diff --git a/LICENSE b/LICENSE
new file mode 100644
--- /dev/null
+++ b/LICENSE
@@ -0,0 +1,28 @@
+Copyright (c) 2015, nedervold
+All rights reserved.
+
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are met:
+
+* Redistributions of source code must retain the above copyright notice, this
+  list of conditions and the following disclaimer.
+
+* Redistributions in binary form must reproduce the above copyright notice,
+  this list of conditions and the following disclaimer in the documentation
+  and/or other materials provided with the distribution.
+
+* Neither the name of context-free-grammar nor the names of its
+  contributors may be used to endorse or promote products derived from
+  this software without specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
+FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
+SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
+OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
diff --git a/Makefile b/Makefile
new file mode 100644
--- /dev/null
+++ b/Makefile
@@ -0,0 +1,83 @@
+.PHONY : all clean configure dist dist-test docs docs-open lint \
+	maintainer-clean test
+
+GEN_CODE = dist/build/generate-code/generate-code
+
+all : configure
+	cabal build
+
+test : all
+	cabal test
+
+################################
+# department of sanitation
+################################
+
+clean :
+	cabal clean
+	# remove emacs cruft
+	-find . -name '*~' -delete
+	-find . -name '\#*' -delete
+
+maintainer-clean : clean
+	-cabal sandbox delete
+	-rm cabal.config
+
+################################
+# the cabal does not exist
+################################
+
+cabal.config :
+	echo 'tests: True' > cabal.config
+
+.cabal-sandbox :
+	cabal sandbox init
+
+configure : .cabal-sandbox cabal.config
+	cabal install --dependencies-only
+	cabal configure
+
+################################
+# distribution
+################################
+
+dist : all
+	-cabal check
+	cabal sdist
+
+TEMPDIR := $(shell mktemp -d /tmp/temp.XXXX)
+
+dist-test : dist
+	$(eval DIR := $(shell (cabal info . | awk '{print $$2 ; exit}')))
+	$(eval TARBALL := $(DIR).tar)
+	$(eval TGZBALL := $(TARBALL).gz)
+	echo $(TEMPDIR)
+	cp dist/$(TGZBALL) $(TEMPDIR)
+	cd $(TEMPDIR) && gunzip $(TGZBALL) && tar -xf $(TARBALL)
+	cd $(TEMPDIR)/$(DIR) && make test
+	rm -rf $(TEMPDIR)
+
+################################
+# documentation
+################################
+
+docs : configure
+	cabal haddock
+
+docs-open : docs
+	open dist/doc/html/context-free-grammar/index.html
+
+################################
+# generate-code
+################################
+
+$(GEN_CODE) : configure
+	cabal build generate-code
+
+################################
+# de-linting
+################################
+
+lint :
+	hlint -i 'Use import/export shortcut' src tests
+	# The import/export shortcut plays poorly with Haddock
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/context-free-grammar.cabal b/context-free-grammar.cabal
new file mode 100644
--- /dev/null
+++ b/context-free-grammar.cabal
@@ -0,0 +1,106 @@
+Name:                   context-free-grammar
+Version:                0.0.1
+Author:                 Eric Nedervold<nedervoldsoftware@gmail.com>
+Maintainer:             Eric Nedervold<nedervoldsoftware@gmail.com>
+License:                BSD3
+License-File:           LICENSE
+Copyright:              (c) 2015 Eric Nedervold
+Stability:              alpha
+Homepage:               http://github.com/nedervold/context-free-grammar
+Bug-Reports:            http://github.com/nedervold/context-free-grammar/issues
+Synopsis:               Basic algorithms on context-free grammars
+Description:            
+
+    Basic algorithms on context-free grammars:
+    .
+    * augmenting a grammar
+    .
+    * calculating nullability
+    .
+    * calculating reachability
+    .
+    * calculating productivity
+    .
+    * calculating first sets
+    .
+    * calculating follow sets
+    .
+    * calculating predict sets
+    .
+    You may define your context-free grammar textually using 'parse'
+    or with the quasiquoter 'bnf' (both in "Data.Cfg.Bnf"), or you may
+    use any data structure you like after making it an instance of
+    'Cfg' (found in "Data.Cfg.Cfg").
+    .
+    Testing is very thin in this version; basically just
+    sanity-checking.
+
+Category:               Language
+Cabal-Version:          >= 1.10
+Build-Type:             Simple
+Extra-Source-Files:     Makefile
+
+Library
+  Default-Language:     Haskell2010
+  HS-Source-Dirs:       src
+  GHC-Options:          -Wall
+  Exposed-Modules:      Data.Cfg
+                      , Data.Cfg.Augment
+                      , Data.Cfg.Bnf
+                      , Data.Cfg.Cfg
+                      , Data.Cfg.CPretty
+                      , Data.Cfg.FirstSet
+                      , Data.Cfg.FollowSet
+                      , Data.Cfg.FreeCfg
+                      , Data.Cfg.LookaheadSet
+                      , Data.Cfg.Nullable
+                      , Data.Cfg.PredictSet
+                      , Data.Cfg.Productive
+                      , Data.Cfg.Reachable
+                      , Data.Cfg.RuleApplication
+  Other-Modules:        Data.Cfg.Bnf.Parser
+                      , Data.Cfg.Bnf.QQ
+                      , Data.Cfg.Bnf.Scanner
+                      , Data.Cfg.Bnf.Syntax
+                      , Data.Cfg.Bnf.Token
+                      , Data.Cfg.Collect
+                      , Data.Cfg.FixedPoint
+  Build-Depends:        base >= 4 && < 5
+                      , array >= 0.5 && < 0.6
+                      , containers >= 0.5 && < 0.6
+                      , control-monad-omega >= 0.3 && < 0.4
+                      , dlist >= 0.7 && < 0.8
+                      , mtl >= 2.1 && < 2.2
+                      , pretty >= 1.1 && < 1.2
+                      , template-haskell
+
+Test-Suite test
+  Type:                 exitcode-stdio-1.0
+  Default-Language:     Haskell2010
+  Hs-Source-Dirs:       tests
+  Ghc-Options:          -Wall
+  Main-Is:              Test.hs
+  Other-Modules:        Data.CfgTests
+                      , Data.Cfg.BnfTests
+                      , Data.Cfg.FirstSetTests
+                      , Data.Cfg.FollowSetTests
+                      , Data.Cfg.LookaheadSetTests
+                      , Data.Cfg.ProductiveTests
+                      , Data.Cfg.ReachableTests
+                      , Data.Cfg.TestGrammars
+  Build-Depends:        base
+                      , containers >= 0.5 && < 0.6
+                      , context-free-grammar
+                      , HUnit
+                      , pretty >= 1.1 && < 1.2
+                      , QuickCheck >= 2.6 && < 2.7
+                      , quickcheck-properties == 0.1
+                      , template-haskell
+                      , test-framework
+                      , test-framework-hunit
+                      , test-framework-quickcheck2 >= 0.3 && < 0.4
+
+Source-Repository head
+  Type:                 git
+  Location:             git://github.com/nedervold/context-free-grammar.git
+
diff --git a/dist/build/Data/Cfg/Bnf/Parser.hs b/dist/build/Data/Cfg/Bnf/Parser.hs
new file mode 100644
--- /dev/null
+++ b/dist/build/Data/Cfg/Bnf/Parser.hs
@@ -0,0 +1,539 @@
+{-# OPTIONS_GHC -w #-}
+{-# OPTIONS -fglasgow-exts -cpp #-}
+-- | Parser for Bnf
+module Data.Cfg.Bnf.Parser(parse) where
+
+import qualified Data.Map as M
+import Data.Cfg.Bnf.Scanner(scan)
+import Data.Cfg.Bnf.Syntax
+import Data.Cfg.Bnf.Token
+import Data.Cfg.Cfg(Production, V(..), Vs)
+import qualified Data.Array as Happy_Data_Array
+import qualified GHC.Exts as Happy_GHC_Exts
+import Control.Applicative(Applicative(..))
+
+-- parser produced by Happy Version 1.19.4
+
+newtype HappyAbsSyn  = HappyAbsSyn HappyAny
+#if __GLASGOW_HASKELL__ >= 607
+type HappyAny = Happy_GHC_Exts.Any
+#else
+type HappyAny = forall a . a
+#endif
+happyIn4 :: (Grammar String String) -> (HappyAbsSyn )
+happyIn4 x = Happy_GHC_Exts.unsafeCoerce# x
+{-# INLINE happyIn4 #-}
+happyOut4 :: (HappyAbsSyn ) -> (Grammar String String)
+happyOut4 x = Happy_GHC_Exts.unsafeCoerce# x
+{-# INLINE happyOut4 #-}
+happyIn5 :: ([Production String String]) -> (HappyAbsSyn )
+happyIn5 x = Happy_GHC_Exts.unsafeCoerce# x
+{-# INLINE happyIn5 #-}
+happyOut5 :: (HappyAbsSyn ) -> ([Production String String])
+happyOut5 x = Happy_GHC_Exts.unsafeCoerce# x
+{-# INLINE happyOut5 #-}
+happyIn6 :: ([Production String String]) -> (HappyAbsSyn )
+happyIn6 x = Happy_GHC_Exts.unsafeCoerce# x
+{-# INLINE happyIn6 #-}
+happyOut6 :: (HappyAbsSyn ) -> ([Production String String])
+happyOut6 x = Happy_GHC_Exts.unsafeCoerce# x
+{-# INLINE happyOut6 #-}
+happyIn7 :: ([Vs String String]) -> (HappyAbsSyn )
+happyIn7 x = Happy_GHC_Exts.unsafeCoerce# x
+{-# INLINE happyIn7 #-}
+happyOut7 :: (HappyAbsSyn ) -> ([Vs String String])
+happyOut7 x = Happy_GHC_Exts.unsafeCoerce# x
+{-# INLINE happyOut7 #-}
+happyIn8 :: ([Vs String String]) -> (HappyAbsSyn )
+happyIn8 x = Happy_GHC_Exts.unsafeCoerce# x
+{-# INLINE happyIn8 #-}
+happyOut8 :: (HappyAbsSyn ) -> ([Vs String String])
+happyOut8 x = Happy_GHC_Exts.unsafeCoerce# x
+{-# INLINE happyOut8 #-}
+happyIn9 :: (Vs String String) -> (HappyAbsSyn )
+happyIn9 x = Happy_GHC_Exts.unsafeCoerce# x
+{-# INLINE happyIn9 #-}
+happyOut9 :: (HappyAbsSyn ) -> (Vs String String)
+happyOut9 x = Happy_GHC_Exts.unsafeCoerce# x
+{-# INLINE happyOut9 #-}
+happyIn10 :: (Vs String String) -> (HappyAbsSyn )
+happyIn10 x = Happy_GHC_Exts.unsafeCoerce# x
+{-# INLINE happyIn10 #-}
+happyOut10 :: (HappyAbsSyn ) -> (Vs String String)
+happyOut10 x = Happy_GHC_Exts.unsafeCoerce# x
+{-# INLINE happyOut10 #-}
+happyIn11 :: (V String String) -> (HappyAbsSyn )
+happyIn11 x = Happy_GHC_Exts.unsafeCoerce# x
+{-# INLINE happyIn11 #-}
+happyOut11 :: (HappyAbsSyn ) -> (V String String)
+happyOut11 x = Happy_GHC_Exts.unsafeCoerce# x
+{-# INLINE happyOut11 #-}
+happyInTok :: (Token) -> (HappyAbsSyn )
+happyInTok x = Happy_GHC_Exts.unsafeCoerce# x
+{-# INLINE happyInTok #-}
+happyOutTok :: (HappyAbsSyn ) -> (Token)
+happyOutTok x = Happy_GHC_Exts.unsafeCoerce# x
+{-# INLINE happyOutTok #-}
+
+
+happyActOffsets :: HappyAddr
+happyActOffsets = HappyA# "\x11\x00\x11\x00\x11\x00\x00\x00\x10\x00\x0c\x00\x00\x00\x00\x00\x0f\x00\x0e\x00\x00\x00\x06\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00"#
+
+happyGotoOffsets :: HappyAddr
+happyGotoOffsets = HappyA# "\x05\x00\x0d\x00\x09\x00\x00\x00\x00\x00\x00\x00\xfe\xff\x00\x00\x00\x00\x00\x00\x00\x00\x02\x00\x00\x00\x00\x00\x00\x00\x07\x00\x00\x00\x00\x00\x00\x00"#
+
+happyDefActions :: HappyAddr
+happyDefActions = HappyA# "\x00\x00\x00\x00\xfe\xff\xfc\xff\x00\x00\x00\x00\xf5\xff\xfd\xff\x00\x00\xfa\xff\xf8\xff\xf7\xff\xf6\xff\xf3\xff\xf4\xff\xf5\xff\xfb\xff\xf9\xff"#
+
+happyCheck :: HappyAddr
+happyCheck = HappyA# "\xff\xff\x03\x00\x04\x00\x05\x00\x06\x00\x00\x00\x01\x00\x02\x00\x02\x00\x07\x00\x04\x00\x02\x00\x05\x00\x06\x00\x01\x00\x02\x00\x01\x00\x03\x00\x06\x00\x02\x00\xff\xff\x05\x00\xff\xff\xff\xff\xff\xff\xff\xff"#
+
+happyTable :: HappyAddr
+happyTable = HappyA# "\x00\x00\x08\x00\x09\x00\x0a\x00\x0b\x00\x05\x00\x02\x00\x03\x00\x0e\x00\x0c\x00\x0f\x00\x07\x00\x11\x00\x0b\x00\x02\x00\x03\x00\x11\x00\x10\x00\xff\xff\x05\x00\x00\x00\x07\x00\x00\x00\x00\x00\x00\x00\x00\x00"#
+
+happyReduceArr = Happy_Data_Array.array (1, 12) [
+	(1 , happyReduce_1),
+	(2 , happyReduce_2),
+	(3 , happyReduce_3),
+	(4 , happyReduce_4),
+	(5 , happyReduce_5),
+	(6 , happyReduce_6),
+	(7 , happyReduce_7),
+	(8 , happyReduce_8),
+	(9 , happyReduce_9),
+	(10 , happyReduce_10),
+	(11 , happyReduce_11),
+	(12 , happyReduce_12)
+	]
+
+happy_n_terms = 7 :: Int
+happy_n_nonterms = 8 :: Int
+
+happyReduce_1 = happySpecReduce_1  0# happyReduction_1
+happyReduction_1 happy_x_1
+	 =  case happyOut5 happy_x_1 of { happy_var_1 -> 
+	happyIn4
+		 (Grammar happy_var_1
+	)}
+
+happyReduce_2 = happySpecReduce_2  1# happyReduction_2
+happyReduction_2 happy_x_2
+	happy_x_1
+	 =  case happyOut5 happy_x_1 of { happy_var_1 -> 
+	case happyOut6 happy_x_2 of { happy_var_2 -> 
+	happyIn5
+		 (happy_var_1 ++ happy_var_2
