Created
May 16, 2012 19:53
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Lambda-calculus beta-reduction algorithm
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import Data.Traversable | |
data Term a = | |
Var a | |
| Lambda a (Term a) | |
| Apply (Term a) (Term a) | |
instance Show a => Show (Term a) where | |
show (Var v) = show v | |
show (Lambda n t) = "/" ++ (show n) ++ "." ++ (show t) | |
show (Apply t1 t2) = "(" ++ (show t1) ++ " " ++ (show t2) ++ ")" | |
--instance Traversable (Term a) where | |
-- traverse f (Var a) = f (Var a) | |
-- traverse f (Lambda n t) = f (Lambda n (traverse t)) | |
-- traverse f (Apply t1 t2) = f (Apply (traverse t1) (traverse t2)) | |
reduce :: Eq a => Term a -> Term a | |
reduce (Var v) = Var v | |
reduce (Lambda a t) = Lambda a (reduce t) | |
reduce (Apply t1 t2) = apply (reduce t1) (reduce t2) | |
apply :: Eq a => Term a -> Term a -> Term a | |
apply (Lambda param t1) t2 = reduce $ rename param t2 t1 | |
apply t1 t2 = Apply t1 t2 | |
fmap' :: (Term a -> Term a) -> Term a -> Term a | |
fmap' f (Var v) = f (Var v) | |
fmap' f (Lambda v t) = Lambda v (fmap' f t) | |
fmap' f (Apply t1 t2) = Apply (fmap' f t1) (fmap' f t2) | |
rename :: Eq a => a -> Term a -> Term a -> Term a | |
rename a t1 t2 = fmap' replace t2 | |
where replace = \(Var x) -> if x == a then t1 else (Var x) |
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how do you run it?
I mean function call and arguments stuff