Replaces all NominalType with Nominal

app/Main.hs

@@ -24,7 +24,7 @@ data Aut = Fifo Int | Stack Int | Running Int | NFA1 | Bollig Int | NonResidual
   deriving (Show, Read)
 
 -- existential wrapper
-data A = forall q i . (NominalType i, Contextual i, Show i, Read i, NominalType q, Show q) => A (Automaton q i)
+data A = forall q i . (Nominal i, Contextual i, Show i, Read i, Nominal q, Show q) => A (Automaton q i)
 
 {- HLINT ignore "Redundant $" -}
 mainExample :: String -> String -> String -> IO ()

app/Main2.hs

@@ -13,7 +13,7 @@ import System.IO
 data Learner = NomLStar | NomLStarCol | NomNLStar
   deriving (Show, Read)
 
-learn :: (Read i, Contextual i, NominalType i, Show i) => Set i -> IO ()
+learn :: (Read i, Contextual i, Nominal i, Show i) => Set i -> IO ()
 learn alphSet = do
     [learnerName] <- getArgs
     let t = teacherWithIO2 alphSet

nominal-lstar.cabal

@@ -2,7 +2,7 @@ cabal-version:       2.2
 name:                nominal-lstar
 version:             0.1.0.0
 author:              Joshua Moerman
-copyright:           (c) 2016 - 2020, Joshua Moerman
+copyright:           (c) 2016 - 2023, Joshua Moerman
 build-type:          Simple
 extra-source-files:  README.md
 
@@ -10,7 +10,8 @@ common stuff
   default-language:  Haskell2010
   ghc-options:       -O2 -Wall
   build-depends:
-    base >= 4.8 && < 5,
+    -- at most 4.17: one transitive dependency breaks with more recent base
+    base >= 4.8 && < 4.17,
     haskeline,
     NLambda >= 1.1
 

src/Angluin.hs

@@ -16,7 +16,7 @@ import Prelude (Bool (..), Maybe (..), error, show, ($), (++), (.))
 
 
 -- This returns all witnesses (of the form sa) for non-closedness
-closednessTest :: (NominalType i, _) => table -> TestResult i
+closednessTest :: (Nominal i, _) => table -> TestResult i
 closednessTest t = case solve (isEmpty defect) of
     Just True  -> Succes
     Just False -> trace "Not closed" $ Failed defect empty
@@ -27,7 +27,7 @@ closednessTest t = case solve (isEmpty defect) of
         defect = filter (not . hasEqRow) (rowsExt t)
 
 -- We look for inconsistencies and return columns witnessing it
-consistencyTestDirect :: (NominalType i, _) => table -> TestResult i
+consistencyTestDirect :: (Nominal i, _) => table -> TestResult i
 consistencyTestDirect t = case solve (isEmpty defect) of
     Just True  -> Succes
     Just False -> trace "Not consistent" $ Failed empty defect
@@ -39,7 +39,7 @@ consistencyTestDirect t = case solve (isEmpty defect) of
 
 -- Given a C&C table, constructs an automaton. The states are given by 2^E (not
 -- necessarily equivariant functions)
-constructHypothesis :: (NominalType i, _) => table -> Automaton (Row table) i
+constructHypothesis :: (Nominal i, _) => table -> Automaton (Row table) i
 constructHypothesis t = simplify $ automaton q (alph t) d i f
     where
         q = map (row t) (rows t)
@@ -48,28 +48,28 @@ constructHypothesis t = simplify $ automaton q (alph t) d i f
         f = filter (`contains` []) q
 
 -- Extends the table with all prefixes of a set of counter examples.
-useCounterExampleAngluin :: (NominalType i, _) => Teacher i -> Set [i] -> table -> table
+useCounterExampleAngluin :: (Nominal i, _) => Teacher i -> Set [i] -> table -> table
 useCounterExampleAngluin teacher ces t =
     let newRows = sum . map (fromList . inits) $ ces
         newRowsRed = newRows \\ rows t
      in addRows (mqToBool teacher) newRowsRed t
 
