FormalGrammars (empty) → 0.0.0.1
raw patch · 15 files changed
+2002/−0 lines, 15 filesdep +ADPfusiondep +HaTeXdep +ansi-wl-pprintsetup-changed
Dependencies added: ADPfusion, HaTeX, ansi-wl-pprint, base, bytestring, cmdargs, containers, data-default, lens, mtl, parsers, repa, template-haskell, text, transformers, trifecta, unordered-containers, vector
Files
- FormalGrammars.cabal +98/−0
- FormalLanguage.hs +11/−0
- FormalLanguage/CFG.hs +2/−0
- FormalLanguage/CFG/Grammar.hs +342/−0
- FormalLanguage/CFG/Parser.hs +357/−0
- FormalLanguage/CFG/PrettyPrint.hs +7/−0
- FormalLanguage/CFG/PrettyPrint/ANSI.hs +79/−0
- FormalLanguage/CFG/PrettyPrint/Haskell.hs +166/−0
- FormalLanguage/CFG/PrettyPrint/LaTeX.hs +68/−0
- FormalLanguage/CFG/QuickCheck.hs +4/−0
- FormalLanguage/CFG/TH.hs +120/−0
- GrammarPP.hs +67/−0
- LICENSE +675/−0
- Setup.hs +2/−0
- changelog +4/−0
+ FormalGrammars.cabal view
@@ -0,0 +1,98 @@+name: FormalGrammars+version: 0.0.0.1+author: Christian Hoener zu Siederdissen, 2013+copyright: Christian Hoener zu Siederdissen, 2013+homepage: http://www.tbi.univie.ac.at/~choener/gramprod/+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:+ (Context-free) grammars in formal language theory+description:+ Context-free grammars in formal language theory are sets of+ production rules, non-terminal and terminal symbols. This+ library provides basic data types and functions to manipulate+ such grammars.+ .+ Grammars can be defined in a small domain-specific language+ that is very close to typical CFG notation.+ .+ In addition, TemplateHaskell and QuasiQuoting functionality+ allow embedding thusly defined grammars in Haskell programs.+ ADPfusion then turns such a grammar into an efficient dynamic+ program. It is also possible to generate Haskell modules that+ contain the resulting grammar, signature and algebra product.+ .+ Alternatives are ansi- or LaTeX-based pretty-printing for users+ that want to implement their CFG in another language than+ Haskell.+ .+ .+ .+ 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 >= 0.2.0.3 ,+ ansi-wl-pprint >= 0.6 ,+ bytestring >= 0.10 ,+ containers ,+ data-default >= 0.5 ,+ HaTeX ,+ lens >= 3.9 ,+ mtl ,+ parsers >= 0.9 ,+ repa >= 3.2 ,+ template-haskell ,+ text ,+ transformers >= 0.3 ,+ trifecta >= 1.2 ,+ unordered-containers >= 0.2 ,+ vector >= 0.10+ exposed-modules:+ FormalLanguage+ FormalLanguage.CFG+ FormalLanguage.CFG.Grammar+ FormalLanguage.CFG.Parser+ FormalLanguage.CFG.PrettyPrint+ FormalLanguage.CFG.PrettyPrint.ANSI+ FormalLanguage.CFG.PrettyPrint.Haskell+ FormalLanguage.CFG.PrettyPrint.LaTeX+ FormalLanguage.CFG.QuickCheck+ FormalLanguage.CFG.TH+ ghc-options:++-- A Simple pretty-printer for formal grammars.++executable GrammarPP+ build-depends:+ cmdargs == 0.10.*+ main-is:+ GrammarPP.hs++source-repository head+ type: git+ location: git://github.com/choener/FormalGrammars+
+ FormalLanguage.hs view
@@ -0,0 +1,11 @@++module FormalLanguage+ ( module FormalLanguage.CFG.Grammar+ , module FormalLanguage.CFG.Parser+ ) where++import FormalLanguage.CFG.Grammar+import FormalLanguage.CFG.PrettyPrint.ANSI+import FormalLanguage.CFG.PrettyPrint.LaTeX+import FormalLanguage.CFG.Parser+
+ FormalLanguage/CFG.hs view
@@ -0,0 +1,2 @@++module FormalLanguage.CFG where
+ FormalLanguage/CFG/Grammar.hs view
@@ -0,0 +1,342 @@+{-# LANGUAGE FlexibleInstances #-}+{-# LANGUAGE GADTs #-}+{-# LANGUAGE LambdaCase #-}+{-# LANGUAGE MultiParamTypeClasses #-}+{-# LANGUAGE NoMonomorphismRestriction #-}+{-# LANGUAGE PatternGuards #-}+{-# LANGUAGE StandaloneDeriving #-}+{-# LANGUAGE TemplateHaskell #-}+{-# LANGUAGE TemplateHaskell #-}+{-# LANGUAGE TypeFamilies #-}++-- | The basic data types for formal languages up to and including context-free+-- grammars.+--+-- TODO we shall have to extend the system for multi-tape grammars to allow+-- combined terminal/non-terminal systems. This will basically mean dealing+-- with context-sensitive grammars, at which we can just fully generalize+-- everything.+--+-- TODO we need a general system to generate fresh variable names of varying+-- dimension. This is very much desired for certain operations (especially on+-- products).+--+-- BIGTODO @E _@ are actually the "None" thing in ADPfusion; while normal+-- epsilons are just terminals.++module FormalLanguage.CFG.Grammar where++import Control.Applicative+import Control.Lens+import Data.Default+import Data.Foldable+import Data.Set (Set)+import Prelude hiding (all)+import qualified Control.Lens.Indexed as Lens+import qualified Data.Set as S++++-- * Basic data types for formal grammars.++-- | Grammar indices are enumerable objects+--+-- TODO should we always assume operations "modulo"?