lambda.hs

data Lambda
  = Var Name
  | App Lambda Lambda
  | Lam Name Lambda
  deriving (Eq, Show)

name :: Parser Name
name = lexeme $ sat \x -> if x `elem` "xyzuvw" then Just $ Name [x] else Nothing

var :: Parser Lambda
var = Var <$> name

lambda :: Parser Lambda
lambda =
  asum
    [ lam
    , app
    , var
    ]

lambdaAll :: Parser Lambda
lambdaAll = lambda <* endOfInput

bracket :: Parser a -> Parser a
bracket p = some (char '(') *> p <* some (char ')')

app :: Parser Lambda
app = foldl1 App <$> do some $ var <|> lam <|> bracket app

lam :: Parser Lambda
lam = do
  char '\\'
  var <- name
  char '.'
  body <- lambda
  pure $ Lam var body