diff --git a/FormalLanguage/GrammarProduct.hs b/FormalLanguage/GrammarProduct.hs
new file mode 100644
--- /dev/null
+++ b/FormalLanguage/GrammarProduct.hs
@@ -0,0 +1,67 @@
+
+-- | This module contains the top-level functionality required to define
+-- "products of grammars" (or more sloppily "how to multiply dynamic
+-- programming algorithms"). Some operators (like '(><)') will check if both
+-- grammars are compatible with the operation and fail if not.
+--
+-- TODO Later on we probably will be able to multiply without restrictions.
+
+module FormalLanguage.GrammarProduct
+ ( (><)
+ , gAdd
+ , gSubtract
+ , gPower
+ ) where
+
+import Data.Monoid
+
+import FormalLanguage.CFG.Grammar
+
+import FormalLanguage.GrammarProduct.Op.Greibach as Greibach
+import FormalLanguage.GrammarProduct.Op.Chomsky as Chomsky
+import FormalLanguage.GrammarProduct.Op.Linear as Linear
+import FormalLanguage.GrammarProduct.Op.Add
+import FormalLanguage.GrammarProduct.Op.Subtract as S
+import FormalLanguage.GrammarProduct.Op.Power as P
+
+
+
+-- |
+
+gAdd g h = runAdd $ (Add g) <> (Add h)
+
+gSubtract g h = S.subtract g h
+
+gPower = P.power
+
+
+
+-- | The product of two grammars.
+--
+-- In general, it is quite hard to define the product of two context-free
+-- grammars in a way that keeps associativity and also "does what we want it to
+-- do" (see paper). For linear grammars it is much easier. Also, for grammars
+-- in certain normal forms, a simpler definition is possible. Due to this, we
+-- make the choice of the actual way on how to multiply based on the type of
+-- grammars given. This, however, should only affect the resulting rules, not
+-- the (multi-tape) language that the operations yields.
+--
+-- TODO I think, left-linear could reasonably be expanded to both, left- and
+-- right-linear and maybe linear in general.
+--
+-- NOTE A proof for associativity is possible, but generally hard, so we prefer
+-- to let the framework perform the proof for us.
+
+(><) :: Grammar -> Grammar -> Grammar
+g >< h
+ | isLeftLinear g && isLeftLinear h = runLinear $ Linear g <> Linear h
+-- | isChomskyNF g && isChomskyNF h = runCNF $ CNF g <> CNF h
+-- | isGreibachNF g && isGreibachNF h = runTwoGNF $ TwoGNF g <> TwoGNF h
+ | otherwise = error "Grammars in general CFG form are not handled. You need to convert into either Greibach- or Chomsky normal form. This might change in the future"
+
+-- | The addition operation defined for two grammars of the same dimension. It
+-- forms a monoid under the 'Add' newtype.
+
+(.+) :: Grammar -> Grammar -> Grammar
+g .+ h = runAdd $ Add g <> Add h
+
diff --git a/FormalLanguage/GrammarProduct/Op/Add.hs b/FormalLanguage/GrammarProduct/Op/Add.hs
new file mode 100644
--- /dev/null
+++ b/FormalLanguage/GrammarProduct/Op/Add.hs
@@ -0,0 +1,60 @@
+{-# LANGUAGE FlexibleInstances #-}
+
+module FormalLanguage.GrammarProduct.Op.Add where
+
+import Control.Lens
+import Control.Lens.Fold
+import Control.Newtype
+import Data.List (genericReplicate)
+import Data.Monoid hiding ((<>))
+import Data.Semigroup
+import qualified Data.Set as S
+import Text.Printf
+
+import FormalLanguage.CFG.Grammar
+
+
+
+-- | Add two grammars. Implemented as the union of production rules without any
+-- renaming.
+
+newtype Add a = Add {runAdd :: a}
+
+
+
+-- | Note that the semigroup on Add will create a new rule S_gh -> S_g | S_h in
+-- case two start symbols with different rhs exist (If S_g, S_h are the same,
+-- there is no problem).
+
+instance Semigroup (Add Grammar) where
+ (Add l) <> (Add r)
+ | gDim l /= gDim r
+ = error $ printf "ERROR: grammars \n%s\n and \n%s\n have different dimensions, cannot unify. (add %d %d)"
+ (show l)
+ (show r)
+ (gDim l)
+ (gDim r)
+ | otherwise = Add $ Grammar (l^.tsyms <> r^.tsyms)
+ (l^.nsyms <> r^.nsyms) -- TODO add the newly created symbol to the non-terminals (or maybe just run ``fix T+N 's from the rules?'')
+ (l^.epsis <> r^.epsis)
+ (l^.rules <> r^.rules <> t)
+ s
+ (l^.name <> r^.name)
+ where s = case (l^.start,r^.start) of
+ (Nothing, Nothing) -> Nothing
+ (Nothing, Just k ) -> Just k
+ (Just k , Nothing) -> Just k
+ (Just k , Just l ) -> if k==l then Just k else error "need to create new symbol, see note on Semigroup (Add Grammar)"
+ t = case (l^.start,r^.start) of
+ (Just k , Just l ) -> if k==l then S.empty else error "this will create the new rule"
+ _ -> S.empty
+ --(if l^.start == r^.start
+ -- then l^.start
+ -- else error "maybe add another rule and a unique start symbol?")
+
+instance Monoid (Add Grammar) where
+ mempty = Add $ Grammar S.empty S.empty S.empty S.empty Nothing ""
+ mappend = (<>)
+
+-- idempotency is not made explicit here
+
diff --git a/FormalLanguage/GrammarProduct/Op/Chomsky.hs b/FormalLanguage/GrammarProduct/Op/Chomsky.hs
new file mode 100644
--- /dev/null
+++ b/FormalLanguage/GrammarProduct/Op/Chomsky.hs
@@ -0,0 +1,157 @@
+{-# LANGUAGE UnicodeSyntax #-}
+{-# LANGUAGE LambdaCase #-}
+{-# LANGUAGE PatternGuards #-}
+
+module FormalLanguage.GrammarProduct.Op.Chomsky where
+
+import Control.Applicative
+import Control.Lens
+import Control.Lens.Fold
+import Control.Newtype ()
+import Data.Function (on)
+import Data.List (genericReplicate,replicate,groupBy)
+import Data.Maybe
+import Data.Monoid hiding ((<>))
+import Data.Semigroup
+import qualified Data.Set as S
+import Text.Printf
+import System.IO.Unsafe
+
+import FormalLanguage.CFG.Grammar
+import FormalLanguage.CFG.Parser
+import FormalLanguage.CFG.PrettyPrint.ANSI
+
+import FormalLanguage.GrammarProduct.Op.Common
+
+
+
+newtype CNF = CNF { runCNF :: Grammar }
+
+instance Semigroup CNF where
+ (CNF g) <> (CNF h) = CNF $ Grammar ts ns es rs s (g^.name ++ h^.name) where
+ ts = S.fromList $ g^..tsyms.folded ++ h^..tsyms.folded
+ ns = collectNonTerminals rs -- this is needed since we generate completely new non-terminal symbols
+ es = S.fromList $ g^..epsis.folded ++ h^..epsis.folded
+ rs = S.fromList
+ . concat
+ $ [ chomskyCombine l r | l <- g^..rules.folded, r <- h^..rules.folded ]
+ s = liftA2 (\l r -> Symb $ l^.symb ++ r^.symb) (g^.start) (h^.start)
+
+instance Monoid CNF where
+ mempty = CNF $ Grammar S.empty S.empty S.empty (S.singleton undefined) (Just $ Symb []) ""
+ mappend = (<>)
+
+-- | Combine production rules a la Chomsky normal form.