++data Enumerable+ = Singular+ | IntBased Integer Integer -- current index, maximum index+-- | Enumerated String [String]+ deriving (Eq,Ord,Show)++_IntBased :: Prism' Enumerable (Integer,Integer)+_IntBased = prism (uncurry IntBased) $ f where+ f Singular = Left Singular+ f (IntBased c m) = Right (c,m)++ibCurrent = _IntBased . _1++ibModulus = _IntBased . _2++instance Default Enumerable where+ def = Singular++-- | A single-dimensional terminal or non-terminal symbol. @E@ is a special+-- symbol denoting that nothing should be done.+--+-- TODO write Eq,Ord by hand. Fail with error if Enumerable is not equal (this+-- should actually be caught in the combination operations).++data TN where+ -- | A terminal symbol (excluding epsilon)+ T :: String -> TN+ -- | A non-terminal symbol (again, excluding non-terminal epsilons)+ N :: String -> Enumerable -> TN+ -- | Epsilon characters, may be named differently+ E :: TN++deriving instance Show TN+deriving instance Eq TN+deriving instance Ord TN++tnName :: Lens' TN String+tnName f (T s ) = T <$> f s+tnName f (N s e) = (\s' -> N s' e) <$> f s+tnName f (E ) = (const E) <$> f "ε"++_T :: Prism' TN String+_T = prism T $ f where+ f (T s) = Right s+ f z = Left z++_N :: Prism' TN (String,Enumerable)+_N = prism (uncurry N) $ f where+ f (N s e) = Right (s,e)+ f z = Left z++_E :: Prism' TN ()+_E = prism (const E) $ f where+ f E = Right ()+ f z = Left z++enumed = _N . _2++-- | A complete grammatical symbol is multi-dimensional with 0.. dimensions.++newtype Symb = Symb { getSymbs :: [TN] }++deriving instance Show Symb+deriving instance Eq Symb+deriving instance Ord Symb++symb :: Lens' Symb [TN]+symb f (Symb xs) = Symb <$> f xs -- are we sure?++type instance Index Symb = Int++type instance IxValue Symb = TN++instance Applicative f => Ixed f Symb where+ ix k f (Symb xs) = Symb <$> ix k f xs+ {-# INLINE ix #-}++-- | A production rule goes from a left-hand side (lhs) to a right-hand side+-- (rhs). The rhs is evaluated using a function (fun).+--+-- TODO These production rules currently do not allow "typical"+-- context-sensitive grammars with terminal symbols on the left-hand side.++data Rule = Rule+ { _lhs :: Symb+ , _fun :: [String] -- Fun+ , _rhs :: [Symb]+ }+ deriving (Eq,Ord,Show)++makeLenses ''Rule++-- | A complete grammar with a set of terminal symbol (tsyms), non-terminal+-- symbol (nsyms), production rules (rules) and a start symbol (start).+--+-- TODO Combined terminal and non-terminal symbols in multi-tape grammars are+-- denoted as non-terminal symbols.+--+-- TODO rename epsis -> esyms+--+-- TODO tsyms, esyms are not symbols but should just be 1-dim things ...+--+-- TODO nsyms should maybe be 1-dim, then have another thing for the multidim things++data Grammar = Grammar+ { _tsyms :: Set Symb+ , _nsyms :: Set Symb+ , _epsis :: Set TN+ , _rules :: Set Rule+ , _start :: Maybe Symb+ , _name :: String+ } deriving (Show)++makeLenses ''Grammar++-- | the dimension of the grammar. Grammars with no symbols have dimension 0.++gDim :: Grammar -> Int+gDim g+ | Just (x,_) <- S.minView (g^.nsyms) = length $ x^.symb+ | Just (x,_) <- S.minView (g^.tsyms) = length $ x^.symb+ | otherwise = 0++++-- * Helper functions on rules and symbols.++-- | Symb is completely in terminal form.++isSymbT :: Symb -> Bool+isSymbT (Symb xs) = allOf folded tTN xs && anyOf folded (\case (T _) -> True ; _ -> False) xs++tTN :: TN -> Bool+tTN (T _ ) = True+tTN (E ) = True+tTN (N _ _) = False++isSymbE :: Symb -> Bool+isSymbE (Symb xs) = allOf folded (\case E -> True ; _ -> False) xs++-- | Symb is completely in non-terminal form.++isSymbN :: Symb -> Bool+isSymbN (Symb xs) = allOf folded nTN xs && anyOf folded (\case (N _ _) -> True ; _ -> False) xs++{-+-- | Generalized non-terminal symbol with at least one non-terminal Symb.++nSymbG :: Symb -> Bool+nSymbG (Symb xs) = allOf folded nTN xs && anyOf folded (\case (N _ _) -> True ; _ -> False) xs+-}++nTN :: TN -> Bool+nTN (N _ _) = True+nTN (E ) = True+nTN (T _ ) = False++++-- * Determine grammar types+--+-- For grammars where the number of non-terminal symbols is restricted, we+-- allow as non-terminal also the generalized variants that have partial+-- terminal symbols.+--+-- TODO maybe restrict those to epsilon-type terminals in generalized+-- non-terminals.++-- | Left-linear grammars have at most one non-terminal on the RHS. It is the+-- first symbol.++isLeftLinear :: Grammar -> Bool+isLeftLinear g = allOf folded isll $ g^.rules where+ isll :: Rule -> Bool+ isll (Rule l _ []) = isSymbN l+ isll (Rule l _ rs) = isSymbN l && (allOf folded (not . isSymbN) $ tail rs) -- at most one non-terminal++-- | Right-linear grammars have at most one non-terminal on the RHS. It is the+-- last symbol.