X-Git-Url: http://git.tomasm.cz/fp.git/blobdiff_plain/16e5b1e83c48bdaf47166d61c780dbbadfa79209..f9d54d61f2feba3f37c9e7c5f4ab87bf7b3e6166:/src/Lambda.hs?ds=inline

diff --git a/src/Lambda.hs b/src/Lambda.hs
index f828f4d..3026b75 100644
--- a/src/Lambda.hs
+++ b/src/Lambda.hs
@@ -1,4 +1,3 @@
-{-# OPTIONS_GHC -fno-warn-unused-do-bind #-}
 {-# LANGUAGE PatternSynonyms #-}
 
 -- |
@@ -15,108 +14,34 @@ module Lambda
   ( -- * Types
     VarName
   , Term(..)
-    -- * Parsing terms
-  , parseTerm
-  , tRead
+  , pattern RedEx
     -- * Reduction
+  , alphaNorm
   , reduce
+  , toNormalForm
+  , Strategy(..)
   ) where
-  
 
-import Data.Text as T
-import Data.Attoparsec.Text
-import Control.Applicative
 import Control.Monad.State 
 
+import Lambda.Term
+
 -- $setup
--- >>> import Test.QuickCheck
 -- >>> import Control.Applicative
--- >>> 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 = 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)
-pattern EmLambda x y t = Lambda x (Lambda y t)
-
-
-instance Show Term where
-  show (Var x) = x
-  show (EmLambda x y t) = show (Lambda (x ++ " " ++ y) t)
-  show (Lambda x t) = "(λ" ++ x ++ "." ++ show t ++ ")"
-  show (AppApp a b c) = show a ++ " " ++ braced (App b c)
-  show (App t r) = show t ++ " " ++ show r
+-- >>> import Lambda.Parser.Fancy
+-- >>> import Test.Term
+-- >>> import Test.QuickCheck
 
-braced :: Term -> String
-braced t = "(" ++ show t ++ ")"
+varnames :: [VarName]
+varnames = map (:[]) ['a'..'z'] ++ [c : s | s <- varnames, c <- ['a'..'z']]
 
--- |
--- prop> t == tRead (show (t :: Term))
-
-tRead :: String -> Term
-tRead s = case parseOnly (parseTerm <* endOfInput) (T.pack s) of
-    (Right t) -> t
-    (Left e) -> error e
-
-parseVar :: Parser Term
-parseVar = do
-  x <- many1 (letter <|> digit)
-  return $! Var x
-
-parseLambda :: Parser Term
-parseLambda = do
-  char '\\' <|> char 'λ'
-  vars <- sepBy1 parseVar (char ' ')
-  char '.'
-  t <- parseTerm
-  return $! createLambda vars t
-
-createLambda :: [Term] -> Term -> Term
-createLambda (Var x : vs) t = Lambda x $ createLambda vs t
-createLambda [] t = t
-createLambda _ _ = error "createLambda failed"
-
-parseApp :: Parser Term
-parseApp = do
-  aps <- sepBy1 (parseBraces <|> parseLambda <|> parseVar) (char ' ')
-  return $! createApp aps
-
-createApp :: [Term] -> Term
-createApp [t] = t
-createApp (t:ts:tss) = createApp (App t ts : tss)
-createApp [] = error "empty createApp"
-
-parseBraces :: Parser Term
-parseBraces = do
-  char '('
-  t <- parseTerm
-  char ')'
-  return t 
-
-parseTerm :: Parser Term
-parseTerm = parseApp <|>
-            parseBraces <|>
-            parseLambda <|>
-            parseVar
-
--------------------------------------------------
+alphaNorm :: Term -> Term
+alphaNorm = alpha varnames
+  where
+    alpha (v:vs) (Lambda x r) = Lambda v . alpha vs $ substitute x (Var v) r
+    alpha vs (App u v) = App (alpha vs u) (alpha vs v)
+    alpha _ (Var x) = Var x
+    alpha [] _ = undefined
 
 isFreeIn :: VarName -> Term -> Bool
 isFreeIn x (Var v) = x == v
@@ -151,24 +76,15 @@ reduce (App t u) = app (reduce t) u
 
 data Strategy = Eager | Lazy
 
-reduceStep :: (Monad m) => Term -> m Term
-reduceStep (RedEx x s t) = return $ substitute x t s
-reduceStep t = return $ t
-
-traversPost :: (Monad m) => (Term -> m Term) -> Term -> m Term
-traversPost f (App t u) = do
-  nt <- traversPost f t
-  nu <- traversPost f u
-  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)
+reduceStep :: Term -> Term
+reduceStep (RedEx x s t) = substitute x t s
+reduceStep t = t
 
 data Z = R Term Z | L Z Term | ZL VarName Z | E
 data D = Up | Down
-data Zip = Zip Z Term
+type TermZipper = (Term, Z, D)
 
+move :: TermZipper -> TermZipper
 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)
@@ -177,36 +93,32 @@ 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 :: TermZipper -> TermZipper
 unmove (t, L c r, Down) = (App t r, c, Down)
 unmove x = x
 
-getF (t, _, _) = t
+-- getTerm :: TermZipper -> Term
 
 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
+    tr f (t@RedEx{}, c, Up) = do
       nt <- f t
-      tr f $ (nt, c, Down)
-    tr f (t, E, Up) = return t
+      tr f (nt, c, Down)
+    tr _ (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
+    tr f (t@RedEx{}, c, Down) = do
       nt <- f t
       tr f $ unmove (nt, c, Down)
-    tr f (t, E, Up) = return t
+    tr _ (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
@@ -215,28 +127,29 @@ printT t = do
 -- >>> toNormalForm Eager 100 $ App cI cI
 -- Just (λx.x)
 --
--- >>> toNormalForm Eager 1000 $ (App (App cK cI) cY)
+-- >>> toNormalForm Eager 100 $ (App (App cK cI) cY)
 -- Nothing
 --
--- >>> toNormalForm Lazy 1000 $ (App (App cK cI) cY)
+-- >>> toNormalForm Lazy 100 $ (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)
+-- prop> within 10000000 $ (\ t u -> t == u || t == Nothing || u == Nothing) (alphaNorm <$> toNormalForm Lazy 1000 x) (alphaNorm <$> toNormalForm Eager 1000 x)
 
+-- inf = tRead "(\\d.a ((\\d c.c d c) (\\x y z.x z (y z)) (\\f.(\\x.f (x x)) (\\x.f (x x))) e))"
 
 toNormalForm :: Strategy -> Int -> Term -> Maybe Term
-toNormalForm Eager n = flip evalStateT 0 . travPost (cnt >=> short n >=> reduceStep)
-toNormalForm Lazy  n = flip evalStateT 0 . travPre  (cnt >=> short n >=> reduceStep)
+toNormalForm Eager n = flip evalStateT 0 . travPost (cnt >=> short n >=> return . reduceStep)
+toNormalForm Lazy  n = flip evalStateT 0 . travPre  (cnt >=> short n >=> return . reduceStep)
 
 cnt :: (Monad m) => Term -> StateT Int m Term
-cnt t@(RedEx _ _ _) = do
+cnt t@RedEx{} = do
   modify (+ 1)
   return t
 cnt t = return t
 
 short :: Int -> Term -> StateT Int Maybe Term
-short max t = do
+short maxN t = do
   n <- get
-  if n > max
+  if n > maxN
     then lift Nothing
     else return t