some cleanup

.stylish-haskell.yaml

@@ -0,0 +1,141 @@
+# stylish-haskell configuration file
+# ==================================
+
+# The stylish-haskell tool is mainly configured by specifying steps. These steps
+# are a list, so they have an order, and one specific step may appear more than
+# once (if needed). Each file is processed by these steps in the given order.
+steps:
+  # Convert some ASCII sequences to their Unicode equivalents. This is disabled
+  # by default.
+  # - unicode_syntax:
+  #     # In order to make this work, we also need to insert the UnicodeSyntax
+  #     # language pragma. If this flag is set to true, we insert it when it's
+  #     # not already present. You may want to disable it if you configure
+  #     # language extensions using some other method than pragmas. Default:
+  #     # true.
+  #     add_language_pragma: true
+
+  # Format record definitions
+  # Disabled: don't like it for simple sum types
+  # - records: {}
+
+  # Align the right hand side of some elements.  This is quite conservative
+  # and only applies to statements where each element occupies a single
+  # line. All default to true.
+  - simple_align:
+      cases: true
+      top_level_patterns: true
+      records: true
+
+  # Import cleanup
+  - imports:
+      # There are different ways we can align names and lists.
+      #
+      # - global: Align the import names and import list throughout the entire
+      #   file.
+      #
+      # - file: Like global, but don't add padding when there are no qualified
+      #   imports in the file.
+      #
+      # - group: Only align the imports per group (a group is formed by adjacent
+      #   import lines).
+      #
+      # - none: Do not perform any alignment.
+      #
+      # Default: global.
+      align: none
+
+      # The following options affect only import list alignment.
+      #
+      # List align has following options:
+      #
+      # - after_alias: Import list is aligned with end of import including
+      #   'as' and 'hiding' keywords.
+      #
+      #   > import qualified Data.List      as List (concat, foldl, foldr, head,
+      #   >                                          init, last, length)
+      #
+      # - with_alias: Import list is aligned with start of alias or hiding.
+      #
+      #   > import qualified Data.List      as List (concat, foldl, foldr, head,
+      #   >                                 init, last, length)
+      #
+      # - with_module_name: Import list is aligned `list_padding` spaces after
+      #   the module name.
+      #
+      #   > import qualified Data.List      as List (concat, foldl, foldr, head,
+      #                          init, last, length)
+      #
+      #   This is mainly intended for use with `pad_module_names: false`.
+      #
+      #   > import qualified Data.List as List (concat, foldl, foldr, head,
+      #                          init, last, length, scanl, scanr, take, drop,
+      #                          sort, nub)
+      #
+      # - new_line: Import list starts always on new line.
+      #
+      #   > import qualified Data.List      as List
+      #   >     (concat, foldl, foldr, head, init, last, length)
+      #
+      # Default: after_alias
+      list_align: after_alias
+
+      # Right-pad the module names to align imports in a group:
+      #
+      # - true: a little more readable
+      #
+      #   > import qualified Data.List       as List (concat, foldl, foldr,
+      #   >                                           init, last, length)
+      #   > import qualified Data.List.Extra as List (concat, foldl, foldr,
+      #   >                                           init, last, length)
+      #
+      # - false: diff-safe
+      #
+      #   > import qualified Data.List as List (concat, foldl, foldr, init,
+      #   >                                     last, length)
+      #   > import qualified Data.List.Extra as List (concat, foldl, foldr,
+      #   >                                           init, last, length)
+      #
+      # Default: true
+      pad_module_names: false
+
+
+  # Language pragmas
+  - language_pragmas:
+      # We can generate different styles of language pragma lists.
+      #
+      # - vertical: Vertical-spaced language pragmas, one per line.
+      #
+      # - compact: A more compact style.
+      #
+      # - compact_line: Similar to compact, but wrap each line with
+      #   `{-#LANGUAGE #-}'.
+      #
+      # Default: vertical.
+      style: vertical
+
+      # Align affects alignment of closing pragma brackets.
+      #
+      # - true: Brackets are aligned in same column.
+      #
+      # - false: Brackets are not aligned together. There is only one space
+      #   between actual import and closing bracket.
+      #
+      # Default: true
+      align: false
+
+      # Language prefix to be used for pragma declaration, this allows you to
+      # use other options non case-sensitive like "language" or "Language".
+      # If a non correct String is provided, it will default to: LANGUAGE.
+      language_prefix: language
+
+  # Remove trailing whitespace
+  - trailing_whitespace: {}
+
+  # Squash multiple spaces between the left and right hand sides of some
+  # elements into single spaces. Basically, this undoes the effect of
+  # simple_align but is a bit less conservative.
+  # - squash: {}
+
+# A common indentation setting. Different steps take this into account.
+indent: 4

