On Tue, 2010-08-31 at 20:39 -0700, Ben wrote:
Hello --
Three related questions, going from most specific to most general :
1 ) Consider the stream processing arrow which computes a running sum, with two implementations : first using generic ArrowCircuits (rSum); second using Automaton (rSum2) :
module Foo where
import Control.Arrow import Control.Arrow.Operations import Control.Arrow.Transformer import Control.Arrow.Transformer.All
rSum :: ArrowCircuit a => a Int Int rSum = proc x -> do rec out <- delay 0 -< out + x returnA -< out
rSum2 = Automaton (f 0) where f s n = let s' = s + n in (s', Automaton (f s'))
runAuto _ [] = [] runAuto (Automaton f) (x:xs) = let (y, a) = f x in y : runAuto a xs
take 10 $ runAuto rSum [1..] [0,1,3,6,10,15,21,28,36,45]
take 10 $ runAuto rSum2 [1..] [1,3,6,10,15,21,28,36,45,55]
Note that the circuit version starts with the initial value zero.
Is there a way to write rSum2 in the general ArrowCircuit form, or using ArrowLoop?
rSum2 :: ArrowCircuit a => a Int Int rSum2 = proc x -> do rec out <- delay 0 -< out + x returnA -< out + x
2) Are the ArrowLoop instances for (->), Kleisli Identity, and Kleisli ((->) r) all morally equivalent? (e.g., up to tagging and untagging?)
Yes
3) One can define fix in terms of trace and trace in terms of fix.
trace f x = fst $ fix (\(m, z) -> f (x, z)) fix f = trace (\(x, y) -> (f y, f y)) undefined
Does this mean we can translate arbitrary recursive functions into ArrowLoop equivalents?
Yes. In fact fix is used on functional languages that do not support recursion to have recursion (or so I heard)
Best regards, Ben
Regards