+--
+-- TODO We need to be able to generate fresh rule name, as we are splitting
+-- rules here! (this means that we need to lift this stuff into a
+-- name-generating monad)
+
+chomskyCombine :: Rule -> Rule -> [Rule]
+chomskyCombine (Rule l f rs) (Rule a g bs)
+ | [r] <- rs, [b] <- bs, isSymbT r, isSymbT b
+ = [Rule (Symb $ l^.symb ++ a^.symb) [] {- (f++g) -} [Symb $ r^.symb ++ b^.symb]]
+ | [r1,r2] <- rs, [b1,b2] <- bs, isSymbN r1, isSymbN r2, isSymbN b1, isSymbN b2
+ = [Rule (Symb $ l^.symb ++ a^.symb) [] {- (f++g) -} [Symb $ r1^.symb ++ b1^.symb, Symb $ r2^.symb ++ b2^.symb]]
+ | [r] <- rs, [b1,b2] <- bs, isSymbT r, isSymbN b1, isSymbN b2
+ = let (z1,zs1) = symbToRules r b1
+ (z2,zs2) = symbToRules r b2
+ in zs1 ++ zs2 ++ {-concatMap (extendRederive (length $ l^.symb) (length $ a^.symb))-}
+ [ Rule (Symb $ l^.symb ++ a^.symb) [] {- (f++g) -} [ {- Symb $ r^.symb ++ b1^.symb -} z1 , Symb $ genEps r ++ b2^.symb]
+ , Rule (Symb $ l^.symb ++ a^.symb) [] {- (f++g) -} [Symb $ genEps r ++ b1^.symb, z2 {- Symb $ r^.symb ++ b2^.symb -} ]
+ ]
+ | [r1,r2] <- rs, [b] <- bs, isSymbN r1, isSymbN r2, isSymbT b
+ = let (z1,zs1) = symbToRules r1 b
+ (z2,zs2) = symbToRules r2 b
+ in zs1 ++ zs2 ++ {-concatMap (extendRederive (length $ l^.symb) (length $ a^.symb))-}
+ [ Rule (Symb $ l^.symb ++ a^.symb) [] {- (f++g) -} [{- Symb $ r1^.symb ++ b^.symb -} z1 , Symb $ r2^.symb ++ genEps b]
+ , Rule (Symb $ l^.symb ++ a^.symb) [] {- (f++g) -} [Symb $ r1^.symb ++ genEps b, z2 {- Symb $ r2^.symb ++ b^.symb -} ]
+ ]
+ --
+ -- extended Chomsky: Non-terminal -> Non-terminal
+ --
+ {-
+ | [r] <- rs, [b] <- bs, nSymb r, nSymb b
+ = [ Rule (Symb $ l^.symb ++ a^.symb) [] [ Symb $ r^.symb ++ b^.symb ] ]
+ | [r] <- rs, [b1,b2] <- bs, nSymb r, nSymb b1, nSymb b2
+ = []
+ | [r1,r2] <- rs, [b] <- bs, nSymb r1, nSymb r2, nSymb b
+ = []
+ | [r] <- rs, [b] <- bs
+ = []
+ -}
+ {-
+ = [ Rule (Symb $ l^.symb ++ a^.symb) [] [ Symb $ r^.symb ++ b1^.symb, Symb $ genEps r ++ b2^.symb ]
+ , Rule (Symb $ l^.symb ++ a^.symb) [] [ Symb $ genEps r ++ b1^.symb, Symb $ r^.symb ++ b2^.symb ]
+ ]
+ -}
+ --
+ -- extended Chomsky above
+ --
+ | otherwise = unsafePerformIO $ do
+ print "======"
+ printDoc $ rulesDoc $ S.singleton $ Rule l f rs
+ printDoc $ rulesDoc $ S.singleton $ Rule a g bs
+ fail "cannot handle (rule is not CNF):"
+ -- | otherwise = error $ "cannot handle (rule is not CNF): " ++ show (printDoc $ rulesDoc $ S.singleton $ Rule l f rs, Rule a g bs)
+
+{-
+-- | Extend mixed rules and rederive CNF
+
+extendRederive :: Int -> Int -> Rule -> [Rule]
+extendRederive α β (Rule l f [r1,r2])
+ | not (tSymb r1) && not (nSymb r1) && nSymb r2
+ = let (newN,epsN,trmN,epsT) = genNewSymbols α β r1
+ in [ Rule l f [newN,r2]
+ , Rule newN ( {- "nwNL_": -} f) [epsN,trmN]
+ , Rule newN ( {- "nwNR_": -} f) [trmN,epsN]
+ , Rule trmN ( {- "trmN_": -} f) [epsT]
+ ]
+ | nSymb r1 && not (tSymb r2) && not (nSymb r2)
+ = let (newN,epsN,trmN,epsT) = genNewSymbols α β r2
+ in [ Rule l f [r1,newN]
+ , Rule newN ( {- "nwNL_": -} f) [epsN,trmN]
+ , Rule newN ( {- "nwNR_": -} f) [trmN,epsN]
+ , Rule trmN ( {- "trmN_": -} f) [epsT]
+ ]
+extendRederive _ _ r = error $ "cannot handle (rule not in extendRederive form for CNF): " ++ show r
+
+genNewSymbols :: Int -> Int -> Symb -> (Symb,Symb,Symb,Symb)
+genNewSymbols α β x = (newN, epsN, trmN, epsT) where
+ -- the new non-terminal, with term TN's replaced by non-term TN with same name (plus extension)
+ newN = Symb . map (\case (T s) -> N ("N"++s) Singular ; z -> z) $ x^.symb
+ -- the new non-terminal, with terms replaced by epsilons
+ epsN = Symb . map (\case (T s) -> eps ; z -> z) $ x^.symb
+ -- the new non-terminal for the terminal symbol, with terms replaced by non-term symbols
+ -- TODO we can't just replace all N here with eps, tome could have been created from other prods.
+ trmN = Symb . map (\case (T s) -> N ("T"++s) Singular ; N _ _ -> eps; z -> z) $ x^.symb
+ -- finally the terminal
+ epsT = Symb . map (\case (N _ _) -> eps ; z -> z) $ x^.symb
+-}
+
+-- |
+
+symbToRules :: Symb -> Symb -> (Symb, [Rule])
+symbToRules u' l'
+ | isSymbN u' && isSymbT l' = go u' l'
+ | isSymbT u' && isSymbN l' = let (s,rs) = go (over symb reverse l') (over symb reverse u')
+ in ( over symb reverse s
+ , map (\(Rule l [] rs) -> Rule (over symb reverse l) [] (map (over symb reverse) rs)) rs
+ )
+ | otherwise = error $ "incompatible upper/lower: " ++ show (u',l')
+ where
+ -- in 'n' we have the partial non-terminal, in 't' the partial terminal
+ go n t =
+ let t' = Symb $ map (\case (T s) -> (N ("T"++s) Singular) ; z -> z) $ t^.symb
+ in ( Symb $ n^.symb ++ t'^.symb
+ , [ Rule (Symb $ n^.symb ++ t'^.symb) [] [ Symb $ n^.symb ++ genEps t, Symb $ genEps n ++ genTermStar t ]
+ , Rule (Symb $ n^.symb ++ t'^.symb) [] [ Symb $ genEps n ++ genTermStar t, Symb $ n^.symb ++ genEps t ]
+ , Rule (Symb $ genEps n ++ genTermStar t) [] [ Symb $ genEps n ++ t^.symb ]
+ ]
+ )
+
+-- | Generate a certain number of epsilons
+
+genTermStar :: Symb -> [TN]
+genTermStar s = map (\case (T s) -> N ("S"++s) Singular ; z -> z) $ s^.symb
+
diff --git a/FormalLanguage/GrammarProduct/Op/Chomsky/Proof.hs b/FormalLanguage/GrammarProduct/Op/Chomsky/Proof.hs
new file mode 100644
--- /dev/null
+++ b/FormalLanguage/GrammarProduct/Op/Chomsky/Proof.hs
@@ -0,0 +1,76 @@
+
+module FormalLanguage.GrammarProduct.Op.Chomsky.Proof where
+
+import Control.Lens
+import Control.Lens.Fold
+import Control.Newtype ()
+import Data.List (genericReplicate)
+import Data.Monoid hiding ((<>))
+import Data.Semigroup
+import qualified Data.Set as S
+import Text.Printf
+import Data.List (groupBy)
+import Data.Function (on)
+import Data.Maybe
+import Control.Applicative
+
+import Text.PrettyPrint.ANSI.Leijen hiding ((<>))
+import Text.Trifecta --
+import qualified Data.ByteString.Char8 as B
+import Control.Monad.Trans.State.Strict
+import Data.Default
+import Text.Trifecta.Delta
+
+import FormalLanguage.CFG.Grammar
+import FormalLanguage.CFG.PrettyPrint.ANSI
+import FormalLanguage.CFG.PrettyPrint.LaTeX
+import FormalLanguage.CFG.Parser
+
+import FormalLanguage.GrammarProduct.Op.Chomsky
+
+
+
+-- * Proof of associativity of the 2-GNF.
