Haskell, Parsec - Parsing application in lambda calculus - parsing

Question

I am writing a simple parser/interpreter for lambda calculus in Haskell.
I am using the syntax "/(x.x)" for a lambda function, "x" for a name and "f y" for application, such that "/(x.x) y" is the application of identity to y and should return y.
My strategy is to have a parser for names, lambda functions and applications. The name and function parsers work, but not the application parser.
When I try to parse "/(x.x) y" it fails. It should try to parse the source as a name, as a lambda function, and after not being able to use both (because it would not parse all the source) try to parse it as an application and then succeed.
My code is:
module Main where
import Text.ParserCombinators.Parsec
data Expression =
Var String
| Lambda Expression Expression
| Application Expression Expression
deriving Eq
instance Show Expression where
show (Var v) = v
show (Lambda v e) = "/(" ++ show v ++ "." ++ show e ++ ")"
show (Application e1 e2) = "" ++ show e1 ++ " " ++ show e2 ++ ""
-- Parser
parseSource :: String -> Expression
parseSource source =
case parse (parseExpression <* eof) "" source of
Right e -> e
_ -> error "Parsing error"
parseExpression :: Parser Expression
parseExpression =
parseVar <|> parseLambda <|> parseApplication
parseVar :: Parser Expression
parseVar = Var <$> many1 letter
parseLambda :: Parser Expression
parseLambda = do
_ <- char '/'
_ <- char '('
arg <- parseVar
_ <- char '.'
body <- parseExpression
_ <- char ')'
return $ Lambda arg body
parseApplication :: Parser Expression
parseApplication = do
e1 <- parseExpression
_ <- spaces
e2 <- parseExpression
return $ Application e1 e2