diff --git a/Data/Regex/Antimirov.hs b/Data/Regex/Antimirov.hs new file mode 100644 --- /dev/null +++ b/Data/Regex/Antimirov.hs @@ -0,0 +1,9 @@ +module Data.Regex.Antimirov + ( module Data.Regex.Antimirov.Regex + , module Data.Regex.Antimirov.Simplify + , module Data.Regex.Antimirov.Subtyping) + where + +import Data.Regex.Antimirov.Regex +import Data.Regex.Antimirov.Simplify +import Data.Regex.Antimirov.Subtyping diff --git a/Data/Regex/Antimirov/Regex.hs b/Data/Regex/Antimirov/Regex.hs new file mode 100644 --- /dev/null +++ b/Data/Regex/Antimirov/Regex.hs @@ -0,0 +1,34 @@ +{-# LANGUAGE NoMonomorphismRestriction #-} +module Data.Regex.Antimirov.Regex where + +data (Eq a, Ord a) => Regex a + = Then (Regex a) (Regex a) + | Or (Regex a) (Regex a) + | Star (Regex a) + | Empty + | Literal a + deriving (Eq, Ord, Show) + +nullable :: (Ord t) => Regex t -> Bool +nullable Empty = True +nullable (Then r1 r2) = nullable r1 && nullable r2 +nullable (Or r1 r2) = nullable r1 || nullable r2 +nullable (Star _) = True +nullable (Literal _) = False + + +( - ) = Then +( ? ) x = x # Empty +( * ) = Star +( # ) = Or +l = Literal + +infixr 7 ? +infixr 7 * +infixr 6 - +infixr 5 # + +toG :: Ord a => [a] -> Regex a +toG [] = Empty +toG l_ = foldl1 Then ((map Literal) l_) + diff --git a/Data/Regex/Antimirov/Simplify.hs b/Data/Regex/Antimirov/Simplify.hs new file mode 100644 --- /dev/null +++ b/Data/Regex/Antimirov/Simplify.hs @@ -0,0 +1,38 @@ +{-# LANGUAGE PatternGuards #-} + +module Data.Regex.Antimirov.Simplify where + +import qualified Data.Set as Set +import Data.Regex.Antimirov.Regex + +simplify (Literal a) = Literal a +simplify Empty = Empty +simplify arg@(Or _ _) = foldl1 Or (map simplify $ Set.elems $ getOr arg) + +simplify (Then r1' r2') + | Empty <- r1 = r2 + | Empty <- r2 = r1 + | otherwise = Then r1 r2 + + where + r1 = simplify r1' + r2 = simplify r2' + +simplify (Star r) + | rset == Set.empty = Empty + | otherwise = Star (simplify $ foldl1 Or $ Set.toList rset) + where + rset = Set.filter (/= Empty) $ cluster r + + +cluster Empty = Set.empty +cluster (Literal a) = Set.singleton (Literal a) +cluster (Or r1 r2) = cluster r1 `Set.union` cluster r2 +cluster a@(Then r1 r2) + | nullable r1 && nullable r2 = cluster r1 `Set.union` cluster r2 + | otherwise = Set.singleton a +cluster (Star r) = cluster r + +getOr :: Ord a => Regex a -> Set.Set (Regex a) +getOr (Or r1 r2) = getOr r1 `Set.union` getOr r2 +getOr r = Set.singleton r diff --git a/Data/Regex/Antimirov/Subtyping.hs b/Data/Regex/Antimirov/Subtyping.hs new file mode 100644 --- /dev/null +++ b/Data/Regex/Antimirov/Subtyping.hs @@ -0,0 +1,75 @@ +{-# LANGUAGE PatternGuards, FlexibleContexts, NoMonomorphismRestriction, FunctionalDependencies #-} + +module Data.Regex.Antimirov.Subtyping + ( (<:) + , match + , RegexSubtyping (..) + ) + + where + +import qualified Data.Set as Set +import Data.Regex.Antimirov.Regex (Regex (..), toG, nullable) + +class Eq a => RegexSubtyping a where + + literalSubtype :: a -> a -> Bool + literalSubtype r s = r == s + +(<:) :: (Ord a, RegexSubtyping a) => Maybe (Regex a) -> Maybe (Regex a) -> Bool +r <: s = subtyping (cl r) r s + + + +cl Nothing = 0 +cl (Just r) = cl' r + +cl' :: Ord a => Regex a -> Integer +cl' (Then r1 r2) = cl' r1 + cl' r2 +cl' (Or r1 r2) = cl' r1 + cl' r2 +cl' (Star r) = cl' r +cl' Empty = 0 +cl' (Literal _) = 1 + +subtyping :: (Ord a, RegexSubtyping a) => Integer -> Maybe (Regex a) -> Maybe (Regex a) -> Bool +subtyping _ Nothing _ = True +subtyping _ (Just _) Nothing = False +subtyping i (Just r) (Just s) + | nullable r && (not.nullable) s = False + | r == Empty = nullable s + | r == s = True + | Star r' <- r, Star s' <- s = Just (Or r' Empty) <: Just (Star s') + | i < 0 = True + | otherwise = setAnd (Set.map (uncurry $ subtyping (i - 1)) (deltaIneqs (r, s))) + +setAnd = Set.fold (&&) True + +type Lin a = Set.Set (a, Regex a) + +lf :: Ord a => Regex a -> Lin a +lf Empty = Set.empty +lf (Literal a) = Set.singleton (a, Empty) +lf (Then t u) + | nullable t = Set.union (lf t *** u) (lf u) + | otherwise = lf t *** u +lf (Or t u) = Set.union (lf t) (lf u) +lf a@(Star r) = lf r *** a + + +concatLf :: Ord a => (a, Regex a) -> Regex a -> (a, Regex a) +concatLf a Empty = a +concatLf (x, Empty) t = (x, t) +concatLf (x, e) t = (x, Then e t) + +(***) :: Ord a => Lin a -> Regex a -> Lin a -- FIXME: INV: r, e, /= Empty +a *** t = Set.map ((flip concatLf) t) a + +deltaIneqs :: (RegexSubtyping a, Ord a) => (Regex a, Regex a) -> Set.Set (Maybe (Regex a), Maybe (Regex a)) +deltaIneqs (r, s) = let ds = lf s in Set.map (\ (a, r') -> (Just r', sigma $ Set.map snd $ Set.filter (literalSubtype a . fst) ds)) (lf r) + +sigma :: Ord a => Set.Set (Regex a) -> Maybe (Regex a) +sigma s = Set.fold (\a b -> case b of Nothing -> Just a; Just b' -> Just (Or b' a)) Nothing s + +match :: (RegexSubtyping a, Ord a) => Maybe (Regex a) -> [a] -> Bool +match Nothing _ = False +match (Just r) l = Just (toG l) <: Just r diff --git a/Data/Regex/Antimirov/SubtypingList.hs b/Data/Regex/Antimirov/SubtypingList.hs new file mode 100644 --- /dev/null +++ b/Data/Regex/Antimirov/SubtypingList.hs @@ -0,0 +1,75 @@ +{-# LANGUAGE PatternGuards, FlexibleContexts, NoMonomorphismRestriction, FunctionalDependencies #-} + +-- This is like Data.Regex.Antimirov.Subtyping but uses Lists instead of Sets for +-- the implentation. + +module Data.Regex.Antimirov.SubtypingList + ( (<:) + , match + , RegexSubtyping (..) + ) + + where + +import Data.Regex.Antimirov.Regex (Regex (..), toG, nullable) + +class Eq a => RegexSubtyping a where + + literalSubtype :: a -> a -> Bool + literalSubtype r s = r == s + +(<:) :: (Ord a, RegexSubtyping a) => Maybe (Regex a) -> Maybe (Regex a) -> Bool +r <: s = subtyping (cl r) r s + + +cl Nothing = 0 +cl (Just r) = cl' r + +cl' :: Ord a => Regex a -> Integer +cl' (Then r1 r2) = cl' r1 + cl' r2 +cl' (Or r1 r2) = cl' r1 + cl' r2 +cl' (Star r) = cl' r +cl' Empty = 0 +cl' (Literal _) = 1 + +subtyping :: (Ord a, RegexSubtyping a) => Integer -> Maybe (Regex a) -> Maybe (Regex a) -> Bool +subtyping _ Nothing _ = True +subtyping _ (Just _) Nothing = False +subtyping i (Just r) (Just