 -- This is the variant by Maler and Pnueli: Adds all suffixes as columns
-useCounterExampleMP :: (NominalType i, _) => Teacher i -> Set [i] -> table -> table
+useCounterExampleMP :: (Nominal i, _) => Teacher i -> Set [i] -> table -> table
 useCounterExampleMP teacher ces t =
     let newColumns = sum . map (fromList . tails) $ ces
         newColumnsRed = newColumns \\ cols t
      in addColumns (mqToBool teacher) newColumnsRed t
 
 -- Default: use counter examples in columns, which is slightly faster
-learnAngluin :: (NominalType i, _) => Teacher i -> Automaton _ i
+learnAngluin :: (Nominal i, _) => Teacher i -> Automaton _ i
 learnAngluin teacher = learnLoop useCounterExampleMP teacher (OT.initialBTable (mqToBool teacher) (alphabet teacher))
 
 -- The "classical" version, where counter examples are added as rows
-learnAngluinRows :: (NominalType i, _) => Teacher i -> Automaton _ i
+learnAngluinRows :: (Nominal i, _) => Teacher i -> Automaton _ i
 learnAngluinRows teacher = learnLoop useCounterExampleAngluin teacher (OT.initialBTable (mqToBool teacher) (alphabet teacher))
 
-learnLoop :: (NominalType i, ObservationTable table i Bool, _) => _ -> Teacher i -> table -> Automaton (Row table) i
+learnLoop :: (Nominal i, ObservationTable table i Bool, _) => _ -> Teacher i -> table -> Automaton (Row table) i
 learnLoop cexHandler teacher t =
     let
         -- No worry, these are computed lazily

src/Bollig.hs

@@ -23,7 +23,7 @@ import Prelude (Bool (..), Int, Maybe (..), Show (..), ($), (++), (.))
 -- This does hinder generalisations to other nominal join semi-
 -- lattices than the Booleans.
 
-rfsaClosednessTest :: (NominalType i, _) => Set (Row table) -> table -> TestResult i
+rfsaClosednessTest :: (Nominal i, _) => Set (Row table) -> table -> TestResult i
 rfsaClosednessTest primesUpp t = case solve (isEmpty defect) of
     Just True  -> Succes
     Just False -> trace "Not closed" $ Failed defect empty
@@ -32,7 +32,7 @@ rfsaClosednessTest primesUpp t = case solve (isEmpty defect) of
     where
         defect = filter (\ua -> row t ua `neq` sum (filter (`isSubsetOf` row t ua) primesUpp)) (rowsExt t)
 
-rfsaConsistencyTest :: (NominalType i, _) => table -> TestResult i
+rfsaConsistencyTest :: (Nominal i, _) => table -> TestResult i
 rfsaConsistencyTest t = case solve (isEmpty defect) of
     Just True  -> Succes
     Just False -> trace "Not consistent" $ Failed empty defect
@@ -43,7 +43,7 @@ rfsaConsistencyTest t = case solve (isEmpty defect) of
         defect = triplesWithFilter (\(u1, u2) a v -> maybeIf (not (tableAt2 (u1 ++ [a]) v) /\ tableAt2 (u2 ++ [a]) v) (a:v)) candidates (alph t) (cols t)
         tableAt2 s e = singleton True `eq` tableAt t s e
 
-constructHypothesisBollig :: (NominalType i, _) => Set (Row table) -> table -> Automaton (Row table) i
+constructHypothesisBollig :: (Nominal i, _) => Set (Row table) -> table -> Automaton (Row table) i
 constructHypothesisBollig primesUpp t = automaton q (alph t) d i f
     where
         q = primesUpp
@@ -55,20 +55,20 @@ constructHypothesisBollig primesUpp t = automaton q (alph t) d i f
 
