Why is the type system refusing my seemingly valid program?

Question

Mind this program:

class Convert a b where
    convert :: a -> b

data A = A deriving Show
data B = B deriving Show
data C = C deriving Show
data D = DA A | D         


        

Answer 1

For that code to work, it would have to work with any argument of the same type. That is, if

get (DB B) :: A

works then

get anyValueOfTypeD :: A

has to work, including

get (DC C) :: A

which can not work because of a missing instance from C to A.

The first line

get anyValueOfTypeD :: B

works because we do have all the three instances to convert A,B,C to B.

I do not think there's any workaround that allows you to leave the type D as it is. If instead you can change that, you could use e.g.

data D a = DA a | DB a | DC a

(mind that it's quite different from the original), or even the GADT

data D x where
  DA :: A -> D A
  DB :: B -> D B
  DC :: C -> D C