Hello all, few days ago I made some experiments with Haskell type classes. I wrote a small Haskell program for searching in sorted lists, defining my own type classes for equality (MyEq) and order (MyOrd) so that they only have one member function: -------------------------------------------------------- class MyEq a where eq :: a -> a -> Bool class MyEq a => MyOrd a where less :: a -> a -> Bool data Nat = Z | S Nat instance MyEq Nat where eq Z Z = True eq Z (S x) = False eq (S x) Z = False eq (S x) (S y) = eq x y instance MyOrd Nat where less Z Z = False less Z (S x) = True less (S x ) Z = False less (S x) (S y) = less x y search :: MyOrd a => a -> [a] -> Bool search x [] = False search x (y:ys) = (eq x y) || (less y x && search x ys) -------------------------------------------------------- I also wrote the translation of this program using the classical approach of dictionaries that appears in "How to make ad-hoc polymorphism less ad hoc", Wadler & Blott 1989 or "Type Classes in Haskell", Cordelia V. Hall et. al. 1996. -------------------------------------------------------- -- From the definition of type class MyEq data DictMyEq a = DictMyEq (a -> a -> Bool) eq :: DictMyEq a -> (a -> a -> Bool) eq (DictMyEq x) = x -- From the definition of type class MyOrd data DictMyOrd a = DictMyOrd (DictMyEq a) (a -> a -> Bool) getMyEqFromMyOrd :: DictMyOrd a -> DictMyEq a getMyEqFromMyOrd (DictMyOrd x y) = x less :: DictMyOrd a -> (a -> a -> Bool) less (DictMyOrd x y) = y data Nat = Z | S Nat -- From the instance MyEq Nat eqNat :: Nat -> Nat -> Bool eqNat Z Z = True eqNat Z (S x) = False eqNat (S x) Z = False eqNat (S x) (S y) = eqNat x y dictMyEqNat :: DictMyEq Nat dictMyEqNat = DictMyEq eqNat -- From the instance MyOrd Nat lessNat :: Nat -> Nat -> Bool lessNat Z Z = False lessNat Z (S x) = True lessNat (S x ) Z = False lessNat (S x) (S y) = lessNat x y dictMyOrdNat :: DictMyOrd Nat dictMyOrdNat = DictMyOrd dictMyEqNat lessNat search :: DictMyOrd a -> a -> [a] -> Bool search _ x [] = False search dict x (y:ys) = (eq (getMyEqFromMyOrd dict) x y) || (less dict y x && search dict x ys) -------------------------------------------------------- I made some tests in GHC 6.8.2 and I noticed that the original program with type classes runs pretty faster than the translated program. For example, reducing the expression search (S Z) (replicate 1000000 Z) needs 2.07 seconds in the original program. However the translated expression search dictMyOrdNat (S Z) (replicate 1000000 Z) needs 3.10 seconds in the translated program, which is one more second. Surprised with the results, I repeated the test this time in Hugs Sept. 2006. I noticed that the difference was not so big: search (S Z) (replicate 100000 Z) --> (2100051 reductions, 2798068 cells, 2 garbage collections) search dictMyOrdNat (S Z) (replicate 100000 Z) --> (2200051 reductions, 2898067 cells, 3 garbage collections) My first idea was that type classes were implemented using the approach of dictionaries, but the test showed me that it is not true (mainly in GHC). Then I discovered the paper "Implementing Haskell overloading", Augustsson 1993, when he describes some ways to improve the speed of Haskell overloading. So my questions are: 1) is the enhancement obtained only using the optimizations of Augustsson's paper? 2) Could anyone tell me where I can find the translation of type classes that GHC and Hugs use? Thank you very much, Enrique M.