[Haskell-cafe] Re: Defining types (newbie)

[apfelmus at quantentunnel.de]

John Fouhy wrote:
> [...]
> data Thing = Thing { field_one :: String, field_two :: String,
> field_three :: Integer }
>
> type BooleanOp a = a -> a -> Bool
> type Field a = Thing -> a
> 
> data ThingCompare a = TC (BooleanOp a) (Field a)
>                    | And (ThingCompare a) (ThingCompare a)
>                    | Or (ThingCompare a) (ThingCompare a)
> [...]
> tcEqOne = TC (==) field_one
> tcEqTwo = TC (==) field_two
> tcGtThree = TC (>) field_three 

I'm not quite sure what you want to do with explicitly represented
comparisons. Maybe optimize them afterwards? Otherwise, BoolOp is likely
to be your best comparison representation.

You can separate the Field and the BoolOp parts with a small combinator

  by :: BoolOp a -> (b -> a) -> BoolOp b
  by f g x y = f (g x) (g y)

Then, the three comparisons become

  tcEqOne   = (==) `by` field_one
  tcEqTwo   = (==) `by` field_two
  tcGtThree = (>)  `by` field_three

Appealing to the famous instance Monad ((->) a), you can also say

  and, or :: BoolOp a -> BoolOp a -> BoolOp a
  and = liftM2 $ liftM2 (&&)
  or  = liftM2 $ liftM2 (||)

Regards,
apfelmus