 -- Adds all suffixes as columns
 -- TODO: do actual Rivest and Schapire
-addCounterExample :: (NominalType i, _) => MQ i Bool -> Set [i] -> table -> table
+addCounterExample :: (Nominal i, _) => MQ i Bool -> Set [i] -> table -> table
 addCounterExample mq ces t =
     let newColumns = sum . map (fromList . tails) $ ces
         newColumnsRed = newColumns \\ cols t
      in addColumns mq newColumnsRed t
 
-learnBollig :: (NominalType i, _) => Int -> Int -> Teacher i -> Automaton _ i
+learnBollig :: (Nominal i, _) => Int -> Int -> Teacher i -> Automaton _ i
 learnBollig k n teacher = learnBolligLoop teacher (BOT.initialBTableSize (mqToBool teacher) (alphabet teacher) k n)
 
 -- Slow version
-learnBolligOld :: (NominalType i, _) => Int -> Int -> Teacher i -> Automaton _ i
+learnBolligOld :: (Nominal i, _) => Int -> Int -> Teacher i -> Automaton _ i
 learnBolligOld k n teacher = learnBolligLoop teacher (SOT.initialBTableSize (mqToBool teacher) (alphabet teacher) k n)
 
-learnBolligLoop :: (NominalType i, _) => Teacher i -> table -> Automaton (Row table) i
+learnBolligLoop :: (Nominal i, _) => Teacher i -> table -> Automaton (Row table) i
 learnBolligLoop teacher t =
     let
         -- These simplify's do speed up

src/BooleanObservationTable.hs

@@ -15,7 +15,7 @@ import Prelude (Bool (..), Eq, Int, Ord, Show (..), (++), (.))
 import qualified Prelude ()
 
 -- Helper function
-mqToSubset :: NominalType i => (Set [i] -> Set ([i], Bool)) -> Set [i] -> Set [i]
+mqToSubset :: Nominal i => (Set [i] -> Set ([i], Bool)) -> Set [i] -> Set [i]
 mqToSubset mq = mapFilter (\(i, o) -> maybeIf (fromBool o) i) . mq
 
 -- A table is nothing more than a part of the language.
@@ -28,9 +28,9 @@ data Table i = Table
     , colIndices :: Set (ColumnIndex i)
     , aa         :: Set i
     }
-    deriving (Show, Ord, Eq, Generic, NominalType, Conditional, Contextual)
+    deriving (Show, Ord, Eq, Generic, Nominal, Conditional, Contextual)
 
-instance (NominalType i, Contextual i) => ObservationTable (Table i) i Bool where
+instance (Nominal i, Contextual i) => ObservationTable (Table i) i Bool where
     type Row (Table i) = Set [i]
     rows = rowIndices
     cols = colIndices
@@ -62,7 +62,7 @@ instance (NominalType i, Contextual i) => ObservationTable (Table i) i Bool wher
             newContent = mqToSubset mq newPartRed
 
 
-initialBTableWith :: NominalType i => MQ i Bool -> Set i -> Set (RowIndex i) -> Set (ColumnIndex i) -> Table i
+initialBTableWith :: Nominal i => MQ i Bool -> Set i -> Set (RowIndex i) -> Set (ColumnIndex i) -> Table i
 initialBTableWith mq alphabet newRows newColumns = Table
     { content = content
     , domain = domain
@@ -75,8 +75,8 @@ initialBTableWith mq alphabet newRows newColumns = Table
         domain = pairsWith (++) newRows (newColumns `union` newColumnsExt)
         content = mqToSubset mq domain
 
-initialBTable :: NominalType i => MQ i Bool -> Set i -> Table i
+initialBTable :: Nominal i => MQ i Bool -> Set i -> Table i
 initialBTable mq alphabet = initialBTableWith mq alphabet (singleton []) (singleton [])
 