NominalAngluin.cabal

@@ -2,7 +2,7 @@ name:                NominalAngluin
 version:             0.1.0.0
 license:             UnspecifiedLicense
 author:              Joshua Moerman
-copyright:           (c) 2016, Joshua Moerman
+copyright:           (c) 2016 - 2020, Joshua Moerman
 build-type:          Simple
 cabal-version:       >=1.10
 
@@ -34,7 +34,7 @@ executable NominalAngluin
     NLambda >= 1.1
   hs-source-dirs:      src
   default-language:    Haskell2010
-  ghc-options:         -O2
+  ghc-options:         -O2 -Wall
 
 executable NominalAngluin2
   ghc-options:
@@ -66,4 +66,4 @@ executable NominalAngluin2
     NLambda >= 1.1
   hs-source-dirs:      src
   default-language:    Haskell2010
-  ghc-options:         -O2
+  ghc-options:         -O2 -Wall

src/Bollig.hs

@@ -6,10 +6,9 @@ import Angluin
 import ObservationTable
 import Teacher
 
-import Data.List (tails)
 import Debug.Trace
 import NLambda
-import Prelude (Bool (..), Int, Maybe (..), fst, show, ($), (++), (.))
+import Prelude (Bool (..), Int, Maybe (..), fst, snd, ($), (++), (.))
 import qualified Prelude hiding ()
 
 rowUnion :: NominalType i => Set (BRow i) -> BRow i
@@ -60,7 +59,7 @@ constructHypothesisBollig State{..} = automaton q a d i f
         i = filter (\r -> r `sublang` row t []) q
         f = filter (\r -> singleton True `eq` mapFilter (\(i,b) -> maybeIf (i `eq` []) b) r) q
         d0 = triplesWithFilter (\s a s2 -> maybeIf (row t s2 `sublang` rowa t s a) (row t s, a, row t s2)) ss aa ss
-        d = filter (\(q1,a,q2) -> q1 `member` q /\ q2 `member` q) d0
+        d = filter (\(q1, _, q2) -> q1 `member` q /\ q2 `member` q) d0
         primesUpp = filter (\r -> nonEmpty r /\ r `neq` rowUnion (sublangs r (allRows \\ orbit [] r))) allRowsUpp
         nonEmpty = isNotEmpty . filter (fromBool . Prelude.snd)
         allRowsUpp = map (row t) ss

src/Examples.hs

@@ -17,7 +17,7 @@ import           Examples.Residual
 import Examples.RunningExample
 import Examples.Stack
 import NLambda (Atom)
-import           Teacher            (teacherWithTarget, Teacher)
+import Teacher (Teacher, teacherWithTarget)
 
 -- Wrapping it in a teacher
 exampleTeacher :: Teacher Atom

src/Examples/Contrived.hs

@@ -1,14 +1,14 @@
-{-# LANGUAGE DeriveGeneric, DeriveAnyClass #-}
+{-# language DeriveAnyClass #-}
+{-# language DeriveGeneric #-}
 module Examples.Contrived where
 
 import NLambda
 
 -- Explicit Prelude, as NLambda has quite some clashes
+import GHC.Generics (Generic)
 import Prelude (Eq, Ord, Show, ($))
 import qualified Prelude ()
 
