[Haskell-cafe] Generics for constructing Rows

Sean Leather leather at cs.uu.nl
Thu Aug 20 07:43:38 EDT 2009

Hi Max,

I've come into trouble defining function `gmap` which will work on these
> data types:
> > data Row = Row
> >      (E Name)
> >      (E Salary)
> >      (E Department)
> > type E a = Either (Maybe RowIndex) (Maybe a)
> > type RowIndex = Int
> `RowIndex`, `Name`, `Salary`, `Department` have kind *
> pseudocode:
> > gmap :: (E a -> E a) -> Row -> Row

> So, generic programming folks, is it even possible to define such
> function?  I don't really care about using GHC extensions, I don't care
> about code being portable, I just want to remove boilerplate and prevent
> introducing bugs.

I'm not sure the problem you're running into is strictly a generic
programming (GP) one. Typically, GP takes code that is often written and
generalizes it, so that it doesn't have to be written for multiple

For your problem, I think the first issue is figuring out how to write the
non-generic function. I don't know if this is exactly what you want, but you
can write a version of gmap using GADTs and rank-2 types. I've simplified
some types, but it should be easily transferable to your code. For example,
change the String, Float, etc. to your Salary, Department, whatever.


{-# LANGUAGE Rank2Types #-}

module Main where

data T a where
  String  :: T String
  Float   :: T Float
  Integer :: T Integer

data Row = Row (Maybe String) (Maybe Float) (Maybe Integer)
  deriving Show

f :: T a -> Maybe a -> Maybe a
f String (Just "a") = Just "z"
f _      x = x

gmap :: (forall a . T a -> Maybe a -> Maybe a) -> Row -> Row
gmap f (Row x y z) = Row (f String x) (f Float y) (f Integer z)

main = do
  print $ gmap f $ Row Nothing (Just 5.4) (Just 3) -- ==> Row Nothing (Just
5.4) (Just 3)
  print $ gmap f $ Row (Just "a") Nothing Nothing -- ==> Row (Just "z")
Nothing Nothing


If this is what you're looking for, then I think it might be possible to do
this more generally, though I haven't looked into it.

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