+
+-- | Run the 2-gnf grammar with the TwoGNF monoid which observes the 2 star
+-- cases.
+
+cNFassociativity :: (Grammar, Grammar, S.Set Rule, S.Set Rule, Bool)
+cNFassociativity = ( l
+ , r
+ , (l^.rules) S.\\ (r^.rules)
+ , (r^.rules) S.\\ (l^.rules)
+ , l^.rules == r^.rules) where
+ l = runCNF $ (CNF g <> CNF g) <> CNF g
+ r = runCNF $ CNF g <> (CNF g <> CNF g)
+ g = cNFgrammar
+
+cNFs = g where
+ g = runCNF $ (CNF h <> CNF h)
+ h = cNFgrammar
+
+showTwo = printDoc $ grammarDoc $ runCNF $ CNF cNFgrammar <> CNF cNFgrammar
+
+-- * The simple 2-gnf grammar to run the proof on.
+
+-- | Very simple 2-gnf form for proofs.
+
+cNFgrammar = case g of
+ Success g' -> g'
+ Failure f -> error $ show f
+ where
+ g = parseGrammar "testGrammar" twoGNF
+ twoGNF = unlines
+ [ "Grammar: CNF"
+ , "N: A"
+ , "N: B"
+ , "N: C"
+-- , "N: Sa"
+ , "T: a"
+ , "A -> twoN <<< B C"
+ , "A -> oneT <<< a"
+-- , "A -> oneN <<< Sa"
+-- , "Sa -> oneT <<< a"
+ , "//"
+ ]
+
diff --git a/FormalLanguage/GrammarProduct/Op/Common.hs b/FormalLanguage/GrammarProduct/Op/Common.hs
new file mode 100644
--- /dev/null
+++ b/FormalLanguage/GrammarProduct/Op/Common.hs
@@ -0,0 +1,37 @@
+{-# LANGUAGE LambdaCase #-}
+
+module FormalLanguage.GrammarProduct.Op.Common where
+
+import qualified Data.Set as S
+import Control.Lens
+
+import FormalLanguage.CFG.Grammar
+
+
+
+-- | Collect all terminal symbols from a set of rules.
+--
+-- TODO move to FormalGrammars library
+--
+-- TODO i guess, this collects multidim stuff for now!!!
+
+collectTerminals :: S.Set Rule -> S.Set Symb
+collectTerminals = S.fromList . filter isSymbT . concatMap _rhs . S.toList
+
+-- | Collect all non-terminal symbols from a set of rules.
+--
+-- TODO move to FormalGrammars library
+
+collectNonTerminals :: S.Set Rule -> S.Set Symb
+collectNonTerminals = S.fromList . filter isSymbN . concatMap (\r -> r^.lhs : r^.rhs) . S.toList
+
+collectEpsilons :: S.Set Rule -> S.Set TN
+collectEpsilons = S.fromList
+ . filter (\case E -> True ; z -> False)
+ . concatMap (view symb)
+ . concatMap _rhs
+ . S.toList
+
+genEps :: Symb -> [TN]
+genEps s = replicate (length $ s^.symb) E
+
diff --git a/FormalLanguage/GrammarProduct/Op/Greibach.hs b/FormalLanguage/GrammarProduct/Op/Greibach.hs
new file mode 100644
--- /dev/null
+++ b/FormalLanguage/GrammarProduct/Op/Greibach.hs
@@ -0,0 +1,135 @@
+{-# LANGUAGE ParallelListComp #-}
+
+module FormalLanguage.GrammarProduct.Op.Greibach where
+
+import Control.Applicative
+import Control.Lens
+import Control.Lens.Fold
+import Control.Newtype ()
+import Data.Function (on)
+import Data.List (genericReplicate)
+import Data.List (groupBy)
+import Data.Maybe
+import Data.Monoid hiding ((<>))
+import Data.Semigroup
+import qualified Data.Set as S
+import Text.Printf
+
+import Text.Trifecta --
+import qualified Data.ByteString.Char8 as B
+import Control.Monad.Trans.State.Strict
+import Data.Default
+import Text.Trifecta.Delta
+
+import FormalLanguage.CFG.Grammar
+import FormalLanguage.CFG.Parser
+
+import FormalLanguage.GrammarProduct.Op.Common
+
+
+
+-- * Proof of associativity of the 2-GNF.
+
+-- | Wrap a grammar in 2-GNF form.
+--
+-- The 2-GNF has rules of the form: X -> a | aY | aYZ with "a" terminal, "Y",
+-- "Z" non-terminals.
+
+newtype TwoGNF = TwoGNF {runTwoGNF :: Grammar}
+
+-- | Construct a grammar product for a grammar in 2-GNF form.
+--
+-- TODO check if grammar is in 2-GNF!
+
+instance Semigroup TwoGNF where
+ (TwoGNF g) <> (TwoGNF h) = TwoGNF $ Grammar ts ns es rs s (g^.name ++ h^.name) where
+ ts = collectTerminals rs
+ ns = collectNonTerminals rs
+ es = g^.epsis <> h^.epsis -- this is kind of sketchy
+ rs = S.fromList
+ . map starRemove
+ . catMaybes
+ $ [ l <.> r
+ | l <- concatMap (starExtend $ gDim g) . S.toList $ g^.rules
+ , r <- concatMap (starExtend $ gDim h) . S.toList $ h^.rules
+ ]
+ s = liftA2 (\l r -> Symb $ l^.symb ++ r^.symb) (g^.start) (h^.start)
+ (<.>) :: Rule -> Rule -> Maybe Rule
+ a <.> b | ((Just $ a^.lhs)==g^.start) `exactlyOne` ((Just $ b^.lhs)==h^.start) = Nothing
+ a <.> b = Just
+ $ Rule (Symb $ a^.lhs.symb ++ b^.lhs.symb)
+ [""]
+ (zipWith (\x y -> Symb $ x^.symb ++ y^.symb) (a^.rhs) (b^.rhs))
+ exactlyOne False True = True
+ exactlyOne True False = True
+ exactlyOne _ _ = False
+ -- | Extend a rule with ``epsilon-type'' productions to create 2-GNF for all rules
+ starExtend :: Int -> Rule -> [Rule]
+ starExtend k (Rule l f [t]) = [ Rule l f [t,stars k, stars k]]
+ starExtend k (Rule l f [t,n]) = [ Rule l f [t,n,stars k]
+ , Rule l f [t,stars k,n]
+ ]
+ -- assuming that we have a 2-gnf at most
+ starExtend k r = [r]
+ stars :: Int -> Symb
+ stars k = Symb $ replicate k E
+ -- | Remove star-online columns.
