Haskell data type and lists

Question

I created a datatype that is a list of other elements say

data Tarr = Tarr [Int] deriving (Show)

I would like to concatenate two of these Lists so

Tarr [0,2,4,2] ++ Tarr [1]

but I get an error

<interactive>:43:1:
    Couldn't match expected type `[a0]' with actual type `Tarr'

If there was a typeclass for (++) (Concat say) as there is for (==) (Eq) I could implement it as something like

class Concat a where
    (+++) :: a -> a -> a

instance Concat Tarr where 
    (+++)  (Tarr a) (Tarr b) = Tarr (a ++ b) 

1) How should I solve my problem?

2) Any reason why (++) isn't defined in a typeclass?

Answer 1

The ++ function applies to lists only, but the <> / mappend function from the Monoid typeclass generalizes it. In fact if you changed your data to a newtype instead, you could do this:

{-# LANGUAGE GeneralizedNewtypeDeriving #-}
import Data.Monoid

newtype Tarr = Tarr [Int] deriving (Show, Monoid)

Answer 2

I don't know why (++) isn't defined as a typeclass. I, however, would suggest implementing a Monoid interface for this. I think Monoid is poorly named, but mappend and mconcat seem like well-known functions for concatenating things.

instance Monoid Tarr where
    mempty = Tarr []
    mappend (Tarr l1) (Tarr l2) = Tarr (l1 ++ l2)

Tarr [1, 2, 3] `mappend` Tarr [4, 5, 6]