-import           GHC.Generics (Generic)
-
 -- Example automaton from the whiteboard. Three orbits with 0, 1 and 2
 -- registers. The third orbit has a local symmetry (S2).
 data Example1 = Initial | S1 Atom | S2 (Atom, Atom)

src/Examples/ContrivedNFAs.hs

@@ -1,14 +1,14 @@
-{-# LANGUAGE DeriveGeneric, DeriveAnyClass #-}
-{-# LANGUAGE TupleSections #-}
+{-# language DeriveAnyClass #-}
+{-# language DeriveGeneric #-}
+{-# language TupleSections #-}
 module Examples.ContrivedNFAs where
 
 import NLambda
 
 -- Explicit Prelude, as NLambda has quite some clashes
-import           Prelude      (Eq, Ord, Show, ($), Int, (+), (-))
-import qualified Prelude      ()
-
 import GHC.Generics (Generic)
+import Prelude (Eq, Int, Ord, Show, (+), (-))
+import qualified Prelude ()
 
 -- Language = u a v a w for any words u,v,w and atom a
 -- The complement of 'all distinct atoms'
@@ -45,6 +45,7 @@ exampleNFA1 = automaton
 data NFA2 = Initial2 | Distinguished Atom | Count Int
   deriving (Show, Eq, Ord, Generic, NominalType, Contextual)
 
+exampleNFA2 :: Int -> Automaton NFA2 Atom
 exampleNFA2 n = automaton
     (singleton Initial2
         `union` map Distinguished atoms

src/Examples/Fifo.hs

@@ -1,10 +1,11 @@
-{-# LANGUAGE DeriveGeneric, DeriveAnyClass #-}
+{-# language DeriveAnyClass #-}
+{-# language DeriveGeneric #-}
 module Examples.Fifo (DataInput(..), fifoExample) where
 
 import GHC.Generics (Generic)
 import NLambda
-import           Prelude      (Eq, Int, Maybe (..), Ord, Show, Read, length, reverse,
-                               ($), (+), (-), (.), (>=))
+import Prelude (Eq, Int, Maybe (..), Ord, Read, Show, length, reverse, ($), (+),
+                (-), (.), (>=))
 import qualified Prelude ()
 
 

src/Examples/RunningExample.hs

@@ -1,5 +1,6 @@
-{-# LANGUAGE DeriveGeneric, DeriveAnyClass #-}
-{-# LANGUAGE TupleSections #-}
+{-# language DeriveAnyClass #-}
+{-# language DeriveGeneric #-}
+{-# language TupleSections #-}
 module Examples.RunningExample where
 
 {- In this file we define the running example of the paper
@@ -12,7 +13,7 @@ import           NLambda
 
 -- Explicit Prelude, as NLambda has quite some clashes
 import Data.List (reverse)
-import           Prelude      (Eq, Ord, Show, ($), (.), (-))
+import Prelude (Eq, Int, Ord, Show, ($), (-), (.))
 import qualified Prelude ()
 
 import GHC.Generics (Generic)
@@ -21,6 +22,7 @@ import           GHC.Generics (Generic)
 data RunningExample a = Store [a] | Check [a] | Accept | Reject
   deriving (Eq, Ord, Show, Generic, NominalType, Contextual)
 
+runningExample :: NominalType a => Set a -> Int -> Automaton (RunningExample a) a
 runningExample alphabet 0 = automaton
     (fromList [Accept, Reject])
     alphabet

src/Examples/Stack.hs

@@ -1,16 +1,16 @@
-{-# LANGUAGE DeriveGeneric, DeriveAnyClass #-}
+{-# language DeriveAnyClass #-}
+{-# language DeriveGeneric #-}
 module Examples.Stack (DataInput(..), stackExample) where
 
 import Examples.Fifo (DataInput (..))
 import GHC.Generics (Generic)
 import NLambda
-import           Prelude       (Eq, Int, Maybe (..), Ord, Show, length, ($),
-                                (.), (>=))
+import Prelude (Eq, Int, Maybe (..), Ord, Show, length, ($), (.), (>=))
 import qualified Prelude ()
 
