Hi Ryan, On Fri, Jun 18, 2010 at 7:57 PM, Ryan Ingram <ryani.s...@gmail.com> wrote:
> Related to this, I really would like to be able to use arrow notation > without "arr"; I was looking into writing a "circuit optimizer" that > modified my arrow-like circuit structure, but since it's impossible to > "look inside" arr, I ran into a brick wall. > > Has anyone done any analysis of what operations arrow notation > actually requires so that they can be made methods of some typeclass, > instead of defining everything in terms of "arr"? > > It seems to me the trickiness comes when you have patterns and complex > expressions in your arrow notation, that is, you write > > (a,b) <- some_arrow <- (c,d) > returnA -< a > The design I've been using for this has been to use data-reify, and observable sharing and to use pure let bindings to build the circuit. full_adder :: Bit -> Bit -> Bit -> (Bit, Bit) full_adder a b cin = (s2, c1 || c2) where (s1,c1) = half_adder a b (s2,c2) = half_adder s1 cin half_adder :: Bit -> Bit -> (Bit, Bit) half_adder a b = (a `xor` b, a && b) foo = do x <- exists y <- exists z <- exists assert $ full_adder x y z === (1,1) assert $ forall $ \ a b c -> (a && b) ==> c === (a ==> b ==> c) return (x,y,z) I perform a similar sharing recovery in the back end code of Numeric.RAD from the 'rad' package and Numeric.AD.Internal.Reverse in the 'ad' package. I have uses in a number of unreleased bottom-up applicative parser combinators as well, so it has a wide arrange of applicable situations. Overall, let bindings tend to be a lot lighter than the accompanying arrow sugar. You might find Andy Gill's write-up on type safe observable sharing in kansas lava to be useful. http://www.ittc.ku.edu/~andygill/papers/reifyGraph.pdf -Edward Kmett
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