++isRightLinear :: Grammar -> Bool+isRightLinear g = allOf folded isrl $ g^.rules where+ isrl :: Rule -> Bool+ isrl (Rule l _ []) = isSymbN l+ isrl (Rule l _ rs) = isSymbN l && (allOf folded (not . isSymbN) $ init rs)++-- | Linear grammars just have a single non-terminal on the right-hand side.++isLinear :: Grammar -> Bool+isLinear g = error "isLinear: write me" -- allOf folded ((<=1) . length . filter nSymbG+++-- * Different normal forms for grammars.++-- | Transform a grammar into CNF. (cf. COL-2007)+--+-- TODO make sure we use a variant that computes small grammars.++chomskyNF :: Grammar -> Grammar+chomskyNF = error "chomsky"++isChomskyNF :: Grammar -> Bool+isChomskyNF g = allOf folded isC $ g^.rules where+ isC :: Rule -> Bool+ isC (Rule _ _ [s]) = isSymbT s+ isC (Rule _ _ [s,t]) = isSymbN s && isSymbN t+ isC _ = False++-- | Transform grammar into GNF.+--+-- http://dl.acm.org/citation.cfm?id=321254++greibachNF :: Grammar -> Grammar+greibachNF = error "gnf"++-- | Check if grammar is in Greibach Normal Form++isGreibachNF :: Grammar -> Bool+isGreibachNF g = allOf folded isG $ g^.rules where+ isG :: Rule -> Bool+ isG (Rule _ _ (t:ns)) = isSymbT t && all isSymbN ns+ isG _ = False++-- | A grammar is epsilon-free if no rule has an empty RHS, resp. any rhs-symb+-- is completely non-empty.+--+-- TODO we should tape-split multi-tape grammars here and make sure that all+-- individual tapes are epsilon-free as otherwise we can generate cases where+-- the epsilon-aligned symbols lead to weird problems. So split into single+-- tapes, then check.++epsilonFree :: Grammar -> Bool+epsilonFree g = allOf folded eFree $ g^.rules where+ eFree :: Rule -> Bool+ eFree (Rule l _ r) = undefined -- l == g^.start || (not $ null r) || anyOf folded (epsFree $ g^.start) r+ epsFree :: Symb -> Symb -> Bool+ epsFree = undefined++{-++-- |++data NTSym where+ TSym :: [String] -> NTSym+ NSym :: [(String, Enumerable)] -> NTSym+ deriving (Eq,Ord,Show)++-- | Grammar indices are enumerable objects+--+-- TODO should we always assume operations "modulo"?++data Enumerable+ = Singular+ | IntBased Integer [Integer]+ | Enumerated String [String]+ deriving (Eq,Ord,Show)++instance Default Enumerable where+ def = Singular++-- |++data Grammar = Grammar+ { _tsyms :: Set NTSym+ , _nsyms :: Set NTSym+ , _productions :: Set Production+ , _start :: NTSym+ } deriving (Show)++makeLenses ''Grammar++-- | Construct regular grammar.++regular :: Set NTSym -> Set NTSym -> Set Production -> NTSym -> Grammar+regular = error "regular: not implemented"++nsym1 :: String -> Enumerable -> NTSym+nsym1 s e = NSym [(s,e)]++isN (NSym _) = True+isN _ = False++isT (TSym _) = True+isT _ = False++-- | The size of a grammar.++size :: Grammar -> Int+size = error "size"++-- | Transform a grammar into 2NF.++twonf :: Grammar -> Grammar+twonf = error "twonf"++-}+
+ FormalLanguage/CFG/Parser.hs view
@@ -0,0 +1,357 @@+{-# LANGUAGE ConstraintKinds #-}+{-# LANGUAGE FlexibleContexts #-}+{-# LANGUAGE GeneralizedNewtypeDeriving #-}+{-# LANGUAGE LambdaCase #-}+{-# LANGUAGE NoMonomorphismRestriction #-}+{-# LANGUAGE RankNTypes #-}+{-# LANGUAGE RecordWildCards #-}+{-# LANGUAGE ScopedTypeVariables #-}+{-# LANGUAGE TemplateHaskell #-}+{-# LANGUAGE TupleSections #-}++-- | We define a simple domain-specific language for context-free languages.+--+-- TODO we still need to make sure to handle NTs correctly. It should be that+-- we write @[X,Y]@ in multidim cases and then we check in rules if @[X,Y]@ is+-- available ... of course for @[X,eps]@ we then need to check if @eps@ is an+-- epsilon symbol.++module FormalLanguage.CFG.Parser+ ( module FormalLanguage.CFG.Parser+ , Result (..)+ ) where++import Control.Applicative+import Control.Arrow+import Control.Lens+import Control.Monad.Identity+import Control.Monad.State.Class (MonadState (..))+import Control.Monad.Trans.Class+import Control.Monad.Trans.State.Strict hiding (get)+import Data.Default+import Data.Either+import Data.List (partition,sort,nub)+import Data.Maybe (catMaybes,isJust)+import Data.Tuple (swap)+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 FormalLanguage.CFG.Grammar++++data Enumerated+ = Sing+ | ZeroBased Integer+-- | Enum [String]+ deriving (Show)++-- | The ++data GrammarState = GrammarState+ { _nsys :: M.Map String Enumerated+ , _tsys :: S.Set String+ , _esys :: S.Set String+ , _grammarNames :: S.Set String+ }+ deriving (Show)++instance Default GrammarState where+ def = GrammarState+ { _nsys = def+ , _tsys = def+ , _esys = def+ , _grammarNames = def+ }++makeLenses ''GrammarState++-- | Parse a single grammar.