-initialBTableSize :: NominalType i => MQ i Bool -> Set i -> Int -> Int -> Table i
+initialBTableSize :: Nominal i => MQ i Bool -> Set i -> Int -> Int -> Table i
 initialBTableSize mq alphabet rs cs = initialBTableWith mq alphabet (replicateSetUntil rs alphabet) (replicateSetUntil cs alphabet)

src/Examples/Contrived.hs

@@ -12,7 +12,7 @@ import qualified Prelude ()
 -- 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)
-  deriving (Show, Eq, Ord, Generic, NominalType, Contextual)
+  deriving (Show, Eq, Ord, Generic, Nominal, Contextual)
 
 example1 :: Automaton Example1 Atom
 example1 = automaton
@@ -37,7 +37,7 @@ example1 = automaton
 -- Accepts all even words (ignores the alphabet). Two orbits, with a
 -- trivial action. No registers.
 data Aut2 = Even | Odd
-  deriving (Eq, Ord, Show, Generic, NominalType, Contextual)
+  deriving (Eq, Ord, Show, Generic, Nominal, Contextual)
 
 example2 :: Automaton Aut2 Atom
 example2 = automaton
@@ -57,7 +57,7 @@ example2 = automaton
 -- Accepts all non-empty words with the same symbol. Three orbits: the initial
 -- state, a state with a register and a sink state.
 data Aut3 = Empty | Stored Atom | Sink
-  deriving (Eq, Ord, Show, Generic, NominalType, Contextual)
+  deriving (Eq, Ord, Show, Generic, Nominal, Contextual)
 
 example3 :: Automaton Aut3 Atom
 example3 = automaton
@@ -86,7 +86,7 @@ data Aut4 = Aut4Init              -- Initial state
           | Second Atom Atom      -- After reading two different symbols
           | Symm Atom Atom Atom   -- Accepting state with C3 symmetry
           | Sorted Atom Atom Atom -- State without symmetry
-  deriving (Eq, Ord, Show, Generic, NominalType, Contextual)
+  deriving (Eq, Ord, Show, Generic, Nominal, Contextual)
 
 example4 :: Automaton Aut4 Atom
 example4 = automaton
@@ -125,7 +125,7 @@ example4 = automaton
 
 -- Accepts all two-symbols words with different atoms
 data Aut5 = Aut5Init | Aut5Store Atom | Aut5T | Aut5F
-    deriving (Eq, Ord, Show, Generic, NominalType, Contextual)
+    deriving (Eq, Ord, Show, Generic, Nominal, Contextual)
 
 example5 :: Automaton Aut5 Atom
 example5 = automaton

src/Examples/ContrivedNFAs.hs

@@ -14,7 +14,7 @@ import qualified Prelude ()
 -- The complement of 'all distinct atoms'
 -- Not determinizable
 data NFA1 = Initial1 | Guessed1 Atom | Final1
-  deriving (Show, Eq, Ord, Generic, NominalType, Contextual)
+  deriving (Show, Eq, Ord, Generic, Nominal, Contextual)
 
 exampleNFA1 :: Automaton NFA1 Atom
 exampleNFA1 = automaton
@@ -43,7 +43,7 @@ exampleNFA1 = automaton
 -- So this one *is* determinizable.
 -- Also used in the Bollig et al paper.
 data NFA2 = Initial2 | Distinguished Atom | Count Int
-  deriving (Show, Eq, Ord, Generic, NominalType, Contextual)
+  deriving (Show, Eq, Ord, Generic, Nominal, Contextual)
 
 exampleNFA2 :: Int -> Automaton NFA2 Atom
 exampleNFA2 n = automaton

src/Examples/Fifo.hs

@@ -14,7 +14,7 @@ import qualified Prelude ()
 -- second list is to pop. If the second list is empty, it will reverse
 -- the first.
 data Fifo a = Fifo [a] [a]
-  deriving (Eq, Ord, Show, Generic, NominalType, Contextual)
+  deriving (Eq, Ord, Show, Generic, Nominal, Contextual)
 
 push :: a -> Fifo a -> Fifo a
 push x (Fifo l1 l2) = Fifo (x:l1) l2
@@ -38,7 +38,7 @@ sizeFifo (Fifo l1 l2) = length l1 + length l2
 
