From: Tomas Musil <tomik.musil@gmail.com>
Date: Fri, 12 Dec 2014 19:25:07 +0000 (+0100)
Subject: Eager and Lazy
X-Git-Url: http://git.tomasm.cz/fp.git/commitdiff_plain/16e5b1e83c48bdaf47166d61c780dbbadfa79209

Eager and Lazy
---

diff --git a/src/Lambda.hs b/src/Lambda.hs
index f89cc7e..f828f4d 100644
--- a/src/Lambda.hs
+++ b/src/Lambda.hs
@@ -31,17 +31,26 @@ import Control.Monad.State
 -- $setup
 -- >>> import Test.QuickCheck
 -- >>> import Control.Applicative
--- >>> let aTerm 0 = pure $ Var "x"
--- >>> let aTerm n = oneof [pure (Var "x"), liftA (Lambda "x") $ aTerm (n - 1), liftA2 App (aTerm (n `div` 2)) (aTerm (n `div` 2))] 
+-- >>> let aTerm 0 = liftA (Var . ("x" ++) . show) (arbitrary :: Gen Int)
+-- >>> let aTerm n = oneof [aTerm 0, liftA (Lambda "x") $ aTerm (n - 1), liftA2 App (aTerm (n `div` 2)) (aTerm (n `div` 2))] 
 -- >>> instance Arbitrary Term where arbitrary = sized aTerm
 
+cY :: Term
+cY = tRead "λf.(λx.f (x x)) (λx.f (x x))"
+
+cI :: Term
+cI = tRead "λx.x"
+
+cK :: Term
+cK = tRead "λx y.x"
+
 type VarName = String
 
 -- | 
 -- >>> print $ Lambda "x" (Var "x")
 -- (λx.x)
 
-data Term = Var VarName | Lambda VarName Term | App Term Term deriving (Eq)
+data Term = EmptyT | Var VarName | Lambda VarName Term | App Term Term deriving (Eq)
 
 pattern RedEx x t s = App (Lambda x t) s
 pattern AppApp a b c = App a (App b c)
@@ -68,7 +77,7 @@ tRead s = case parseOnly (parseTerm <* endOfInput) (T.pack s) of
 
 parseVar :: Parser Term
 parseVar = do
-  x <- many1 letter
+  x <- many1 (letter <|> digit)
   return $! Var x
 
 parseLambda :: Parser Term
@@ -150,17 +159,74 @@ traversPost :: (Monad m) => (Term -> m Term) -> Term -> m Term
 traversPost f (App t u) = do
   nt <- traversPost f t
   nu <- traversPost f u
-  f (App nt nu)
-traversPost f (Lambda x t) = f . Lambda x =<< traversPost f t
-traversPost f (Var x) = f (Var x)
+  case App nt nu of
+    l@(RedEx _ _ _) -> traversPost f =<< f l
+    r -> return r
+traversPost f (Lambda x t) = return . Lambda x =<< traversPost f t
+traversPost f (Var x) = return $ (Var x)
+
+data Z = R Term Z | L Z Term | ZL VarName Z | E
+data D = Up | Down
+data Zip = Zip Z Term
+
+move (App l r, c, Down) = (l, L c r, Down)
+move (Lambda x t, c, Down) = (t, ZL x c, Down)
+move (Var x, c, Down) = (Var x, c, Up)
+move (t, L c r, Up) = (r, R t c, Down)
+move (t, R l c, Up) = (App l t, c, Up)
+move (t, ZL x c, Up) = (Lambda x t, c, Up)
+move (t, E, Up) = (t, E, Up)
+
+unmove (t, L c r, Down) = (App t r, c, Down)
+unmove x = x
+
+getF (t, _, _) = t
+
+travPost :: (Monad m) => (Term -> m Term) -> Term -> m Term
+travPost fnc term = tr fnc (term, E, Down)
+  where 
+    tr f (t@(RedEx _ _ _), c, Up) = do
+      nt <- f t
+      tr f $ (nt, c, Down)
+    tr f (t, E, Up) = return t
+    tr f (t, c, Up) = tr f $ move (t, c, Up)
+    tr f (t, c, Down) = tr f $ move (t, c, Down)
+
+travPre :: (Monad m) => (Term -> m Term) -> Term -> m Term
+travPre fnc term = tr fnc (term, E, Down)
+  where 
+    tr f (t@(RedEx _ _ _), c, Down) = do
+      nt <- f t
+      tr f $ unmove (nt, c, Down)
+    tr f (t, E, Up) = return t
+    tr f (t, c, Up) = tr f $ move (t, c, Up)
+    tr f (t, c, Down) = tr f $ move (t, c, Down)
 
 printT :: Term -> IO Term
 printT t = do
   print t
   return t
 
+-- |
+--
+-- >>> toNormalForm Eager 100 cI
+-- Just (λx.x)
+--
+-- >>> toNormalForm Eager 100 $ App cI cI
+-- Just (λx.x)
+--
+-- >>> toNormalForm Eager 1000 $ (App (App cK cI) cY)
+-- Nothing
+--
+-- >>> toNormalForm Lazy 1000 $ (App (App cK cI) cY)
+-- Just (λx.x)
+--
+-- prop> (\ t u -> t == u || t == Nothing || u == Nothing) (toNormalForm Lazy 1000 x) (toNormalForm Eager 1000 x)
+
+
 toNormalForm :: Strategy -> Int -> Term -> Maybe Term
-toNormalForm Eager n = flip evalStateT 0 . traversPost (short n >=> cnt >=> reduceStep)
+toNormalForm Eager n = flip evalStateT 0 . travPost (cnt >=> short n >=> reduceStep)
+toNormalForm Lazy  n = flip evalStateT 0 . travPre  (cnt >=> short n >=> reduceStep)
 
 cnt :: (Monad m) => Term -> StateT Int m Term
 cnt t@(RedEx _ _ _) = do
@@ -171,6 +237,6 @@ cnt t = return t
 short :: Int -> Term -> StateT Int Maybe Term
 short max t = do
   n <- get
-  if n == max
+  if n > max
     then lift Nothing
     else return t