newtype Predicate a = Predicate { getPredicate :: a -> Bool } instance Contravariant Predicate where contramap :: (a' -> a) -> (Predicate a -> Predicate a') contramap f (Predicate p) = Predicate (p . f) | `- First, map the input... `----- then apply the predicate. overdrawn :: Predicate Person overdrawn = contramap personBankBalance negativeAny instance should be subject to the following laws: Note, that the second law follows from the free theorem of the type of contramap and the first law, so you need only check that the former condition holds.
data MyException = ThisException | ThatException deriving Show instance Exception MyExceptionThe default method definitions in the Exception class do what we need in this case. You can now throw and catch ThisException and ThatException as exceptions:
*Main> throw ThisException `catch` \e -> putStrLn ("Caught " ++ show (e :: MyException)) Caught ThisExceptionIn more complicated examples, you may wish to define a whole hierarchy of exceptions:
--------------------------------------------------------------------- -- Make the root exception type for all the exceptions in a compiler data SomeCompilerException = forall e . Exception e => SomeCompilerException e instance Show SomeCompilerException where show (SomeCompilerException e) = show e instance Exception SomeCompilerException compilerExceptionToException :: Exception e => e -> SomeException compilerExceptionToException = toException . SomeCompilerException compilerExceptionFromException :: Exception e => SomeException -> Maybe e compilerExceptionFromException x = do SomeCompilerException a <- fromException x cast a --------------------------------------------------------------------- -- Make a subhierarchy for exceptions in the frontend of the compiler data SomeFrontendException = forall e . Exception e => SomeFrontendException e instance Show SomeFrontendException where show (SomeFrontendException e) = show e instance Exception SomeFrontendException where toException = compilerExceptionToException fromException = compilerExceptionFromException frontendExceptionToException :: Exception e => e -> SomeException frontendExceptionToException = toException . SomeFrontendException frontendExceptionFromException :: Exception e => SomeException -> Maybe e frontendExceptionFromException x = do SomeFrontendException a <- fromException x cast a --------------------------------------------------------------------- -- Make an exception type for a particular frontend compiler exception data MismatchedParentheses = MismatchedParentheses deriving Show instance Exception MismatchedParentheses where toException = frontendExceptionToException fromException = frontendExceptionFromExceptionWe can now catch a MismatchedParentheses exception as MismatchedParentheses, SomeFrontendException or SomeCompilerException, but not other types, e.g. IOException:
*Main> throw MismatchedParentheses `catch` \e -> putStrLn ("Caught " ++ show (e :: MismatchedParentheses)) Caught MismatchedParentheses *Main> throw MismatchedParentheses `catch` \e -> putStrLn ("Caught " ++ show (e :: SomeFrontendException)) Caught MismatchedParentheses *Main> throw MismatchedParentheses `catch` \e -> putStrLn ("Caught " ++ show (e :: SomeCompilerException)) Caught MismatchedParentheses *Main> throw MismatchedParentheses `catch` \e -> putStrLn ("Caught " ++ show (e :: IOException)) *** Exception: MismatchedParentheses
fail s >>= f = fail sIf your Monad is also MonadPlus, a popular definition is
fail _ = mzero
>>> const 42 "hello" 42
>>> map (const 42) [0..3] [42,42,42,42]
>>> mconcat ["Hello", " ", "Haskell", "!"] "Hello Haskell!"