+	)}}
+
+happyReduce_3 = happySpecReduce_1  1# happyReduction_3
+happyReduction_3 happy_x_1
+	 =  case happyOut6 happy_x_1 of { happy_var_1 -> 
+	happyIn5
+		 (happy_var_1
+	)}
+
+happyReduce_4 = happyReduce 4# 2# happyReduction_4
+happyReduction_4 (happy_x_4 `HappyStk`
+	happy_x_3 `HappyStk`
+	happy_x_2 `HappyStk`
+	happy_x_1 `HappyStk`
+	happyRest)
+	 = case happyOutTok happy_x_1 of { (Token LOWER_IDENTIFIER happy_var_1) -> 
+	case happyOut7 happy_x_3 of { happy_var_3 -> 
+	happyIn6
+		 ([ (happy_var_1, alt) | alt <- happy_var_3 ]
+	) `HappyStk` happyRest}}
+
+happyReduce_5 = happySpecReduce_1  3# happyReduction_5
+happyReduction_5 happy_x_1
+	 =  case happyOut8 happy_x_1 of { happy_var_1 -> 
+	happyIn7
+		 (happy_var_1
+	)}
+
+happyReduce_6 = happySpecReduce_3  4# happyReduction_6
+happyReduction_6 happy_x_3
+	happy_x_2
+	happy_x_1
+	 =  case happyOut8 happy_x_1 of { happy_var_1 -> 
+	case happyOut9 happy_x_3 of { happy_var_3 -> 
+	happyIn8
+		 (happy_var_1 ++ [ happy_var_3 ]
+	)}}
+
+happyReduce_7 = happySpecReduce_1  4# happyReduction_7
+happyReduction_7 happy_x_1
+	 =  case happyOut9 happy_x_1 of { happy_var_1 -> 
+	happyIn8
+		 ([ happy_var_1 ]
+	)}
+
+happyReduce_8 = happySpecReduce_1  5# happyReduction_8
+happyReduction_8 happy_x_1
+	 =  case happyOut10 happy_x_1 of { happy_var_1 -> 
+	happyIn9
+		 (happy_var_1
+	)}
+
+happyReduce_9 = happySpecReduce_2  6# happyReduction_9
+happyReduction_9 happy_x_2
+	happy_x_1
+	 =  case happyOut10 happy_x_1 of { happy_var_1 -> 
+	case happyOut11 happy_x_2 of { happy_var_2 -> 
+	happyIn10
+		 (happy_var_1 ++ [ happy_var_2 ]
+	)}}
+
+happyReduce_10 = happySpecReduce_0  6# happyReduction_10
+happyReduction_10  =  happyIn10
+		 ([]
+	)
+
+happyReduce_11 = happySpecReduce_1  7# happyReduction_11
+happyReduction_11 happy_x_1
+	 =  case happyOutTok happy_x_1 of { (Token UPPER_IDENTIFIER happy_var_1) -> 
+	happyIn11
+		 (T happy_var_1
+	)}
+
+happyReduce_12 = happySpecReduce_1  7# happyReduction_12
+happyReduction_12 happy_x_1
+	 =  case happyOutTok happy_x_1 of { (Token LOWER_IDENTIFIER happy_var_1) -> 
+	happyIn11
+		 (NT happy_var_1
+	)}
+
+happyNewToken action sts stk [] =
+	happyDoAction 6# notHappyAtAll action sts stk []
+
+happyNewToken action sts stk (tk:tks) =
+	let cont i = happyDoAction i tk action sts stk tks in
+	case tk of {
+	Token FULL_STOP happy_dollar_dollar -> cont 1#;
+	Token LOWER_IDENTIFIER happy_dollar_dollar -> cont 2#;
+	Token OR happy_dollar_dollar -> cont 3#;
+	Token UPPER_IDENTIFIER happy_dollar_dollar -> cont 4#;
+	Token YIELDS happy_dollar_dollar -> cont 5#;
+	_ -> happyError' (tk:tks)
+	}
+
+happyError_ 6# tk tks = happyError' tks
+happyError_ _ tk tks = happyError' (tk:tks)
+
+newtype HappyIdentity a = HappyIdentity a
+happyIdentity = HappyIdentity
+happyRunIdentity (HappyIdentity a) = a
+
+instance Functor HappyIdentity where
+    fmap f (HappyIdentity a) = HappyIdentity (f a)
+
+instance Applicative HappyIdentity where
+    pure    = return
+    a <*> b = (fmap id a) <*> b
+instance Monad HappyIdentity where
+    return = HappyIdentity
+    (HappyIdentity p) >>= q = q p
+
+happyThen :: () => HappyIdentity a -> (a -> HappyIdentity b) -> HappyIdentity b
+happyThen = (>>=)
+happyReturn :: () => a -> HappyIdentity a
+happyReturn = (return)
+happyThen1 m k tks = (>>=) m (\a -> k a tks)
+happyReturn1 :: () => a -> b -> HappyIdentity a
+happyReturn1 = \a tks -> (return) a
+happyError' :: () => [(Token)] -> HappyIdentity a
+happyError' = HappyIdentity . parseError
+
+parseTokens tks = happyRunIdentity happySomeParser where
+  happySomeParser = happyThen (happyParse 0# tks) (\x -> happyReturn (happyOut4 x))
+
+happySeq = happyDontSeq
+
+
+parseError :: [Token] -> a
+parseError ts = error $ "parseError at: " ++ show ts
+
+-- | Parses Bnf source into a 'Grammar'.
+parse :: String -> Grammar String String
+parse = parseTokens . scan
+
+-- | Parses a list of 'Token's into a 'Grammar'.
+parseTokens :: [Token] -> Grammar String String
+{-# LINE 1 "templates/GenericTemplate.hs" #-}
+-- Id: GenericTemplate.hs,v 1.26 2005/01/14 14:47:22 simonmar Exp 
+
+
+
+
+
+
+
+-- Do not remove this comment. Required to fix CPP parsing when using GCC and a clang-compiled alex.
+#if __GLASGOW_HASKELL__ > 706
+#define LT(n,m) ((Happy_GHC_Exts.tagToEnum# (n Happy_GHC_Exts.<# m)) :: Bool)
+#define GTE(n,m) ((Happy_GHC_Exts.tagToEnum# (n Happy_GHC_Exts.>=# m)) :: Bool)
+#define EQ(n,m) ((Happy_GHC_Exts.tagToEnum# (n Happy_GHC_Exts.==# m)) :: Bool)
+#else
+#define LT(n,m) (n Happy_GHC_Exts.<# m)
+#define GTE(n,m) (n Happy_GHC_Exts.>=# m)
+#define EQ(n,m) (n Happy_GHC_Exts.==# m)
+#endif
+
+
+
+data Happy_IntList = HappyCons Happy_GHC_Exts.Int# Happy_IntList
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+infixr 9 `HappyStk`
+data HappyStk a = HappyStk a (HappyStk a)
+
+-----------------------------------------------------------------------------
+-- starting the parse
+
+happyParse start_state = happyNewToken start_state notHappyAtAll notHappyAtAll
+
+-----------------------------------------------------------------------------
+-- Accepting the parse
+
+-- If the current token is 0#, it means we've just accepted a partial
+-- parse (a %partial parser).  We must ignore the saved token on the top of
+-- the stack in this case.
+happyAccept 0# tk st sts (_ `HappyStk` ans `HappyStk` _) =
+        happyReturn1 ans
+happyAccept j tk st sts (HappyStk ans _) = 
+        (happyTcHack j (happyTcHack st)) (happyReturn1 ans)
+
+-----------------------------------------------------------------------------
+-- Arrays only: do the next action
+
+
+
+happyDoAction i tk st
+        = {- nothing -}
+          
+
+          case action of
+                0#           -> {- nothing -}
+                                     happyFail i tk st
+                -1#          -> {- nothing -}
+                                     happyAccept i tk st
+                n | LT(n,(0# :: Happy_GHC_Exts.Int#)) -> {- nothing -}
+                                                   
+                                                   (happyReduceArr Happy_Data_Array.! rule) i tk st
+                                                   where rule = (Happy_GHC_Exts.I# ((Happy_GHC_Exts.negateInt# ((n Happy_GHC_Exts.+# (1# :: Happy_GHC_Exts.Int#))))))
+                n                 -> {- nothing -}
+                                     
+
+                                     happyShift new_state i tk st
+                                     where new_state = (n Happy_GHC_Exts.-# (1# :: Happy_GHC_Exts.Int#))
+   where off    = indexShortOffAddr happyActOffsets st
+         off_i  = (off Happy_GHC_Exts.+# i)
+         check  = if GTE(off_i,(0# :: Happy_GHC_Exts.Int#))
+                  then EQ(indexShortOffAddr happyCheck off_i, i)
+                  else False
+         action
+          | check     = indexShortOffAddr happyTable off_i
+          | otherwise = indexShortOffAddr happyDefActions st
+
+
+indexShortOffAddr (HappyA# arr) off =
+        Happy_GHC_Exts.narrow16Int# i
+  where
+        i = Happy_GHC_Exts.word2Int# (Happy_GHC_Exts.or# (Happy_GHC_Exts.uncheckedShiftL# high 8#) low)
+        high = Happy_GHC_Exts.int2Word# (Happy_GHC_Exts.ord# (Happy_GHC_Exts.indexCharOffAddr# arr (off' Happy_GHC_Exts.+# 1#)))
+        low  = Happy_GHC_Exts.int2Word# (Happy_GHC_Exts.ord# (Happy_GHC_Exts.indexCharOffAddr# arr off'))
+        off' = off Happy_GHC_Exts.*# 2#
+
+
+
+
+
+data HappyAddr = HappyA# Happy_GHC_Exts.Addr#
+
+
+
+
+-----------------------------------------------------------------------------
+-- HappyState data type (not arrays)
+
+
+
+-----------------------------------------------------------------------------
+-- Shifting a token
+
+happyShift new_state 0# tk st sts stk@(x `HappyStk` _) =
+     let i = (case Happy_GHC_Exts.unsafeCoerce# x of { (Happy_GHC_Exts.I# (i)) -> i }) in
+--     trace "shifting the error token" $
+     happyDoAction i tk new_state (HappyCons (st) (sts)) (stk)
+
+happyShift new_state i tk st sts stk =
+     happyNewToken new_state (HappyCons (st) (sts)) ((happyInTok (tk))`HappyStk`stk)
+
+-- happyReduce is specialised for the common cases.
+
+happySpecReduce_0 i fn 0# tk st sts stk
+     = happyFail 0# tk st sts stk
+happySpecReduce_0 nt fn j tk st@((action)) sts stk
+     = happyGoto nt j tk st (HappyCons (st) (sts)) (fn `HappyStk` stk)
+
+happySpecReduce_1 i fn 0# tk st sts stk
+     = happyFail 0# tk st sts stk
+happySpecReduce_1 nt fn j tk _ sts@((HappyCons (st@(action)) (_))) (v1`HappyStk`stk')
+     = let r = fn v1 in
+       happySeq r (happyGoto nt j tk st sts (r `HappyStk` stk'))
+
+happySpecReduce_2 i fn 0# tk st sts stk
+     = happyFail 0# tk st sts stk
+happySpecReduce_2 nt fn j tk _ (HappyCons (_) (sts@((HappyCons (st@(action)) (_))))) (v1`HappyStk`v2`HappyStk`stk')
+     = let r = fn v1 v2 in
+       happySeq r (happyGoto nt j tk st sts (r `HappyStk` stk'))
+
+happySpecReduce_3 i fn 0# tk st sts stk
+     = happyFail 0# tk st sts stk
+happySpecReduce_3 nt fn j tk _ (HappyCons (_) ((HappyCons (_) (sts@((HappyCons (st@(action)) (_))))))) (v1`HappyStk`v2`HappyStk`v3`HappyStk`stk')
+     = let r = fn v1 v2 v3 in
+       happySeq r (happyGoto nt j tk st sts (r `HappyStk` stk'))
+
+happyReduce k i fn 0# tk st sts stk
+     = happyFail 0# tk st sts stk
+happyReduce k nt fn j tk st sts stk
+     = case happyDrop (k Happy_GHC_Exts.-# (1# :: Happy_GHC_Exts.Int#)) sts of
+         sts1@((HappyCons (st1@(action)) (_))) ->
+                let r = fn stk in  -- it doesn't hurt to always seq here...
+                happyDoSeq r (happyGoto nt j tk st1 sts1 r)
+
+happyMonadReduce k nt fn 0# tk st sts stk
+     = happyFail 0# tk st sts stk
+happyMonadReduce k nt fn j tk st sts stk =
+      case happyDrop k (HappyCons (st) (sts)) of
+        sts1@((HappyCons (st1@(action)) (_))) ->
+          let drop_stk = happyDropStk k stk in
+          happyThen1 (fn stk tk) (\r -> happyGoto nt j tk st1 sts1 (r `HappyStk` drop_stk))
+
+happyMonad2Reduce k nt fn 0# tk st sts stk
+     = happyFail 0# tk st sts stk
+happyMonad2Reduce k nt fn j tk st sts stk =
+      case happyDrop k (HappyCons (st) (sts)) of
+        sts1@((HappyCons (st1@(action)) (_))) ->
+         let drop_stk = happyDropStk k stk
+
+             off = indexShortOffAddr happyGotoOffsets st1
+             off_i = (off Happy_GHC_Exts.+# nt)
+             new_state = indexShortOffAddr happyTable off_i
+
+
+
+          in
+          happyThen1 (fn stk tk) (\r -> happyNewToken new_state sts1 (r `HappyStk` drop_stk))
+
+happyDrop 0# l = l
+happyDrop n (HappyCons (_) (t)) = happyDrop (n Happy_GHC_Exts.-# (1# :: Happy_GHC_Exts.Int#)) t
+
+happyDropStk 0# l = l
+happyDropStk n (x `HappyStk` xs) = happyDropStk (n Happy_GHC_Exts.-# (1#::Happy_GHC_Exts.Int#)) xs
+
+-----------------------------------------------------------------------------
+-- Moving to a new state after a reduction
+
+
+happyGoto nt j tk st = 
+   {- nothing -}
+   happyDoAction j tk new_state
+   where off = indexShortOffAddr happyGotoOffsets st
+         off_i = (off Happy_GHC_Exts.+# nt)
+         new_state = indexShortOffAddr happyTable off_i
+
+
+
+
+-----------------------------------------------------------------------------
+-- Error recovery (0# is the error token)
+
+-- parse error if we are in recovery and we fail again
+happyFail 0# tk old_st _ stk@(x `HappyStk` _) =
+     let i = (case Happy_GHC_Exts.unsafeCoerce# x of { (Happy_GHC_Exts.I# (i)) -> i }) in
+--      trace "failing" $ 
+        happyError_ i tk
+
+{-  We don't need state discarding for our restricted implementation of
+    "error".  In fact, it can cause some bogus parses, so I've disabled it
+    for now --SDM
+
+-- discard a state
+happyFail  0# tk old_st (HappyCons ((action)) (sts)) 
+                                                (saved_tok `HappyStk` _ `HappyStk` stk) =
+--      trace ("discarding state, depth " ++ show (length stk))  $
+        happyDoAction 0# tk action sts ((saved_tok`HappyStk`stk))
+-}
+
+-- Enter error recovery: generate an error token,
+--                       save the old token and carry on.