 
 -- Functional stack data type is simply a list.
-data Stack a = Stack [a]
+newtype Stack a = Stack [a]
   deriving (Eq, Ord, Show, Generic, NominalType, Contextual)
 
 push :: a -> Stack a -> Stack a

src/Main.hs

@@ -1,16 +1,13 @@
-{-# LANGUAGE ExistentialQuantification #-}
+{-# language ExistentialQuantification #-}
 import Angluin
 import Bollig
 import Examples
-import           Teacher
 import ObservationTable
-import           NLStar
+import Teacher
 
-import           Data.IORef (readIORef)
-import           System.Environment
 import NLambda
-
 import Prelude hiding (map)
+import System.Environment
 
 data Learner
   = NomLStar     -- nominal L* for nominal automata
@@ -18,14 +15,17 @@ data Learner
   | NomNLStar    -- NL* for nominal automata, counterexamples as columns (suffix closed)
   deriving (Show, Read)
 
-data Teacher = EqDFA | EqNFA Int
+data Teacher
+  = EqDFA         -- Automatic teacher with membership and equivalence (only for DFAs)
+  | EqNFA Int     -- Automatic teacher with membership and bounded equivalence
+  | EquivalenceIO -- Teacher with automatic membership but manual equivalence
   deriving (Show, Read)
 
 data Aut = Fifo Int | Stack Int | Running Int | NFA1 | Bollig Int | NonResidual | Residual1 | Residual2
   deriving (Show, Read)
 
 -- existential wrapper
-data A = forall q i . (LearnableAlphabet i, NominalType q, Show q) => A (Automaton q i)
+data A = forall q i . (LearnableAlphabet i, Read i, NominalType q, Show q) => A (Automaton q i)
 
 mainExample :: String -> String -> String -> IO ()
 mainExample learnerName teacherName autName = do
@@ -41,6 +41,7 @@ mainExample learnerName teacherName autName = do
     let teacher = case read teacherName of
             EqDFA         -> teacherWithTarget automaton
             EqNFA k       -> teacherWithTargetNonDet k automaton
+            EquivalenceIO -> teacherWithTargetAndIO automaton
     let h = case read learnerName of
             NomLStar    -> learnAngluinRows teacher
             NomLStarCol -> learnAngluin teacher
@@ -49,7 +50,7 @@ mainExample learnerName teacherName autName = do
 
 mainWithIO :: String -> IO ()
 mainWithIO learnerName = do
-    let t = teacherWithIO (atoms)
+    let t = teacherWithIO atoms
     let h = case read learnerName of
             NomLStar    -> learnAngluinRows t
             NomLStarCol -> learnAngluin t

src/Main2.hs

@@ -2,16 +2,15 @@ import           Angluin
 import Bollig
 import Examples
 import Teacher
-import           ObservationTable
-import           NLStar
 
+import NLambda
 import System.Environment
 import System.IO
-import           NLambda
 
 data Learner = NomLStar | NomLStarCol | NomNLStar
   deriving (Show, Read)
 
+learn :: (Read i, Contextual i, NominalType i, Show i) => Set i -> IO ()
 learn alphSet = do
     [learnerName] <- getArgs
     let t = teacherWithIO2 alphSet
@@ -23,7 +22,6 @@ learn alphSet = do
 
 main :: IO ()
 main = do
-    [learnerName] <- getArgs
     putStrLn "ALPHABET" -- ask for the alphabet from the teacher
     hFlush stdout
     alph <- getLine

src/NLStar.hs

@@ -1,4 +1,4 @@
-{-# LANGUAGE RecordWildCards #-}
+{-# language RecordWildCards #-}
 module NLStar where
 
 import AbstractLStar
@@ -7,12 +7,9 @@ import           Bollig
 import ObservationTable
 import Teacher
 
-import           NLambda
-
 import Debug.Trace
-import           Data.List        (inits, tails)
-import           Prelude          hiding (and, curry, filter, lookup, map, not,
-                                   sum)
+import NLambda
+import Prelude hiding (and, curry, filter, lookup, map, not, sum)
 
