2013/10/8 Thiago Negri <evohunz@gmail.com>

I think I'm starting to get the "way of arrows".

My implementation was incorrect. I've seen it with the hand made test listed below [1].

The output of "first arrA" and "first arrB" should be joined together and form a new stream with the length of the shortest output of both ("arrA *** arrB"), and this wasn't happening.

I've found package "streamproc" at Hackage and that gave me some insights.
Yet I think "streamproc" is also wrong, as it does not buffer the second stream.
You can check it at line 58 of SP.hs [3] that it ignores the first element of the pair.

But I didn't write a test to check what is the implication of this, I'll try to do this as a next step into understanding arrows.

That exercise really helped me!

My new implementation, wich I think is correct now, is listed below [2].

Thanks!

Thiago

[1]:
inputA :: [String]

inputA = ["a", "b", "hello", "c", "d", "e", "hello", "f", "g", "e", "x"]

arrA :: SP String String

arrA = Get (\a -> if a == "hello" then (Put a (Put "world" arrA))
else (Put "unknown" arrA))

arrB :: SP String String

arrB = Get (\a -> if a == "my" then (Get (\a -> if a == "name" then (Get (\a -> if a == "is" then Get (\a -> Put ("name: " ++ a) arrB)
else arrB))

else arrB))
else arrB)

inputB :: [String]
inputB = ["a", "b", "my", "name", "is", "thiago", "and", "I", "am", "so", "cool"]

inputAB :: [(String, String)]
inputAB = zip inputA inputB

main :: IO ()
main = let actualOutputB = runSP arrB inputB
actualOutputB1 = runSP (first arrB) (zip inputB (repeat "a"))

actualOutputA = runSP arrA inputA
actualOutputA1 = runSP (first arrA) (zip inputA (repeat "a"))
actualOutputAB = runSP (arrA *** arrB) inputAB
in do putStrLn $ "inputAB: " ++ show inputAB
putStrLn $ "outputA: " ++ show actualOutputA
putStrLn $ "outputA1: " ++ show actualOutputA1

putStrLn $ "outputB: " ++ show actualOutputB
putStrLn $ "outputB1: " ++ show actualOutputB1
putStrLn $ "outputAB: " ++ show actualOutputAB

[2]:
module SP where

import Prelude hiding (id, (.))
import Control.Category
import Control.Arrow

import Test.QuickCheck

data SP a b = Put b (SP a b) | Get (a -> SP a b)

runSP :: SP a b -> [a] -> [b]
runSP (Put b s) as = b:runSP s as

runSP (Get k) (a:as) = runSP (k a) as

runSP (Get k) [] = []

compose :: SP b c -> SP a b -> SP a c
compose (Put a s) g = Put a (compose s g)
compose (Get k) (Put a s) = compose (k a) s
compose f (Get k) = Get (\a -> compose f (k a))

instance Category SP where
id = arr id
(.) = compose

instance Arrow SP where
arr f = Get (\a -> Put (f a) (arr f))
first = queued empty empty

queued :: Queue a -> Queue c -> SP a b -> SP (a, c) (b, c)
queued qa qc (Put a s) = case pop qc of Nothing -> Get (\(a', c) -> Put (a, c) (queued (push a' qa) qc s))

Just (c, qc') -> Put (a, c) (queued qa qc' s)
queued qa qc (Get k) = case pop qa of Nothing -> Get (\(a, c) -> queued qa (push c qc) (k a))
Just (a, qa') -> queued qa' qc (k a)

data Queue a = Queue [a]

empty :: Queue a
empty = Queue []

push :: a -> Queue a -> Queue a
push a (Queue as) = Queue (a:as)

pop :: Queue a -> Maybe (a, Queue a)
pop (Queue []) = Nothing
pop (Queue (a:as)) = Just (a, Queue as)

delayed :: (a, c) -> SP a b -> SP (a, c) (b, c)
delayed (a, c) (Put b s) = Put (b, c) (delayed (a, c) s)
delayed (a, c) (Get k) = firstWithValue (k a) c

firstWithValue :: SP a b -> c -> SP (a, c) (b, c)
firstWithValue (Put a s) c = Put (a, c) (firstWithValue s c)
firstWithValue (Get k) _ = Get (\(a, c) -> firstWithValue (k a) c)

input :: [(String, String)]
input = [("a1", "a2"), ("b1", "b2"), ("c1", "c2"), ("d1", "d2")]

