Defining an instance for a composite type in Haskell

Question

I have a type that has a mappend-like function but not a real mappend, so it is not a Semigroup. For instance:

data MyType = MyType Int deriving Show

myMerge :: MyType -> MyType -> Maybe MyType
myMerge (MyType x) (MyType y)
  | (x < 0) || (y < 0) = Nothing
  | otherwise          = Just $ MyType $ x + y

I always deal with MyType when it is wrapped in Maybe. I need semantics that would be perfectly represented if I could define a Semigroup instance on the "combined" type Maybe MyType like this:

instance Semigroup (Maybe MyType) where
  (Just x) <> (Just y) = myMerge x y
  Nothing  <> Nothing  = Nothing
  Nothing  <> (Just _) = Nothing
  (Just _) <> Nothing  = Nothing

I.e. when both parameters are Just's, I can get either a Just or Nothing, otherwise I always get Nothing. But this is not possible, I get an error:

All instance types must be of the form (T a1 ... an)

How can I represent the semantics that I need?

Answer 1

The instance you defined is illegal because it is basically trying to define a different (partial) Semigroup instance for Maybe, but Maybe already has one. Instead, use a newtype wrapper:

newtype MaybeMyType = MaybeMyType (Maybe MyType)

instance Semigroup MaybeMyType where
  ...

You will have to interact with your type through this MaybeMyType wrapper in the cases where you want to use its Semigroup instance.