++grammar :: Parse Grammar+grammar = do+ reserveGI "Grammar:"+ _name :: String <- identGI+ _nsyms <- S.fromList . concat <$> many nts+ _tsyms <- S.fromList . concat <$> many ts+ _epsis <- S.fromList <$> many epsP+ _start <- try (Just <$> startSymbol) <|> pure Nothing+ _rules <- (S.fromList . concat) <$> some rule+ reserveGI "//"+ grammarNames <>= S.singleton _name+ return Grammar { .. }++-- | Start symbol. Only a single symbol may be given+--+-- TODO for indexed symbols make sure we actually have one index to start with.++startSymbol :: Parse Symb+startSymbol = do+ reserveGI "S:"+ name :: String <- identGI+ -- TODO go and allow indexed NTs as start symbols, with one index given+ -- return $ nsym1 name Singular+ return $ Symb [N name Singular]++-- | The non-terminal declaration "NT: ..." returns a list of non-terms as+-- indexed non-terminals are expanded.++nts :: Parse [Symb]+nts = do+ reserveGI "N:"+ name <- identGI+ enumed <- option Sing $ braces enumeration+ let zs = expandNT name enumed+ nsys <>= M.singleton name enumed+ return zs++-- | expand set of non-terminals based on type of enumerations++expandNT :: String -> Enumerated -> [Symb]+expandNT name = go where+ go Sing = [Symb [N name Singular]]+ go (ZeroBased k) = [Symb [N name (IntBased z k)] | z <- [0..(k-1)]]+ --go (Enum es) = [Symb [N name (Enumerated z es )] | z <- es ]++-- | Figure out if we are dealing with indexed (enumerable) non-terminals++enumeration = ZeroBased <$> natural+-- <|> Enum <$> sepBy1 identGI (string ",")++-- | Parse declared terminal symbols.++ts :: Parse [Symb]+ts = do+ reserveGI "T:"+ n <- identGI+ let z = Symb [T n]+ tsys <>= S.singleton n+ return [z]++-- | Parse epsilon symbols++epsP :: Parse TN+epsP = do+ reserveGI "E:"+ e <- identGI+ esys <>= S.singleton e+ return E++-- | Parse a single rule. Some rules come attached with an index. In that case,+-- each rule is inflated according to its modulus (or more general the set of+-- indices indicated.+--+-- TODO add @fun@ to each PR++rule :: P m => m [Rule] -- Parse [Rule]+rule = do+ lhs <- runUnlined $ parsePreNN+ reserveGI "->"+ fun :: String <- identGI+ reserveGI "<<<"+ -- rhs <- runUnlined $ some (try (lift $ parsePreNN) <|> (lift $ parsePreTT))+ rhs <- runUnlined $ some (try parsePreNN <|> try parsePreTT <|> parsePreEE)+ whiteSpace+ s <- get+ return $ generateRules s lhs fun rhs++-- | Actually create a rule given both lhs and rhs. This means we need to+-- expand rules according to what we allow.+--+-- TODO need to handle epsilons correctly++generateRules :: GrammarState -> PreSymb -> String -> [PreSymb] -> [Rule]+generateRules gs lhs fun rhs = map buildRules js where+ -- gives (index,NT) list; from (NT,(index,integer)) list+ is = nub . map swap . over (mapped._2) indexName $ (lhs : rhs) ^.. folded.folded._OnlyIndexedPreN+ js = sequence $ map (expandIndex $ gs^.nsys) is+ expandIndex ns (i,n) =+ let expand Sing = error "expanded index on singular"+ expand (ZeroBased z) = [0 .. (z-1)]+ in map (i,) . expand $ ns M.! n+ buildTNE _ (PreE s) = E+ buildTNE _ (PreT s) = T s+ buildTNE _ (PreN s NotIndexed) = N s Singular+ buildTNE zs (PreN s (FixedInPreN k)) =+ let ZeroBased m = (gs^.nsys) M.! s+ in N s (IntBased k m)+ buildTNE zs (PreN s (IndexedPreN t k)) =+ let Just z = lookup t zs+ ZeroBased m = (gs^.nsys) M.! s+ l :: Integer = (z+k) `mod` m+ in N s (IntBased l m)+ buildRules j = Rule (Symb $ map (buildTNE j) lhs) [fun] (map (Symb . map (buildTNE j)) rhs)++data IndexedPreN+ = NotIndexed+ | FixedInPreN Integer+ | IndexedPreN String Integer+ deriving (Show,Eq,Ord)++indexName (IndexedPreN s i) = s++_IndexedPreN :: Prism' IndexedPreN (String,Integer)+_IndexedPreN = prism (uncurry IndexedPreN) $ \case (IndexedPreN s i) -> Right (s,i)+ other -> Left other++data PreTNE+ = PreN String IndexedPreN+ | PreT String+ | PreE String+ deriving (Show,Eq,Ord)++_PreN :: Prism' PreTNE (String,IndexedPreN)+_PreN = prism (uncurry PreN) $ \case (PreN s i) -> Right (s,i)+ other -> Left other++_OnlyIndexedPreN :: Prism' PreTNE (String,IndexedPreN)+_OnlyIndexedPreN = prism (uncurry PreN) $ \case (PreN s (IndexedPreN t i)) -> Right (s, IndexedPreN t i)+ other -> Left other++_PreT :: Prism' PreTNE String+_PreT = prism PreT $ \case (PreT s) -> Right s+ other -> Left other++_PreE :: Prism' PreTNE String+_PreE = prism PreE $ \case (PreE s) -> Right s+ other -> Left other++type PreSymb = [PreTNE]++--parsePreN :: P m => m PreTNE+parsePreN = lift (use nsys) >>= \ks -> (PreN <$> (choice . map string . M.keys $ ks) <*> parseIndexedPreN)++--parsePreT :: P m => m PreTNE+parsePreT = PreT <$> (lift (use tsys) >>= choice . map string . S.elems)++--parsePreE :: P m => m PreTNE+parsePreE = PreE <$> (lift (use esys) >>= choice . map string . S.elems)++--parseIndexedPreN :: P m => m IndexedPreN+parseIndexedPreN = option NotIndexed ( (try . braces $ IndexedPreN <$> identGI <*> option 0 integer)+ <|> (braces $ FixedInPreN <$> integer)+ )++-- parsePreNN :: P m => m [PreTNE]+parsePreNN = do+ ns <- (:[]) <$> parsePreN <* whiteSpace <|> listP (try parsePreN <|> parsePreE)+ guard (notNullOf (folded._PreN) ns) <?