documentation

[fp.git] / src / Lambda.hs

diff --git a/src/Lambda.hs b/src/Lambda.hs
index 54c4065..c570199 100644 (file)
--- a/src/Lambda.hs
+++ b/src/Lambda.hs
@@ -1,20 +1,65 @@
 {-# OPTIONS_GHC -fno-warn-unused-do-bind #-}
-
-module Lambda where
+{-# LANGUAGE PatternSynonyms #-}
+
+-- |
+-- Module      :  Lambda
+-- Copyright   :  Tomáš Musil 2014
+-- License     :  BSD-3
+--
+-- Maintainer  :  tomik.musil@gmail.com
+-- Stability   :  experimental
+--
+-- This is a toy λ-calculus implementation.
+
+module Lambda 
+  ( -- * Types
+    VarName
+  , Term(..)
+    -- * Parsing terms
+  , parseTerm
+  , tRead
+    -- * Reduction
+  , reduce
+  ) where
+  
 
 import Data.Text as T
 import Data.Attoparsec.Text
 import Control.Applicative
 
+-- $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
+
 type VarName = String
-data Term = Var VarName | Lambda VarName Term | App Term Term
+
+-- | 
+-- >>> 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)
+
 
 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 ++ ")"
+
+-- |
+-- prop> t == tRead (show (t :: Term))
 
---instance Read Term where
 tRead :: String -> Term
 tRead s = case parseOnly (parseTerm <* endOfInput) (T.pack s) of
     (Right t) -> t
@@ -27,7 +72,7 @@ parseVar = do
 
 parseLambda :: Parser Term
 parseLambda = do
-  char '\\'
+  char '\\' <|> char 'λ'
   vars <- sepBy1 parseVar (char ' ')
   char '.'
   t <- parseTerm