[Haskell-cafe] Re: questions about Arrows

[Maciej Piechotka]

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
-------------- next part --------------
A non-text attachment was scrubbed...
Name: not available
Type: application/pgp-signature
Size: 836 bytes
Desc: This is a digitally signed message part
Url : http://www.haskell.org/pipermail/haskell-cafe/attachments/20100901/4c238fc7/attachment.bin