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

master
Joshua Moerman 12 years ago
parent
commit
e5bcd02578
  1. 11
      Automata.hs
  2. 3
      Coalgebra.hs
  3. 11
      Streams.hs

11
Automata.hs

@ -10,15 +10,6 @@ type F a = (,) Bool `O` ((->) a)
-- Fixpoint, ie languages -- Fixpoint, ie languages
type Language a = Mu (F a) 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 -- auciliry function
is_member :: [a] -> Language a -> Bool is_member :: [a] -> Language a -> Bool
is_member [] l = b where O (b, _) = psi l is_member [] l = b where O (b, _) = psi l
@ -49,7 +40,7 @@ instance Coalgebra (F A) X where
-- Test a word against it -- 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 main = do
let words = [[A], [A,B], [A,B,B], [A,B,B,A], [A,B,A,B,A]] let words = [[A], [A,B], [A,B,B], [A,B,B,A], [A,B,A,B,A]]

3
Coalgebra.hs

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

11
Streams.hs

@ -9,15 +9,6 @@ type F a = (,) a
-- This will give the fixpoint, ie a coalgebra, because F is a functor -- This will give the fixpoint, ie a coalgebra, because F is a functor
type Stream a = Mu (F a) 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 -- auxilary functions
toList :: Stream a -> [a] toList :: Stream a -> [a]
toList s = a0 : toList a' where (a0, a') = psi s toList s = a0 : toList a' where (a0, a') = psi s
@ -32,4 +23,4 @@ instance Coalgebra (F Int) X where
main :: IO () main :: IO ()
main = do main = do
putStrLn $ show $ take 20 $ toList $ (sem One :: Stream Int) putStrLn $ show $ take 20 $ toList $ (semantics One :: Stream Int)