 {- This is not NL* from the Bollig et al paper. This is a very naive
    approximation. You see, the consistency in their paper is quite weak,

src/ObservationTable.hs

@@ -1,9 +1,9 @@
-{-# LANGUAGE ConstraintKinds   #-}
-{-# LANGUAGE DeriveGeneric     #-}
-{-# LANGUAGE DeriveAnyClass    #-}
-{-# LANGUAGE FlexibleContexts  #-}
-{-# LANGUAGE FlexibleInstances #-}
-{-# LANGUAGE RecordWildCards   #-}
+{-# language ConstraintKinds #-}
+{-# language DeriveAnyClass #-}
+{-# language DeriveGeneric #-}
+{-# language FlexibleContexts #-}
+{-# language FlexibleInstances #-}
+{-# language RecordWildCards #-}
 
 module ObservationTable where
 
@@ -13,7 +13,7 @@ import           Teacher
 import Data.Maybe (fromJust)
 import Debug.Trace (trace)
 import GHC.Generics (Generic)
-import           Prelude      (Bool (..), Eq, Ord, Show (..), ($), (++), (.), uncurry, id)
+import Prelude (Bool (..), Eq, Ord, Show (..), id, uncurry, ($), (++), (.))
 import qualified Prelude ()
 
 
@@ -66,7 +66,7 @@ type BRow i = Row i Bool
 fillTable :: LearnableAlphabet i => Teacher i -> Set [i] -> Set [i] -> BTable i
 fillTable teacher sssa ee = Prelude.uncurry union . map2 (map slv) . map2 simplify . partition (\(_, _, f) -> f) $ base
     where
-        base0 = pairsWith (\s e -> (s++e)) sssa ee
+        base0 = pairsWith (++) sssa ee
         base1 = membership teacher base0
         base1b s e = forAll id $ mapFilter (\(i,f) -> maybeIf (i `eq` (s++e)) f)  base1
         base = pairsWith (\s e -> (s, e, base1b s e)) sssa ee

src/Teacher.hs

@@ -1,5 +1,5 @@
-{-# LANGUAGE RankNTypes #-}
-{-# LANGUAGE FlexibleInstances         #-}
+{-# language FlexibleInstances #-}
+{-# language RankNTypes #-}
 
 module Teacher
     ( module Teachers.Teacher
@@ -11,8 +11,8 @@ module Teacher
     ) where
 
 import Teachers.Teacher
-import Teachers.Whitebox
 import Teachers.Terminal
+import Teachers.Whitebox
 
 import NLambda hiding (alphabet)
 import qualified NLambda (alphabet)
@@ -65,13 +65,14 @@ teacherWithIO2 alph = Teacher
 -- 3. A teacher uses a target for the mebership queries, but you for equivalence
 -- Useful as long as you don't have an equivalence check
 -- used for NFAs when there was no bounded bisimulation yet
-teacherWithTargetAndIO :: NominalType q => Automaton q Atom -> Teacher Atom
+teacherWithTargetAndIO :: (Show i, Read i, NominalType i, Contextual i, NominalType q) => Automaton q i -> Teacher i
 teacherWithTargetAndIO aut = Teacher
     { membership = foreachQuery $ accepts aut
     , equivalent = ioEquivalent
-    , alphabet   = atoms
+    , alphabet   = NLambda.alphabet aut
     }
 
+automaticEquivalent :: (p1 -> p2 -> Set a) -> p1 -> p2 -> Maybe (Set a)
 automaticEquivalent bisimlator aut hypo = case solve isEq of
         Nothing    -> error "should be solved"
         Just True  -> Nothing

src/Teachers/Teacher.hs

@@ -1,4 +1,4 @@
-{-# LANGUAGE RankNTypes #-}
+{-# language RankNTypes #-}
 module Teachers.Teacher where
 
 import NLambda
@@ -25,4 +25,4 @@ data Teacher i = Teacher
 -- Often a membership query is defined by a function [i] -> Formula. This wraps
 -- such a function to the required type for a membership query (see above).
 foreachQuery :: NominalType i => ([i] -> Formula) -> Set[i] -> Set ([i], Formula)
-foreachQuery f qs = map (\q -> (q, f q)) qs
+foreachQuery f = map (\q -> (q, f q))

