more work on Hindley-Milner

[fp.git] / src / Lambda.hs

diff --git a/src/Lambda.hs b/src/Lambda.hs
index 5c3ecda..3026b75 100644 (file)
--- a/src/Lambda.hs
+++ b/src/Lambda.hs
@@ -14,42 +14,29 @@ module Lambda
   ( -- * Types
     VarName
   , Term(..)
   ( -- * Types
     VarName
   , Term(..)

+  , pattern RedEx

     -- * Reduction
   , alphaNorm
   , reduce
   , toNormalForm
   , Strategy(..)
   ) where
     -- * Reduction
   , alphaNorm
   , reduce
   , toNormalForm
   , Strategy(..)
   ) where

-  

 
 import Control.Monad.State 
 
 import Lambda.Term
 
 -- $setup
 
 import Control.Monad.State 
 
 import Lambda.Term
 
 -- $setup

--- >>> import Test.QuickCheck

 -- >>> import Control.Applicative
 -- >>> import Lambda.Parser.Fancy
 -- >>> import Control.Applicative
 -- >>> import Lambda.Parser.Fancy

--- >>> import Lambda.Term
--- >>> let cP = tRead "(λa d c.(λa.e) b (λc.d)) ((λa.(λd.a) (λd c.b ((λa.a) a)) (a ((λa.(λd.e) ((λe.(λd b.a) (λa c.(λa a d.(λd.b (λa d.c) e) (λb b.c a (a d (λb d d e a.d (λb b.d))))) ((λb.a) c)) (d ((λc.(λd.a (λe.e)) (c d)) ((λe.b) a))) c (λa.d (e (λe.(λd c.b) a))) (c (b a)) a (λe.(λa b e b a.d) b)) ((λe.b) (λa.b)) ((λe d.b) b) e) b) ((λc c.a e) (λb.(λb.e) a)))) (λe.e) b (λd c e e c a.c)) a)"
--- >>> cY = tRead "λf.(λx.f (x x)) (λx.f (x x))"
--- >>> cI = tRead "λx.x"
--- >>> cK = tRead "λx y.x"
--- >>> cS = tRead "λx y z.x z (y z)"
--- >>> let aVarName = oneof . map (pure . (:[])) $ ['a'..'e']
--- >>> let aVar = liftA Var aVarName
--- >>> let aComb = oneof . map pure $ [cS, cK, cI, cY]
--- >>> let aTerm 0 = aVar 
--- >>> let aTerm n = oneof [aVar, aComb, liftA2 Lambda aVarName $ aTerm (n - 1), liftA2 App (aTerm (n `div` 2)) (aTerm (n `div` 2))] 
--- >>> instance Arbitrary Term where arbitrary = sized aTerm
---
--- TODO: shrink Terms
+-- >>> import Test.Term
+-- >>> import Test.QuickCheck

 
 varnames :: [VarName]
 varnames = map (:[]) ['a'..'z'] ++ [c : s | s <- varnames, c <- ['a'..'z']]
 
 alphaNorm :: Term -> Term
 
 varnames :: [VarName]
 varnames = map (:[]) ['a'..'z'] ++ [c : s | s <- varnames, c <- ['a'..'z']]
 
 alphaNorm :: Term -> Term

-alphaNorm t = alpha varnames t
+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)
   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)


@@ -89,9 +76,9 @@ 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


@@ -110,12 +97,14 @@ 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)


@@ -123,20 +112,13 @@ 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


@@ -151,15 +133,16 @@ 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) (alphaNorm <$> toNormalForm Lazy 1000 x) (alphaNorm <$> 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 :: 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 :: (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