myArrow :: SP (String, String) (String, String)

myArrow = (delay "db1" >>> delay "da1") *** (delay "db2" >>> delay "da2")

delay :: a -> SP a a
delay b = Put b (arr id)

inputA :: [String]
inputA = ["a", "b", "hello", "c", "d", "e", "hello", "f", "g", "e", "x"]

arrA :: SP String String
arrA = Get (\a -> if a == "hello" then (Put a (Put "world" arrA))
else (Put "unknown" arrA))

arrB :: SP String String
arrB = Get (\a -> if a == "my" then (Get (\a -> if a == "name" then (Get (\a -> if a == "is" then Get (\a -> Put ("name: " ++ a) arrB)

else arrB))
else arrB))
else arrB)

inputB :: [String]
inputB = ["a", "b", "my", "name", "is", "thiago", "and", "I", "am", "so", "cool"]

inputAB :: [(String, String)]
inputAB = zip inputA inputB

main :: IO ()
main = let actualOutputB = runSP arrB inputB
actualOutputB1 = runSP (first arrB) (zip inputB (repeat "a"))

actualOutputA = runSP arrA inputA
actualOutputA1 = runSP (first arrA) (zip inputA (repeat "a"))
actualOutputAB = runSP (arrA *** arrB) inputAB
in do putStrLn $ "inputAB: " ++ show inputAB
putStrLn $ "outputA: " ++ show actualOutputA
putStrLn $ "outputA1: " ++ show actualOutputA1

putStrLn $ "outputB: " ++ show actualOutputB
putStrLn $ "outputB1: " ++ show actualOutputB1
putStrLn $ "outputAB: " ++ show actualOutputAB

[3]: https://github.com/peti/streamproc/blob/master/Control/Arrow/SP.hs#L58

2013/10/7 Thiago Negri <evohunz@gmail.com>

This is my first contact with QuickCheck, but does this test count as a proof that my implementation is correct?

QuickCheck shows 100 tests passed.

prop_a xs = runSP (f *** g) xs == runSP (first f >>> swap >>> first g >>> swap) xs

where swap = arr (\(a,b) -> (b,a))
f = arr (++"a")
g = arr (++"b")

2013/10/7 Thiago Negri <evohunz@gmail.com>

"On the one hand, indeterminate a's need to be fed in before indeterminate b's get pulled out. On the other hand, the c's need to behave as if they were in a no-op assembly line. One c goes in, the one (and same!) c drops out."

I agree with "no-op assembly line", but when I'm using `first` on a processor, I want to process the first stream *only*. The second stream should remain as it was not touched, so future processors will receive the same sequence from the second stream.

I mean, I think I need to guarantee that this definition holds:

`g *** f` is the same as `first g >>> swap >>> first f >>> swap`

If my implementation of `first` uses a real no-op assembly line for `c` (i.e., `arr id`), then I would lose the stream. As you said, I need to buffer the second stream while processing the first one.

Is my line of tought correct?

I'll try to write some tests to verify this.

Thanks!

2013/10/7 Kim-Ee Yeoh <ky3@atamo.com>

Hey Thiago,

First of all, congratulations for reading Hughes! Many of his papers are worth reading and re-reading for both beginners and experts alike.

On Tue, Oct 8, 2013 at 12:05 AM, Thiago Negri <evohunz@gmail.com> wrote:
Exercise 2 (section 2.5) is asking to create a Stream Processor that can map more than one output per input (e.g. 3 outcomes for a single consume of the stream).

Given

> data SP a b = Put b (SP a b) | Get (a -> SP a b)

it's easy to see that it's not just about more than one output per input. It's about n pieces of input producing m pieces of output, where (n,m) may even -- and probably does -- depend on previous inputs!

The exercise asks for an implementation of the following Arrow instance:

> first :: arr a b -> arr (a,c) (b,c)

which, specialized to our case, is just SP a b -> SP (a,c) (b,c).

It should now be apparent what the 'trickiness' is. On the one hand, indeterminate a's need to be fed in before indeterminate b's get pulled out. On the other hand, the c's need to behave as if they were in a no-op assembly line. One c goes in, the one (and same!) c drops out.

So one way to look at this is as a buffering problem.

At this point, I'd encourage you to think of some quickcheck tests you can write to convince yourself whether you have a right implementation or not.

Your main function doesn't seem adequate for the task.

-- Kim-Ee

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