 -- The alphabet:
 data DataInput = Put Atom | Get Atom
-  deriving (Eq, Ord, Show, Read, Generic, NominalType, Contextual)
+  deriving (Eq, Ord, Show, Read, Generic, Nominal, Contextual)
 
 -- The automaton: States consist of fifo queues and a sink state.
 -- This representation is not minimal at all, but that's OK, since the

src/Examples/NonResidual.hs

@@ -18,7 +18,7 @@ import qualified Prelude ()
 
 -- Parametric in the alphabet, because why not?
 data NonResidual a = Q1 | Q2 a | Q3 a a | Q4 a | Q5
-  deriving (Eq, Ord, Show, Generic, NominalType, Contextual)
+  deriving (Eq, Ord, Show, Generic, Nominal, Contextual)
 
 exampleNonResidual :: Automaton (NonResidual Atom) Atom
 exampleNonResidual = automaton

src/Examples/Residual.hs

@@ -13,7 +13,7 @@ import Prelude (Eq, Ord, Read, Show)
 import qualified Prelude ()
 
 data Res1 a = QR1 a | QR2 | QEmpty
-  deriving (Eq, Ord, Show, Generic, NominalType, Contextual)
+  deriving (Eq, Ord, Show, Generic, Nominal, Contextual)
 
 -- Language L = { w a | a fresh for w } + {eps}, but anchored with a new symbol
 exampleResidual1 :: Automaton (Res1 Atom) DataInput
@@ -35,10 +35,10 @@ exampleResidual1 = automaton
 
 -- Example when learning breaks
 data Res2 a = Guess a | GuessConfused a | Accept
-  deriving (Eq, Ord, Show, Generic, NominalType, Contextual)
+  deriving (Eq, Ord, Show, Generic, Nominal, Contextual)
 
 data AlphabetR a = A a | Anc a
-  deriving (Eq, Ord, Show, Read, Generic, NominalType, Contextual)
+  deriving (Eq, Ord, Show, Read, Generic, Nominal, Contextual)
 
 exampleResidual2 :: Automaton (Res2 Atom) (AlphabetR Atom)
 exampleResidual2 = automaton

src/Examples/RunningExample.hs

@@ -18,9 +18,9 @@ import qualified Prelude ()
 
 
 data RunningExample a = Store [a] | Check [a] | Accept | Reject
-  deriving (Eq, Ord, Show, Generic, NominalType, Contextual)
+  deriving (Eq, Ord, Show, Generic, Nominal, Contextual)
 
-runningExample :: NominalType a => Set a -> Int -> Automaton (RunningExample a) a
+runningExample :: Nominal a => Set a -> Int -> Automaton (RunningExample a) a
 runningExample alphabet 0 = automaton
     (fromList [Accept, Reject])
     alphabet

src/Examples/Stack.hs

@@ -12,7 +12,7 @@ import qualified Prelude ()
 
 -- Functional stack data type is simply a list.
 newtype Stack a = Stack [a]
-  deriving (Eq, Ord, Show, Generic, NominalType, Contextual)
+  deriving (Eq, Ord, Show, Generic, Nominal, Contextual)
 
 push :: a -> Stack a -> Stack a
 push x (Stack l1) = Stack (x:l1)

src/ObservationTableClass.hs

@@ -3,7 +3,8 @@
 
 module ObservationTableClass where
 
-import NLambda (NominalType, Set, pairsWith)
+import Data.Kind (Type)
+import NLambda (Nominal, Set, pairsWith)
 import Prelude ((++))
 
 -- Words are indices to our table
@@ -14,9 +15,9 @@ type ColumnIndex i = [i]
 type MQ i o = Set [i] -> Set ([i], o)
 
 -- This is a fat class, so that instances could give more efficient implementations
-class (NominalType table, NominalType i, NominalType o) => ObservationTable table i o | table -> i o where
+class (Nominal table, Nominal i, Nominal o) => ObservationTable table i o | table -> i o where
   -- The type of data in a row is determined by the table
-  type Row table :: *
+  type Row table :: Type
 