+happyFail  i tk (action) sts stk =
+--      trace "entering error recovery" $
+        happyDoAction 0# tk action sts ( (Happy_GHC_Exts.unsafeCoerce# (Happy_GHC_Exts.I# (i))) `HappyStk` stk)
+
+-- Internal happy errors:
+
+notHappyAtAll :: a
+notHappyAtAll = error "Internal Happy error\n"
+
+-----------------------------------------------------------------------------
+-- Hack to get the typechecker to accept our action functions
+
+
+happyTcHack :: Happy_GHC_Exts.Int# -> a -> a
+happyTcHack x y = y
+{-# INLINE happyTcHack #-}
+
+
+-----------------------------------------------------------------------------
+-- Seq-ing.  If the --strict flag is given, then Happy emits 
+--      happySeq = happyDoSeq
+-- otherwise it emits
+--      happySeq = happyDontSeq
+
+happyDoSeq, happyDontSeq :: a -> b -> b
+happyDoSeq   a b = a `seq` b
+happyDontSeq a b = b
+
+-----------------------------------------------------------------------------
+-- Don't inline any functions from the template.  GHC has a nasty habit
+-- of deciding to inline happyGoto everywhere, which increases the size of
+-- the generated parser quite a bit.
+
+
+{-# NOINLINE happyDoAction #-}
+{-# NOINLINE happyTable #-}
+{-# NOINLINE happyCheck #-}
+{-# NOINLINE happyActOffsets #-}
+{-# NOINLINE happyGotoOffsets #-}
+{-# NOINLINE happyDefActions #-}
+
+{-# NOINLINE happyShift #-}
+{-# NOINLINE happySpecReduce_0 #-}
+{-# NOINLINE happySpecReduce_1 #-}
+{-# NOINLINE happySpecReduce_2 #-}
+{-# NOINLINE happySpecReduce_3 #-}
+{-# NOINLINE happyReduce #-}
+{-# NOINLINE happyMonadReduce #-}
+{-# NOINLINE happyGoto #-}
+{-# NOINLINE happyFail #-}
+
+-- end of Happy Template.
+
diff --git a/dist/build/Data/Cfg/Bnf/Scanner.hs b/dist/build/Data/Cfg/Bnf/Scanner.hs
new file mode 100644
--- /dev/null
+++ b/dist/build/Data/Cfg/Bnf/Scanner.hs
@@ -0,0 +1,360 @@
+{-# LANGUAGE CPP,MagicHash #-}
+{-# LINE 1 "src/Data/Cfg/Bnf/Scanner.x" #-}
+
+{-# OPTIONS_GHC -w #-}
+-- | Scanner for Bnf
+module Data.Cfg.Bnf.Scanner(scan) where
+
+import Data.Cfg.Bnf.Token
+
+#if __GLASGOW_HASKELL__ >= 603
+#include "ghcconfig.h"
+#elif defined(__GLASGOW_HASKELL__)
+#include "config.h"
+#endif
+#if __GLASGOW_HASKELL__ >= 503
+import Data.Array
+import Data.Char (ord)
+import Data.Array.Base (unsafeAt)
+#else
+import Array
+import Char (ord)
+#endif
+#if __GLASGOW_HASKELL__ >= 503
+import GHC.Exts
+#else
+import GlaExts
+#endif
+{-# LINE 1 "templates/wrappers.hs" #-}
+-- -----------------------------------------------------------------------------
+-- Alex wrapper code.
+--
+-- This code is in the PUBLIC DOMAIN; you may copy it freely and use
+-- it for any purpose whatsoever.
+
+import Data.Word (Word8)
+
+
+import qualified Data.Bits
+
+-- | Encode a Haskell String to a list of Word8 values, in UTF8 format.
+utf8Encode :: Char -> [Word8]
+utf8Encode = map fromIntegral . go . ord
+ where
+  go oc
+   | oc <= 0x7f       = [oc]
+
+   | oc <= 0x7ff      = [ 0xc0 + (oc `Data.Bits.shiftR` 6)
+                        , 0x80 + oc Data.Bits..&. 0x3f
+                        ]
+
+   | oc <= 0xffff     = [ 0xe0 + (oc `Data.Bits.shiftR` 12)
+                        , 0x80 + ((oc `Data.Bits.shiftR` 6) Data.Bits..&. 0x3f)
+                        , 0x80 + oc Data.Bits..&. 0x3f
+                        ]
+   | otherwise        = [ 0xf0 + (oc `Data.Bits.shiftR` 18)
+                        , 0x80 + ((oc `Data.Bits.shiftR` 12) Data.Bits..&. 0x3f)
+                        , 0x80 + ((oc `Data.Bits.shiftR` 6) Data.Bits..&. 0x3f)
+                        , 0x80 + oc Data.Bits..&. 0x3f
+                        ]
+
+
+
+type Byte = Word8
+
+-- -----------------------------------------------------------------------------
+-- The input type
+
+
+
+
+
+
+
+
+
+-- -----------------------------------------------------------------------------
+-- Token positions
+
+-- `Posn' records the location of a token in the input text.  It has three
+-- fields: the address (number of chacaters preceding the token), line number
+-- and column of a token within the file. `start_pos' gives the position of the
+-- start of the file and `eof_pos' a standard encoding for the end of file.
+-- `move_pos' calculates the new position after traversing a given character,
+-- assuming the usual eight character tab stops.
+
+
+
+-- -----------------------------------------------------------------------------
+-- Default monad
+
+
+
+
+-- -----------------------------------------------------------------------------
+-- Monad (with ByteString input)
+
+
+
+
+-- -----------------------------------------------------------------------------
+-- Basic wrapper
+
+
+type AlexInput = (Char,[Byte],String)
+
+alexInputPrevChar :: AlexInput -> Char
+alexInputPrevChar (c,_,_) = c
+
+-- alexScanTokens :: String -> [token]
+alexScanTokens str = go ('\n',[],str)
+  where go inp@(_,_bs,s) =
+          case alexScan inp 0 of
+                AlexEOF -> []
+                AlexError _ -> error "lexical error"
+                AlexSkip  inp' len     -> go inp'
+                AlexToken inp' len act -> act (take len s) : go inp'
+
+alexGetByte :: AlexInput -> Maybe (Byte,AlexInput)
+alexGetByte (c,(b:bs),s) = Just (b,(c,bs,s))
+alexGetByte (c,[],[])    = Nothing
+alexGetByte (_,[],(c:s)) = case utf8Encode c of
+                             (b:bs) -> Just (b, (c, bs, s))
+                             [] -> Nothing
+
+
+
+-- -----------------------------------------------------------------------------
+-- Basic wrapper, ByteString version
+
+
+
+
+
+
+-- -----------------------------------------------------------------------------
+-- Posn wrapper
+
+-- Adds text positions to the basic model.
+
+
+
+
+-- -----------------------------------------------------------------------------
+-- Posn wrapper, ByteString version
+
+
+
+
+-- -----------------------------------------------------------------------------
+-- GScan wrapper
+
+-- For compatibility with previous versions of Alex, and because we can.
+
+
+alex_base :: AlexAddr
+alex_base = AlexA# "\x01\x00\x00\x00\x44\x00\x00\x00\x76\x00\x00\x00\xf6\x00\x00\x00\x76\x01\x00\x00\xe7\x01\x00\x00\x00\x00\x00\x00\x67\x02\x00\x00\x00\x00\x00\x00\xd8\x02\x00\x00\x00\x00\x00\x00\xc3\xff\xff\xff\x00\x00\x00\x00\x19\x03\x00\x00\x19\x04\x00\x00\xd9\x03\x00\x00\x00\x00\x00\x00\xd9\x04\x00\x00\x99\x04\x00\x00\x00\x00\x00\x00\x90\x05\x00\x00\x94\x05\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x6f\x05\x00\x00\x64\x06\x00\x00\x7c\x05\x00\x00\x00\x00\x00\x00\x70\x05\x00\x00"#
+
+alex_table :: AlexAddr
+alex_table = AlexA# 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+
+alex_check :: AlexAddr
+alex_check = AlexA# 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f\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff"#
+
+alex_deflt :: AlexAddr
+alex_deflt = AlexA# "\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\x0a\x00\x0a\x00\xff\xff\x0c\x00\x0c\x00\x10\x00\x10\x00\x13\x00\x13\x00\x1c\x00\x1c\x00\x1c\x00\x15\x00\x15\x00\x15\x00\xff\xff\x15\x00\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff"#
+
+alex_accept = listArray (0::Int,29) [AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccNone,AlexAccSkip,AlexAccSkip,AlexAcc (alex_action_2),AlexAcc (alex_action_3),AlexAcc (alex_action_4),AlexAcc (alex_action_5),AlexAcc (alex_action_6),AlexAcc (alex_action_7),AlexAcc (alex_action_7),AlexAcc (alex_action_7)]
+{-# LINE 26 "src/Data/Cfg/Bnf/Scanner.x" #-}
+
+-- | Tokenizes a source string.
+scan :: String -> [Token]
+scan = alexScanTokens
+
+alex_action_2 =  Token YIELDS 
+alex_action_3 =  Token OR 
+alex_action_4 =  Token FULL_STOP 
+alex_action_5 =  Token LOWER_IDENTIFIER 
+alex_action_6 =  Token UPPER_IDENTIFIER 
+alex_action_7 =  Token ERROR 
+{-# LINE 1 "templates/GenericTemplate.hs" #-}
+-- -----------------------------------------------------------------------------
+-- ALEX TEMPLATE
+--
+-- This code is in the PUBLIC DOMAIN; you may copy it freely and use
+-- it for any purpose whatsoever.
+
+-- -----------------------------------------------------------------------------
+-- INTERNALS and main scanner engine
+
+
+
+
+
+
+
+-- Do not remove this comment. Required to fix CPP parsing when using GCC and a clang-compiled alex.
+#if __GLASGOW_HASKELL__ > 706
+#define GTE(n,m) (tagToEnum# (n >=# m))
+#define EQ(n,m) (tagToEnum# (n ==# m))
+#else
+#define GTE(n,m) (n >=# m)
+#define EQ(n,m) (n ==# m)
+#endif
+
+
+
+data AlexAddr = AlexA# Addr#
+-- Do not remove this comment. Required to fix CPP parsing when using GCC and a clang-compiled alex.
+#if __GLASGOW_HASKELL__ < 503
+uncheckedShiftL# = shiftL#
+#endif
+
+{-# INLINE alexIndexInt16OffAddr #-}
+alexIndexInt16OffAddr (AlexA# arr) off =
+#ifdef WORDS_BIGENDIAN
+  narrow16Int# i
+  where
+        i    = word2Int# ((high `uncheckedShiftL#` 8#) `or#` low)
+        high = int2Word# (ord# (indexCharOffAddr# arr (off' +# 1#)))
+        low  = int2Word# (ord# (indexCharOffAddr# arr off'))
+        off' = off *# 2#
+#else
+  indexInt16OffAddr# arr off
+#endif
+
+
+
+
+
+{-# INLINE alexIndexInt32OffAddr #-}
+alexIndexInt32OffAddr (AlexA# arr) off = 
+#ifdef WORDS_BIGENDIAN
+  narrow32Int# i
+  where
+   i    = word2Int# ((b3 `uncheckedShiftL#` 24#) `or#`
+		     (b2 `uncheckedShiftL#` 16#) `or#`
+		     (b1 `uncheckedShiftL#` 8#) `or#` b0)
+   b3   = int2Word# (ord# (indexCharOffAddr# arr (off' +# 3#)))
+   b2   = int2Word# (ord# (indexCharOffAddr# arr (off' +# 2#)))
+   b1   = int2Word# (ord# (indexCharOffAddr# arr (off' +# 1#)))
+   b0   = int2Word# (ord# (indexCharOffAddr# arr off'))
+   off' = off *# 4#
+#else
+  indexInt32OffAddr# arr off
+#endif
+
+
+
+
+
+
+#if __GLASGOW_HASKELL__ < 503
+quickIndex arr i = arr ! i
+#else
+-- GHC >= 503, unsafeAt is available from Data.Array.Base.
+quickIndex = unsafeAt
+#endif
+
+
+
+
+-- -----------------------------------------------------------------------------
+-- Main lexing routines
+
+data AlexReturn a
+  = AlexEOF
+  | AlexError  !AlexInput
+  | AlexSkip   !AlexInput !Int
+  | AlexToken  !AlexInput !Int a
+
+-- alexScan :: AlexInput -> StartCode -> AlexReturn a
+alexScan input (I# (sc))
+  = alexScanUser undefined input (I# (sc))
+
+alexScanUser user input (I# (sc))
+  = case alex_scan_tkn user input 0# input sc AlexNone of
+	(AlexNone, input') ->
+		case alexGetByte input of
+			Nothing -> 
+
+
+
+				   AlexEOF
+			Just _ ->
+
+
+
+				   AlexError input'
+
+	(AlexLastSkip input'' len, _) ->
+
+
+
+		AlexSkip input'' len
+
+	(AlexLastAcc k input''' len, _) ->
+
+
+
+		AlexToken input''' len k
+
+
+-- Push the input through the DFA, remembering the most recent accepting
+-- state it encountered.