+ starRemove :: Rule -> Rule
+ starRemove = over rhs (filter (any (not . isEpsilon) . getSymbs))
+ isEpsilon E = True
+ isEpsilon _ = False
+
+-- | The start symbol for this instance needs to be "Just []" so as to preserve
+-- the start symbol in a chain of (<>) operations.
+
+instance Monoid TwoGNF where
+ mempty = TwoGNF $ Grammar S.empty S.empty S.empty (S.singleton undefined) (Just $ Symb []) ""
+ mappend = (<>)
+
+
+
+-- | Takes lists of symbols and aligns according to being
+-- terminal/non-terminal:
+--
+-- aXbc / aXYb =>
+--
+-- aX-bc a-Xbc
+-- aXYb- aXYb-
+--
+-- That is, create all alignments of non-terminals, but just ``left-align'' all
+-- terminals. This will create all possible "alignments" of symbols. This is
+-- why we return a list of lists.
+
+{-
+aligned :: [Symb] -> [Symb] -> [[Symb]]
+aligned ls' rs' = go (groupBy ((==) `on` isSymbT) ls') (groupBy ((==) `on` isSymbT) rs') where
+ dl = length . getSymbs . head $ ls'
+ dr = length . getSymbs . head $ rs'
+ go :: [[Symb]] -> [[Symb]] -> [[Symb]]
+ go [] [] = []
+ go (l:ls) [] = epsR l : go ls []
+ go [] (r:rs) = epsL r : go [] rs
+ go (l:ls) (r:rs)
+ | all isSymbT l
+ && all isSymbT r = goT l r : go ls rs
+ | all isSymbN l
+ && all isSymbN r = undefined -- [ ns : gs | ns <- goN l r, gs <- go ls rs ]
+ | all isSymbT l = epsR l : go ls (r:rs)
+ | all isSymbT r = epsL r : go (l:ls) rs
+ goT [] [] = []
+ goT ls [] = epsR ls
+ goT [] rs = epsL rs
+ goT (l:ls) (r:rs) = (Symb $ l^.symb ++ r^.symb) : goT ls rs
+ goN :: [Symb] -> [Symb] -> [[Symb]]
+ goN [] [] = [[]]
+ goN (l:ls) [] = epsR [l] : goN ls []
+ goN [] (r:rs) = epsL [r] : goN [] rs
+ goN lls rrs
+ | length lls == length rrs = [[ Symb $ l^.symb ++ r^.symb | l <- lls | r <- rrs ]]
+ goN lls@(l:ls) rrs@(r:rs)
+ | length lls < length rrs = undefined
+ | length lls > length rrs = undefined
+ epsR ls = map (\(Symb s) -> Symb $ s ++ replicate dr (T "")) ls
+ epsL rs = map (\(Symb s) -> Symb $ replicate dl (T "") ++ s) rs
+-}
+
diff --git a/FormalLanguage/GrammarProduct/Op/Greibach/Proof.hs b/FormalLanguage/GrammarProduct/Op/Greibach/Proof.hs
new file mode 100644
--- /dev/null
+++ b/FormalLanguage/GrammarProduct/Op/Greibach/Proof.hs
@@ -0,0 +1,161 @@
+{-# LANGUAGE PatternGuards #-}
+{-# LANGUAGE ParallelListComp #-}
+
+module FormalLanguage.GrammarProduct.Op.Greibach.Proof where
+
+import Control.Lens
+import Control.Lens.Fold
+import Control.Newtype ()
+import Data.List (genericReplicate)
+import Data.Monoid hiding ((<>))
+import Data.Semigroup
+import qualified Data.Set as S
+import Text.Printf
+import Data.List (groupBy)
+import Data.Function (on)
+import Data.Maybe
+import Control.Applicative
+
+import Text.PrettyPrint.ANSI.Leijen hiding ((<>))
+import Text.Trifecta --
+import qualified Data.ByteString.Char8 as B
+import Control.Monad.Trans.State.Strict
+import Data.Default
+import Text.Trifecta.Delta
+
+import FormalLanguage.CFG.Grammar
+import FormalLanguage.CFG.PrettyPrint.ANSI
+import FormalLanguage.CFG.PrettyPrint.LaTeX
+import FormalLanguage.CFG.Parser
+
+import FormalLanguage.GrammarProduct.Op.Greibach
+import FormalLanguage.GrammarProduct.Op.Common
+
+
+
+-- * Proof of associativity of the 2-GNF.
+
+-- | Run the 2-gnf grammar with the TwoGNF monoid which observes the 2 star
+-- cases.
+
+twoGNFassociativity :: (Grammar, Grammar, S.Set Rule, S.Set Rule, Bool)
+twoGNFassociativity = ( l
+ , r
+ , (l^.rules) S.\\ (r^.rules)
+ , (r^.rules) S.\\ (l^.rules)
+ , l^.rules == r^.rules) where
+ l = runTwoGNF $ (TwoGNF g <> TwoGNF g) <> TwoGNF g
+ r = runTwoGNF $ TwoGNF g <> (TwoGNF g <> TwoGNF g)
+ g = twoGNFgrammar
+
+twoGNFs = g where
+ g = runTwoGNF $ (TwoGNF h <> TwoGNF h)
+ h = twoGNFgrammar
+
+assocHelper l r = ( l
+ , r
+ , (l^.rules) S.\\ (r^.rules)
+ , (r^.rules) S.\\ (l^.rules)
+ , l^.rules == r^.rules)
+
+-- * Proof that the 2 star cases are actually needed. We loose associativity
+-- without those. As this version does not preserve associativity, we keep it
+-- here, instead of the general Greibach version.
+
+newtype FailGNF = FailGNF { runFailGNF :: Grammar }
+
+-- |
+--
+-- TODO check correctness
+
+instance Semigroup FailGNF where
+ (FailGNF g) <> (FailGNF h) = FailGNF $ Grammar ts ns es rs s (g^.name ++ h^.name) where
+ ts = collectTerminals rs
+ ns = collectNonTerminals rs
+ es = g^.epsis <> h^.epsis
+ rs = S.fromList
+ . map starRemove
+ . concat
+ $ [ l <.> r
+ | l <- S.toList $ g^.rules
+ , r <- S.toList $ h^.rules
+ ]
+ s = liftA2 (\l r -> Symb $ l^.symb ++ r^.symb) (g^.start) (h^.start)
+ (<.>) :: Rule -> Rule -> [Rule]
+ a <.> b | ((Just $ a^.lhs)==g^.start) `exactlyOne` ((Just $ b^.lhs)==h^.start) = []
+ a <.> b
+ | [s,m] <- a^.rhs
+ , [t,n,o] <- b^.rhs
+ = [ Rule (Symb $ a^.lhs.symb ++ b^.lhs.symb)
+ [""]
+ [Symb $ s^.symb ++ t^.symb, Symb $ m^.symb ++ n^.symb, Symb $ stars (length $ m^.symb) ^.symb ++ o^.symb ]
+ , Rule (Symb $ a^.lhs.symb ++ b^.lhs.symb)
+ [""]
+ [Symb $ s^.symb ++ t^.symb, Symb $ stars (length $ m^.symb) ^.symb ++ n^.symb, Symb $ m^.symb ++ o^.symb ]
+ ]
+ | [s,m,o] <- a^.rhs
+ , [t,n] <- b^.rhs
+ = [ Rule (Symb $ a^.lhs.symb ++ b^.lhs.symb)
+ [""]
+ [ Symb $ s^.symb ++ t^.symb
+ , Symb $ m^.symb ++ n^.symb
+ , Symb $ o^.symb ++ stars (length $ t^.symb) ^.symb
+ ]
+ , Rule (Symb $ a^.lhs.symb ++ b^.lhs.symb)
+ [""]
+ [ Symb $ s^.symb ++ t^.symb
+ , Symb $ m^.symb ++ stars (length $ t^.symb) ^.symb
+ , Symb $ o^.symb ++ n^.symb
+ ]
+ ]
+ a <.> b = [ Rule (Symb $ a^.lhs.symb ++ b^.lhs.symb)
+ [""]
+ (take 3 $ zipWith (\l r -> Symb $ l^.symb ++ r^.symb) (a^.rhs ++ repeat (stars (gDim g)))
+ (b^.rhs ++ repeat (stars (gDim h)))
+ )
+ ]
+ exactlyOne False True = True
+ exactlyOne True False = True
+ exactlyOne _ _ = False
+ stars :: Int -> Symb
+ stars k = Symb $ replicate k E
+ -- | Remove star-online columns.
