closepath+fill+gsave 10 dict begin+1273 1011 moveto (Epsilon) 42 14.00 -0.50 alignedtext+end grestore++% 20+gsave 10 dict begin+1340 959 20 20 ellipse_path+stroke+gsave 10 dict begin+1340 960 moveto (20) 14 14.00 -0.50 alignedtext+end grestore+end grestore++% 17 -> 20+newpath 1226 966 moveto+1248 965 1285 963 1311 961 curveto+stroke+newpath 1310 959 moveto+1320 960 lineto+1310 964 lineto+closepath+fill+gsave 10 dict begin+1273 972 moveto (Epsilon) 42 14.00 -0.50 alignedtext+end grestore++% 47 -> 48+newpath 3357 976 moveto+3379 916 3448 728 3474 656 curveto+stroke+newpath 3471 656 moveto+3477 647 lineto+3476 657 lineto+closepath+fill+gsave 10 dict 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441 moveto+7421 442 7496 443 7539 444 curveto+stroke+newpath 7538 442 moveto+7548 444 lineto+7538 447 lineto+closepath+fill+gsave 10 dict begin+7429 465 moveto (Epsilon) 42 14.00 -0.50 alignedtext+end grestore++% 103+gsave 10 dict begin+7501 386 24 24 ellipse_path+stroke+gsave 10 dict begin+7501 387 moveto (103) 21 14.00 -0.50 alignedtext+end grestore+end grestore++% 100 -> 103+newpath 7374 423 moveto+7382 417 7391 410 7400 405 curveto+7422 395 7447 390 7468 388 curveto+stroke+newpath 7466 386 moveto+7476 387 lineto+7466 391 lineto+closepath+fill+gsave 10 dict begin+7429 417 moveto (Epsilon) 42 14.00 -0.50 alignedtext+end grestore++% 130 -> 131+newpath 9685 509 moveto+9709 512 9745 516 9772 519 curveto+stroke+newpath 9771 516 moveto+9781 520 lineto+9771 521 lineto+closepath+fill+gsave 10 dict begin+9733 527 moveto (Epsilon) 42 14.00 -0.50 alignedtext+end grestore++% 103 -> 104+newpath 7526 387 moveto+7549 389 7585 391 7611 392 curveto+stroke+newpath 7610 389 moveto+7620 393 lineto+7610 394 lineto+closepath+fill+gsave 10 dict begin+7573 401 moveto (Epsilon) 42 14.00 -0.50 alignedtext+end grestore++% 106+gsave 10 dict begin+7645 328 24 24 ellipse_path+stroke+gsave 10 dict begin+7645 329 moveto (106) 21 14.00 -0.50 alignedtext+end grestore+end grestore++% 103 -> 106+newpath 7524 377 moveto+7548 367 7586 352 7613 340 curveto+stroke+newpath 7612 338 moveto+7622 337 lineto+7613 343 lineto+closepath+fill+gsave 10 dict begin+7573 379 moveto (Epsilon) 42 14.00 -0.50 alignedtext+end grestore++% 129 -> 130+newpath 9542 457 moveto+9563 460 9593 465 9618 476 curveto+9624 479 9629 482 9634 485 curveto+stroke+newpath 9636 483 moveto+9642 491 lineto+9633 487 lineto+closepath+fill+gsave 10 dict begin+9589 485 moveto (Epsilon) 42 14.00 -0.50 alignedtext+end grestore++% 106 -> 107+newpath 7670 329 moveto+7709 330 7784 333 7827 335 curveto+stroke+newpath 7826 333 moveto+7836 335 lineto+7826 338 lineto+closepath+fill+gsave 10 dict begin+7717 360 moveto (Epsilon) 42 14.00 -0.50 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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 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+ scripts/Make_Animation view
@@ -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
+ scripts/faAnim.lefty view
@@ -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');+};