+
+alex_scan_tkn user orig_input len input s last_acc =
+  input `seq` -- strict in the input
+  let 
+	new_acc = (check_accs (alex_accept `quickIndex` (I# (s))))
+  in
+  new_acc `seq`
+  case alexGetByte input of
+     Nothing -> (new_acc, input)
+     Just (c, new_input) -> 
+
+
+
+      case fromIntegral c of { (I# (ord_c)) ->
+        let
+                base   = alexIndexInt32OffAddr alex_base s
+                offset = (base +# ord_c)
+                check  = alexIndexInt16OffAddr alex_check offset
+		
+                new_s = if GTE(offset,0#) && EQ(check,ord_c)
+			  then alexIndexInt16OffAddr alex_table offset
+			  else alexIndexInt16OffAddr alex_deflt s
+	in
+        case new_s of
+	    -1# -> (new_acc, input)
+		-- on an error, we want to keep the input *before* the
+		-- character that failed, not after.
+    	    _ -> alex_scan_tkn user orig_input (if c < 0x80 || c >= 0xC0 then (len +# 1#) else len)
+                                                -- note that the length is increased ONLY if this is the 1st byte in a char encoding)
+			new_input new_s new_acc
+      }
+  where
+	check_accs (AlexAccNone) = last_acc
+	check_accs (AlexAcc a  ) = AlexLastAcc a input (I# (len))
+	check_accs (AlexAccSkip) = AlexLastSkip  input (I# (len))
+
+
+data AlexLastAcc a
+  = AlexNone
+  | AlexLastAcc a !AlexInput !Int
+  | AlexLastSkip  !AlexInput !Int
+
+instance Functor AlexLastAcc where
+    fmap f AlexNone = AlexNone
+    fmap f (AlexLastAcc x y z) = AlexLastAcc (f x) y z
+    fmap f (AlexLastSkip x y) = AlexLastSkip x y
+
+data AlexAcc a user
+  = AlexAccNone
+  | AlexAcc a
+  | AlexAccSkip
+
+
+-- used by wrappers
+iUnbox (I# (i)) = i
+
diff --git a/src/Data/Cfg.hs b/src/Data/Cfg.hs
new file mode 100644
--- /dev/null
+++ b/src/Data/Cfg.hs
@@ -0,0 +1,28 @@
+-- | Context-free grammars.
+module Data.Cfg(
+    module Data.Cfg.Augment,
+    module Data.Cfg.Cfg,
+    module Data.Cfg.CPretty,
+    module Data.Cfg.FirstSet,
+    module Data.Cfg.FollowSet,
+    module Data.Cfg.FreeCfg,
+    module Data.Cfg.LookaheadSet,
+    module Data.Cfg.Nullable,
+    module Data.Cfg.PredictSet,
+    module Data.Cfg.Productive,
+    module Data.Cfg.Reachable,
+    module Data.Cfg.RuleApplication
+    ) where
+
+import Data.Cfg.Augment
+import Data.Cfg.Cfg
+import Data.Cfg.CPretty
+import Data.Cfg.FirstSet
+import Data.Cfg.FollowSet
+import Data.Cfg.FreeCfg
+import Data.Cfg.LookaheadSet
+import Data.Cfg.Nullable
+import Data.Cfg.PredictSet
+import Data.Cfg.Productive
+import Data.Cfg.Reachable
+import Data.Cfg.RuleApplication
diff --git a/src/Data/Cfg/Augment.hs b/src/Data/Cfg/Augment.hs
new file mode 100644
--- /dev/null
+++ b/src/Data/Cfg/Augment.hs
@@ -0,0 +1,64 @@
+-- | Augmented grammars.
+{-# LANGUAGE ScopedTypeVariables #-}
+module Data.Cfg.Augment (
+    -- * Augmenting grammars
+    augmentCfg,
+    -- * Augmenting symbols
+    AugNT(..),
+    AugT(..),
+    -- * Type synonyms
+    AugV,
+    AugVs,
+    AugProduction,
+    AugFreeCfg
+    ) where
+
+import Data.Cfg.Cfg(Cfg(..), Production, V(..), Vs)
+import Data.Cfg.FreeCfg(FreeCfg(..))
+import qualified Data.Set as S
+
+-- | Nonterminal symbols augmented with a special 'StartSymbol'
+data AugNT nt = StartSymbol | AugNT nt
+    deriving (Eq, Ord, Show)
+
+-- | Terminal symbols augmented with a special end-of-file symbol
+data AugT t = EOF | AugT t
+    deriving (Eq, Ord, Show)
+
+-- | A convenience synonym for an augmented vocabulary symbol
+type AugV t nt = V (AugT t) (AugNT nt)
+
+-- | A convenience synonym for augmented vocabulary symbols
+type AugVs t nt = Vs (AugT t) (AugNT nt)
+
+-- | A convenience synonym for augmented productions
+type AugProduction t nt = Production (AugT t) (AugNT nt)
+
+-- | A convenience symbol for an augmented grammar
+type AugFreeCfg t nt = FreeCfg (AugT t) (AugNT nt)
+
+-- | Returns the /augmented/ grammar: a grammar for the same language
+-- but using explicit start and end-of-file symbols.
+augmentCfg :: forall cfg t nt . (Cfg cfg t nt, Ord nt, Ord t)
+	   => cfg t nt -> FreeCfg (AugT t) (AugNT nt)
+augmentCfg cfg = FreeCfg {
+    nonterminals' = S.insert StartSymbol $ S.map AugNT $ nonterminals cfg,
+    terminals' = S.insert EOF $ S.map AugT $ terminals cfg,
+    productionRules' = pr,
+    startSymbol' = StartSymbol
+    }
+
+    where
+    pr :: AugNT nt -> S.Set (Vs (AugT t) (AugNT nt))
+    pr StartSymbol = S.singleton [NT $ AugNT $ startSymbol cfg, T EOF]
+    pr (AugNT nt) = S.map augmentVs oldRhss
+	where
+	oldRhss :: S.Set (Vs t nt)
+	oldRhss = productionRules cfg nt
+
+	augmentVs :: Vs t nt -> Vs (AugT t) (AugNT nt)
+	augmentVs = map augmentV
+
+	augmentV :: V t nt -> V (AugT t) (AugNT nt)
+	augmentV (NT nt') = NT $ AugNT nt'
+        augmentV (T t') = T $ AugT t'
diff --git a/src/Data/Cfg/Bnf.hs b/src/Data/Cfg/Bnf.hs
new file mode 100644
--- /dev/null
+++ b/src/Data/Cfg/Bnf.hs
@@ -0,0 +1,29 @@
+{- | A simple, concrete instance of 'Cfg' that can be parsed from source.
+
+The grammar of Bnf source is:
+
+@
+grammar ::= (production)+.
+production ::= LOWER_CASE_STRING "::=" right_hand_sides ".".
+right_hand_sides ::= right_hand_side ("|" right_hand_side)*.
+right_hand_side ::= term*.
+term ::= UPPER_CASE_STRING | LOWER_CASE_STRING.
+@
+
+where /*/ means zero or more repetitions and /+/ means one or more
+repetitions.  Terminals are indicated by strings of upper-case
+characters and underscores; nonterminals by strings of lower-case
+characters and underscores.  Quoted strings are literal tokens.
+
+-}
+
+module Data.Cfg.Bnf (
+    Grammar(..),
+    bnf,
+    parse
+    ) where
+
+import Data.Cfg.Bnf.Parser
+import Data.Cfg.Bnf.QQ
+import Data.Cfg.Bnf.Syntax
+
diff --git a/src/Data/Cfg/Bnf/Parser.y b/src/Data/Cfg/Bnf/Parser.y
new file mode 100644
--- /dev/null
+++ b/src/Data/Cfg/Bnf/Parser.y
@@ -0,0 +1,66 @@
+{
+-- | Parser for Bnf
+module Data.Cfg.Bnf.Parser(parse) where
+
+import qualified Data.Map as M
+import Data.Cfg.Bnf.Scanner(scan)
+import Data.Cfg.Bnf.Syntax
+import Data.Cfg.Bnf.Token
+import Data.Cfg.Cfg(Production, V(..), Vs)
+}
+
+%name parseTokens grammar
+
+%error { parseError }
+
+%tokentype { Token }
+
+%token
+    FULL_STOP           { Token FULL_STOP $$ }
+    LOWER_IDENTIFIER    { Token LOWER_IDENTIFIER $$ }
+    OR                  { Token OR $$ }
+    UPPER_IDENTIFIER    { Token UPPER_IDENTIFIER $$ }
+    YIELDS              { Token YIELDS $$ }
+
+%%
+
+grammar :: { Grammar String String  }
+        : prods { Grammar $1 }
+
+prods :: { [Production String String] }
+      : prods prod { $1 ++ $2 }
+      | prod { $1 }
+
+prod :: { [Production String String] }
+     : LOWER_IDENTIFIER YIELDS rhs FULL_STOP { [ ($1, alt) | alt <- $3 ] }
+
+rhs :: { [Vs String String] }
+    : alts { $1 }
+
+alts :: { [Vs String String] }
+     : alts OR alt { $1 ++ [ $3 ] }
+     | alt { [ $1 ] }
+
+alt :: { Vs String String }
+    : terms { $1 }
+
+terms :: { Vs String String }
+      : terms term { $1 ++ [ $2 ] }
+      | { [] }
+
+term :: { V String String }
+     : UPPER_IDENTIFIER { T $1 }
+     | LOWER_IDENTIFIER { NT $1 }
+
+{
+
+parseError :: [Token] -> a
+parseError ts = error $ "parseError at: " ++ show ts
+
+-- | Parses Bnf source into a 'Grammar'.
+parse :: String -> Grammar String String
+parse = parseTokens . scan
+
+-- | Parses a list of 'Token's into a 'Grammar'.
+parseTokens :: [Token] -> Grammar String String
+}
diff --git a/src/Data/Cfg/Bnf/QQ.hs b/src/Data/Cfg/Bnf/QQ.hs
new file mode 100644
--- /dev/null
+++ b/src/Data/Cfg/Bnf/QQ.hs
@@ -0,0 +1,17 @@
+-- | 'QuasiQuoter' for BNF source.
+module Data.Cfg.Bnf.QQ(bnf) where
+
+import Data.Cfg.Bnf.Parser
+import Language.Haskell.TH.Quote
+
+-- | 'QuasiQuoter' for BNF source.  Generates a value of type
+-- 'Grammar'.  Not usable in pattern, type or declaration positions.
+bnf :: QuasiQuoter
+bnf = QuasiQuoter {
+    quoteExp = dataToExpQ (const Nothing) . parse,
+    quotePat = err,
+    quoteType = err,
+    quoteDec = err
+    }
+    where
+    err _ = error "The bnf quasiquoter is only allowed in Exp position."
diff --git a/src/Data/Cfg/Bnf/Scanner.x b/src/Data/Cfg/Bnf/Scanner.x
new file mode 100644
--- /dev/null
+++ b/src/Data/Cfg/Bnf/Scanner.x
@@ -0,0 +1,30 @@
+{
+{-# OPTIONS_GHC -w #-}
+-- | Scanner for Bnf
+module Data.Cfg.Bnf.Scanner(scan) where
+
+import Data.Cfg.Bnf.Token
+}
+
+%wrapper "basic"
+
+$lower = [a-z]
+$upper = [A-Z]
+$lowerTail = [a-z_0-9]
+$upperTail = [A-Z_0-9]
+
+tokens :-
+       $white+          ;
+       \-\-.*           ;
+       \:\:\=           { Token YIELDS }
+       \|               { Token OR }
+       \.               { Token FULL_STOP }
+       $lower $lowerTail*               { Token LOWER_IDENTIFIER }
+       $upper $upperTail*               { Token UPPER_IDENTIFIER }
+       .                { Token ERROR }
+
+{
+-- | Tokenizes a source string.
+scan :: String -> [Token]
+scan = alexScanTokens
+}
diff --git a/src/Data/Cfg/Bnf/Syntax.hs b/src/Data/Cfg/Bnf/Syntax.hs
new file mode 100644
--- /dev/null
+++ b/src/Data/Cfg/Bnf/Syntax.hs
@@ -0,0 +1,39 @@
+-- | Syntax structures of Bnf.
+{-# LANGUAGE DeriveDataTypeable #-}
+{-# LANGUAGE FlexibleInstances #-}
+{-# LANGUAGE MultiParamTypeClasses #-}
+module Data.Cfg.Bnf.Syntax(Grammar(..)) where
+
+import Data.Cfg.Cfg(Cfg(..), Production, V(..), Vs)
+import Data.Data(Data, Typeable)
+import qualified Data.Set as S
+
+-- | A simple, concrete instance of 'Cfg'.  The terminal and
+-- nonterminal symbols of a 'Grammar' are defined to be exactly those
+-- appearing the productions.  The start symbol is defined to be the
+-- head of the first of the productions.
+newtype Grammar t nt = Grammar {
+    grammarProductions :: [Production t nt]
+	-- ^ the productions of the 'Grammar'
+    }
+    deriving (Data, Typeable)
+
+instance (Ord nt, Ord t) => Cfg Grammar t nt where
+    terminals = S.fromList . concatMap terminalsProd . grammarProductions
+    nonterminals = S.fromList . concatMap nonterminalsProd . grammarProductions
+    productionRules g nt
+	= S.fromList [ rhs | (nt', rhs) <- grammarProductions g,
+			     nt == nt' ]
+    startSymbol = fst . head . grammarProductions
+
+nonterminalsVs :: Vs t nt -> [nt]
+nonterminalsVs vs = [ nt | NT nt <- vs ]
+
+terminalsVs :: Vs t nt -> [t]
+terminalsVs vs = [ t | T t <- vs ]
+
+nonterminalsProd :: Production t nt -> [nt]
+nonterminalsProd (nt, rhs) = nt : nonterminalsVs rhs
+
+terminalsProd :: Production t nt -> [t]
+terminalsProd = terminalsVs . snd
diff --git a/src/Data/Cfg/Bnf/Token.hs b/src/Data/Cfg/Bnf/Token.hs
new file mode 100644
--- /dev/null
+++ b/src/Data/Cfg/Bnf/Token.hs
@@ -0,0 +1,26 @@
+-- | Bnf tokens
+module Data.Cfg.Bnf.Token(
+    Token(..),
+    TokenType(..)
+    ) where
+
+-- | Token types
+data TokenType = ERROR
+    | FULL_STOP			-- ^ @.@
+    | LOWER_IDENTIFIER
+
+	-- ^ an identifier made of lower-case characters possibly
+	-- separated by underscores
+
+    | OR			-- ^ @|@
+    | UPPER_IDENTIFIER
+
+	-- ^ an identifier made of upper-case characters possibly
+	-- separated by underscores
+
+    | YIELDS			-- ^ @::=@
+    deriving (Eq, Show)
+
+-- | Basic Bnf tokens.	They do not contain location information.
