I wrote:
1. Find a way to model strictness/laziness properties of Haskell functions in a category in a way that is reasonably rich.
Duncan Coutts wrote:
The reason it's not obvious for categories is because the semantics for Haskell comes from domain theory (CPOs etc) not categories.
The category we have been discussing seems to do the trick quite easily for (1): Let Empty be the empty type. Let undef = \x -> undefined, and as before, f .! g = f `seq` g `seq` (\x -> f (g x)) Then we can take HaskL - Haskell with Laziness - to be the category Haskell types and Haskell functions (including seq), with .! as composition. It is easy to check that this is a category, using the left-monoid laws for seq: (x `seq` y) `seq` z = x `seq` (y `seq` z) (x `seq` y) `seq` z = (y `seq` x) `seq` z (\x -> expr) `seq` y = y Empty is bi-universal in HaskL, with undef the unique morphism in either direction. We have undef .! f = undef for any three types and any morphism f. We say that a morphism f is strict iff f .! undef = undef. We will only consider functors (F, fmap) on HaskL that are natural, in the sense that fmap is a morphism from (A -> B) to (F(A) -> F(B)) for all A, B. Similarly for return and join with monads. It is easy to show that a functor (F, fmap) preserves strictness if fmap is strict as a morphism. -Yitz _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
