Haskell type classes hierarchy

Question

I have 2 classes:

class (IsColor (ColorType a)) => ColorList a where
    type ColorType a :: *
    foreground :: a -> (ColorType a)
    background :: a -> (ColorType a)

class (ColorList (ThemeColorList a)) => Theme a where
    type ThemeColorList a :: *
    renderTheme :: a -> b

I have function dosomething with type signature:

 dosomething :: (IsColor a) => a -> Int

I define instance of Theme class for data type SimpleTheme:

data SimpleTheme a = SimpleTheme a

instance (ColorList a) => Theme (SimpleTheme a) where
    type ThemeColorList (SimpleTheme a) = a
    renderTheme theme = dosomething $ background theme

If in renderTheme I do something with background or foreground, I get compilation error:

Could not deduce (IsColor (ColorType (SimpleTheme a)))
      arising from a use of ‘dosomething’
    from the context (ColorList (ThemeColorList (SimpleTheme a)),
                      ColorList a)
      bound by the instance declaration at

How to solve problem?

Answer 1

You can fix that single problem by changing the definition of renderTheme in the SimpleTheme instance. The context only requires that there be a ColorList a instance, not a ColorList (SimpleTheme a), so we can use background on the a held in a SimpleTheme, but can't use background on the whole SimpleTheme.

    renderTheme (SimpleTheme a) = dosomething $ background a

Explanation of the error

From the context

(ColorList (ThemeColorList (SimpleTheme a)),
 ColorList a)

We can deduce the following.

• Since there's a ColorList a there must be what is required for a ColorList. That is, there's a type ColorType a and an instance IsColor (ColorType a).
• Since there's a ColorList (ThemeColorList (SimpleTheme a)) there must be what is required for a ColorList. that is, there's a type ColorType (ThemeColorList (SimpleTheme a)) and an instance IsColor (ThemeColorList (SimpleTheme a)).

None of these is an instance for IsColor (ColorType (SimpleTheme a)), which is why you get the error.