+data Token = Token TokenType String
+  deriving (Eq, Show)
diff --git a/src/Data/Cfg/CPretty.hs b/src/Data/Cfg/CPretty.hs
new file mode 100644
--- /dev/null
+++ b/src/Data/Cfg/CPretty.hs
@@ -0,0 +1,12 @@
+-- | Pretty-printing that requires a context
+{-# LANGUAGE MultiParamTypeClasses #-}
+{-# LANGUAGE RankNTypes #-}
+module Data.Cfg.CPretty(CPretty(..)) where
+
+import Control.Monad.Reader
+import Text.PrettyPrint
+
+-- | Pretty-printing that requires a context
+class CPretty p ctxt where
+    cpretty :: (MonadReader ctxt m) => p -> m Doc
+	-- ^ pretty-print in a monad providing the context
diff --git a/src/Data/Cfg/Cfg.hs b/src/Data/Cfg/Cfg.hs
new file mode 100644
--- /dev/null
+++ b/src/Data/Cfg/Cfg.hs
@@ -0,0 +1,183 @@
+-- | Context-free grammars.
+{-# LANGUAGE DeriveDataTypeable #-}
+{-# LANGUAGE FlexibleInstances #-}
+{-# LANGUAGE MultiParamTypeClasses #-}
+{-# LANGUAGE ScopedTypeVariables #-}
+module Data.Cfg.Cfg(
+    -- * Class
+    Cfg(..),
+    -- * Vocabulary
+    V(..),
+    Vs,
+    isNT,
+    isT,
+    bimapV,
+    bimapVs,
+    vocabulary,
+    usedVocabulary,
+    undeclaredVocabulary,
+    isFullyDeclared,
+    -- * Productions
+    Production,
+    productions,
+    -- * Utility functions
+    eqCfg {- ,
+    compareCfg -}) where
+
+import Control.Monad(liftM4)
+import Control.Monad.Reader(ask)
+import Data.Cfg.CPretty
+import Data.Data(Data, Typeable)
+import qualified Data.Set as S
+import Text.PrettyPrint
+
+------------------------------------------------------------
+
+-- | Represents a context-free grammar with its nonterminal and
+-- terminal types.
+class Cfg cfg t nt where
+    nonterminals :: cfg t nt -> S.Set nt
+	-- ^ the nonterminals of the grammar
+    terminals :: cfg t nt -> S.Set t
+	-- ^ the terminals of the grammar
+    productionRules :: cfg t nt -> nt -> S.Set (Vs t nt)
+	-- ^ the productions of the grammar
+    startSymbol :: cfg t nt -> nt
+	-- ^ the start symbol of the grammar; must be an element of
+	-- 'nonterminals' 'cfg'
+
+instance (Cfg cfg t nt) => CPretty (cfg t nt) (V t nt -> Doc) where
+    cpretty cfg = liftM4 vcat' ss ts nts prods
+	where
+	vcat' a b c d = vcat [a, b, c, d]
+	ss = do
+	    prettyV <- ask
+	    return (text "Start symbol:" <+> prettyV (NT $ startSymbol cfg))
+	ts = do
+	    prettyV <- ask
+	    return (text "Terminals:"
+		       <+> fsep (punctuate comma
+				   $ map (prettyV . T)
+					 (S.toList $ terminals cfg)))
+	nts = do
+	    prettyV <- ask
+	    return (text "Nonterminals:"
+		       <+> fsep (punctuate comma
+				   $ map (prettyV . NT)
+					 (S.toList $ nonterminals cfg)))
+
+	prods = do
+	    prettyV <- ask
+	    return (text "Productions:"
+			 $$ nest 4
+				 (vcat (map (prettyProd prettyV)
+					    (zip [1..] $ productions cfg))))
+	    where
+	    prettyProd pv (n, (hd, rhs))
+		= hsep [parens (int n),
+			pv (NT hd), text "::=", rhs' <> text "."]
+		where
+		rhs' = hsep $ map pv rhs
+
+------------------------------------------------------------
+
+------------------------------------------------------------
+
+-- | Vocabulary symbols of the grammar.
+data V t nt = T t	-- ^ a terminal
+    | NT nt		-- ^ a nonterminal
+    deriving (Eq, Ord, Show, Data, Typeable)
+
+-- | Returns 'True' iff the vocabularly symbols is a terminal.
+isT :: V t nt -> Bool
+isT (T _) = True
+isT _ = False
+
+-- | Returns 'True' iff the vocabularly symbols is a nonterminal.
+isNT :: V t nt -> Bool
+isNT (NT _) = True
+isNT _ = False
+
+instance Functor (V t) where
+    fmap _f (T t) = T t
+    fmap f (NT nt) = NT $ f nt
+
+-- | Maps over the terminal and nonterminal symbols in a 'V'.
+bimapV :: (t -> t') -> (nt -> nt') -> V t nt -> V t' nt'
+bimapV f _g (T t) = T $ f t
+bimapV _f g (NT nt) = NT $ g nt
+
+-- | Returns the vocabulary symbols of the grammar: elements of
+-- 'terminals' and 'nonterminals'.
+vocabulary :: (Cfg cfg t nt, Ord nt, Ord t) => cfg t nt -> S.Set (V t nt)
+vocabulary cfg = S.map T (terminals cfg)
+		     `S.union` S.map NT (nonterminals cfg)
+
+-- | Synonym for lists of vocabulary symbols.
+type Vs t nt = [V t nt]
+
+-- | Maps over the terminal and nonterminal symbols in a list of 'V's.
+bimapVs :: (t -> t') -> (nt -> nt') -> Vs t nt -> Vs t' nt'
+bimapVs f g = map (bimapV f g)
+
+-- | Productions over vocabulary symbols
+type Production t nt = (nt, Vs t nt)
+
+-- | Returns the productions of the grammar.
+productions :: (Cfg cfg t nt) => cfg t nt -> [Production t nt]
+productions cfg = do
+    nt <- S.toList $ nonterminals cfg
+    vs <- S.toList $ productionRules cfg nt
+    return (nt, vs)
+
+-- | Returns 'True' iff the two inhabitants of 'Cfg' are equal.
+eqCfg :: forall cfg cfg' t nt
+      . (Cfg cfg t nt, Cfg cfg' t nt, Eq nt, Eq t)
+      => cfg t nt -> cfg' t nt -> Bool
+eqCfg cfg cfg' = to4Tuple cfg == to4Tuple cfg'
+
+{------------------------------------------------------------
+
+-- | Compares the two inhabitants of 'Cfg'.
+compareCfg :: forall cfg cfg' t nt
+	   . (Cfg cfg t nt, Cfg cfg' t nt, Ord nt, Ord t)
+	   => cfg t nt -> cfg' t nt -> Ordering
+compareCfg cfg cfg' = compare (to4Tuple cfg) (to4Tuple cfg')
+
+------------------------------------------------------------}
+
+-- | Converts the 'Cfg' to a 4-tuple that inhabits both 'Eq' and 'Ord'
+-- if 't' and 'nt' do.
+to4Tuple :: forall cfg t nt . (Cfg cfg t nt)
+	 => cfg t nt -> (nt, S.Set nt, S.Set t, [Production t nt])
+
+    -- We move the start symbol first to optimize the operations
+    -- since it's most likely to differ.
+
+to4Tuple cfg = (
+    startSymbol cfg,
+    nonterminals cfg,
+    terminals cfg,
+    productions cfg)
+
+-- | Returns all vocabulary used in the productions plus the start
+-- symbol.
+usedVocabulary :: (Cfg cfg t nt, Ord nt, Ord t)
+	       => cfg t nt -> S.Set (V t nt)
+usedVocabulary cfg
+    = S.fromList
+	  $ NT (startSymbol cfg) :
+	      concat [ NT nt : vs | (nt, vs) <- productions cfg]
+
+-- | Returns all vocabulary used in the productions plus the start
+-- symbol but not declared in 'nonterminals' or 'terminals'.
+undeclaredVocabulary :: (Cfg cfg t nt, Ord nt, Ord t)
+                     => cfg t nt -> S.Set (V t nt)
+undeclaredVocabulary cfg = usedVocabulary cfg S.\\ vocabulary cfg
+
+------------------------------------------------------------
+
+-- | Returns 'True' all the vocabulary used in the grammar is
+-- declared.
+isFullyDeclared :: (Cfg cfg t nt, Ord nt, Ord t) => cfg t nt -> Bool
+isFullyDeclared = S.null . undeclaredVocabulary
diff --git a/src/Data/Cfg/Collect.hs b/src/Data/Cfg/Collect.hs
new file mode 100644
--- /dev/null
+++ b/src/Data/Cfg/Collect.hs
@@ -0,0 +1,39 @@
+-- | Data-shuffling
+module Data.Cfg.Collect (
+    collectOnFirst,
+    collectOnSecond,
+    collectOnFirst',
+    collectOnSecond'
+    ) where
+
+import Data.List(nub)
+import qualified Data.Set as S
+
+-- | Collects a list of pairs on the first element.
+collectOnFirst :: Eq a => [(a, b)] -> [(a, [b])]
+collectOnFirst pairs = [(a, bsFor a) | a <- as]
+    where
+    as = nub $ map fst pairs
+    bsFor a = [ b | (a', b) <- pairs, a == a' ]
+
+-- | Collects a list of pairs on the second element.
+collectOnSecond :: Eq b => [(a, b)] -> [([a], b)]
+collectOnSecond pairs = [(asFor b, b) | b <- bs]
+    where
+    bs = nub $ map snd pairs
+    asFor b = [ a | (a, b') <- pairs, b == b' ]
+
+-- | Collects a list of pairs on the first element.
+collectOnFirst' :: (Eq a, Ord b) => [(a, b)] -> [(a, S.Set b)]
+collectOnFirst' pairs = [(a, bsFor a) | a <- as]
+    where
+    as = nub $ map fst pairs
+    bsFor a = S.fromList [ b | (a', b) <- pairs, a == a' ]
+
+-- | Collects a list of pairs on the second element.
+collectOnSecond' :: (Ord a, Eq b) => [(a, b)] -> [(S.Set a, b)]
+collectOnSecond' pairs = [(asFor b, b) | b <- bs]
+    where
+    bs = nub $ map snd pairs
+    asFor b = S.fromList [ a | (a, b') <- pairs, b == b' ]
+
diff --git a/src/Data/Cfg/FirstSet.hs b/src/Data/Cfg/FirstSet.hs
new file mode 100644
--- /dev/null
+++ b/src/Data/Cfg/FirstSet.hs
@@ -0,0 +1,57 @@
+-- | First sets of a context-free grammar.
+{-# LANGUAGE FlexibleContexts #-}
+{-# LANGUAGE ScopedTypeVariables #-}
+module Data.Cfg.FirstSet(firstSet, firstSetMap, firstsOfVs) where
+
+import Data.Cfg.Augment
+import Data.Cfg.Cfg
+import Data.Cfg.FixedPoint(fixedPoint)
+import Data.Cfg.LookaheadSet hiding(unions)
+import qualified Data.Cfg.LookaheadSet as LA
+import qualified Data.Map as M
+import Data.Maybe(fromMaybe)
+import Data.Monoid(Monoid(mconcat))
+import qualified Data.Set as S
+
+-- | Returns the first set of the nonterminal for the grammar as a
+-- map.
+firstSetMap :: forall cfg t nt
+	    . (Cfg cfg (AugT t) (AugNT nt), Ord nt, Ord t, Show nt)
+	    => cfg (AugT t) (AugNT nt) -> M.Map (AugNT nt) (LookaheadSet t)
+firstSetMap cfg = fixedPoint go M.empty
+    where
+    go :: M.Map (AugNT nt) (LookaheadSet t)
+       -> M.Map (AugNT nt) (LookaheadSet t)
+    go knownFirsts
+	= M.fromList [(nt, firstAlts rhss)
+	      | nt <- S.toList $ nonterminals cfg,
+		let rhss = S.toList $ productionRules cfg nt,
+		not $ null rhss ]
+	where
+	firstAlts :: [Vs (AugT t) (AugNT nt)] -> LookaheadSet t
+	firstAlts = LA.unions . map (mconcat . map (firstsV knownFirsts))
+
+-- | Returns the first set of the nonterminal for the grammar.	To
+-- avoid recalculations, hold a copy of @firstSet cfg@.
+firstSet :: forall cfg t nt
+	 . (Cfg cfg (AugT t) (AugNT nt), Ord nt, Ord t, Show nt)
+	 => cfg (AugT t) (AugNT nt) -> AugNT nt -> LookaheadSet t
+firstSet cfg nt = firstSetMap cfg M.! nt
+
+firstsV :: Ord nt
+	=> M.Map (AugNT nt) (LookaheadSet t) -> V (AugT t) (AugNT nt)
+					     -> LookaheadSet t
+firstsV _ (T t) = LA.singleton t
+firstsV fs (NT nt) = fromMaybe LA.empty (M.lookup nt fs)
+
+    -- TODO I need a consistent story here of what I define and
+    -- export.	FollowSet needs this one below, but you can see the
+    -- code duplication with firstsV.  Resolve.
+
+-- | Given a firsts function, find the first set of a list of symbols.
+firstsOfVs :: Ord t
+	   => (AugNT nt -> LookaheadSet t) -> AugVs t nt -> LookaheadSet t
+firstsOfVs firsts vs = mconcat $ map firstsV' vs
+    where
+    firstsV' (T t) = LA.singleton t
+    firstsV' (NT nt) = firsts nt
diff --git a/src/Data/Cfg/FixedPoint.hs b/src/Data/Cfg/FixedPoint.hs
new file mode 100644
--- /dev/null
+++ b/src/Data/Cfg/FixedPoint.hs
@@ -0,0 +1,17 @@
+-- | The iterative fixed-point function.
+module Data.Cfg.FixedPoint (
+    fixedPoint
+    ) where
+
+-- | Given a function and an initial value, find the fixed point of
+-- the function.
+fixedPoint :: Eq a => (a -> a) -> a -> a
+fixedPoint f = go
+    where
+    go s = if s == s'
+	       then s
+	       else go s'
+	where
+	s' = f s
+
+-- TODO When I can use fix instead?
diff --git a/src/Data/Cfg/FollowSet.hs b/src/Data/Cfg/FollowSet.hs
new file mode 100644
--- /dev/null
+++ b/src/Data/Cfg/FollowSet.hs
@@ -0,0 +1,94 @@
+-- | Follow sets of a context-free grammar.