> "no non-terminal encountered"+ return ns++--parsePreTT :: P m => m [PreTNE]+parsePreTT = do+ ts <- (:[]) <$> parsePreT <* whiteSpace <|> listP (try parsePreT <|> parsePreE)+ guard (notNullOf (folded._PreT) ts) <?> "no terminal encountered"+ return ts++parsePreEE = do+ es <- (:[]) <$> parsePreE <* whiteSpace <|> listP parsePreE+ guard (allOf (folded._PreT) (const True) es) <?> ""+ return es++-- | Parses a list of a la @[a,b,c]@++listP = brackets . commaSep++++-- * Monadic Parsing Machinery++-- | Parser with 'GrammarState'++newtype GrammarParser m a = GrammarP { runGrammarP :: StateT GrammarState m a }+ deriving ( Monad+ , MonadPlus+ , Alternative+ , Applicative+ , Functor+ , MonadState GrammarState+ , TokenParsing+ , CharParsing+ , Parsing+ , MonadTrans+ )++-- | Functions that parse using the 'GrammarParser'++type Parse a = ( Monad m+ , MonadPlus m+ , TokenParsing m+ ) => GrammarParser m a++-- | Parsing where we stop at a newline (which needs to be parsed explicitly)++type ParseU a = (Monad m+ , MonadPlus m+ , TokenParsing m+ ) => Unlined (GrammarParser m) a++type P m = ( Monad m+ , MonadPlus m+ , Alternative m+ , Parsing m+ , TokenParsing m+ , MonadState GrammarState m+ )++-- | grammar identifiers++grammarIdentifiers = set styleReserved rs emptyIdents where+ rs = H.fromList ["Grammar:", "N:", "T:", "E:"]++-- | partial binding of 'reserve' to idents++reserveGI = reserve grammarIdentifiers++identGI = ident grammarIdentifiers++++parseGrammar :: String -> String -> Result Grammar+parseGrammar fname cnts = parseString+ ((evalStateT . runGrammarP) grammar def)+ (Directed (B.pack fname) 0 0 0 0)+ cnts+++--+-- test stuff+--++testGrammar = unlines+ [ "Grammar: Align"+ , "N: X{2}"+ , "N: Y{2}"+ , "N: Z"+ , "T: a"+ , "T: e"+ , "E: ε"+ , "S: X"+ , "[X{i},Y{j}] -> many <<< [X{j+1},Y{i-1}]"+ , "[X{i},Y{i}] -> eeee <<< [e,e]"+ , "[X{1},Y{0}] -> blar <<< [X{0},Y{1}]"+ , "[X{1},Y{0}] -> blub <<< [X{0},Y{i}]"+ , "Z -> step <<< Z a Z a Z"+-- , "Z -> done <<< ε" -- this shouldn't actually be done, as @E@ symbols are to denote that nothing happens (so this is actually rather undefined)+-- , "X -> stand <<< X"+-- , "[X] -> oned <<< [X]"+-- , "X -> eps <<< epsilon"+ , "//"+ ]++testParsing :: Result Grammar+testParsing = parseString+ ((evalStateT . runGrammarP) grammar def)+ (Directed (B.pack "testGrammar") 0 0 0 0)+ testGrammar++asG = let (Success g) = testParsing in g
+ FormalLanguage/CFG/PrettyPrint.hs view
@@ -0,0 +1,7 @@++module FormalLanguage.CFG.PrettyPrint+ ( renderLaTeX+ ) where++import FormalLanguage.CFG.PrettyPrint.LaTeX as LaTeX+
+ FormalLanguage/CFG/PrettyPrint/ANSI.hs view
@@ -0,0 +1,79 @@+{-# LANGUAGE PatternGuards #-}++module FormalLanguage.CFG.PrettyPrint.ANSI+ ( grammarDoc+ , rulesDoc+ , printDoc+ ) where++import Control.Lens+import qualified Data.Set as S+import System.IO (stdout)+import Text.PrettyPrint.ANSI.Leijen++import FormalLanguage.CFG.Grammar+import FormalLanguage.CFG.Parser++++-- | Prettyprint a grammar ANSI-style.+--+-- TODO Later on, it would be really nice to better align the LHS, fun, and RHS+-- of the rules++grammarDoc :: Grammar -> Doc+grammarDoc g = text "Grammar: " <$> indent 2 (ns <$> ts <$> es <$> ss <$> rs) <$> line where+ ns = ind "non terminals:" 2 . vcat $ zipWith (\k z -> (fill 5 $ int k) <+> (symbolDoc z <+> (text . show $ z))) [1..] (g^..nsyms.folded)+ ts = ind "terminals:" 2 . vcat . map (\z -> symbolDoc z <+> (text . show $ z)) $ g^..tsyms.folded+ es = ind "epsilons:" 2 . vcat . map (\z -> tnDoc z <+> (text . show $ z)) $ g^..epsis.folded+ ss = ind "start symbol:" 2 . startDoc $ g^.start+ rs = ind "rules:" 2 . vcat $ zipWith (\k r -> (fill 5 $ int k) <+> (ruleDoc r)) [1..] (g^..rules.folded)+ ind s k d = text s <$> indent k d++-- | Print just a set of rules (for the GrammarProducts Proofs).++rulesDoc :: S.Set Rule -> Doc+rulesDoc rs = text "rules:" <$> (indent 2 . vcat . map ruleDoc $ rs^..folded) <$> line++-- | Prettify the start symbol, or give warning.++startDoc :: Maybe Symb -> Doc+startDoc Nothing = red $ text "no start symbol is set!"+startDoc (Just s) = symbolDoc s++-- | Render a rule.++ruleDoc :: Rule -> Doc+ruleDoc r = fill 10 l <+> text "->" <+> fill 10 f <+> rs where+ l = symbolDoc $ r^.lhs+ f = case r^.fun of+ [] -> text "MISSING!"+ [z] -> text z+ xs -> list . map text $ xs+ rs = hcat $ punctuate space $ map symbolDoc $ r^.rhs++-- | A symbol is rendered either as a ``symbol'' or a list of symbols for+-- multi-tape grammars.++symbolDoc :: Symb -> Doc+symbolDoc s+ | [z] <- s^.symb = tnDoc z+ | otherwise = list $ map tnDoc $ s^.symb++-- | Prettyprint a (non-)terminal symbol.++tnDoc :: TN -> Doc+tnDoc (E ) = blue $ text "ε"+tnDoc (T s ) = green $ text s+tnDoc (N s e)+ | Singular <- e = red $ text s+ | IntBased k z <- e = (red $ text s) <+> (magenta $ text $ show k)++-- |++printDoc :: Doc -> IO ()+printDoc d = displayIO stdout (renderPretty 0.8 160 $ d <> linebreak)++-- Print the test grammar from the parser.++test = printDoc $ grammarDoc asG