src/Teachers/Terminal.hs

@@ -1,11 +1,9 @@
 module Teachers.Terminal where
 
-import NLambda
-
 import Control.Monad
 import Data.IORef
-import Data.List (intersperse, concat)
-import Prelude hiding (filter, map, and, sum)
+import NLambda
+import Prelude hiding (and, filter, map, sum)
 import System.Console.Haskeline
 import System.IO.Unsafe (unsafePerformIO)
 import Text.Read (readMaybe)
@@ -14,7 +12,7 @@ import Text.Read (readMaybe)
 ioMembership :: (Show i, NominalType i, Contextual i) => Set [i] -> Set ([i], Formula)
 ioMembership queries = unsafePerformIO $ do
     cache <- readIORef mqCache
-    let cachedAnswers = filter (\(a, f) -> a `member` queries) cache
+    let cachedAnswers = filter (\(a, _) -> a `member` queries) cache
     let newQueries = simplify $ queries \\ map fst cache
     let representedInputs = toList . mapFilter id . setOrbitsRepresentatives $ newQueries
     putStrLn "\n# Membership Queries:"
@@ -27,7 +25,7 @@ ioMembership queries = unsafePerformIO $ do
                 case x of
                     Nothing -> error "Bye bye, have a good day!"
                     Just Nothing -> do
-                        outputStrLn $ "Unable to parse, try again"
+                        outputStrLn "Unable to parse, try again"
                         loop
                     Just (Just f) -> return f
         answer <- runInputT defaultSettings loop
@@ -46,11 +44,11 @@ ioMembership queries = unsafePerformIO $ do
 ioMembership2 :: (Show i, NominalType i, Contextual i) => Set [i] -> Set ([i], Formula)
 ioMembership2 queries = unsafePerformIO $ do
     cache <- readIORef mqCache
-    let cachedAnswers = filter (\(a, f) -> a `member` queries) cache
+    let cachedAnswers = filter (\(a, _) -> a `member` queries) cache
     let newQueries = simplify $ queries \\ map fst cache
     let representedInputs = toList . mapFilter id . setOrbitsRepresentatives $ newQueries
     answers <- forM representedInputs $ \input -> do
-        let str = Data.List.concat . intersperse " " . fmap show $ input
+        let str = unwords . fmap show $ input
         putStrLn $ "MQ \"" ++ str ++ "\""
         let askit = do
                 x <- getInputLine ""
@@ -70,28 +68,40 @@ ioMembership2 queries = unsafePerformIO $ do
         mqCache = unsafePerformIO $ newIORef empty
 
 
+newtype TestIO i = T [i]
+  deriving (Show, Read, Eq, Ord)
+
 -- Poses a query to the terminal, waiting for the user to provide a counter example
--- TODO: extend to any alphabet type (hard because of parsing)
+-- User can pose a "test query" which is evaluated on the hypothesis
 ioEquivalent :: (Show q, NominalType q, Show i, Read i, NominalType i) => Automaton q i -> Maybe (Set [i])
 ioEquivalent hypothesis = unsafePerformIO $ do
     putStrLn "\n# Is the following automaton correct?"
     putStr "# "
     print hypothesis
-    putStrLn "# \"^D\" for equivalent, \"[...]\" for a counter example (eg \"[0,1,0]\")"
+    putStrLn "# \"^D\" for equivalent; \"[...]\" for a counter example (eg \"[0,1,0]\"); \"T [...]\" for a test query."
     let loop = do
-            x <- fmap readMaybe <$> getInputLine "> "
-            case x of
+            resp <- getInputLine "> "
+            case resp of
                 Nothing -> do
-                    outputStrLn $ "Ok, we're done"
+                    outputStrLn "Ok, we're done"
                     return Nothing
-                Just Nothing -> do
-                    outputStrLn $ "Unable to parse (88), try again"
+                Just inp ->
+                    case readMaybe inp of
+                        Just (T w) -> do
+                            let a = accepts hypothesis w
+                            outputStrLn $ show a
+                            loop
+                        Nothing ->
+                            case readMaybe inp of
+                                Just f -> return (Just f)
+                                Nothing -> do
+                                    outputStrLn "Unable to parse (88), try again"
                                     loop
-                Just (Just f) -> return (Just f)
     answer <- runInputT defaultSettings loop
     return (orbit [] <$> answer)
 