+{-# LANGUAGE FlexibleContexts #-}
+{-# LANGUAGE ScopedTypeVariables #-}
+module Data.Cfg.FollowSet (
+    followSet, followSetMap
+    ) where
+
+import Control.Monad(guard)
+import Data.Cfg.Augment
+import Data.Cfg.Cfg
+import Data.Cfg.Collect(collectOnFirst)
+import Data.Cfg.FirstSet(firstsOfVs)
+import Data.Cfg.FixedPoint(fixedPoint)
+import Data.List(tails)
+import Data.Cfg.LookaheadSet hiding(unions)
+import qualified Data.Cfg.LookaheadSet as LA
+import qualified Data.Map as M
+import qualified Data.Set as S
+
+-- | Represents the environment following a nonterminal symbol.	 A
+-- production @foo ::= <vs> bar <vs'>@ will contribute a 'FollowSite' record
+-- with @ntTail == <vs'>@ and @prodHead == foo@, where @<vs>@ is a
+-- (possibly empty) list of vocabulary symbols.
+data FollowSite t nt = FollowSite {
+    ntTail :: AugVs t nt,
+    prodHead :: AugNT nt
+    }
+
+-- | Calculates a map that gives all the follow sites in the grammar
+-- for the given nonterminal.
+followSitesMap :: (Cfg cfg (AugT t) (AugNT nt), Ord nt)
+      => cfg (AugT t) (AugNT nt)
+      -> M.Map (AugNT nt) [FollowSite t nt]
+followSitesMap cfg = M.fromList . collectOnFirst $ do
+    prodHd <- S.toList $ nonterminals cfg
+    let rhss = S.toList $ productionRules cfg prodHd
+    guard (not $ null rhss)
+    rhs <- rhss
+    NT nt : tl <- tails rhs
+    return (nt, FollowSite { ntTail = tl, prodHead = prodHd })
+
+-- | Given what we know of firsts and follows, find the first set of a
+-- follow site.
+firstsOfFollowSite :: forall t nt . (Ord t, Ord nt)
+		   => (AugNT nt -> LookaheadSet t)
+		   -> M.Map (AugNT nt) (LookaheadSet t)
+		   -> FollowSite t nt
+		   -> LookaheadSet t
+firstsOfFollowSite firsts knownFollows followSite
+    = firstsOfNTTail <> firstsOfProdHead
+    where
+    firstsOfNTTail, firstsOfProdHead  :: LookaheadSet t
+    firstsOfNTTail = firstsOfVs firsts (ntTail followSite)
+    firstsOfProdHead = knownFollows M.! prodHead followSite
+
+-- | Returns the follow sets for the grammar as a
+-- map.
+followSetMap :: forall cfg t nt
+	     . (Cfg cfg (AugT t) (AugNT nt), Ord nt, Ord t, Show nt)
+	     => cfg (AugT t) (AugNT nt)
+		     -- ^ the grammar
+	     -> (AugNT nt -> LookaheadSet t)
+		     -- ^ 'firstSet' for the grammar
+	     -> M.Map (AugNT nt) (LookaheadSet t)
+followSetMap cfg fs = fixedPoint go initMap
+    where
+    go :: M.Map (AugNT nt) (LookaheadSet t)
+       -> M.Map (AugNT nt) (LookaheadSet t)
+    go oldFols = M.mapWithKey (\ k v -> LA.unions $ f k v) oldFols
+	where
+	f :: AugNT nt -> LookaheadSet t -> [LookaheadSet t]
+	f nt oldFollows = oldFollows : map (firstsOfFollowSite fs oldFols) folSites
+	    where
+	    folSites = M.findWithDefault [] nt followSitesMap'
+
+    initMap :: M.Map (AugNT nt) (LookaheadSet t)
+    initMap = M.fromList [(nt, case nt of
+				   StartSymbol -> singleton EOF
+				   _ -> empty) | nt <- nts]
+	where
+	nts = S.toList $ nonterminals cfg
+
+    followSitesMap' :: M.Map (AugNT nt) [FollowSite t nt]
+    followSitesMap' = followSitesMap cfg
+
+-- | Returns the follow set of the nonterminal for the grammar. To
+-- avoid recalculations, hold a copy of @followSet cfg@.
+followSet :: forall cfg t nt
+	  . (Cfg cfg (AugT t) (AugNT nt), Ord nt, Ord t, Show nt)
+	  => cfg (AugT t) (AugNT nt)          -- ^ the grammar
+          -> (AugNT nt -> LookaheadSet t)     -- ^ 'firstSet' for the grammar
+          -> AugNT nt                         -- ^ the nonterminal
+          -> LookaheadSet t
+followSet cfg fs nt = followSetMap cfg fs M.! nt
diff --git a/src/Data/Cfg/FreeCfg.hs b/src/Data/Cfg/FreeCfg.hs
new file mode 100644
--- /dev/null
+++ b/src/Data/Cfg/FreeCfg.hs
@@ -0,0 +1,40 @@
+{-# LANGUAGE FlexibleInstances #-}
+{-# LANGUAGE MultiParamTypeClasses #-}
+-- | The free 'Cfg'
+module Data.Cfg.FreeCfg (
+    FreeCfg(..),
+    toFreeCfg
+    ) where
+
+import Data.Cfg.Cfg(Cfg(..), Vs)
+import qualified Data.Set as S
+
+-- | Represents a context-free grammar with its nonterminal and
+-- terminal types.  The canonical instance of 'Cfg': a record that
+-- collects up implementations of each class method.
+data FreeCfg t nt = FreeCfg {
+    nonterminals' :: S.Set nt,
+	-- ^ the nonterminals of the grammar
+    terminals' :: S.Set t,
+	-- ^ the terminals of the grammar
+    productionRules' :: nt -> S.Set (Vs t nt),
+	-- ^ the productions of the grammar
+    startSymbol' :: nt
+	-- ^ the start symbol of the grammar; must be an element of
+	-- 'nonterminals' 'cfg'
+    }
+
+instance Cfg FreeCfg t nt where
+    nonterminals = nonterminals'
+    terminals = terminals'
+    productionRules = productionRules'
+    startSymbol = startSymbol'
+
+-- | Converts any 'Cfg' into a 'FreeCfg'.
+toFreeCfg :: Cfg cfg t nt => cfg t nt -> FreeCfg t nt
+toFreeCfg cfg = FreeCfg {
+    nonterminals' = nonterminals cfg,
+    terminals' = terminals cfg,
+    productionRules' = productionRules cfg,
+    startSymbol' = startSymbol cfg
+    }
diff --git a/src/Data/Cfg/LookaheadSet.hs b/src/Data/Cfg/LookaheadSet.hs
new file mode 100644
--- /dev/null
+++ b/src/Data/Cfg/LookaheadSet.hs
@@ -0,0 +1,57 @@
+-- | Sets of lookahead symbols.
+module Data.Cfg.LookaheadSet (
+    LookaheadSet,
+    mkLookaheadSet,
+    fromList,
+    toSet,
+    (<>),	-- reexport
+    -- * Set operations
+    empty,
+    singleton,
+    unions
+    ) where
+
+import Data.Cfg.Augment(AugT(..))
+import Data.Monoid(Monoid(..), (<>))
+import qualified Data.Set as S
+
+-- | Set of lookahead symbols providing different 'Monoid' semantics
+-- than 'Data.Set.Set'.	 ('mappend' implements concatenation, not set
+-- union.)
+newtype LookaheadSet t = LookaheadSet {
+    toSet :: S.Set (AugT t)
+	-- ^ Converts the 'LookaheadSet' to a regular 'Data.Set.Set'
+    }
+    deriving (Eq, Ord, Show)
+
+instance Ord t => Monoid (LookaheadSet t) where
+    mempty = LookaheadSet $ S.singleton EOF
+    l@(LookaheadSet s) `mappend` LookaheadSet s'
+	= if EOF `S.member` s
+	      then LookaheadSet $ S.delete EOF s `S.union` s'
+	      else l
+
+-- | Creates a 'LookaheadSet'
+mkLookaheadSet :: (Ord t)
+	       => Bool	-- ^ true iff it has 'EOF'
+	       -> [t]	-- ^ terminal symbols
+	       -> LookaheadSet t
+mkLookaheadSet hasEOF = LookaheadSet . S.fromList . f . map AugT
+    where
+    f = if hasEOF then (EOF:) else id
+
+-- | Creates a 'LookaheadSet' from a list of augmented terminals.
+fromList :: Ord t => [AugT t] -> LookaheadSet t
+fromList = LookaheadSet . S.fromList
+
+-- | The empty lookahead set.
+empty :: LookaheadSet t
+empty = LookaheadSet S.empty
+
+-- | Creates a singleton lookahead set.
+singleton :: AugT t -> LookaheadSet t
+singleton = LookaheadSet . S.singleton
+
+-- | Returns the union of all the lookahead sets.
+unions :: Ord t => [LookaheadSet t] -> LookaheadSet t
+unions = LookaheadSet . S.unions . map toSet
diff --git a/src/Data/Cfg/Nullable.hs b/src/Data/Cfg/Nullable.hs
new file mode 100644
--- /dev/null
+++ b/src/Data/Cfg/Nullable.hs
@@ -0,0 +1,29 @@
+-- | Nullable nonterminals
+{-# LANGUAGE ScopedTypeVariables #-}
+module Data.Cfg.Nullable(nullables) where
+
+import Control.Monad(guard)
+import Data.Cfg.Cfg
+import Data.Cfg.FixedPoint(fixedPoint)
+import qualified Data.Set as S
+
+-- | Returns the nonterminals in the grammar that can produce the
+-- empty string.
+nullables :: forall cfg t nt . (Cfg cfg t nt, Ord nt)
+	  => cfg t nt -> S.Set nt
+nullables cfg = fixedPoint go S.empty
+    where
+    go :: S.Set nt -> S.Set nt
+    go knownNullables = calculatedNullables
+	where
+	isKnownNullable :: V t nt -> Bool
+	isKnownNullable (NT nm) = nm `S.member` knownNullables
+	isKnownNullable _ = False
+
+	calculatedNullables :: S.Set nt
+	calculatedNullables = S.fromList $ do
+	    nt <- S.toList $ nonterminals cfg
+	    let rhss = S.toList $ productionRules cfg nt
+	    guard $ any (all isKnownNullable) rhss
+            return nt
+
diff --git a/src/Data/Cfg/PredictSet.hs b/src/Data/Cfg/PredictSet.hs
new file mode 100644
--- /dev/null
+++ b/src/Data/Cfg/PredictSet.hs
@@ -0,0 +1,76 @@
+{-# LANGUAGE FlexibleContexts #-}
+{-# LANGUAGE ScopedTypeVariables #-}
+-- | Predict sets of a context-free grammar.
+module Data.Cfg.PredictSet (
+    Prediction,
+    Predictions,
+    predictSet,
+    ll1Info,
+    ll1InfoMap,
+    isLL1
+    ) where
+
+import Data.Cfg.Augment
+import Data.Cfg.Cfg(Cfg(..))
+import Data.Cfg.Collect
+import Data.Cfg.FirstSet(firstsOfVs)
+import Data.Cfg.LookaheadSet
+import qualified Data.Map as M
+import qualified Data.Set as S
+
+-- | Returns the predict set of a production.
+predictSet :: (Ord t)
+	   => (AugNT nt -> LookaheadSet t)    -- ^ 'firstSet' for the grammar
+	   -> (AugNT nt -> LookaheadSet t)    -- ^ 'followSet' for the grammar
+	   -> AugProduction t nt	      -- ^ the production
+	   -> LookaheadSet t
+predictSet firstSet' followSet' (hd, vs)
+    = firstsOfVs firstSet' vs <> followSet' hd
+
+-- | A lookahead set with the productions it predicts
+type Prediction t nt = (LookaheadSet t, S.Set (AugProduction t nt))
+
+-- | A set of 'Prediction's.  The 'LookaheadSet's of the 'Prediction's
+-- will be pairwise disjoint.
+type Predictions t nt = S.Set (Prediction t nt)
+
+-- | Returns the production 'Predictions' for a nonterminal symbol.
+ll1Info :: (Cfg cfg (AugT t) (AugNT nt), Ord nt, Ord t)
+	=> cfg (AugT t) (AugNT nt)
+	-> (AugProduction t nt -> LookaheadSet t)
+	-> AugNT nt
+	-> Predictions t nt
+ll1Info cfg predictSet' nt = ll1InfoMap cfg predictSet' M.! nt
+
+-- | Returns the production 'Predictions' for the grammar as a map.
+ll1InfoMap :: forall cfg t nt
+	   . (Cfg cfg (AugT t) (AugNT nt), Ord nt, Ord t)
+	   => cfg (AugT t) (AugNT nt)
+	   -> (AugProduction t nt -> LookaheadSet t)
+	   -> M.Map (AugNT nt) (Predictions t nt)
+ll1InfoMap cfg predictSet' = mkMap mkPredictions $ S.toList $ nonterminals cfg
+    where
+    mkPredictions :: AugNT nt -> Predictions t nt
+	-- Mostly reshuffling data
+    mkPredictions nt
+	= S.fromList $ f $ collectOnSecond $ collectOnFirst' lookaheadProds
+	where
+	-- Possible lookahead symbols for productions of this nonterminal
+	lookaheadProds :: [(AugT t, AugProduction t nt)]
+	lookaheadProds	= do
+	    rhs <- S.toList $ productionRules cfg nt
+	    let prod = (nt, rhs)
+	    t <- S.toList $ toSet $ predictSet' prod
+	    return (t, prod)
+
+	f :: [([AugT t], S.Set (AugProduction t nt))]
+	  -> [(LookaheadSet t, S.Set (AugProduction t nt))]
+	f pairs = [(fromList la, ps) | (la, ps) <- pairs]
+
+    mkMap :: Ord k => (k -> v) -> [k] -> M.Map k v
+    mkMap f ks = M.fromList [(k, f k) | k <- ks]
+
+-- | Returns true iff the predictions are unambiguous, true iff the
+-- grammar is LL(1).
+isLL1 :: M.Map (AugNT nt) (Predictions t nt) -> Bool
+isLL1 m = all (\ ps -> S.size ps == 1) $ M.elems m
diff --git a/src/Data/Cfg/Productive.hs b/src/Data/Cfg/Productive.hs
new file mode 100644
--- /dev/null
+++ b/src/Data/Cfg/Productive.hs
@@ -0,0 +1,87 @@
+-- | Productivity of productions in the grammar.
