calc v scheme in Haskell

CalcVScheme.hs

module CalcVScheme where

import Prelude hiding (lookup)

data Term
 = Var Var
 | Lambda Var Term
 | Apply Term Term
 | Closure Env Var Term
 deriving (Eq, Show)

type Env = [(Var, Term)]
type Var = String

eval e (Var v) = lookup e v
eval e (Lambda v t) = Closure e v t
eval e (Apply t0 t1) = apply (eval e t0) (eval e t1)

apply (Closure e v t0) t1 = eval (extend e v t1) t0

lookup ((v0, t) : e) v1
  | v0 == v1 = t
  | otherwise = lookup e v1

extend e v t = (v, t):e
empty = []


i n = Lambda n $ Var n
k a b = Lambda a $ Lambda b $ Var a
s x y z = Lambda x $ Lambda y $ Lambda z $ Apply (Apply (Var x) (Var z)) $ Apply (Var y) (Var z)

main = do
  print $ eval empty (Apply (Lambda "x" (Var "x")) (Lambda "y" (Var "y")))
  print $ eval empty (Apply (Apply (k "a" "b") (i "x")) (i "y"))