doctest

[fp.git] / src / Lambda.hs

diff --git a/src/Lambda.hs b/src/Lambda.hs
index f9fbe2b..f54a100 100644 (file)
--- a/src/Lambda.hs
+++ b/src/Lambda.hs
@@ -1,4 +1,5 @@
 {-# OPTIONS_GHC -fno-warn-unused-do-bind #-}
 {-# OPTIONS_GHC -fno-warn-unused-do-bind #-}

+{-# LANGUAGE PatternSynonyms #-}

 
 module Lambda where
 
 
 module Lambda where
 


@@ -7,12 +8,35 @@ import Data.Attoparsec.Text
 import Control.Applicative
 
 type VarName = String
 import Control.Applicative
 
 type VarName = String

-data Term = Var VarName | Lambda VarName Term | App Term Term
+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)
+
+-- $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))] 
+-- >>> instance Arbitrary Term where arbitrary = sized aTerm
+
+-- | Read and show λ-terms
+--
+--   >>> print $ Lambda "x" (Var "x")
+--   (λx.x)
+--
+--   prop> t == tRead (show (t :: Term))

 
 instance Show Term where
   show (Var x) = x
 
 instance Show Term where
   show (Var x) = x

-  show (Lambda x t) = "\\" ++ x ++ "." ++ show t
-  show (App t r) = "(" ++ show t ++ " " ++ show r ++ ")"
+  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
+
+braced :: Term -> String
+braced t = "(" ++ show t ++ ")"

 
 --instance Read Term where
 tRead :: String -> Term
 
 --instance Read Term where
 tRead :: String -> Term


@@ -27,8 +51,8 @@ parseVar = do
 
 parseLambda :: Parser Term
 parseLambda = do
 
 parseLambda :: Parser Term
 parseLambda = do

-  char '\\'
-  vars <- many1 (parseVar <* char ' ')
+  char '\\' <|> char 'λ'
+  vars <- sepBy1 parseVar (char ' ')

   char '.'
   t <- parseTerm
   return $! createLambda vars t
   char '.'
   t <- parseTerm
   return $! createLambda vars t


@@ -40,15 +64,26 @@ createLambda _ _ = error "createLambda failed"
 
 parseApp :: Parser Term
 parseApp = do
 
 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 '('
   t <- parseTerm

-  char ' '
-  r <- parseTerm

   char ')'
   char ')'

-  return $! App t r
+  return t 

 
 parseTerm :: Parser Term
 
 parseTerm :: Parser Term

-parseTerm = parseVar <|> parseLambda <|> parseApp
+parseTerm = parseApp <|>
+            parseBraces <|>
+            parseLambda <|>
+            parseVar

 
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