[Haskell-beginners] Need help with code duplication (types and typeclasses)

[Brent Yorgey]

On Sat, Oct 23, 2010 at 11:24:05PM -0400, Edward Turpin wrote:
> I can't seem to get my head around types and typeclasses (as well as
> many other things in Haskell).  Here's the following code I need help
> with.
> 
> In module 1:
> //////////////////////// Start of Code //////////////////////////////
> data NewtonRow = NewtonRow { iteration :: Integer,
>                              xn :: Double,
>                              fxn :: Double,
>                              errEst :: Double
>                            }
> 
> instance Show NewtonRow where
>     show row = show (iteration row) ++ "\t" ++
>                showEFloat (Just 8) (xn row) "\t" ++
>                showEFloat (Just 2) (fxn row) "\t" ++
>                showEFloat (Just 2) (errEst row) "\n"
> 
> newtype NewtonTable = NewtonTable { getNewtonTable :: [NewtonRow] }
> 
> instance Show NewtonTable where
>     show table = "n\t" ++ "xn\t\t\t" ++ "fxn\t\t" ++ "xn - xn-1\n" ++
>                  concatMap show (getNewtonTable table)
> 
> instance Monoid NewtonTable where
>     mempty = NewtonTable []
>     table1 `mappend` table2 = NewtonTable $ (getNewtonTable table1) ++
> (getNewtonTable table2)
> 
> cons :: NewtonRow -> NewtonTable -> NewtonTable
> row `cons` table = NewtonTable (row : getNewtonTable table)

How about something like this?  The idea is to make the Table type
polymorphic, and to abstract the row-type-specific table header into a
new type class.

  {-# LANGUAGE GeneralizedNewtypeDeriving #-}

  newtype Table a = Table { getTable :: [a] }
    deriving Monoid   -- derive the Monoid instance from the
                      -- underlying list instance

  cons :: a -> Table a -> Table a
  row `cons` (Table t) = Table (row : t)

  class HasTableHeader a where
    tableHeader :: a -> String

  instance TableHeader NewtonRow where
    tableHeader _ = "n\t" ++ "wn\t\t\t" ++ "fxn\t\t" ++ "xn - xn-1\n"

  instance HasTableHeader a => Show (Table a) where
    show (Table []) = "---"
    show (Table (r:rs)) = showHeader r ++ concatMap show (r:rs)

I think you can see how to extend this to work with the other row type
as well.

-Brent