diff --git a/FormalGrammars.cabal b/FormalGrammars.cabal new file mode 100644 --- /dev/null +++ b/FormalGrammars.cabal @@ -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 + diff --git a/FormalLanguage.hs b/FormalLanguage.hs new file mode 100644 --- /dev/null +++ b/FormalLanguage.hs @@ -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 + diff --git a/FormalLanguage/CFG.hs b/FormalLanguage/CFG.hs new file mode 100644 --- /dev/null +++ b/FormalLanguage/CFG.hs @@ -0,0 +1,2 @@ + +module FormalLanguage.CFG where diff --git a/FormalLanguage/CFG/Grammar.hs b/FormalLanguage/CFG/Grammar.hs new file mode 100644 --- /dev/null +++ b/FormalLanguage/CFG/Grammar.hs @@ -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" + +-} + diff --git a/FormalLanguage/CFG/Parser.hs b/FormalLanguage/CFG/Parser.hs new file mode 100644 --- /dev/null +++ b/FormalLanguage/CFG/Parser.hs @@ -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 diff --git a/FormalLanguage/CFG/PrettyPrint.hs b/FormalLanguage/CFG/PrettyPrint.hs new file mode 100644 --- /dev/null +++ b/FormalLanguage/CFG/PrettyPrint.hs @@ -0,0 +1,7 @@ + +module FormalLanguage.CFG.PrettyPrint + ( renderLaTeX + ) where + +import FormalLanguage.CFG.PrettyPrint.LaTeX as LaTeX + diff --git a/FormalLanguage/CFG/PrettyPrint/ANSI.hs b/FormalLanguage/CFG/PrettyPrint/ANSI.hs new file mode 100644 --- /dev/null +++ b/FormalLanguage/CFG/PrettyPrint/ANSI.hs @@ -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 diff --git a/FormalLanguage/CFG/PrettyPrint/Haskell.hs b/FormalLanguage/CFG/PrettyPrint/Haskell.hs new file mode 100644 --- /dev/null +++ b/FormalLanguage/CFG/PrettyPrint/Haskell.hs @@ -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) + diff --git a/FormalLanguage/CFG/PrettyPrint/LaTeX.hs b/FormalLanguage/CFG/PrettyPrint/LaTeX.hs new file mode 100644 --- /dev/null +++ b/FormalLanguage/CFG/PrettyPrint/LaTeX.hs @@ -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..] ] + diff --git a/FormalLanguage/CFG/QuickCheck.hs b/FormalLanguage/CFG/QuickCheck.hs new file mode 100644 --- /dev/null +++ b/FormalLanguage/CFG/QuickCheck.hs @@ -0,0 +1,4 @@ + +-- | Create random grammars. + +module FormalLanguage.CFG.QuickCheck where diff --git a/FormalLanguage/CFG/TH.hs b/FormalLanguage/CFG/TH.hs new file mode 100644 --- /dev/null +++ b/FormalLanguage/CFG/TH.hs @@ -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 + diff --git a/GrammarPP.hs b/GrammarPP.hs new file mode 100644 --- /dev/null +++ b/GrammarPP.hs @@ -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 + diff --git a/LICENSE b/LICENSE new file mode 100644 --- /dev/null +++ b/LICENSE @@ -0,0 +1,675 @@ + 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/changelog b/changelog new file mode 100644 --- /dev/null +++ b/changelog @@ -0,0 +1,4 @@ +0.0.0.1 +------- + +Basic operations on context-free formal grammars.