+{-# LANGUAGE ScopedTypeVariables #-}
+module Data.Cfg.Productive (
+    productives,
+    unproductives,
+    removeUnproductives
+    ) where
+
+import Control.Monad(guard, unless)
+import Data.Cfg.Cfg(Cfg(..), Production, V(..), Vs, productions)
+import Data.Cfg.FixedPoint(fixedPoint)
+import Data.Cfg.FreeCfg(FreeCfg(..))
+import qualified Data.Set as S
+
+-- | Returns the productive productions of this grammar.
+productives :: forall cfg t nt
+	    . (Cfg cfg t nt, Ord nt, Ord t)
+	    => cfg t nt -> S.Set (Production t nt)
+productives cfg = S.fromList
+		      $ filter (isProductiveProduction productiveNTs)
+			  $ productions cfg
+    where
+    productiveNTs :: S.Set nt
+    productiveNTs = productiveNonterminals cfg
+
+-- | Returns the unproductive productions of this grammar.
+unproductives :: forall cfg t nt
+	      . (Cfg cfg t nt, Ord nt, Ord t)
+	      => cfg t nt -> S.Set (Production t nt)
+unproductives cfg = S.fromList (productions cfg) S.\\ productives cfg
+
+-- | Returns an equivalent grammar not including unproductive
+-- productions.
+removeUnproductives :: forall cfg t nt
+		    . (Cfg cfg t nt, Ord nt, Ord t)
+		    => cfg t nt -> FreeCfg t nt
+removeUnproductives cfg = FreeCfg {
+    terminals' = terminals cfg,
+    startSymbol' = startSymbol cfg,
+    nonterminals' = nts,
+    productionRules' = rules
+    }
+    where
+    nts :: S.Set nt
+    nts = productiveNonterminals cfg
+
+    rules :: nt -> S.Set (Vs t nt)
+    rules nt = if nt `S.member` nts
+	then S.filter (isProductiveVs nts) $ productionRules cfg nt
+	else S.empty
+
+-- | Returns the productive nonterminals of the grammar
+productiveNonterminals :: forall cfg t nt
+		       . (Cfg cfg t nt, Ord nt, Ord t)
+		       => cfg t nt -> S.Set nt
+productiveNonterminals cfg = fixedPoint f S.empty
+    where
+    f :: S.Set nt -> S.Set nt
+    f productiveNTs = S.fromList $ do
+	nt <- S.toList $ nonterminals cfg
+	unless (nt `S.member` productiveNTs) $ do
+	    let rhss = productionRules cfg nt
+	    guard (any (isProductiveVs productiveNTs) $ S.toList rhss)
+	return nt
+
+isProductiveProduction :: forall t nt
+		       . (Ord nt)
+		       => S.Set nt -> Production t nt -> Bool
+isProductiveProduction productiveNTs (hd, rhs)
+    = hd `S.member` productiveNTs
+	  && isProductiveVs productiveNTs rhs
+
+-- | Given a set of known productive nonterminals, is the vocabulary
+-- symbol productive?
+isProductiveVs :: forall t nt
+	       . (Ord nt)
+	       => S.Set nt -> Vs t nt -> Bool
+isProductiveVs productiveNTs = all isProductiveV
+    where
+    -- | Given a set of known productive nonterminals, is the vocabulary
+    -- symbol productive?
+    isProductiveV :: V t nt -> Bool
+    isProductiveV v = case v of
+        NT nt -> nt `S.member` productiveNTs
+        _ -> True
+
+
diff --git a/src/Data/Cfg/Reachable.hs b/src/Data/Cfg/Reachable.hs
new file mode 100644
--- /dev/null
+++ b/src/Data/Cfg/Reachable.hs
@@ -0,0 +1,55 @@
+-- | Reachability of nonterminals in the grammar.
+{-# LANGUAGE ScopedTypeVariables #-}
+module Data.Cfg.Reachable (
+    reachables,
+    unreachables,
+    removeUnreachables
+    ) where
+
+import Data.Cfg.Cfg(Cfg(..), V(..), Vs)
+import Data.Cfg.FreeCfg(FreeCfg(..))
+import qualified Data.Set as S
+
+-- | Returns the nonterminals of this grammar reachable from the start
+-- symbol.
+reachables :: forall cfg t nt . (Cfg cfg t nt, Ord nt)
+	   => cfg t nt -> S.Set nt
+reachables cfg = go [startSymbol cfg] S.empty
+    where
+    go :: [nt] -> S.Set nt -> S.Set nt
+    go [] seen = seen
+    go (nt : nts) seen
+	= if nt `S.member` seen
+	      then go nts seen
+	      else do
+		  let seen' = S.insert nt seen
+		  let vs = concat $ S.toList $ productionRules cfg nt
+		  go (nts ++ [nt' | NT nt' <- vs]) seen'
+
+-- | Returns the nonterminals of this grammar unreachable from the
+-- start symbol.
+unreachables :: forall cfg t nt . (Cfg cfg t nt, Ord nt)
+	     => cfg t nt -> S.Set nt
+unreachables cfg = nonterminals cfg S.\\ reachables cfg
+
+
+-- | Returns an equivalent grammar not including unreachable
+-- nonterminals.
+removeUnreachables :: forall cfg t nt . (Cfg cfg t nt, Ord nt)
+		   => cfg t nt -> FreeCfg t nt
+removeUnreachables cfg = FreeCfg {
+    nonterminals' = res,
+    terminals' = terminals cfg,
+    productionRules' = pr,
+    startSymbol' = startSymbol cfg
+    }
+    where
+    res :: S.Set nt
+    res = reachables cfg
+
+    pr :: nt -> S.Set (Vs t nt)
+    pr nt = if nt `S.member` res
+                then productionRules cfg nt
+                else S.empty
+
+
diff --git a/src/Data/Cfg/RuleApplication.hs b/src/Data/Cfg/RuleApplication.hs
new file mode 100644
--- /dev/null
+++ b/src/Data/Cfg/RuleApplication.hs
@@ -0,0 +1,66 @@
+-- | Results of application of the production rules of a grammar.
+{-# LANGUAGE ScopedTypeVariables #-}
+module Data.Cfg.RuleApplication(
+    language,
+    yields,
+    directlyYields
+    ) where
+
+import Control.Monad(liftM, msum)
+import Control.Monad.Omega
+import Data.Cfg.Cfg
+import qualified Data.DList as DL
+import qualified Data.Map as M
+import qualified Data.Set as S
+
+-- | Given a grammar and a string of symbols, returns the strings
+-- yielded by application of a production rule; that is, by expanding
+-- one nonterminal in the string.
+directlyYields :: (Cfg cfg t nt) => cfg t nt -> Vs t nt -> [Vs t nt]
+directlyYields cfg vs = do
+    i <- [0..length vs - 1]
+    let (pre, NT nt : post) = splitAt i vs
+    expansion <- S.toList $ productionRules cfg nt
+    return (pre ++ expansion ++ post)
+
+-- | Given a grammar, returns all strings yielded by application of
+-- production rules.
+yields :: forall cfg t nt . (Cfg cfg t nt, Ord nt)
+        => cfg t nt -> [Vs t nt]
+yields cfg = map DL.toList $ runOmega $ yieldNT (startSymbol cfg)
+    where
+    yieldNT :: nt -> Omega (DL.DList (V t nt))
+    yieldNT nt = memoMap M.! nt
+	where
+	memoMap :: M.Map nt (Omega (DL.DList (V t nt)))
+	memoMap = M.fromList
+		      [(nt', yieldNT' nt')
+			  | nt' <- S.toList $ nonterminals cfg]
+
+	yieldNT' :: nt -> Omega (DL.DList (V t nt))
+	yieldNT' nt' = msum (return (DL.singleton (NT nt'))
+			       : map yieldVs rhss)
+	    where
+	    rhss = S.toList $ productionRules cfg nt'
+
+
+    yieldV :: V t nt -> Omega (DL.DList (V t nt))
+    yieldV v = case v of
+		   NT nt -> yieldNT nt
+		   t -> return $ DL.singleton t
+
+    yieldVs :: Vs t nt -> Omega (DL.DList (V t nt))
+    yieldVs = liftM DL.concat . mapM yieldV
+
+
+-- NOTE: you shouldn't get symbol strings repeating if the grammar is
+-- unambiguous.
+
+-- | Given a grammar, returns all strings of terminals yielded by
+-- application of the production rules to the start symbol.  This is
+-- the /language/ of the grammar.
+language :: (Cfg cfg t nt, Ord nt) => cfg t nt -> [Vs t nt]
+    -- TODO There's certainly a more efficient way to do this.
+language = filter (all isT) . yields
+
+
diff --git a/tests/Data/Cfg/BnfTests.hs b/tests/Data/Cfg/BnfTests.hs
new file mode 100644
--- /dev/null
+++ b/tests/Data/Cfg/BnfTests.hs
@@ -0,0 +1,38 @@
+{-# LANGUAGE QuasiQuotes #-}
+module Data.Cfg.BnfTests(tests) where
+
+import Data.Cfg.Bnf
+import Data.Cfg.Cfg
+import Data.Cfg.FreeCfg
+import qualified Data.Set as S
+import Test.Framework(Test, testGroup)
+import Test.Framework.Providers.HUnit(testCase)
+import Test.HUnit(assertEqual)
+
+tests :: Test
+tests = testGroup "Data.Cfg.Bnf" [ test ]
+
+test :: Test
+test = testCase "bnf quasiquoter sanity test" $ do
+    assertEqual "startSymbol works" "foo" (startSymbol cfg')
+    assertEqual "terminals works" 5 (S.size $ terminals cfg')
+    assertEqual "nonterminals works" 2 (S.size $ nonterminals cfg')
+    assertEqual "productions count works" 3 (length $ productions cfg')
+    where
+    cfg' = toFreeCfg gram'
+    gram' = [bnf|foo ::= A B C D bar.
+		  foo ::= .
+		  bar ::= E A B. |]
+
+{- Test code for yieldCfg.
+import Data.Cfg.RuleApplication
+
+py :: Int -> IO ()
+py n = mapM_ print $ take n y
+    where
+    y = yieldCfg cfg
+    cfg = gramToCfg' gram'
+    gram' = [gram|digits ::= digit | digit digits .
+	          digit ::= O | I . |]
+
+-}
diff --git a/tests/Data/Cfg/FirstSetTests.hs b/tests/Data/Cfg/FirstSetTests.hs
new file mode 100644
--- /dev/null
+++ b/tests/Data/Cfg/FirstSetTests.hs
@@ -0,0 +1,62 @@
+module Data.Cfg.FirstSetTests (
+    tests
+    ) where
+
+import Data.Cfg.Augment
+import Data.Cfg.FirstSet
+import Data.Cfg.LookaheadSet
+import Data.Cfg.TestGrammars
+import Test.Framework(Test, testGroup)
+import Test.Framework.Providers.HUnit(testCase)
+import Test.HUnit(assertEqual)
+
+tests :: Test
+tests = testGroup "Data.Cfg.FirstSet" [
+    g0FirstSetTest,
+    microFirstSetTest
+    ]
+
+g0FirstSetTest :: Test
+g0FirstSetTest = testCase "g0 first-set test" $ mapM_ f tab
+    where
+    f :: (String, LookaheadSet String) -> IO ()
+    f (nt, expected) = assertEqual msg expected (fs $ AugNT nt)
+	where
+	msg = "g0: firstSet(" ++ nt ++ ")"
+
+    tab :: [(String, LookaheadSet String)]
+    tab = [("e", mkLookaheadSet False $ words "F LPAREN V"),
+	   ("prefix", mkLookaheadSet True ["F"]),
+	   ("tail", mkLookaheadSet True ["PLUS"])]
+
+    fs :: AugNT String -> LookaheadSet String
+    fs = firstSet g0
+
+microFirstSetTest :: Test
+microFirstSetTest = testCase "micro first-set test" $ mapM_ f tab
+    where
+    f :: (String, LookaheadSet String) -> IO ()
+    f (nt, expected) = assertEqual msg expected (fs $ AugNT nt)
+	where
+	msg = "micro: firstSet(" ++ nt ++ ")"
+
+    tab :: [(String, LookaheadSet String)]
+    tab = [
+	    ("program", mkLookaheadSet False $ words "BEGIN"),
+	    ("statement_list", mkLookaheadSet False $ words "ID READ WRITE"),
+	    ("statement", mkLookaheadSet False $ words "ID READ WRITE"),
+	    ("statement_tail", mkLookaheadSet True $ words "ID READ WRITE"),
+	    ("expression",
+		 mkLookaheadSet False $ words "ID INT_LITERAL LPAREN"),
+	    ("id_list", mkLookaheadSet False $ words "ID"),
+	    ("expr_list",
+		 mkLookaheadSet False $ words "ID INT_LITERAL LPAREN"),
+	    ("id_tail", mkLookaheadSet True $ words "COMMA"),
+	    ("expr_tail", mkLookaheadSet True $ words "COMMA"),
+	    ("primary", mkLookaheadSet False $ words "ID INT_LITERAL LPAREN"),
+	    ("primary_tail", mkLookaheadSet True $ words "PLUS MINUS"),
+            ("add_op", mkLookaheadSet False $ words "PLUS MINUS") ]
+
+    fs :: AugNT String -> LookaheadSet String
+    fs = firstSet micro
+
diff --git a/tests/Data/Cfg/FollowSetTests.hs b/tests/Data/Cfg/FollowSetTests.hs
new file mode 100644
--- /dev/null
+++ b/tests/Data/Cfg/FollowSetTests.hs
@@ -0,0 +1,67 @@
+module Data.Cfg.FollowSetTests (
+    tests
+    ) where
+
+import Data.Cfg.Augment
+import Data.Cfg.FirstSet
+import Data.Cfg.FollowSet
+import Data.Cfg.LookaheadSet
+import Data.Cfg.TestGrammars
+import Test.Framework(Test, testGroup)
+import Test.Framework.Providers.HUnit(testCase)
+import Test.HUnit(assertEqual)
+
+tests :: Test
+tests = testGroup "Data.Cfg.FollowSet" [
+    g0FollowSetTest,
+    microFollowSetTest
+    ]
+
+g0FollowSetTest :: Test
+g0FollowSetTest = testCase "g0 follow-set test" $ mapM_ f tab
+    where
+    f :: (String, LookaheadSet String) -> IO ()
+    f (nt, expected) = assertEqual msg expected (fols $ AugNT nt)
+	where
+	msg = "g0: followSet(" ++ nt ++ ")"
+
+    tab :: [(String, LookaheadSet String)]
+    tab = [("e", mkLookaheadSet True ["RPAREN"]),
+	   ("prefix", mkLookaheadSet False ["LPAREN"]),
+	   ("tail", mkLookaheadSet True ["RPAREN"])]
+
+    fs :: AugNT String -> LookaheadSet String
+    fs = firstSet g0
+
+    fols :: AugNT String -> LookaheadSet String
+    fols = followSet g0 fs
+
+microFollowSetTest :: Test
+microFollowSetTest = testCase "micro follow-set test" $ mapM_ f tab
+    where
+    f :: (String, LookaheadSet String) -> IO ()
+    f (nt, expected) = assertEqual msg expected (fols $ AugNT nt)
+	where
+	msg = "micro: followSet(" ++ nt ++ ")"
+
+    tab :: [(String, LookaheadSet String)]
+    tab = [ ("program", mkLookaheadSet True []),
+	    ("statement_list", mkLookaheadSet False $ words "END"),
+	    ("statement", mkLookaheadSet False $ words "ID READ WRITE END"),
+	    ("statement_tail", mkLookaheadSet False $ words "END"),
+	    ("expression", mkLookaheadSet False $ words "COMMA SEMI RPAREN"),
+	    ("id_list", mkLookaheadSet False $ words "RPAREN"),
+	    ("expr_list", mkLookaheadSet False $ words "RPAREN"),
+	    ("id_tail", mkLookaheadSet False $ words "RPAREN"),
+	    ("expr_tail", mkLookaheadSet False $ words "RPAREN"),
+	    ("primary",
+		 mkLookaheadSet False $ words "COMMA SEMI PLUS MINUS RPAREN"),
+	    ("primary_tail", mkLookaheadSet False $ words "COMMA SEMI RPAREN"),
+	    ("add_op", mkLookaheadSet False $ words "ID INT_LITERAL LPAREN") ]
+
+    fs :: AugNT String -> LookaheadSet String
+    fs = firstSet micro
+
+    fols :: AugNT String -> LookaheadSet String
+    fols = followSet micro fs
+
diff --git a/tests/Data/Cfg/LookaheadSetTests.hs b/tests/Data/Cfg/LookaheadSetTests.hs
new file mode 100644
--- /dev/null
+++ b/tests/Data/Cfg/LookaheadSetTests.hs
@@ -0,0 +1,21 @@
+{-# LANGUAGE FlexibleInstances #-}
+{-# OPTIONS_GHC -fno-warn-orphans #-}
+module Data.Cfg.LookaheadSetTests (
+    tests
+    ) where
+
+import Control.Monad(liftM2)
+import Data.Cfg.LookaheadSet(LookaheadSet, mkLookaheadSet)
+import Test.Framework(Test, testGroup)
+import Test.Framework.Providers.QuickCheck2(testProperty)
+import Test.QuickCheck(Arbitrary(..), listOf)
+import Test.QuickCheck.Property.Monoid(T(..), eq, prop_Monoid)
+
+instance Arbitrary (LookaheadSet Int) where
+    arbitrary = liftM2 mkLookaheadSet arbitrary $ listOf arbitrary
+
+tests :: Test
+tests = testGroup "Data.Cfg.Lookahead" [
+    testProperty "monoid laws for lookahead sets"
+	$ eq $ prop_Monoid (T :: T (LookaheadSet Int))
+    ]
diff --git a/tests/Data/Cfg/ProductiveTests.hs b/tests/Data/Cfg/ProductiveTests.hs
new file mode 100644
--- /dev/null
+++ b/tests/Data/Cfg/ProductiveTests.hs
@@ -0,0 +1,53 @@
+{-# LANGUAGE QuasiQuotes #-}
+module Data.Cfg.ProductiveTests (
+    tests
+    ) where
+
+import Data.Cfg.Bnf(Grammar(..), bnf)
+import Data.Cfg.Cfg(Cfg(..), V(..))