+ starRemove :: Rule -> Rule
+ starRemove = over rhs (filter (any (not . isEpsilon) . getSymbs))
+ isEpsilon E = True
+ isEpsilon _ = False
+
+
+-- | Run the 2-gnf grammar without the star cases.
+
+-- noStarFailure :: (S.Set Rule, S.Set Rule,
+noStarFailure = assocHelper l r where
+ l = runFailGNF $ (FailGNF g <> FailGNF g) <> FailGNF g
+ r = runFailGNF $ FailGNF g <> (FailGNF g <> FailGNF g)
+ g = twoGNFgrammar
+
+-- * The simple 2-gnf grammar to run the proof on.
+
+-- | Very simple 2-gnf form for proofs.
+
+twoGNFgrammar = case g of
+ Success g' -> g'
+ Failure f -> error $ show f
+ where
+ g = parseGrammar "testGrammar" twoGNF
+ twoGNF = unlines
+ [ "Grammar: TwoGNF"
+ , "N: A"
+ , "N: B"
+ , "N: C"
+ , "N: D"
+ , "T: a"
+ , "T: b"
+ , "T: c"
+-- , "S: X"
+ , "A -> three <<< a B C"
+ , "A -> two <<< b D"
+ , "A -> one <<< c"
+ , "//"
+ ]
+
diff --git a/FormalLanguage/GrammarProduct/Op/Linear.hs b/FormalLanguage/GrammarProduct/Op/Linear.hs
new file mode 100644
--- /dev/null
+++ b/FormalLanguage/GrammarProduct/Op/Linear.hs
@@ -0,0 +1,73 @@
+{-# LANGUAGE FlexibleInstances #-}
+
+-- | Direct product of two grammars.
+--
+-- Currently implemented for linear grammars. Once we move to context-free
+-- grammars with more than one non-terminal on the RHS, things become
+-- interesting.
+
+module FormalLanguage.GrammarProduct.Op.Linear where
+
+import Data.Semigroup
+import Control.Lens
+import Control.Applicative
+import qualified Data.Set as S
+import Data.List (groupBy)
+import Data.Function (on)
+
+import FormalLanguage.CFG.Grammar
+
+import FormalLanguage.GrammarProduct.Op.Common
+
+
+
+newtype Linear a = Linear {runLinear :: a}
+
+
+
+instance Semigroup (Linear Grammar) where
+ (Linear g) <> (Linear h) = Linear $ Grammar ts ns es rs s (g^.name <> h^.name) where
+ ts = g^.tsyms <> h^.tsyms
+ ns = collectNonTerminals rs
+ es = g^.epsis <> h^.epsis
+ rs = S.fromList [ direct l r | l <- g^..rules.folded, r <- h^..rules.folded ]
+ s = liftA2 (\l r -> Symb $ l^.symb ++ r^.symb) (g^.start) (h^.start)
+ direct (Rule l f rs) (Rule a g bs) = Rule (Symb $ l^.symb ++ a^.symb) (f++g) (mergeRHS rs bs)
+
+instance Monoid (Linear Grammar) where
+ mempty = Linear $ Grammar S.empty S.empty S.empty (S.singleton $ Rule (Symb []) [] []) Nothing ""
+ mappend = (<>)
+
+-- | Merges right-hand sides in a linear direct product. For full-fledged CFGs
+-- in different normal forms, see the GNF and CNF implementations.
+
+mergeRHS :: [Symb] -> [Symb] -> [Symb]
+mergeRHS [] rs = rs -- neutral element
+mergeRHS ls [] = ls -- neutral element
+mergeRHS ls' rs' = concat $ go (groupRHS ls') (groupRHS rs') where
+ dl = head ls'
+ dr = head rs'
+ go [] [] = []
+ go [] (r:rs)
+ | all isSymbT r = map (\(Symb z) -> Symb $ genEps dl ++ z) r : go [] rs
+ | all isSymbN r = let [Symb z] = r
+ in [Symb $ genEps dl ++ z] : go [] rs
+ go (l:ls) []
+ | all isSymbT l = map (\(Symb z) -> Symb $ z ++ genEps dr) l : go ls []
+ | all isSymbN l = let [Symb z] = l
+ in [Symb $ z ++ genEps dr] : go ls []
+ go (l:ls) (r:rs)
+ | all isSymbT l && all isSymbT r = goT l r : go ls rs
+ | all isSymbN l && all isSymbN r = let [Symb y] = l
+ [Symb z] = r
+ in [Symb $ y++z] : go ls rs
+ | all isSymbN l = go [l] [] ++ go ls (r:rs)
+ | all isSymbN r = go [] [r] ++ go (l:ls) rs
+ | otherwise = go [l] [] ++ go [] [r] ++ go ls rs
+ goT [] [] = []
+ goT [] (Symb t : rs) = Symb (genEps dl ++ t) : goT [] rs
+ goT (Symb t : ls) [] = Symb (t ++ genEps dr) : goT ls []
+ goT (Symb u : ls) (Symb v : rs) = Symb (u++v) : goT ls rs
+
+groupRHS = groupBy ((==) `on` isSymbT)
+
diff --git a/FormalLanguage/GrammarProduct/Op/Power.hs b/FormalLanguage/GrammarProduct/Op/Power.hs
new file mode 100644
--- /dev/null
+++ b/FormalLanguage/GrammarProduct/Op/Power.hs
@@ -0,0 +1,27 @@
+
+module FormalLanguage.GrammarProduct.Op.Power where
+
+import Control.Newtype
+import Data.Semigroup
+import Control.Lens
+import Control.Lens.Fold
+import qualified Data.Set as S
+import Data.List (genericReplicate)
+import Text.Printf
+
+import FormalLanguage.CFG.Grammar
+
+
+
+-- |
+
+power :: Grammar -> Integer -> Grammar
+power g k = Grammar ts ns es rs s nm where
+ ts = g^.tsyms
+ ns = S.map go $ g^.nsyms
+ es = g^.epsis
+ rs = S.map (\(Rule l f rs) -> Rule (go l) (f++f) (map go rs)) $ g^.rules
+ s = fmap go $ g^.start
+ nm = concat . genericReplicate k $ g^.name
+ go (Symb z) = Symb . concat $ genericReplicate k z
+
diff --git a/FormalLanguage/GrammarProduct/Op/Subtract.hs b/FormalLanguage/GrammarProduct/Op/Subtract.hs
new file mode 100644
--- /dev/null
+++ b/FormalLanguage/GrammarProduct/Op/Subtract.hs
@@ -0,0 +1,34 @@
+{-# LANGUAGE FlexibleInstances #-}
+
+module FormalLanguage.GrammarProduct.Op.Subtract where
+
+import Control.Newtype
+import Data.Semigroup
+import Control.Lens
+import Control.Lens.Fold
+import qualified Data.Set as S
+import Data.List (genericReplicate)
+import Text.Printf
+
+import FormalLanguage.CFG.Grammar
+
+import FormalLanguage.GrammarProduct.Op.Common
+
+
+
+-- | Subtract two grammars.
