lambda-viewer.hs

-- lambda 
data Term = Lam Var Term
          | Var Var
          | App Term Term -- func application

data Var = V String

instance Show Var where
    show (V s) = s
    
instance Show Term where
    show (Var v) = show v
    show (Lam v t) = "λ" ++ show v ++ "." ++ show t
    show (App t1 t2) = "(" ++ show t1 ++ " " ++ show t2 ++ ")"


-- exercises
-- a b c d e f
(App (App (App (App (App (Var (V "a"))
                         (Var (V "b")))
                    (Var (V "c")))
               (Var (V "d")))
          (Var (V "e")))
     (Var (V "f")))

-- (g h) (i j)
(App (App (Var (V "g"))
          (Var (V "h")))
     (App (Var (V "i"))
          (Var (V "j"))))

-- λx.f (λy.f y)
(Lam (V "x")
     (App (f)
          (Lam (y)
               (App (f)
                    (Var (y)))))
where f = Var (V "f")
      y = V "y"

-- (λf.f x y) (λx.λy.x)
(App (Lam (f)
          (App (App (Val f)
                    (Val (V "x")))
               (Val (V "y"))))
     (Lam (x)
          (Lam (V "y")
               (Val x))))
where f = V "f"
      x = V "x"

-- f g λx.y z
(App (App (App (Val (V "f"))
               (Val (V "g")))
          (Lam (V "x")
               (Val (V "y"))))
     (Val (V "z")))