   -- getters
   rows :: table -> Set (RowIndex i)

src/SimpleObservationTable.hs

@@ -22,7 +22,7 @@ import qualified Prelude ()
 -- Except when o = Bool, more on that later
 type Fun i o = Set (i, o)
 
-dom :: (NominalType i, NominalType o) => Fun i o -> Set i
+dom :: (Nominal i, Nominal o) => Fun i o -> Set i
 dom = map fst
 
 -- A table is nothing more than a part of the language.
@@ -34,9 +34,9 @@ data Table i o = Table
     , colIndices :: Set (ColumnIndex i)
     , aa         :: Set i
     }
-    deriving (Show, Ord, Eq, Generic, NominalType, Conditional, Contextual)
+    deriving (Show, Ord, Eq, Generic, Nominal, Conditional, Contextual)
 
-instance (NominalType i, NominalType o) => ObservationTable (Table i o) i o where
+instance (Nominal i, Nominal o) => ObservationTable (Table i o) i o where
     type Row (Table i o) = Fun [i] o
     rows = rowIndices
     cols = colIndices
@@ -70,11 +70,11 @@ instance (NominalType i, NominalType o) => ObservationTable (Table i o) i o wher
 -- We can reuse the above tables for the Boolean case and
 -- perform some minor optimisations.
 newtype Boolean table = B { unB :: table }
-    deriving (Show, Ord, Eq, Generic, NominalType, Conditional, Contextual)
+    deriving (Show, Ord, Eq, Generic, Nominal, Conditional, Contextual)
 
 type BTable i = Boolean (Table i Bool)
 
-instance (NominalType i) => ObservationTable (BTable i) i Bool where
+instance (Nominal i) => ObservationTable (BTable i) i Bool where
     -- Special case of a boolean: functions to Booleans are subsets
     type Row (BTable i) = Set [i]
 
@@ -94,7 +94,7 @@ instance (NominalType i) => ObservationTable (BTable i) i Bool where
     rowEps (B Table{..}) = mapFilter (\(i, o) -> maybeIf (fromBool o /\ i `member` colIndices) i) content
 
 
-initialTableWith :: (NominalType i, NominalType o) => MQ i o -> Set i -> Set (RowIndex i) -> Set (ColumnIndex i) -> Table i o
+initialTableWith :: (Nominal i, Nominal o) => MQ i o -> Set i -> Set (RowIndex i) -> Set (ColumnIndex i) -> Table i o
 initialTableWith mq alphabet newRows newColumns = Table
     { content = content
     , rowIndices = newRows
@@ -106,17 +106,17 @@ initialTableWith mq alphabet newRows newColumns = Table
         domain = pairsWith (++) newRows (newColumns `union` newColumnsExt)
         content = mq domain
 
-initialTable :: (NominalType i, NominalType o) => MQ i o -> Set i -> Table i o
+initialTable :: (Nominal i, Nominal o) => MQ i o -> Set i -> Table i o
 initialTable mq alphabet = initialTableWith mq alphabet (singleton []) (singleton [])
 
-initialTableSize :: (NominalType i, NominalType o) => MQ i o -> Set i -> Int -> Int -> Table i o
+initialTableSize :: (Nominal i, Nominal o) => MQ i o -> Set i -> Int -> Int -> Table i o
 initialTableSize mq alphabet rs cs = initialTableWith mq alphabet (replicateSetUntil rs alphabet) (replicateSetUntil cs alphabet)
 
-initialBTableWith :: NominalType i => MQ i Bool -> Set i -> Set (RowIndex i) -> Set (ColumnIndex i) -> BTable i
+initialBTableWith :: Nominal i => MQ i Bool -> Set i -> Set (RowIndex i) -> Set (ColumnIndex i) -> BTable i
 initialBTableWith = coerce initialTableWith
 
-initialBTable :: NominalType i => MQ i Bool -> Set i -> BTable i
+initialBTable :: Nominal i => MQ i Bool -> Set i -> BTable i
 initialBTable = coerce initialTable
 