+
+subtract :: Grammar -> Grammar -> Grammar
+subtract l r
+ | gDim l /= gDim r = error $ printf "grammars %s and %s have different dimensions, cannot unify. (subtract)" (show l) (show r)
+ | otherwise = Grammar ts ns es rs s (l^.name ++ r^.name) where
+ ts = collectTerminals rs
+ ns = collectNonTerminals rs
+ es = collectEpsilons rs
+ rs = (l^.rules) S.\\ (r^.rules)
+ s = case (l^.start) of
+ Nothing -> Nothing
+ Just s' -> if anyOf (rules.folded.lhs) (==s') l
+ then l^.start
+ else Nothing
+
diff --git a/FormalLanguage/GrammarProduct/Parser.hs b/FormalLanguage/GrammarProduct/Parser.hs
new file mode 100644
--- /dev/null
+++ b/FormalLanguage/GrammarProduct/Parser.hs
@@ -0,0 +1,355 @@
+{-# LANGUAGE ScopedTypeVariables #-}
+{-# LANGUAGE StandaloneDeriving #-}
+{-# LANGUAGE RankNTypes #-}
+{-# LANGUAGE TemplateHaskell #-}
+{-# LANGUAGE GeneralizedNewtypeDeriving #-}
+{-# LANGUAGE NoMonomorphismRestriction #-}
+{-# LANGUAGE OverloadedStrings #-}
+
+-- | This parser extends the @FormalLanguage.Parser@ parser of single- and
+-- multi-dim grammars to accept grammar product definitions as well.
+
+module FormalLanguage.GrammarProduct.Parser where
+
+import Control.Arrow
+import Control.Applicative
+import Control.Lens
+import Control.Monad (MonadPlus(..), guard, when)
+import Control.Monad.Trans.Class
+import Control.Monad.Trans.State.Strict
+import Control.Monad.Trans.Reader
+import Data.Default
+import Data.Either
+import Data.Map (Map)
+import Data.Set (Set)
+import Debug.Trace
+import Data.List
+import qualified Data.ByteString.Char8 as B
+--import qualified Data.HashSet as H
+import qualified Data.Map as M
+import qualified Data.Set as S
+import Text.Parser.Expression
+import Text.Parser.Token.Highlight
+import Text.Parser.Token.Style
+import Text.Printf
+import Text.Trifecta
+import Text.Trifecta.Delta
+import Text.Trifecta.Result
+import Data.Semigroup ((<>),times1p)
+import qualified Control.Newtype as T
+--import Numeric.Natural.Internal
+import Prelude hiding (subtract)
+import Control.Monad
+
+import FormalLanguage.CFG.Grammar
+import FormalLanguage.CFG.Parser
+
+import FormalLanguage.GrammarProduct
+
+
+
+-- | Parse a product grammar.
+
+parseProduct :: String -> String -> Result [Grammar]
+parseProduct fname cnts = parseString
+ ((evalStateT . runGrammarP) productParser def)
+ (Directed (B.pack fname) 0 0 0 0)
+ cnts
+
+-- | Parse all grammars and grammar products, prepending to the list.
+
+productParser = go [] <* eof where
+ go gs = do
+ whiteSpace
+ g' <- option Nothing $ Just <$> (try grammar <|> grammarProduct gs)
+ case g' of
+ Nothing -> return gs
+ Just g -> go (g:gs)
+
+grammarProduct gs = do
+ reserveGI "Product:"
+ n <- identGI
+ e <- getGrammar <$> expr (M.fromList [(g^.name,g) | g<-gs])
+ reserveGI "//"
+ return $ over (name) (const n) e
+
+expr :: Map String Grammar -> Parse ExprGrammar
+expr g = e where
+ e = buildExpressionParser table term
+ table = [ [ binary "^><" highDirect AssocLeft
+ ]
+ , [ binary "><" exprDirect AssocLeft
+ , binary "*" exprPower AssocLeft
+ ]
+ , [ binary "+" exprPlus AssocLeft
+ , binary "-" exprMinus AssocLeft
+ ]
+ ]
+ term = parens e
+ <|> (choice gts "previously defined grammar")
+ <|> (ExprNumber <$> natural "integral power of grammar")
+ gts = map (fmap ExprGrammar . gterm) $ M.assocs g
+ binary n f a = Infix (f <$ reserveGI n) a
+ exprDirect l r = ExprGrammar $ (getGrammar l >< getGrammar r)
+ exprPlus l r = ExprGrammar $ gAdd (getGrammar l) (getGrammar r)
+ exprMinus l r = ExprGrammar $ gSubtract (getGrammar l) (getGrammar r)
+ exprPower l r = ExprGrammar $ gPower (getGrammar l) (getNumber r)
+ highDirect l r = error "highDirect (not active)!" -- ExprGrammar . unDirect $ times1p (Natural $ getNumber r -1) (Direct $ getGrammar l)
+
+data ExprGrammar
+ = ExprGrammar { getGrammar :: Grammar }
+ | ExprNumber { getNumber :: Integer }
+
+gterm :: (String,Grammar) -> Parse Grammar
+gterm (s,g) = g <$ reserveGI s
+
+{-
+data GS = GS
+ { _ntsyms :: Map String Integer
+ , _tsyms :: Set String
+ , _gs :: Map String Grammar
+ , _gCount :: Integer
+ , _grammarUid :: Integer
+ }
+ deriving (Show)
+
+instance Default GS where
+ def = GS
+ { _ntsyms = def
+ , _tsyms = def
+ , _gs = def
+ , _gCount = def
+ , _grammarUid = def
+ }
+
+makeLenses ''GS
+
+-- | Parsing product expressions, producing a grammar, again
+
+{-
+expr :: Map String Grammar -> Parse Grammar
+expr g = choice [directprod] where
+ directprod = do
+ gl <- choice gts
+ reserve gi "><"
+ gr <- choice gts
+ return . unDirect $ Direct gl <> Direct gr
+ gts = map gterm $ M.assocs g
+-}
+
+expr :: Map String Grammar -> Parse ExprGrammar
+expr g = e where
+ e = buildExpressionParser table term
+ table = [ [ binary "^><" highDirect AssocLeft
+ ]
+ , [ binary "><" exprDirect AssocLeft
+ , binary "*" exprPower AssocLeft
+ ]
+ , [ binary "+" exprPlus AssocLeft
+ , binary "-" exprMinus AssocLeft
+ ]
+ ]
+ term = parens e
+ <|> (choice gts "previously defined grammar")
+ <|> (ExprNumber <$> natural "integral power of grammar")
+ gts = map (fmap ExprGrammar . gterm) $ M.assocs g
+ binary n f a = Infix (f <$ reserve gi n) a
+ exprDirect l r = ExprGrammar . unDirect $ (Direct $ getGrammar l) <> (Direct $ getGrammar r)
+ exprPlus l r = ExprGrammar . unAdd $ (Add $ getGrammar l) <> (Add $ getGrammar r)
+ exprMinus l r = ExprGrammar $ subtract (getGrammar l) (getGrammar r)
+ exprPower l r = ExprGrammar $ power (getGrammar l) (getNumber r)
+ highDirect l r = ExprGrammar . unDirect $ times1p (Natural $ getNumber r -1) (Direct $ getGrammar l)
+
+data ExprGrammar
+ = ExprGrammar { getGrammar :: Grammar }
+ | ExprNumber { getNumber :: Integer }
+
+gterm :: (String,Grammar) -> Parse Grammar
+gterm (s,g) = g <$ reserve gi s
+
+-- | Grammar product
+
+gprod :: Parse Grammar
+gprod = do
+ reserve gi "Product:"
+ n <- ident gi
+ g <- use gs
+ e <- getGrammar <$> expr g
+ reserve gi "//"
+ let g = e & gname .~ n
+ gs <>= M.singleton (g ^. gname) g
+ return g
+
+data Product = Product
+ deriving (Show)
+
+-- |
+--
+-- TODO complain on indexed NTs with modulus '1'
+
+grammar :: Parse Grammar
+grammar = do
+ -- reset some information
+ ntsyms .= def
+ tsyms .= def
+ -- new grammar
+ gCount += 1
+ -- begin parsing
+ reserve gi "Grammar:"
+ n <- ident gi
+ (nts,ts) <- partitionEithers <$> ntsts
+ rs <- concat <$> some rule
+ reserve gi "//"
+ let g = Grammar (S.fromList rs) n
+ gs <>= M.singleton (g ^. gname) g
+ return g
+
+-- | Parse a single rule. Some rules come attached with an index. In that case,
+-- each rule is inflated according to its modulus.