+ FormalLanguage/CFG/PrettyPrint/Haskell.hs view
@@ -0,0 +1,166 @@+{-# LANGUAGE LambdaCase #-}++-- | A PrettyPrinter that generates "almost useable" Haskell modules. The+-- signature and grammar are created but the algebras are (obviously) missing.++module FormalLanguage.CFG.PrettyPrint.Haskell+ ( grammarHaskell+ ) where++import Control.Lens+import Data.Function (on)+import Data.List (nub,sort,intersperse,nubBy,groupBy,foldl')+import qualified Data.Set as S+import System.IO (stdout)+import Text.PrettyPrint.ANSI.Leijen+import Text.Printf+import Control.Arrow hiding ((<+>))++import FormalLanguage.CFG.Grammar+import FormalLanguage.CFG.Parser++++-- | Render grammar++grammarHaskell :: Grammar -> Doc+grammarHaskell g = signatureD g <$> empty <$> grammarD g <$> empty <$> productD g++signatureD :: Grammar -> Doc+signatureD g = hdr <$> indent 2 fns where+ hdr = text $ printf "data Sig%s {-Monad-} m {-NT-} nt hResT {-T-} %s = Sig%s" (g^.name) {- ns -} ts (g^.name)+ ns = concat . intersperse " " . nub . sort . map ntS . filter isSymbN $ (g^..rules.folded.lhs) ++ (g^..rules.folded.rhs.folded)+ ts = concat . intersperse " " . nub . sort+ . map (view tnName) . filter (\case (T _) -> True ; z -> False)+ $ g^..tsyms.folded.symb.folded+-- es = concat . intersperse " " . map (addEps . view tnName) $ g^..epsis.folded+-- fns = encloseSep lbrace rbrace comma . map (text . concat) . (++[["h"]]) . nub . sort $ g^..rules.folded.fun+ fns = encloseSep lbrace rbrace comma . (++[h]) . map ruleSigDoc . nubBy ((==) `on` _fun) . sort $ g^..rules.folded+ h = text "h :: Data.Vector.Fusion.Stream.Monadic.Stream m nt -> m hResT"++-- | Generate rule signatures for the 'Signature' data ctor.+--+-- TODO extend to allow classified dp (need more than one NT type)++ruleSigDoc :: Rule -> Doc+ruleSigDoc (Rule lhs fun rhs) =+ text (concat fun) <+>+ text "::" <+>+ cat (punctuate (text " -> ") rs) <+>+ text "-> nt"+ where+ rs = map tOrNt rhs+ tOrNt r+ {-+ | isSymbE r = case (r^.symb) of+ [x] -> text $ addEps $ x^.tnName+ xs -> encloseSep (text "(Z:.") rparen (text ":.") $ map (text . addEps . view tnName) xs+ -}+ | isSymbN r = text "nt"+ | isSymbT r = case (r^.symb) of+ [x] -> text $ x^.tnName+ xs -> encloseSep (text "(Z:.") rparen (text ":.") $ map sigT xs+ | otherwise = error $ "ruleSigDoc: " ++ show r+ where sigT (T s) = text s+ sigT E = text "()" -- important, EMIT NOTHING emits @()@++ntS :: Symb -> String+ntS (Symb []) = error "zero-dim symbol"+ntS (Symb xs) = "_" ++ concatMap (\x -> x^.tnName ++ addIndex x) xs++addIndex :: TN -> String+addIndex (N _ Singular) = ""+addIndex (N _ (IntBased k _)) = show k+addIndex _ = ""++-- |+--+-- TODO collect all rules with same lhs ++grammarD :: Grammar -> Doc+grammarD g = text ("grammar" ++ g^.name) <+>+ text ("Sig" ++ g^.name ++ "{..}") <+>+ text "{-NT-}" <+> hsep (map (text . ntS) . nub . sort $ g^..rules.folded.lhs) <+>+ text "{-T-}" <+> hsep (map (text . view tnName) . nub . sort+ . filter (\case (T _) -> True ; z -> False)+ $ g^..tsyms.folded.symb.folded) <+>+-- text "{-E-}" <+> hsep (map (text . addEps . view tnName) . nub . sort $ g^..epsis.folded) <+>+ text "="<$>+ indent 2 (tupled xs)+ where+ xs = map genForNT . groupBy ((==) `on` _lhs) $ g^..rules.folded++addEps "" = "eps"+addEps s = s++genForNT xs = tupled [l,r] where+ l = text . ntS $ head xs ^. lhs+ r = encloseSep empty (text " ... h") (text " ||| ") $ map genApp xs++genApp x = (text $ concat $ x^.fun)+ <+> text "<<<"+ <+> (encloseSep empty empty (text " % ") $ map genSymb $ x^.rhs)++genSymb x+ {-+ | isSymbE x = case (x^.symb) of+ [z] -> text $ theName z+ zs -> encloseSep (text "(Z:.") rparen (text ":.") $ map (text . theName) zs+ -}+ | isSymbN x = text $ ntS x+ | isSymbT x = case (x^.symb) of+ [z] -> text $ theName z+ zs -> encloseSep (text "(T:!") rparen (text ":!") $ map (text . theName) zs+ where+ theName (E ) = "None"+ theName (T s ) = s++productD g = (text $ printf "(<**) f g = Sig%s" (g^.name)) <$> indent 2 fs <$> bnd where+ fs = encloseSep lbrace rbrace comma $ (map productFun . nubBy ((==) `on` _fun) . sort $ g^..rules.folded) ++ [h]+ h = vcat $ map text+ [ "h xs = do"+ , " hfs <- _Fh . Data.Vector.Fusion.Stream.Monadic.map fst $ xs"+ , " let phfs = Data.Vector.Fusion.Stream.Monadic.concatMapM snd"+ , " . Data.Vector.Fusion.Stream.Monadic.filter ((hfs==) . fst) $ xs"+ , " _Gh phfs"+ ]+ bnd = indent 2 ((text "where") <$> indent 2 (bF <$> bG))+ bF = vcat $ map (\f -> let z = concat $ _fun f in text $ printf "_F%s = %s f" z z)+ $ fnubs ++ [Rule undefined ["h"] undefined]+ bG = vcat $ map (\f -> let z = concat $ _fun f in text $ printf "_G%s = %s g" z z)+ $ fnubs ++ [Rule undefined ["h"] undefined]+ {-+ bF = text (printf "Sig%s" (g^.name))+ <> (encloseSep lbrace rbrace comma . map text . (++["h_F"]) . map (("_F"++) . concat . _fun) $ fnubs)+ <> text " =f"+ bG = text (printf "Sig%s" (g^.name))+ <> (encloseSep lbrace rbrace comma . map text . (++["h_G"]) . map (("_G"++) . concat . _fun) $ fnubs)+ <> text " =g"+ -}+ fnubs = nubBy ((==) `on` _fun) . sort $ g^..rules.folded++productFun (Rule l f rs) = text (concat f) <> text " = \\" <> vars <> text " -> " <> parens (callF <> comma <> callG)+ where+ vars = hsep $ zipWith mkVars rs vs+ callF = text (concat $ "_F" : f) <+> (hcat . punctuate space . map text $ take (length rs) vs)+ callG = let ns = map snd . filter (isSymbN . fst) $ zip rs vs+ in text . genS $ zip rs vs+ vs = let az = ['a'..'z'] ; bs = [[]] ++ [ a:b | b<-bs, a<-az ] in drop 1 bs+ mkVars r v+ | isSymbT r = text v+ | isSymbN r = parens (text v <> comma <> text (v++"N"))+ genS zs = let go (ns,as) (r,v)+ | isSymbT r = (ns, as ++ [v])+ | isSymbN r = (ns++ [v++"N", ">>= Data.Vector.Fusion.Stream.Monadic.concatMap (\\", v, "->"], as ++ [v])+ postAddBrackets = (++ (replicate (length . filter isSymbN . map fst $ zs) ')'))+ in postAddBrackets+ . concat+ . intersperse " "+ . uncurry (++)+ . foldl' go ([],["Data.Vector.Fusion.Stream.Monadic.singleton $", (concat $ "_S" : f)])+ $ zs++test = printDoc $ grammarHaskell asG where+ printDoc :: Doc -> IO ()+ printDoc d = displayIO stdout (renderPretty 0.8 160 $ d <> linebreak)+
+ FormalLanguage/CFG/PrettyPrint/LaTeX.hs view
@@ -0,0 +1,68 @@+{-# LANGUAGE NoMonomorphismRestriction #-}+{-# LANGUAGE OverloadedStrings #-}+{-# LANGUAGE ParallelListComp #-}+{-# LANGUAGE PatternGuards #-}++module FormalLanguage.CFG.PrettyPrint.LaTeX+ ( renderFile+ , renderLaTeX+ ) where++import Control.Lens hiding ((&), to)+import Data.List (intersperse)+import Data.Set (toList)+import Data.Text (pack)+import Text.LaTeX.Base+import Text.LaTeX.Base.Class+import Text.LaTeX.Base.Syntax+import Text.LaTeX.Packages.AMSMath hiding (align)++import FormalLanguage.CFG.Grammar++++renderLaTeX :: Int -> Grammar -> LaTeX+renderLaTeX = renderGrammar++-- | Transform a grammar to some LaTeX code.++renderGrammar :: LaTeXC l => Int -> Grammar -> l+renderGrammar k g -- (Grammar ps gname)+ | k == 1 = align xs+ | k == 2 = align2 xs+ where -- subsubsection (raw $ pack gname) <> raw "\n" <> align2 xs <> raw "\n" where+ xs = [ (renderNtT l, mconcat (map renderNtT r)) | Rule l _ r <- toList (g^.rules) ]++-- | Transform a single 'Symb'. This will produce a column of terminal /+-- non-terminal symbols.++renderNtT :: LaTeXC l => Symb -> l+renderNtT (Symb xs) = ll <> (mci $ map go xs) <> rr+ where+ go (T s ) = render s+ go (N s e)+ | Singular <- e = render s+ | IntBased k zs <- e = render s !: (raw . pack $ show k)+ go (E ) = render "-"+-- | Enumerated k zs <- e = render s !: (raw . pack $ k)+ ll = raw "\\begingroup \\left ( \\begin{smallmatrix}"+ rr = raw "\\end{smallmatrix} \\right ) \\endgroup" where+ render x+ | x == "empty" = varepsilon+ | null x = epsilon -- raw $ pack "-"+ | otherwise = raw $ pack x++mci = mconcat . intersperse (raw "\\\\\n")++align :: LaTeXC l => [(l,l)] -> l+align = (liftL $ TeXEnv "align*" []) . go where+ go xs = mci [ l & to <> r | (l,r) <- xs ]++align2 :: LaTeXC l => [(l,l)] -> l+align2 = (liftL $ TeXEnv "align*" []) . go where+ go xs = let len = length xs+ (as,bs) = splitAt ((len +1) `div` 2) $ xs ++ repeat ("","")+ to' c = if c > len `div` 2 then "" else to+ in+ mci [ ll & to <> lr & rl & to' c <> rr | (ll,lr) <- as | ((rl,rr),c) <- zip bs [1..] ]+
+ FormalLanguage/CFG/QuickCheck.hs view
@@ -0,0 +1,4 @@++-- | Create random grammars.++module FormalLanguage.CFG.QuickCheck where
+ FormalLanguage/CFG/TH.hs view
@@ -0,0 +1,120 @@+{-# LANGUAGE PatternGuards #-}++module FormalLanguage.CFG.TH where++import Control.Lens hiding (Strict)+import Data.List (intersperse,nub,nubBy,groupBy)+import Language.Haskell.TH+import Data.Vector.Fusion.Stream.Monadic (Stream)+import Control.Arrow+import Control.Applicative+import Control.Monad+import qualified Data.Set as S+import Data.Function (on)+import Control.Monad.Trans.Class+import Data.Maybe++import FormalLanguage.CFG.Grammar++++-- | Given a grammar, create the Signature of data type+--+-- @data Signature a b = Signature { ...}@+--+-- TODO we assume that all signature functions have same arity and type; a+-- function to check this is currently missing and needs to be added!