s) + | nullable r && (not.nullable) s = False + | r == Empty = nullable s + | r == s = True + | Star r' <- r, Star s' <- s = Just (Or r' Empty) <: Just (Star s') + | i < 0 = True + | otherwise = and (map (uncurry $ subtyping (i - 1)) (deltaIneqs (r, s))) + + +type Lin a = [(a, Regex a)] + +lf :: Ord a => Regex a -> Lin a +lf Empty = [] +lf (Literal a) = [(a, Empty)] +lf (Then t u) + | nullable t = (lf t *** u) ++ lf u + | otherwise = lf t *** u +lf (Or t u) = lf t ++ lf u +lf a@(Star r) = lf r *** a + + +concatLf :: Ord a => (a, Regex a) -> Regex a -> (a, Regex a) +concatLf a Empty = a +concatLf (x, Empty) t = (x, t) +concatLf (x, e) t = (x, Then e t) + +(***) :: Ord a => Lin a -> Regex a -> Lin a -- FIXME: INV: r, e, /= Empty +a *** t = map ((flip concatLf) t) a + +deltaIneqs :: (RegexSubtyping a, Ord a) => (Regex a, Regex a) -> [(Maybe (Regex a), Maybe (Regex a))] +deltaIneqs (r, s) = let ds = lf s in map (\ (a, r') -> (Just r', sigma $ map snd $ filter (literalSubtype a . fst) ds)) (lf r) + +sigma :: Ord a => [(Regex a)] -> Maybe (Regex a) +sigma s = foldl (\a b -> case a of Nothing -> Just b; Just a' -> Just (Or a' b)) Nothing s + +match :: (RegexSubtyping a, Ord a) => Maybe (Regex a) -> [a] -> Bool +match Nothing _ = False +match (Just r) l = Just (toG l) <: Just r diff --git a/LICENSE b/LICENSE new file mode 100644 --- /dev/null +++ b/LICENSE @@ -0,0 +1,674 @@ + GNU GENERAL PUBLIC LICENSE + Version 3, 29 June 2007 + + Copyright (C) 2007 Free Software Foundation, Inc. + Everyone is permitted to copy and distribute verbatim copies + of this license document, but changing it is not allowed. + + Preamble + + The GNU General Public License is a free, copyleft license for +software and other kinds of works. + + The licenses for most software and other practical works are designed +to take away your freedom to share and change the works. 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If your program is a subroutine library, you +may consider it more useful to permit linking proprietary applications with +the library. If this is what you want to do, use the GNU Lesser General +Public License instead of this License. But first, please read +. diff --git a/Setup.hs b/Setup.hs new file mode 100644 --- /dev/null +++ b/Setup.hs @@ -0,0 +1,2 @@ +import Distribution.Simple +main = defaultMain diff --git a/antimirov.cabal b/antimirov.cabal new file mode 100644 --- /dev/null +++ b/antimirov.cabal @@ -0,0 +1,26 @@ +name: antimirov +version: 0.1.0 +license: GPL +license-file: LICENSE +copyright: Copyright (c) 2009 Marcel Manthe +maintainer: Rick Kaudewitz +stability: experimental +category: Language, Math +synopsis: Define the language containment (=subtyping) relation on regulare expressions. +description: This is a generalization of regex-"matching". We use Antimirovs algorithm. + Tests are provided, too. +ghc-options: -Wall -fno-warn-missing-signatures +exposed-Modules: + Data.Regex.Antimirov + Data.Regex.Antimirov.Regex + Data.Regex.Antimirov.Subtyping + Data.Regex.Antimirov.SubtypingList + Data.Regex.Antimirov.Simplify +build-depends: containers, base, QuickCheck +hs-source-dirs: . +build-type: Simple + +executable: test +ghc-options: -Wall -fno-warn-orphans -fno-warn-missing-signatures +main-is: TestAntimirov.hs +hs-source-dirs: test . diff --git a/test/TestAntimirov.hs b/test/TestAntimirov.hs new file mode 100644 --- /dev/null +++ b/test/TestAntimirov.hs @@ -0,0 +1,174 @@ +{-# LANGUAGE TypeSynonymInstances, PostfixOperators #-} +module Main where + +import Control.Monad +import Prelude hiding ((+), (-), (*)) + +import Test.QuickCheck hiding (test, ok) + +import Data.Regex.Antimirov hiding ( (<:), match ) +import qualified Data.Regex.Antimirov as R + +(<:) a b = (Just a) R.<: (Just b) +match r l_ = R.match (Just r) l_ + +test :: (RegexSubtyping sy, Show sy, Ord sy) => Regex sy -> ([[sy]], [[sy]]) -> IO () +test r (pos, neg) = + let + fun = map (\g -> (match r g, g)) + (mPos, mNeg) = (fun pos, fun neg) + errPos = filter (not . fst) mPos + errNeg = filter fst mNeg + in unless (null $ errPos ++ errNeg) (do + putStr $ show r + -- putStrLn $ show ndfa + putStrLn $ show errPos ++ " " ++ show errNeg) + +trick, t, p', p :: Regex Char +trick = (((l 'A')?)*) +t = l 'A' - l 'B' + +p' = ((l 'A') ?) - ((l 'B') ?) +p = (p'*) + +assert :: String -> Bool -> a -> a +assert s b r = if b then r else error s + +instance RegexSubtyping () + +instance RegexSubtyping String + +instance RegexSubtyping Char where + literalSubtype _ '.' = True + literalSubtype r s = r == s + + +data T = Element String (Regex T) | Any deriving (Ord, Eq, Show) + +instance RegexSubtyping T where + + literalSubtype (Element n1 c1) (Element n2 c2) = n1 == n2 && c1 <: c2 + literalSubtype _ Any = True + literalSubtype r s = r == s + +compare' :: (RegexSubtyping sy, Show sy, Ord sy, Eq sy) => Regex sy -> Regex sy -> Maybe Ordering +compare' a1 a2 = case (a2 <: a1, a1 <: a2) of + (False, False) -> Nothing + (True, False) -> Just GT + (False, True) -> Just LT + (True, True) -> Just EQ + +testCmp :: (RegexSubtyping sy, Ord sy, Show sy, Eq sy) => Maybe Ordering -> Regex sy -> Regex sy -> IO () +testCmp o a1 a2 = let o' = compare' a1 a2 in do + when (o /= o') (putStrLn $ "testCmp fail: " ++ show (a1, o, a2, o')) + + + + + +main :: IO () +main = do + test t (["AB"], ["AC"]) + test ((l 'A' - ((l 'B')?) - l 'C')*) (["ACAC", "ABCAC"], ["ACC"]) + test trick (["", "A", "AAAAAA"], ["AC", "C", "AAAAC"]) + test (((l 'X') *) *) (["X"], ["A"]) + test (((l 'X') *) ?) (["XX", ""], ["A"]) + test p (["AB", "BA", "BBBB", ""], ["C"]) + let + t1 = (l 'A' - ((l 'B')*) - l 'C') + r1 = (["ABC", "ABBBBBBC", "AC"], ["BC", "C", "AABC", "ABBBBBBBBBBBBBBCC"]) + t2 = ((l 'A' `Or` l 'B') - l 'C') + r2 = (["AC", "BC"], ["ABC", "C"]) + test t1 r1 + test t2 r2 + test (t1 `Or` t2) (fst r1 ++ fst r2, []) + test (t1 `Then` t2) (zipWith (++) (fst r1) (fst r2), []) + test (t2 `Then` t1) (zipWith (++) (fst r2) (fst r1), []) + test (Empty) ([""], ["A"]) + test (Literal 'A' `Or` (Literal 'A' `Then` Literal 'B')) (["AB", "A"], ["", "B", "AA"]) + test ((Literal 'A' `Then` Literal 'B') `Or` Literal 'A') (["AB", "A"], ["", "B", "AA"]) + test (Literal 'A' `Then` (Literal 'A' *)) (["AAAAAAAAAAAA"], ["", "B"]) +-- test (Empty) (["Test the test"], [""]) + + testCmp (Just GT) (Literal 'A' `Or` Literal 'B' `Or` Literal 'C') (Literal 'A' `Or` Literal 'B') + testCmp (Just GT) ((Literal 'A' ?) `Then` (Literal 'B' ?)) (Literal 'A' `Or` Literal 'B') + testCmp (Just EQ) Empty (Empty::Regex ()) + testCmp Nothing (Literal 'A') (Literal 'B') -- not equal, not gt not lt + testCmp (Just LT) Empty (Literal 'A' *) +-- testCmp (Just EQ) (Literal "Test this test, too") Empty + testCmp Nothing ((l 'C' ?) - l 'A') ((l 'A' ?) - l 'A') + testCmp Nothing ((l 'C' *) # l 'A') (l 'C' - l 'A') + + testCmp (Just GT) (l 'C' - l '.') (l 'C' - l 'A') + testCmp (Just GT) (l '.' - l '.') (l 'C' - l 'A') + testCmp (Just GT) (l '.' *) (l 'C' - l 'A') + + testCmp (Just LT) (l 'A') (l '.' ?) + + + testCmp (Just EQ) (l 'a' - l 'b') (l 'a' - l 'b' # l 'a' - l 'b' # l 'a' - l 'b') + testCmp (Just GT) ((l "first" *) - (l "second" *)) ((l "first" - l "second")?) + + + testCmp (Just GT) (l Any *) (Then (l $ Element "e1" Empty) (l $ Element "e2" Empty)) + + testCmp (Just GT) (l Any *) (Then (l $ Element "e1" Empty) (l $ Element "e2" Empty)) + + testCmp (Just GT) (l $ Element "e1" (l Any)) (l $ Element "e1" (l $ Element "e2" Empty)) + testCmp (Just GT) (l $ Element "e1" ((l $ Element "e2" (l Any)) # Empty)) (l $ Element "e1" (Empty)) + + + testCmp (Just GT) ((l 'A' *) # (l 'B' *)) (l 'A') + testCmp (Just GT) ((l 'A' *) # (l 'B' *)) (l 'B') + testCmp (Just EQ) s_ s_ + testCmp (Just EQ) te tf + testCmp (Just LT) (l 'a' - l 'a' - l 'a') (l 'a' *) + testCmp (Just EQ) ((l 'a' - l 'b') *) ((l 'a' - l 'b') *) + testCmp Nothing ((l 'a' - l 'b') *) (((l 'a' - l 'b') *) - l 'c') + + quickCheck ((\e -> e <: e) :: Regex Char -> Bool) + + let f a b c = if a <: b && b <: c then a <: c else True + quickCheck ((\a' -> let a = simplify a' in a <: a' && a' <: a) :: Regex Char -> Bool) + quickCheck ((\a' b' c' -> let a = simplify a'; b = simplify b'; c = simplify c' in f a b c && f a c b && f b a c && f b c a && f c a b && f c b a) :: Regex Char -> Regex Char -> Regex Char -> Bool) + + testCmp (Just EQ) case1 case1 + testCmp (Just EQ) case2 case2 + testCmp (Just EQ) case3 case3 + testCmp (Just EQ) case4 case4 + + +te, tf :: Regex String +te = l "out" - ((l "in" - l "out")*) +tf = ((l "out" - l "in")*) - l "out" + + +case2, case3 :: Regex Char +case2 = ((Literal 'a' *) `Then` Literal 'c') `Then` ((Literal 'a' ?)*) + + +case3 = ((l 'b' # l 'c')*) +case4 = ((l 'b' - ((l 'a') *))*) + +case1 :: Regex Char +case1 = Or ((Then (Or (Literal 'c') (Then (Literal 'b' *) Empty)) (Literal 'c'))) (Or Empty (Literal 'c')*) + +s_ :: Regex Char +s_ = (l 'a' *) + + +instance (Arbitrary sy, Ord sy) => Arbitrary (Regex sy) where + arbitrary = frequency [ + (2, liftM Star arbitrary), + (7, liftM Literal arbitrary), + (2, liftM2 Then arbitrary arbitrary), + (2, liftM2 Or arbitrary arbitrary), + (3, return Empty)] + coarbitrary = undefined + + + +instance Arbitrary Char where + arbitrary = elements "abcd." + coarbitrary = undefined +