-initialBTableSize :: NominalType i => MQ i Bool -> Set i -> Int -> Int -> BTable i
+initialBTableSize :: Nominal i => MQ i Bool -> Set i -> Int -> Int -> BTable i
 initialBTableSize = coerce initialTableSize

src/Teacher.hs

@@ -23,7 +23,7 @@ import Prelude hiding (map)
 -- The teacher interface is slightly inconvenient
 -- But this is for a good reason. The type [i] -> o
 -- doesn't work well in nlambda
-mqToBool :: NominalType i => Teacher i -> Set [i] -> Set ([i], Bool)
+mqToBool :: Nominal i => Teacher i -> Set [i] -> Set ([i], Bool)
 mqToBool teacher qs = answer
     where
         realQ = membership teacher qs
@@ -41,7 +41,7 @@ mqToBool teacher qs = answer
 
 -- 1. This is a fully automatic teacher, which has an internal automaton
 -- Only works for DFAs for now, as those can be checked for equivalence
-teacherWithTarget :: (NominalType i, NominalType q) => Automaton q i -> Teacher i
+teacherWithTarget :: (Nominal i, Nominal q) => Automaton q i -> Teacher i
 teacherWithTarget aut = Teacher
     { membership = foreachQuery $ accepts aut
     , equivalent = automaticEquivalent bisim aut
@@ -50,7 +50,7 @@ teacherWithTarget aut = Teacher
 
 -- 1b. This is a fully automatic teacher, which has an internal automaton
 -- NFA have undecidable equivalence, n is a bound on deoth of bisimulation.
-teacherWithTargetNonDet :: (Show i, Show q, NominalType i, NominalType q) => Int -> Automaton q i -> Teacher i
+teacherWithTargetNonDet :: (Show i, Show q, Nominal i, Nominal q) => Int -> Automaton q i -> Teacher i
 teacherWithTargetNonDet n aut = Teacher
     { membership = foreachQuery $ accepts aut
     , equivalent = automaticEquivalent (bisimNonDet n) aut
@@ -62,7 +62,7 @@ teacherWithTargetNonDet n aut = Teacher
 -- Note that parsing is very unforgiving, one mistake, and there is no way back
 -- Atoms are referenced by Ints. When the user provides a counter example, we
 -- consider the whole orbit generated by it.
-teacherWithIO :: (Show i, Read i, NominalType i, Contextual i) => Set i -> Teacher i
+teacherWithIO :: (Show i, Read i, Nominal i, Contextual i) => Set i -> Teacher i
 teacherWithIO alph = Teacher
     { membership = ioMembership
     , equivalent = ioEquivalent
@@ -70,7 +70,7 @@ teacherWithIO alph = Teacher
     }
 
 -- 2b. Same as above. But with machine readable queries (except for EQs maybe)
-teacherWithIO2 :: (Show i, Read i, NominalType i, Contextual i) => Set i -> Teacher i
+teacherWithIO2 :: (Show i, Read i, Nominal i, Contextual i) => Set i -> Teacher i
 teacherWithIO2 alph = Teacher
     { membership = ioMembership2
     , equivalent = ioEquivalent2
@@ -80,7 +80,7 @@ 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 :: (Show i, Read i, NominalType i, Contextual i, NominalType q) => Automaton q i -> Teacher i
+teacherWithTargetAndIO :: (Show i, Read i, Nominal i, Contextual i, Nominal q) => Automaton q i -> Teacher i
 teacherWithTargetAndIO aut = Teacher
     { membership = foreachQuery $ accepts aut
     , equivalent = ioEquivalent

src/Teachers/Teacher.hs

@@ -17,12 +17,12 @@ data Teacher i = Teacher
     -- Given a hypothesis, returns Nothing when equivalence or a (equivariant)
     -- set of counter examples. Needs to be quantified over q, because the
     -- learner may choose the type of the state space.
-    , equivalent :: forall q. (Show q, NominalType q) => Automaton q i -> Maybe (Set [i])
+    , equivalent :: forall q. (Show q, Nominal q) => Automaton q i -> Maybe (Set [i])
     -- Returns the alphabet to the learner
     , alphabet   :: Set i
     }
 