+--
+-- TODO add @fun@ to each PR
+
+rule :: Parse [PR]
+rule = do
+ ln <- ident gi "rule: lhs non-terminal"
+ uses ntsyms (M.member ln) >>= guard (printf "undeclared NT: %s" ln)
+ i <- nTindex
+ reserve gi "->"
+ fun <- ident gi
+ reserve gi "<<<"
+ zs <- runUnlined $ some (Left <$> try ruleNts <|> Right <$> try ruleTs)
+ whiteSpace
+ s <- get
+ let ret = runReaderT (genPR fun ln i zs) s
+ return ret
+
+-- | Generate one or more production rules from a parsed line.
+
+genPR :: String -> String -> NtIndex -> [Either (String,NtIndex) String] -> ReaderT GS [] PR
+genPR f ln i xs = go where
+ go = do
+ (l,(m,k)) <- genL i
+ r <- genR m k xs
+ return $ PR [l] r [f]
+ genL NoIdx = do
+ g <- view grammarUid
+ return (Nt 1 [NTSym ln 1 0], (1,0))
+ genL (WithVar v 0) = do
+ g <- view grammarUid
+ m <- views ntsyms (M.! ln)
+ k <- lift [0 .. m-1]
+ return (Nt 1 [NTSym ln m k], (m,k))
+ genL (Range xs) = do
+ g <- view grammarUid
+ m <- views ntsyms (M.! ln)
+ k <- lift xs
+ return (Nt 1 [NTSym ln m k], (m,k))
+ genR m k [] = do
+ return []
+ genR m k (Left (n,WithVar k' p) :rs) = do
+ let (WithVar v 0) = i
+ g <- view grammarUid
+ nm <- views ntsyms (M.! n)
+ when (v/=k') $ error "oops, index var wrong"
+ rs' <- genR m k rs
+ return (Nt 1 [NTSym n m ((k+p) `mod` m)] :rs')
+ genR m k (Left (n,Range ls) :rs) = do
+ g <- view grammarUid
+ nm <- views ntsyms (M.! n)
+ l <- lift ls
+ rs' <- genR m k rs
+ return (Nt 1 [NTSym n m l] :rs')
+ genR m k (Left (n,NoIdx) :rs) = do
+ g <- view grammarUid
+ nm <- views ntsyms (M.! n)
+ when (nm>1) $ error $ printf "oops, NoIdx given, but indexed NT in: %s" (show (nm,m,k,n,rs))
+ rs' <- genR m k rs
+ return (Nt 1 [NTSym n 1 0] :rs')
+ genR m k (Right t :rs) = do
+ g <- view grammarUid
+ rs' <- genR m k rs
+ return (T 1 [TSym t] :rs')
+
+ruleNts :: ParseU (String,NtIndex)
+ruleNts = do
+ n <- ident gi "rule: nonterminal identifier"
+ i <- nTindex "rule:" -- option ("",1) $ braces ((,) <$> ident gi <*> option 0 integer) "rule: nonterminal index"
+ lift $ uses ntsyms (M.member n) >>= guard (printf "undeclared NT: %s" n)
+ return (n,i)
+
+nTindex :: ParseG NtIndex
+nTindex = option NoIdx
+ $ try (braces $ WithVar <$> ident gi <*> option 0 integer)
+ <|> try (Range <$> braces (commaSep1 integer))
+ "non-terminal index"
+
+data NtIndex
+ = WithVar String Integer
+ | Range [Integer]
+ | NoIdx
+ deriving (Show)
+
+ruleTs :: ParseU String
+ruleTs = do
+ n <- ident gi "rule: terminal identifier"
+ lift $ uses tsyms (S.member n) >>= guard (printf "undeclared T: %s" n)
+ return n
+
+ntsts :: Parse [Either NTSym TSym]
+ntsts = concat <$> some (map Left <$> nts <|> map Right <$> ts)
+
+-- |
+--
+-- TODO expand @NT@ symbols here or later?
+
+nts :: Parse [NTSym]
+nts = do
+ reserve gi "NT:"
+ n <- ident gi
+ mdl <- option 1 $ braces natural
+ let zs = map (NTSym n mdl) [0 .. mdl-1]
+ ntsyms <>= M.singleton n mdl
+ return zs
+
+ts :: Parse [TSym]
+ts = do
+ reserve gi "T:"
+ n <- ident gi
+ let z = TSym n
+ tsyms <>= S.singleton n
+ return [z]
+
+parseDesc = do
+ whiteSpace
+ {-
+ gs <- some grammar
+ let g = undefined -- M.fromList $ map ((^. gname) &&& id) gs
+ ps <- some (gprod g)
+ -}
+ gsps <- some (grammar <|> gprod)
+ eof
+ let (gs,ps) = partition ((==1) . grammarDim) gsps
+ return (gs,ps)
+
+gi = set styleReserved rs emptyIdents where
+ rs = H.fromList ["Grammar:", "NT:", "T:"]
+
+newtype GrammarLang m a = GrammarLang {runGrammarLang :: m a }
+ deriving (Functor,Applicative,Alternative,Monad,MonadPlus,Parsing,CharParsing)
+
+instance MonadTrans GrammarLang where
+ lift = GrammarLang
+ {-# INLINE lift #-}
+
+instance TokenParsing m => TokenParsing (GrammarLang m) where
+ someSpace = GrammarLang $ someSpace `buildSomeSpaceParser` haskellCommentStyle
+
+type Parse a = (Monad m, TokenParsing m, MonadPlus m) => StateT GS m a
+type ParseU a = (Monad m, TokenParsing m, MonadPlus m) => Unlined (StateT GS m) a
+type ParseG a = (Monad m, TokenParsing m, MonadPlus m) => m a
+
+instance MonadTrans Unlined where
+ lift = Unlined
+ {-# INLINE lift #-}
+-}
+
diff --git a/GramProd.hs b/GramProd.hs
new file mode 100644
--- /dev/null
+++ b/GramProd.hs
@@ -0,0 +1,130 @@
+{-# LANGUAGE OverloadedStrings #-}
+{-# LANGUAGE RecordWildCards #-}
+{-# LANGUAGE DeriveDataTypeable #-}
+
+-- | The @GramProd@ executable reads a grammatical description (from stdin or a
+-- file) and produces a set of grammars, each written into a separate file.
+--
+-- It is possible to both, produce @LaTeX@ and @Haskell@ output. The Haskell
+-- grammars require "ADPfusion" to be useful -- and you have to provide
+-- algebras that actually evaluate parses.
