gitignore

[fp.git] / src / Lambda.hs

diff --git a/src/Lambda.hs b/src/Lambda.hs
index 0cedf4a..428ac99 100644 (file)
--- a/src/Lambda.hs
+++ b/src/Lambda.hs
@@ -1,4 +1,3 @@
-{-# OPTIONS_GHC -fno-warn-unused-do-bind #-}

 {-# LANGUAGE PatternSynonyms #-}
 
 -- |
 {-# LANGUAGE PatternSynonyms #-}
 
 -- |


@@ -15,112 +14,37 @@ module Lambda
   ( -- * Types
     VarName
   , Term(..)
   ( -- * Types
     VarName
   , Term(..)

-    -- * Parsing terms
-  , parseTerm
-  , tRead
+  , pattern RedEx

     -- * Reduction
     -- * Reduction

+  , alphaNorm

   , reduce
   , toNormalForm
   , Strategy(..)
   ) where
   , reduce
   , toNormalForm
   , Strategy(..)
   ) where

-  

 
 

-import Data.Text as T hiding (map)
-import Data.Attoparsec.Text
-import Control.Applicative

 import Control.Monad.State 
 
 import Control.Monad.State 
 

--- $setup
--- >>> import Test.QuickCheck
--- >>> import Control.Applicative
--- >>> let aVarName = oneof . map (pure . (:[])) $ ['a'..'e']
--- >>> let aVar = liftA Var aVarName
--- >>> let aTerm 0 = aVar 
--- >>> let aTerm n = oneof [aVar, liftA2 Lambda aVarName $ 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)
-
-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)
+import Lambda.Term

 
 

+import Debug.Trace
+import Lambda.Parser.Fancy ()

 
 

-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
+-- $setup
+-- >>> import Control.Applicative
+-- >>> 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
 
 isFreeIn :: VarName -> Term -> Bool
 isFreeIn x (Var v) = x == v


@@ -155,9 +79,9 @@ reduce (App t u) = app (reduce t) u
 
 data Strategy = Eager | Lazy
 
 
 data Strategy = Eager | Lazy
 

-reduceStep :: (Monad m) => Term -> m Term
-reduceStep (RedEx x s t) = return $ substitute x t s
-reduceStep t = return $ t
+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 Z = R Term Z | L Z Term | ZL VarName Z | E
 data D = Up | Down


@@ -176,12 +100,14 @@ unmove :: TermZipper -> TermZipper
 unmove (t, L c r, Down) = (App t r, c, Down)
 unmove x = x
 
 unmove (t, L c r, Down) = (App t r, c, Down)
 unmove x = x
 

+-- getTerm :: TermZipper -> Term
+

 travPost :: (Monad m) => (Term -> m Term) -> Term -> m Term
 travPost fnc term = tr fnc (term, E, Down)
   where 
 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
       nt <- f t

-      tr f $ (nt, c, Down)
+      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)
     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)


@@ -189,18 +115,13 @@ travPost fnc term = tr fnc (term, E, Down)
 travPre :: (Monad m) => (Term -> m Term) -> Term -> m Term
 travPre fnc term = tr fnc (term, E, Down)
   where 
 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 _ (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)
 
       nt <- f t
       tr f $ unmove (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)
 

-printT :: Term -> IO Term
-printT t = do
-  print t
-  return t
-

 -- |
 --
 -- >>> toNormalForm Eager 100 cI
 -- |
 --
 -- >>> toNormalForm Eager 100 cI


@@ -215,15 +136,24 @@ printT t = do
 -- >>> toNormalForm Lazy 100 $ (App (App cK cI) cY)
 -- Just (λx.x)
 --
 -- >>> 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 <$> toNormalForm Lazy 100 x) (alphaNorm <$> toNormalForm Eager 100 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))"

 
 
 
 

+toNormalFormDebug :: Strategy -> Int -> Term -> Maybe Term
+toNormalFormDebug Eager n = flip evalStateT 0 . travPost (prnt >=> cnt >=> short n >=> return . reduceStep)
+toNormalFormDebug Lazy  n = flip evalStateT 0 . travPre  (prnt >=> cnt >=> short n >=> return . reduceStep)
+

 toNormalForm :: Strategy -> Int -> Term -> Maybe Term
 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)
+
+prnt :: (Monad m) => Term -> StateT Int m Term
+prnt t = traceShow t $ return t

 
 cnt :: (Monad m) => Term -> StateT Int m Term
 
 cnt :: (Monad m) => Term -> StateT Int m Term

-cnt t@(RedEx _ _ _) = do
+cnt t@RedEx{} = do

   modify (+ 1)
   return t
 cnt t = return t
   modify (+ 1)
   return t
 cnt t = return t