 -- 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 :: Nominal i => ([i] -> Formula) -> Set[i] -> Set ([i], Formula)
 foreachQuery f = map (\q -> (q, f q))

src/Teachers/Terminal.hs

@@ -9,7 +9,7 @@ import System.IO.Unsafe (unsafePerformIO)
 import Text.Read (readMaybe)
 
 -- Posing a membership query to the terminal and waits for used to input a formula
-ioMembership :: (Show i, NominalType i, Contextual i) => Set [i] -> Set ([i], Formula)
+ioMembership :: (Show i, Nominal i, Contextual i) => Set [i] -> Set ([i], Formula)
 ioMembership queries = unsafePerformIO $ do
     cache <- readIORef mqCache
     let cachedAnswers = filter (\(a, _) -> a `member` queries) cache
@@ -41,7 +41,7 @@ ioMembership queries = unsafePerformIO $ do
 
 
 -- Same as above, but with a machine-readable format
-ioMembership2 :: (Show i, NominalType i, Contextual i) => Set [i] -> Set ([i], Formula)
+ioMembership2 :: (Show i, Nominal i, Contextual i) => Set [i] -> Set ([i], Formula)
 ioMembership2 queries = unsafePerformIO $ do
     cache <- readIORef mqCache
     let cachedAnswers = filter (\(a, _) -> a `member` queries) cache
@@ -73,7 +73,7 @@ newtype TestIO i = T [i]
 
 -- Poses a query to the terminal, waiting for the user to provide a counter example
 -- 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 :: (Show q, Nominal q, Show i, Read i, Nominal i) => Automaton q i -> Maybe (Set [i])
 ioEquivalent hypothesis = unsafePerformIO $ do
     putStrLn "\n# Is the following automaton correct?"
     putStr "# "
@@ -102,7 +102,7 @@ ioEquivalent hypothesis = unsafePerformIO $ do
 
 -- 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 :: (Show q, Nominal q, Show i, Read i, Nominal i) => Automaton q i -> Maybe (Set [i])
 ioEquivalent2 hypothesis = unsafePerformIO $ do
     putStrLn "EQ\n\"Is the following automaton correct?"
     print hypothesis

src/Teachers/Whitebox.hs

@@ -8,7 +8,7 @@ import Prelude hiding (filter, map, not, sum)
 -- Checks bisimulation of initial states (only for DFAs)
 -- returns some counterexamples if not bisimilar
 -- returns empty set iff bisimilar
-bisim :: (NominalType i, NominalType q1, NominalType q2) => Automaton q1 i -> Automaton q2 i -> Set [i]
+bisim :: (Nominal i, Nominal q1, Nominal q2) => Automaton q1 i -> Automaton q2 i -> Set [i]
 bisim aut1 aut2 = go empty (pairsWith addEmptyWord (initialStates aut1) (initialStates aut2))
     where
         go rel todo =
@@ -37,7 +37,7 @@ bisim aut1 aut2 = go empty (pairsWith addEmptyWord (initialStates aut1) (initial
 -- I am not sure about correctness, but that is not really an issue for our
 -- use-case. Note that deciding equivalence of NFAs is undecidable, so we
 -- bound the bisimulation depth.
-bisimNonDet :: (Show i, Show q1, Show q2, NominalType i, NominalType q1, NominalType q2) => Int -> Automaton q1 i -> Automaton q2 i -> Set [i]
+bisimNonDet :: (Show i, Show q1, Show q2, Nominal i, Nominal q1, Nominal q2) => Int -> Automaton q1 i -> Automaton q2 i -> Set [i]
 bisimNonDet n aut1 aut2 = go empty (singleton ([], initialStates aut1, initialStates aut2))
     where
         go rel todo0 =