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module HW (
fv,
subst,
normalstep,
pickFresh,
repeatedly,
printnormal,
) where
import AST
import qualified Data.Set as Set
import Parse (parse)
-- | Return the free variables in an expression
fv :: Expr -> Set.Set String
fv (Var x) = Set.singleton x
fv (Lam x m) = x `Set.delete` (fv m)
fv (App m1 m2) = (fv m1) `Set.union` (fv m2)
{- | Substitute n for x in e, avoiding name capture
subst n x e e[x := n]
-}
subst :: Expr -> String -> Expr -> Expr
-- subst _ _ _ = Var "UNIMPLEMENTED" -- Replace with your solution to problem 2
subst n x (Var e)
| x == e = n
| otherwise = Var e
-- | Take a single step in normal order reduction or return Nothing
normalstep :: Expr -> Maybe Expr
normalstep _ = Just (Var "UNIMPLEMENTED") -- Replace with your solution to problem 3
{- | Return a "fresh" name not already in the set.
Tries x' then x'', etc.
-}
pickFresh :: Set.Set String -> String -> String
pickFresh s = pickFresh'
where
pickFresh' n | n `Set.notMember` s = n
pickFresh' n = pickFresh' $ n ++ "'"
{- | Repeatedly apply a function to transform a value, returning the list
of steps it took. The result list starts with the given initial value
-}
repeatedly :: (a -> Maybe a) -> a -> [a]
repeatedly f = repeatedly'
where
repeatedly' x =
x : case f x of
Nothing -> []
Just y -> repeatedly' y
-- | Print out the series of normal order reduction steps
printnormal :: String -> IO ()
printnormal = mapM_ print . repeatedly normalstep . parse
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