Here is a solution to your problem in Generic Haskell, see www.generic-haskell.org. You use gmap to traverse the structure, and have a special case for the type Expr, which does the optimization. I'm surprised the `real world' is this easy :-) --------------------------------------------- module Optimize where import GH.Library.Map data Expr = Const Int | Var String | Add Expr Expr deriving Show data Stm = Assign String Expr | Seq Stm Stm deriving Show stmt :: Stm stmt = Seq (Assign "y" (Add (Var "x") (Const 0))) (Assign "z" (Add (Const 0) (Var "y"))) optimize {| t :: * |} :: (optimize{|t|}) => t -> t optimize extends gmap optimize {|Expr|} e = case e of Add x (Const 0) -> x Add (Const 0) x -> x e' -> e' mymain = optimize{|Stm|} stmt ------------------------------------------ -- Johan
I'm playing with generic programming. At the moment I'm interested in reusable transformations on data types. Provided for example a toy datatype Expr like this:
data Expr = Const Int | Var String | Add Expr Expr
Plus a function "optimize" that optimizes a pattern "x + 0" into "x":
optimize (Add x (Const 0)) = x
You would now want this to be this generic, so the function should be recursive for all other constructors *and* other data types. For example, suppose that Expr is included in other datatype:
data Stm = Assign String Expr | Seq Stm Stm
I now want the "optimize" transformation to work on Stm, like this:
x = optimize (Seq (Assign (Add (Var "x") (Const 0))) blah blah)
For sure, I don't want to write specific code for type Stm. The thing I want is to generically walk through values of those types into Expr where it can apply the pattern.
Haskell does not seem to have an easy way to do this. After looking through some papers I found lots of things that *might* handle this, like Generic Haskell, "scrap your boilerplate", Drift, etc. Now I'm not sure what works best for real world, bread and butter programming. None of them seem ideal. I know it's trivial in Scheme (my usual language). Vast amounts of the research literature concerns itself only with toy problems. Extensibility (i.e., reuse) however seems not to be a big concern. Really, this shouldn't be so hard. So I even asked a Haskell programming friend of mine, and he could not come up with a sensible solution in an hour, while I can do this in two minutes in Scheme. After all, writing compilers is supposed to be a *strong* point of Haskell. Real world is knocking on your door, guys!
Yours truly,
Arka.