that's why Ross chose a fresh variable in FD range position: in the old translation, the class-based FD improvement rule no longer applies after reduction because there's only one C constraint left, and the instance-based FD improvement rule will only instantiate the 'b' or 'c' in the constraint with a fresh 'b_123', 'b_124', .., unrelated to 'b', 'c', or any previously generated variables in the constraint store. hth, claus another way to interpret your message: to show equivalence of the two constraint sets, you need to show that one implies the other, or that both are equivalent to a common constraint set - you cannot use constraints from one set to help discharging constraints in the other.
class B a b | a -> b class C a b c | a -> b
instance B a b => C [a] b Bool
Starting from a constraint set C [a] b Bool, C [a] c d, we have two possible reductions:
1) C [a] b Bool, C [a] c d => c = b, C [a] b Bool, C [a] b d (use FD on C) => c = b, B a b, C [a] b d (reduce instance)
2) C [a] b Bool, C [a] c d => B a b, C [a] c d (reduce instance)
(changed C to B to fix a typo) It seems to me that the constraint sets {B a b, C [a] b d} and {B a b, C [a] c d} are equivalent in the sense that if we assume the first set we can discharge the constraints in the second, and vice versa. So why are we saying that we have lost confluence? Is there perhaps a different example that illustrates the porblem? -Iavor PS: To show that C [a] b d |- C [a] c d we can apply the improving substitution 'b=c' (using the FD on class C), and then solve the goal by assumption, the proof the other way is symmetric. _______________________________________________ Haskell-prime mailing list Haskell-prime@haskell.org http://haskell.org/mailman/listinfo/haskell-prime