Small cleanup

app/ExampleAutomata.hs

@@ -62,19 +62,21 @@ doubleWordAut n = Automaton {..} where
 
 
 -- alphetbet for the Fifo queue example
-data Fifo = Put Atom | Get Atom
+data FifoA = Put Atom | Get Atom
   deriving (Eq, Ord, Show, GHC.Generic)
-  deriving Nominal via Generic Fifo
+  deriving Nominal via Generic FifoA
 
-instance ToStr Fifo where
+instance ToStr FifoA where
   toStr (Put a) = "Put " ++ toStr a
   toStr (Get a) = "Get " ++ toStr a
 
-instance FromStr Fifo where
+instance FromStr FifoA where
   fromStr ('P':'u':'t':' ':a) = let (x, r) = fromStr a in (Put x, r)
   fromStr ('G':'e':'t':' ':a) = let (x, r) = fromStr a in (Get x, r)
   fromStr _ = error "Cannot parse Fifo"
 
+fifoAlph = map Put rationals <> map Get rationals
+
 data FifoS = FifoS [Atom] [Atom]
   deriving (Eq, Ord, GHC.Generic)
   deriving Nominal via Generic FifoS
@@ -82,8 +84,6 @@ data FifoS = FifoS [Atom] [Atom]
 instance ToStr FifoS where
   toStr (FifoS l1 l2) = "F " ++ toStr l1 ++ " - " ++ toStr l2
 
-fifoAlph = map Put rationals <> map Get rationals
-
 fifoAut n = Automaton {..} where
   states0 = filter (\(FifoS l1 l2) -> length l1 + length l2 <= n) $ productWith (\l1 l2 -> FifoS l1 l2) (words n) (words n)
   states = fromList [Nothing] <> map Just states0

src/EquivariantMap.hs

@@ -28,8 +28,10 @@ import Support
 -- Very similar to EquivariantSet, but then the map analogue. The important
 -- thing is that we have to store which values are preserved under a map. This
 -- is done with the list of bit vector. Otherwise, it is an orbit-wise
--- representation, just like sets.
+-- representation, just like sets. This action is trivial, since equivariant
+-- maps are equivariant.
 newtype EquivariantMap k v = EqMap { unEqMap :: Map (Orbit k) (Orbit v, [Bool]) }
+  deriving Nominal via Trivial (EquivariantMap k v)
 
 -- Need undecidableIntances for this
 deriving instance (Eq (Orbit k), Eq (Orbit v)) => Eq (EquivariantMap k v)
@@ -41,9 +43,6 @@ deriving instance (Show (Orbit k), Show (Orbit v)) => Show (EquivariantMap k v)
 deriving instance Ord (Orbit k) => Monoid (EquivariantMap k v)
 deriving instance Ord (Orbit k) => Semigroup (EquivariantMap k v)
 
--- This action is trivial, since equivariant maps are equivariant
-deriving via (Trivial (EquivariantMap k v)) instance Nominal (EquivariantMap k v) 
-
 
 -- Query
 

src/EquivariantSet.hs

@@ -22,8 +22,10 @@ import OrbitList (OrbitList(..))
 -- represented. Although internally it is just a set of orbits, the interface
 -- will always work directly with elements. This way we model infinite sets.
 -- Note that functions such as toList do not return an ordered list since the
--- representatives are chosen arbitrarily.
+-- representatives are chosen arbitrarily. This action is trivial, since
+-- equivariant sets are equivariant :-).
 newtype EquivariantSet a = EqSet { unEqSet :: Set (Orbit a) }
+  deriving Nominal via Trivial (EquivariantSet a)
 
 -- Need undecidableIntances for this
 deriving instance Eq (Orbit a) => Eq (EquivariantSet a)
@@ -35,9 +37,6 @@ deriving instance Show (Orbit a) => Show (EquivariantSet a)
 deriving instance Ord (Orbit a) => Monoid (EquivariantSet a)
 deriving instance Ord (Orbit a) => Semigroup (EquivariantSet a)
 
--- This action is trivial, since equivariant sets are equivariant
-deriving via (Trivial (EquivariantSet a)) instance Nominal (EquivariantSet a) 
-
 
 -- Query
 

src/Nominal/Class.hs

@@ -87,12 +87,12 @@ instance Nominal (Trivial a) where
 
 -- We can now define trivial instances for some basic types. (Some of these
 -- could equivalently be derived with generics.)
-deriving via (Trivial Void) instance Nominal Void
-deriving via (Trivial ()) instance Nominal ()
-deriving via (Trivial Bool) instance Nominal Bool
-deriving via (Trivial Char) instance Nominal Char
-deriving via (Trivial Int) instance Nominal Int -- NB: Trivial instance!
-deriving via (Trivial Ordering) instance Nominal Ordering
+deriving via Trivial Void instance Nominal Void
+deriving via Trivial () instance Nominal ()
+deriving via Trivial Bool instance Nominal Bool
+deriving via Trivial Char instance Nominal Char
+deriving via Trivial Int instance Nominal Int -- NB: Trivial instance!
+deriving via Trivial Ordering instance Nominal Ordering
 
 
 -- The generic instance unfolds the algebraic data type in sums and products,
@@ -107,14 +107,12 @@ instance (GHC.Generic a, GNominal (Rep a)) => Nominal (Generic a) where
 
 
 -- Some instances we can derive via generics
-deriving via (Generic (a, b)) instance (Nominal a, Nominal b) => Nominal (a, b)
-deriving via (Generic (a, b, c)) instance (Nominal a, Nominal b, Nominal c) => Nominal (a, b, c)
-deriving via (Generic (a, b, c, d)) instance (Nominal a, Nominal b, Nominal c, Nominal d) => Nominal (a, b, c, d)
-
-deriving via (Generic (Either a b)) instance (Nominal a, Nominal b) => Nominal (Either a b)
-
-deriving via (Generic [a]) instance Nominal a => Nominal [a]
-deriving via (Generic (Maybe a)) instance Nominal a => Nominal (Maybe a)
+deriving via Generic (a, b) instance (Nominal a, Nominal b) => Nominal (a, b)
+deriving via Generic (a, b, c) instance (Nominal a, Nominal b, Nominal c) => Nominal (a, b, c)
+deriving via Generic (a, b, c, d) instance (Nominal a, Nominal b, Nominal c, Nominal d) => Nominal (a, b, c, d)
+deriving via Generic (Either a b) instance (Nominal a, Nominal b) => Nominal (Either a b)
+deriving via Generic [a] instance Nominal a => Nominal [a]
+deriving via Generic (Maybe a) instance Nominal a => Nominal (Maybe a)
 
 
 -- Generic class, so that custom data types can be derived

src/OrbitList.hs

@@ -18,11 +18,11 @@ import Support (Rat(..))
 -- Similar to EquivariantSet, but merely a list structure. It is an
 -- equivariant data type, so the Nominal instance is trivial.
 newtype OrbitList a = OrbitList { unOrbitList :: [Orbit a] }
+  deriving Nominal via Trivial (OrbitList a)
 
 deriving instance Eq (Orbit a) => Eq (OrbitList a)
 deriving instance Ord (Orbit a) => Ord (OrbitList a)
 deriving instance Show (Orbit a) => Show (OrbitList a)
-deriving via (Trivial (OrbitList a)) instance Nominal (OrbitList a)
 
 -- Simply concatenation of the list
 deriving instance Semigroup (OrbitList a)