+
+module Main where
+
+import Control.Lens
+import Control.Monad
+import Control.Monad.IO.Class
+import Control.Monad.Trans.State.Strict
+import Data.Default
+import Data.Semigroup
+import qualified Text.LaTeX.Base.Render as Latex
+import System.Console.CmdArgs hiding (def)
+import System.IO
+import Text.PrettyPrint.ANSI.Leijen as Pretty hiding (line, (<>), (<$>))
+import Text.Printf
+import Text.Trifecta
+import Text.Trifecta.Delta
+
+import FormalLanguage.CFG.Grammar
+import FormalLanguage.CFG.PrettyPrint.ANSI
+import FormalLanguage.CFG.PrettyPrint.LaTeX
+import FormalLanguage.CFG.PrettyPrint.Haskell
+import FormalLanguage.GrammarProduct.Parser
+
+
+
+data Options
+ = LaTeX
+ { inFile :: String
+ , outFile ::String
+ }
+ | Ansi
+ { inFile :: String
+ }
+ | Haskell
+ { inFile :: String
+ , outFile :: String
+ }
+ deriving (Show,Data,Typeable)
+
+optionLatex = LaTeX
+ { inFile = ""
+ , outFile = ""
+ }
+
+optionAnsi = Ansi
+ { inFile = ""
+ }
+
+optionHaskell = Haskell
+ { inFile = ""
+ , outFile = ""
+ }
+
+main = do
+ o <- cmdArgs $ modes [optionLatex,optionAnsi,optionHaskell]
+ pr <- case (inFile o) of
+ "" -> getContents >>= return . parseProduct "stdin"
+ fn -> readFile fn >>= return . parseProduct fn
+ case pr of
+ Failure f -> putStrLn "failed:" >> printDoc f
+ Success [] -> error "you did provide input?!"
+ Success (s:ss) -> case o of
+ LaTeX{..} -> case outFile of
+ "" -> error "need to set output file name"
+ fn -> renderFile fn $ renderLaTeX 2 s
+ Ansi {..} -> printDoc $ grammarDoc s
+ Haskell{..} -> case outFile of
+ "" -> printDoc $ grammarHaskell s
+ fn -> do h <- openFile fn WriteMode
+ hPutDoc h $ grammarHaskell s
+ hClose h
+
+
+
+{-
+main :: IO ()
+main = do
+ o <- cmdArgs $ modes [optionLatex, optionHaskell]
+ let g = runGrammarLang $ flip evalStateT def $ parseDesc
+ r <- case infile o of
+ "" -> getContents >>= return . parseString g (Directed "stdin" 0 0 0 0)
+ fn -> parseFromFileEx g fn
+ case r of
+ Failure e -> liftIO $ displayIO stdout $ renderPretty 0.8 80 $ e <> linebreak
+ Success (gs,ps) -> case o of
+ Latex{..} -> do
+ let latex g = Latex.renderFile (printf "%s/%s.tex" outdir (g^.gname)) . renderGrammarLaTeX columns $ g
+ when withatoms $ mapM_ latex gs
+ mapM_ latex ps
+ Haskell{..} -> do
+ let s = renderGrammarHaskell (if withatoms then gs else [] ++ ps)
+ -- writeFile (printf "%s/%s.hs" outdir (g^.gname)) s
+ putStrLn s
+
+data Options
+ = Latex
+ { infile :: String
+ , outdir :: String
+ , withatoms :: Bool
+ , columns :: Int
+ }
+ | Haskell
+ { infile :: String
+-- , outdir :: String
+ , withatoms :: Bool
+ }
+ deriving (Show,Data,Typeable)
+
+optionLatex = Latex
+ { infile = "" &= help "grammar file to read (stdin if not given)"
+ , outdir = "." &= help "directory to put grammars in (./ if not given)"
+ , withatoms = False &= help "if set, source grammars (atoms) are written to target, too"
+ , columns = 1 &= help "align grammar to 1 or 2 columns?"
+ }
+
+optionHaskell = Haskell
+ {
+ }
+-}
+
diff --git a/GrammarProducts.cabal b/GrammarProducts.cabal
new file mode 100644
--- /dev/null
+++ b/GrammarProducts.cabal
@@ -0,0 +1,116 @@
+name: GrammarProducts
+version: 0.0.0.2
+author: Christian Hoener zu Siederdissen, 2013
+copyright: Christian Hoener zu Siederdissen, Ivo L. Hofacker, Peter F. Stadler, 2013
+homepage: http://www.tbi.univie.ac.at/~choener/
+maintainer: choener@tbi.univie.ac.at
+category: Formal Languages, Bioinformatics
+license: GPL-3
+license-file: LICENSE
+build-type: Simple
+stability: experimental
+cabal-version: >= 1.6.0
+synopsis:
+ Grammar products and higher-dimensional grammars
+description:
+ An algebra of liner and context-free grammars.
+ .
+ This library provides the implementation of our theory of
+ algebraic operations over linear and context-free grammars.
+ Using algebraic operations, it is possible to construct complex
+ dynamic programming algorithms from simpler "atomic" grammars.
+ .
+ Our most important contribution is the definition of a product
+ of grammars which naturally leads to alignment-like algorithms
+ on multiple tapes.
+ .
+ An efficient implementation of the resulting grammars is
+ possible via the ADPfusion framework. The @FormalGrammars@
+ library provides the required "Template Haskell" machinary.
+ .
+ Alternatively, the resulting grammars can also be
+ pretty-printed in various ways (LaTeX, ANSI, Haskell module
+ with signature and grammar).
+ .
+ .
+ .
+ Formal background can be found in two papers:
+ @
+ Christian Höner zu Siederdissen, Ivo L. Hofacker, and Peter F. Stadler
+ .
+ Product Grammars for Alignment and Folding
+ .
+ submitted
+ @
+ .
+ and
+ .
+ @
+ Christian Höner zu Siederdissen, Ivo L. Hofacker, and Peter F. Stadler
+ .
+ How to Multiply Dynamic Programming Algorithms
+ .
+ Brazilian Symposium on Bioinformatics (BSB 2013)
+ .
+ Lecture Notes in Bioinformatics 8213, Springer, Heidelberg
+ @
+
+
+
+Extra-Source-Files:
+ changelog
+
+library
+ build-depends:
+ base >= 4 && < 5 ,
+ ADPfusion >= 0.2.0 ,
+ ansi-wl-pprint ,
+ bytestring ,
+ containers ,
+ data-default ,
+ FormalGrammars >= 0.0.0.1 ,
+ HaTeX ,
+ lens ,
+ newtype ,
+ parsers ,
+ PrimitiveArray >= 0.5.1.0 ,
+ semigroups ,
+ transformers ,
+ trifecta
+ exposed-modules:
+ FormalLanguage.GrammarProduct
+ FormalLanguage.GrammarProduct.Op.Add
+ FormalLanguage.GrammarProduct.Op.Chomsky
+ FormalLanguage.GrammarProduct.Op.Chomsky.Proof
+ FormalLanguage.GrammarProduct.Op.Common
+ FormalLanguage.GrammarProduct.Op.Greibach
+ FormalLanguage.GrammarProduct.Op.Greibach.Proof
+ FormalLanguage.GrammarProduct.Op.Linear
+ FormalLanguage.GrammarProduct.Op.Power
+ FormalLanguage.GrammarProduct.Op.Subtract
+ FormalLanguage.GrammarProduct.Parser
+-- BioInf.GrammarProducts
+-- BioInf.GrammarProducts.Grammar
+-- BioInf.GrammarProducts.Haskell
+-- BioInf.GrammarProducts.Helper
+-- BioInf.GrammarProducts.LaTeX
+-- BioInf.GrammarProducts.Tools
+-- BioInf.GrammarProducts.TH
+ ghc-options:
+ -O2
+
+-- With grammar products, we need a refined way of turning input source files
+-- into LaTeX and Haskell modules.
+
+executable GrammarProductPP
+ build-depends:
+ cmdargs == 0.10.*
+ main-is:
+ GramProd.hs
+ ghc-options:
+ -O2
+
+source-repository head
+ type: git
+ location: git://github.com/choener/GrammarProducts
+
diff --git a/LICENSE b/LICENSE
new file mode 100644
--- /dev/null
+++ b/LICENSE
@@ -0,0 +1,675 @@
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+.
+
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/changelog b/changelog
new file mode 100644
--- /dev/null
+++ b/changelog
@@ -0,0 +1,2 @@
+0.0.0.2
+ * Products of linear and context-free grammars