Removed the sem functions, replaced them with a general one.

Automata.hs

@@ -10,15 +10,6 @@ type F a = (,) Bool `O` ((->) a)
 -- Fixpoint, ie languages
 type Language a = Mu (F a)
 
--- basic constructor
-ctor :: Bool -> (a -> Language a) -> Language a
-ctor b t = phi (O (b, t))
-
--- For every (F a)-coalgebra x, there is a arrow x -> Language a
--- and it is unique, so `Language a` is the final (F a)-coalgebra!
-sem :: (Coalgebra (F a) x) => x -> Language a
-sem s = ctor b (\w -> sem $ trans w) where O (b, trans) = psi s
-
 -- auciliry function
 is_member :: [a] -> Language a -> Bool
 is_member [] l = b where O (b, _) = psi l
@@ -49,7 +40,7 @@ instance Coalgebra (F A) X where
 
 
 -- Test a word against it
-show_member word = putStrLn $ show (word, is_member word (sem One :: Language A))
+show_member word = putStrLn $ show (word, is_member word (semantics One :: Language A))
 
 main = do
 	let words = [[A], [A,B], [A,B,B], [A,B,B,A], [A,B,A,B,A]]

Coalgebra.hs

@@ -21,3 +21,6 @@ instance Functor f => Algebra f (Mu f) where
  
 instance Functor f => Coalgebra f (Mu f) where
     psi (In x) = x
+
+semantics :: (Functor f, Coalgebra f x) => x -> (Mu f)
+semantics x = phi (fmap semantics (psi x))

Streams.hs

@@ -9,15 +9,6 @@ type F a = (,) a
 -- This will give the fixpoint, ie a coalgebra, because F is a functor
 type Stream a = Mu (F a)
 
--- basic constructor
-(+:+) :: a -> Stream a -> Stream a
-(+:+) a s = phi (a, s)
-
--- For every (F a)-coalgebra x, there is a arrow x -> Stream a
--- and it is unique, so `Stream a` is the final (F a)-coalgebra!
-sem :: (Coalgebra (F a) x) => x -> Stream a
-sem x = x0 +:+ sem x' where (x0, x') = psi x
-
 -- auxilary functions
 toList :: Stream a -> [a]
 toList s = a0 : toList a' where (a0, a') = psi s
@@ -32,4 +23,4 @@ instance Coalgebra (F Int) X where
 
 main :: IO ()
 main = do
-	putStrLn $ show $ take 20 $ toList $ (sem One :: Stream Int)
+	putStrLn $ show $ take 20 $ toList $ (semantics One :: Stream Int)