 -- Same as above but in different format.
+-- This is used for automation and benchmarking different nominal tools
 ioEquivalent2 :: (Show q, NominalType q, Show i, Read i, NominalType i) => Automaton q i -> Maybe (Set [i])
 ioEquivalent2 hypothesis = unsafePerformIO $ do
     putStrLn "EQ\n\"Is the following automaton correct?"

src/Teachers/Whitebox.hs

@@ -3,7 +3,7 @@ module Teachers.Whitebox where
 import NLambda
 
 import Control.Monad.Identity
-import Prelude hiding (map, sum, filter, not)
+import Prelude hiding (filter, map, not, sum)
 
 -- I found it a bit easier to write a do-block below. So I needed this
 -- Conditional instance.
@@ -21,7 +21,7 @@ bisim aut1 aut2 = runIdentity $ go empty (pairsWith addEmptyWord (initialStates
             -- if elements are already in R, we can skip them
             let todo2 = filter (\(_, x, y) -> (x, y) `notMember` rel) todo
             -- split into correct pairs and wrong pairs
-            let (cont, ces) = partition (\(_, x, y) -> (x `member` (finalStates aut1)) <==> (y `member` (finalStates aut2))) todo2
+            let (cont, ces) = partition (\(_, x, y) -> (x `member` finalStates aut1) <==> (y `member` finalStates aut2)) todo2
             let aa = NLambda.alphabet aut1
             -- the good pairs should make one step
             let dtodo = sum (pairsWith (\(w, x, y) a -> pairsWith (\x2 y2 -> (a:w, x2, y2)) (d aut1 a x) (d aut2 a y)) cont aa)
@@ -32,7 +32,7 @@ bisim aut1 aut2 = runIdentity $ go empty (pairsWith addEmptyWord (initialStates
                 -- else continue with good pairs
                 (ite (isEmpty dtodo)
                     (return empty)
-                    (go (rel `union` map stripWord cont) (dtodo))
+                    (go (rel `union` map stripWord cont) dtodo)
                 )
         d aut a x = mapFilter (\(s, l, t) -> maybeIf (s `eq` x /\ l `eq` a) t) (delta aut)
         stripWord (_, x, y) = (x, y)
@@ -63,7 +63,7 @@ bisimNonDet n aut1 aut2 = runIdentity $ go empty (singleton ([], initialStates a
             -- filter out things expressed as sums
             let todo2 = filter (\(_, x, y) -> notSums x y) todo1
             -- split into correct pairs and wrong pairs
-            let (cont, ces) = partition (\(_, x, y) -> (x `intersect` (finalStates aut1)) <==> (y `intersect` (finalStates aut2))) todo2
+            let (cont, ces) = partition (\(_, x, y) -> (x `intersect` finalStates aut1) <==> (y `intersect` finalStates aut2)) todo2
             let aa = NLambda.alphabet aut1
             -- the good pairs should make one step
             let dtodo = pairsWith (\(w, x, y) a -> (a:w, sumMap (d aut1 a) x, sumMap (d aut2 a) y)) cont aa
@@ -75,10 +75,9 @@ bisimNonDet n aut1 aut2 = runIdentity $ go empty (singleton ([], initialStates a
                 -- else continue with good pairs
                 (ite (isEmpty dtodo)
                     (return empty)
-                    (go (rel `union` map stripWord cont) (dtodo))
+                    (go (rel `union` map stripWord cont) dtodo)
                 )
         d aut a x = mapFilter (\(s, l, t) -> maybeIf (s `eq` x /\ l `eq` a) t) (delta aut)
         stripWord (_, x, y) = (x, y)
         getRevWord (w, _, _) = reverse w
-        addEmptyWord x y = ([], x, y)
-        sumMap f = sum . (map f)
+        sumMap f = sum . map f