+--+-- TODO need varnames for all NTs and Ts+--+-- TODO allow only one type of NTs (as in one type ctor)+--+-- TODO need monad vartype also (for opt)++genSignature :: Grammar -> Q Dec+genSignature g = do+ let ts = map (PlainTV . mkName . ("t"++)) $ g^..tsyms.folded.symb.folded.tnName+ let ns = map (PlainTV . mkName . genNname) $ g^..nsyms.folded -- PlainTV (mkName "xX")+ let ns = map (PlainTV . mkName) ["_m", "_x", "_r"]+ let fs = map genFname . nub $ g^..rules.folded+ let h = genObjectiveFun+ s <- dataD (cxt []) (mkName "Signature") (ns++ts) [recC (mkName "Signature") (fs++[h])] []+ return s++-- | Generate the grammar.++genGrammar :: Grammar -> Q Dec+genGrammar g = do+ ns <- mapM (\n -> newName (genNname n) >>= \z -> return (n,z)) $ g^..nsyms.folded+ ts <- mapM (\t -> newName t >>= \z -> return (t,z)) $ g^..tsyms.folded.symb.folded.tnName+ runIO $ print ts+ let bd = normalB $ tupE $ map (genPair ns ts) $ groupBy ((==) `on` _lhs) $ S.toList $ g^.rules+ f <- funD (mkName "grammar") [clause (map varP $ map snd ns ++ map snd ts) bd [{-decQs-}]]+ return f++-- |++genPair :: [(Symb,Name)] -> [(String,Name)] -> [Rule] -> ExpQ+genPair ns ts rs = do+ let l = fromJust $ lookup (head rs ^. lhs) ns+ tupE [varE l, tupE []]++-- |++genTname = PlainTV . mkName . ("t"++)++-- | Generate a non-terminal name. Can be used for the type ctor as well as for+-- the functions and grammar.++genNname :: Symb -> String+genNname s = ("n_"++) . concat . intersperse "_" $ s^..symb.folded.tnName++-- | Terminal names are composites either of @t@ or of @(Z:.t1:.t2:. ...)@. The+-- correct version is created here. We can not use this for the type ctor.++genTType :: Symb -> Type+genTType s+ | [z] <- s^.symb = VarT . mkName $ "t"++ z^.tnName+ | zs <- s^.symb = foldl+ (\l r -> AppT (AppT (ConT . mkName $ ":.") l) r)+ (ConT . mkName $ "Z")+ (map (VarT . mkName . ("t"++)) $ (zs^..folded.tnName))++-- | +--+-- TODO the return type is the type of the LHS++-- ( AppT ( AppT ArrowT (VarT a_7) )+-- ( AppT ( AppT ArrowT (VarT b_8) ) +-- ( VarT c_9 )+-- )+-- ) ++genFname :: Rule -> Q (Name,Strict,Type)+genFname r = do+ let name = ("f_"++) . concat . intersperse "_" $ r^.fun+ let rtrn = VarT . mkName $ "_x" -- . genNname $ r^.lhs+ let args = map (AppT ArrowT . genArg) $ r^.rhs+ return (mkName name, NotStrict, foldr AppT rtrn args)++-- |++genObjectiveFun :: Q (Name,Strict,Type)+genObjectiveFun = do+ let name = "h"+ let mnd = VarT . mkName $ "_m"+ let rtrn = AppT mnd $ VarT . mkName $ "_r"+ let strm = ConT . mkName $ "Stream"+ let args = AppT ArrowT . AppT (AppT strm mnd) . VarT . mkName $ "_x"+ return (mkName name, NotStrict, AppT args rtrn)++-- | Create the correct argument.+--+-- TODO make sure to handle multi-dim terms using Z:.++genArg :: Symb -> Type+genArg s+ | isSymbT s = genTType s+ | isSymbN s = VarT . mkName $ "_x" -- . genNname $ s+ | otherwise = error $ "incompatible symbol: " ++ show s+
+ GrammarPP.hs view
@@ -0,0 +1,67 @@+{-# LANGUAGE DeriveDataTypeable #-}+{-# LANGUAGE RecordWildCards #-}++-- | This small utility allows us to turn a formal language description into+-- either a LaTeX source file or a Haskell module.++module Main where++import System.Console.CmdArgs+import System.IO (openFile, hClose, IOMode (..))+import Text.PrettyPrint.ANSI.Leijen (hPutDoc)++import FormalLanguage.CFG.Grammar+import FormalLanguage.CFG.Parser+import FormalLanguage.CFG.PrettyPrint.ANSI (printDoc, grammarDoc)+import FormalLanguage.CFG.PrettyPrint.Haskell (grammarHaskell)+import FormalLanguage.CFG.PrettyPrint.LaTeX (renderFile, renderLaTeX)++++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]+ print o+ pr <- case (inFile o) of+ "" -> getContents >>= return . parseGrammar "stdin"+ fn -> readFile fn >>= return . parseGrammar fn+ case pr of+ Failure f -> printDoc f+ Success s -> 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+
+ LICENSE view
@@ -0,0 +1,675 @@+ GNU GENERAL PUBLIC LICENSE+ Version 3, 29 June 2007++ Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/>+ 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. By contrast,+the GNU General Public License is intended to guarantee your freedom to+share and change all versions of a program--to make sure it remains free+software for all its users. We, the Free Software Foundation, use the+GNU General Public License for most of our software; it applies also to+any other work released this way by its authors. You can apply it to+your programs, too.++ When we speak of free software, we are referring to freedom, not+price. 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+ Setup.hs view
@@ -0,0 +1,2 @@+import Distribution.Simple+main = defaultMain
+ changelog view
@@ -0,0 +1,4 @@+0.0.0.1+-------++Basic operations on context-free formal grammars.