+import Data.Cfg.FreeCfg(FreeCfg(..), toFreeCfg)
+import Data.Cfg.Productive
+import Data.Cfg.TestGrammars(assertEqCfg, wiki)
+import qualified Data.Set as S
+import Test.Framework(Test, testGroup)
+import Test.Framework.Providers.HUnit(testCase)
+import Test.HUnit(assertEqual)
+import Text.PrettyPrint
+
+tests :: Test
+tests = testGroup "Data.Cfg.Productive" [
+    wikiTest
+    ]
+
+wikiTest :: Test
+wikiTest = testCase "wiki productivity test" $ do
+    assertEqual "productives" (S.fromList $ grammarProductions prods')
+			      (productives wiki)
+    assertEqual "unproductives" (S.fromList $ grammarProductions unprods')
+				(unproductives wiki)
+    assertEqCfg ctxt ctxt "productivity" expected $ removeUnproductives wiki
+
+    where
+    ctxt :: V String String -> Doc
+    ctxt v = text $ case v of
+			NT nt -> nt
+			T t -> t
+
+    expected :: FreeCfg String String
+    expected = (toFreeCfg prods') {
+	terminals' = terminals wiki
+	}
+
+    prods' :: Grammar String String
+    prods' = [bnf|
+	s ::= b B | c C.
+	b ::= b B | B.
+	c ::= c C | C.
+	d ::= b D | c D | D.
+        |]
+
+    unprods' :: Grammar String String
+    unprods' = [bnf|
+        s ::= e E.
+        e ::= e E.
+        |]
diff --git a/tests/Data/Cfg/ReachableTests.hs b/tests/Data/Cfg/ReachableTests.hs
new file mode 100644
--- /dev/null
+++ b/tests/Data/Cfg/ReachableTests.hs
@@ -0,0 +1,45 @@
+{-# LANGUAGE QuasiQuotes #-}
+module Data.Cfg.ReachableTests (
+    tests
+    ) where
+
+import Data.Cfg.Bnf(bnf)
+import Data.Cfg.Cfg(Cfg(..), V(..))
+import Data.Cfg.FreeCfg(FreeCfg(..), toFreeCfg)
+import Data.Cfg.Reachable
+import Data.Cfg.TestGrammars(assertEqCfg, wiki)
+import qualified Data.Set as S
+import Test.Framework(Test, testGroup)
+import Test.Framework.Providers.HUnit(testCase)
+import Test.HUnit(assertEqual)
+import Text.PrettyPrint
+
+tests :: Test
+tests = testGroup "Data.Cfg.Reachable" [
+    wikiTest
+    ]
+
+wikiTest :: Test
+wikiTest = testCase "wiki reachability test" $ do
+    assertEqual "reachables" (S.fromList $ words "s b c e")
+			     (reachables wiki)
+    assertEqual "unreachables" (S.fromList $ words "d")
+			       (unreachables wiki)
+    assertEqCfg ctxt ctxt "reachability" expected $ removeUnreachables wiki
+
+    where
+    ctxt :: V String String -> Doc
+    ctxt v = text $ case v of
+			NT nt -> nt
+			T t -> t
+    reach = [bnf|
+	s ::= b B | c C | e E.
+	b ::= b B | B.
+	c ::= c C | C.
+	e ::= e E.
+	|]
+
+    expected :: FreeCfg String String
+    expected = (toFreeCfg reach){
+            terminals' = terminals wiki
+        }
diff --git a/tests/Data/Cfg/TestGrammars.hs b/tests/Data/Cfg/TestGrammars.hs
new file mode 100644
--- /dev/null
+++ b/tests/Data/Cfg/TestGrammars.hs
@@ -0,0 +1,93 @@
+-- | Sample grammars for tests
+{-# LANGUAGE QuasiQuotes #-}
+module Data.Cfg.TestGrammars (
+    -- * Assertion for equality in 'Cfg'
+    assertEqCfg,
+    -- * Grammars for sanity checks
+    g0,
+    micro,
+    wiki,
+    -- * Convenience functions for the REPL
+    pretty'
+    ) where
+
+import Data.Cfg.Augment
+import Data.Cfg.Bnf
+import Data.Cfg.Cfg(Cfg(..), V(..), eqCfg)
+import Data.Cfg.CPretty
+import Data.Cfg.FreeCfg
+import Text.PrettyPrint
+import Test.HUnit(assertBool)
+
+-- | An assertion for testing equality of 'Cfg'.
+assertEqCfg :: (Cfg cfg t nt, CPretty (cfg t nt) ctxt,
+		Cfg cfg' t nt, CPretty (cfg' t nt) ctxt',
+		Eq t, Eq nt)
+		=> ctxt -> ctxt' -> String -> cfg t nt -> cfg' t nt -> IO ()
+assertEqCfg ctxt ctxt' msg expected actual =
+    assertBool msg' (eqCfg expected actual)
+    where
+    msg' = show $ vcat [text msg, expected', actual']
+    expected' = text "Expected:" <+> cpretty expected ctxt
+    actual' = text "Actual:" <+> cpretty actual ctxt'
+
+pretty' :: AugFreeCfg String String -> Doc
+pretty' cfg = cpretty cfg ctxt
+    where
+    ctxt :: AugV String String -> Doc
+    ctxt v = text $ case v of
+		 NT nt -> case nt of
+		     StartSymbol -> "$start"
+		     AugNT s -> s
+		 T t -> case t of
+		     EOF -> "$EOF"
+		     AugT s -> s
+
+-- | A test grammar.  Found in Crafting a compiler, by Charles
+-- N. Fischer and Richard J. LeBlanc, Jr., (c) 1998, pg. 95.
+g0 :: FreeCfg (AugT String) (AugNT String)
+g0 = augmentCfg [bnf|
+    e ::= prefix LPAREN e RPAREN.
+    e ::= V tail.
+    prefix ::= F.
+    prefix ::= .
+    tail ::= PLUS e.
+    tail ::= .
+   |]
+
+-- | A test grammar.  Found in Fischer and LeBlanc, pg. 111.
+micro :: FreeCfg (AugT String) (AugNT String)
+micro = augmentCfg [bnf|
+    program ::= BEGIN statement_list END.
+    statement_list ::= statement statement_tail.
+    statement_tail ::= statement statement_tail.
+    statement_tail ::=.
+    statement ::= ID ASSIGN expression SEMI.
+    statement ::= READ LPAREN id_list RPAREN SEMI.
+    statement ::= WRITE LPAREN expr_list RPAREN SEMI.
+    id_list ::= ID id_tail.
+    id_tail ::= COMMA ID id_tail.
+    id_tail ::=.
+    expr_list ::= expression expr_tail.
+    expr_tail ::= COMMA expression expr_tail.
+    expr_tail ::=.
+    expression ::= primary primary_tail.
+    primary_tail ::= add_op primary primary_tail.
+    primary_tail ::=.
+    primary ::= LPAREN expression RPAREN.
+    primary ::= ID.
+    primary ::= INT_LITERAL.
+    add_op ::= PLUS.
+    add_op ::= MINUS.
+    |]
+
+-- | A test grammar.  Found at
+-- http://en.wikipedia.org/wiki/Useless_rules; retrieved 2015-03-14.
+wiki :: Grammar String String
+wiki = [bnf|
+    s ::= b B | c C | e E.
+    b ::= b B | B.
+    c ::= c C | C.
+    d ::= b D | c D | D.
+    e ::= e E.
+    |]
diff --git a/tests/Data/CfgTests.hs b/tests/Data/CfgTests.hs
new file mode 100644
--- /dev/null
+++ b/tests/Data/CfgTests.hs
@@ -0,0 +1,79 @@
+{-# LANGUAGE FlexibleInstances #-}
+{-# OPTIONS_GHC -fno-warn-orphans #-}
+module Data.CfgTests (sampleCfg, tests) where
+
+import Control.Monad(forM)
+import Data.Char(toLower, toUpper)
+import qualified Data.Cfg.BnfTests
+import Data.Cfg.Cfg(V(..))
+import Data.Cfg.CPretty(cpretty)
+import Data.Cfg.FreeCfg
+import qualified Data.Cfg.FirstSetTests
+import qualified Data.Cfg.FollowSetTests
+import qualified Data.Cfg.LookaheadSetTests
+import qualified Data.Cfg.ProductiveTests
+import qualified Data.Cfg.ReachableTests
+import qualified Data.Map as M
+import qualified Data.Set as S
+import Test.Framework(Test, testGroup)
+import Test.QuickCheck
+import Text.PrettyPrint
+
+instance Arbitrary (FreeCfg Int Int) where
+    arbitrary = do
+	tCnt <- choose (1, 25)
+	let ts = [0..tCnt-1]
+	ntCnt <- choose (1, 100)
+	let nts = [0..ntCnt-1]
+	let vs = map T ts ++ map NT nts
+	let genV = elements vs
+	let genVs = listOf genV
+	pairs <- forM nts $ \nt -> do
+	    altCnt <- choose (1, 5)
+	    rhss <- vectorOf altCnt genVs
+	    return (nt, S.fromList rhss)
+
+	let map' = M.fromList pairs
+	return FreeCfg {
+	    nonterminals' = S.fromList nts,
+	    terminals' = S.fromList ts,
+	    productionRules' = (map' M.!),
+	    startSymbol' = 0
+	    }
+
+ctxt :: V Int Int -> Doc
+ctxt v = text $ map f $ base26 n
+    where
+    (f, n) = case v of
+		 NT n' -> (toLower, n')
+		 T n' -> (toUpper, n')
+
+    base26 :: Int -> String
+    base26 n'
+	| n' < 26	= [digitToChar n']
+	| otherwise = if msds == 0
+			  then [digitToChar lsd]
+			  else base26 msds ++ [digitToChar lsd]
+	where
+	(msds, lsd) = n' `divMod` 26
+
+	digitToChar :: Int -> Char
+	digitToChar digit = toEnum (fromEnum 'a' + digit)
+
+pretty :: FreeCfg Int Int -> Doc
+pretty cfg = cpretty cfg ctxt
+
+sampleCfg :: IO ()
+sampleCfg = do
+    cfgs <- sample' (arbitrary :: Gen (FreeCfg Int Int))
+    mapM_ (print . pretty) (take 3 cfgs)
+
+tests :: Test
+tests = testGroup "Data.Cfg" [
+    Data.Cfg.BnfTests.tests,
+    Data.Cfg.FirstSetTests.tests,
+    Data.Cfg.FollowSetTests.tests,
+    Data.Cfg.LookaheadSetTests.tests,
+    Data.Cfg.ProductiveTests.tests,
+    Data.Cfg.ReachableTests.tests
+    ]
diff --git a/tests/Test.hs b/tests/Test.hs
new file mode 100644
--- /dev/null
+++ b/tests/Test.hs
@@ -0,0 +1,9 @@
+module Main where
+
+import Data.CfgTests(tests)
+import Test.Framework(defaultMain)
+
+main :: IO ()
+main = defaultMain [tests]
+
+