fix doctests

diff --git a/src/Lambda.hs b/src/Lambda.hs
index f828f4d..0cedf4a 100644 (file)
--- a/src/Lambda.hs
+++ b/src/Lambda.hs
@@ -20,10 +20,12 @@ module Lambda
   , tRead
     -- * Reduction
   , reduce
   , tRead
     -- * Reduction
   , reduce

+  , toNormalForm
+  , Strategy(..)

   ) where
   
 
   ) where
   
 

-import Data.Text as T
+import Data.Text as T hiding (map)

 import Data.Attoparsec.Text
 import Control.Applicative
 import Control.Monad.State 
 import Data.Attoparsec.Text
 import Control.Applicative
 import Control.Monad.State 


@@ -31,8 +33,10 @@ import Control.Monad.State
 -- $setup
 -- >>> import Test.QuickCheck
 -- >>> import Control.Applicative
 -- $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))] 
+-- >>> 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
 -- >>> instance Arbitrary Term where arbitrary = sized aTerm
 
 cY :: Term


@@ -50,7 +54,7 @@ type VarName = String
 -- >>> print $ Lambda "x" (Var "x")
 -- (λx.x)
 
 -- >>> print $ Lambda "x" (Var "x")
 -- (λx.x)
 

-data Term = EmptyT | Var VarName | Lambda VarName Term | App Term Term deriving (Eq)
+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 RedEx x t s = App (Lambda x t) s
 pattern AppApp a b c = App a (App b c)


@@ -155,20 +159,11 @@ reduceStep :: (Monad m) => Term -> m Term
 reduceStep (RedEx x s t) = return $ substitute x t s
 reduceStep t = return $ t
 
 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)
-

 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

-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)
 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)


@@ -177,18 +172,17 @@ 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)
 
 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
 
 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)
 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 _ (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 f (t, c, Up) = tr f $ move (t, c, Up)
     tr f (t, c, Down) = tr f $ move (t, c, Down)
 


@@ -198,7 +192,7 @@ travPre fnc term = tr fnc (term, E, Down)
     tr f (t@(RedEx _ _ _), c, Down) = do
       nt <- f t
       tr f $ unmove (nt, c, Down)
     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)
 
     tr f (t, c, Up) = tr f $ move (t, c, Up)
     tr f (t, c, Down) = tr f $ move (t, c, Down)
 


@@ -215,10 +209,10 @@ printT t = do
 -- >>> toNormalForm Eager 100 $ App cI cI
 -- Just (λx.x)
 --
 -- >>> 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
 --
 -- 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)
 -- Just (λx.x)
 --
 -- prop> (\ t u -> t == u || t == Nothing || u == Nothing) (toNormalForm Lazy 1000 x) (toNormalForm Eager 1000 x)


@@ -235,8 +229,8 @@ cnt t@(RedEx _ _ _) = do
 cnt t = return t
 
 short :: Int -> Term -> StateT Int Maybe Term
 cnt t = return t
 
 short :: Int -> Term -> StateT Int Maybe Term

-short max t = do
+short maxN t = do

   n <- get
   n <- get

-  if n > max
+  if n > maxN

     then lift Nothing
     else return t
     then lift Nothing
     else return t