[Haskell-cafe] Monad vs ArrowChoice

2008-05-14 Thread Ronald Guida 
I have read that Monad is stronger than Idiom because Monad lets me
use the results of a computation to choose between the side effects of
alternative future computations, while Idiom does not have this
feature.  Arrow does not have this feature either.

ArrowChoice has the feature that the sum type, Either, can be used to
choose between alternative computations, including their side effects.
 I know that Monad is supposed to be stronger than ArrowChoice, but I
have to ask, what exactly can Monad do that ArrowChoice can't do?

Let me set up an example to illustrate where I'm coming from.

 import Control.Monad.Writer
 import Control.Applicative
 import Control.Arrow hiding (pure)

The missileControl function accepts a flag to determine whether
missiles actually get launched, and it returns the number of
casualties.

 missileControl :: Bool - IO Integer
 missileControl b = do
  showFlag b
  casualties - if b
  then launchMissiles
  else doNotLaunch
  return casualties

 showFlag :: Bool - IO Bool
 showFlag b = (putStrLn $ Launch flag =  ++ show b)  return b

 launchMissiles :: IO Integer
 launchMissiles = do
   putStrLn Missiles have been launched.
   putStrLn Casualties = 6,700,000,000.
   return 67

 doNotLaunch :: IO Integer
 doNotLaunch = putStrLn Missiles not launched.  return 0

If I try to use an Idiom, or even an Arrow, instead of a Monad, then I
don't get to choose between the alternative side effects, and the
results will be similar to this:

 missileControl' :: Bool - IO Integer
 missileControl' b = do
   showFlag b
   casualties - launchMissiles
   casualties' - doNotLaunch
   if b
 then return casualties
 else return casualties'

If I use ArrowChoice, then I can do this:

 missileControl2 :: Bool - IO Integer
 missileControl2 b = runKleisli a b
 where a = (Kleisli $ showFlag)  (arr boolToEither) 
   ((Kleisli $ const launchMissiles) |||
(Kleisli $ const doNotLaunch))

 boolToEither :: Bool - Either () ()
 boolToEither True = Left ()
 boolToEither False = Right ()

GHCi missileControl2 True
Launch flag = True
Missiles have been launched.
Casualties = 6,700,000,000.
67

GHCi missileControl2 False
Launch flag = False
Missiles not launched.
0
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Re: [Haskell-cafe] Monad vs ArrowChoice

2008-05-14 Thread Twan van Laarhoven 

Ronald Guida wrote:

I have read that Monad is stronger than Idiom because Monad lets me
use the results of a computation to choose between the side effects of
alternative future computations, while Idiom does not have this
feature.  Arrow does not have this feature either.

ArrowChoice has the feature that the sum type, Either, can be used to
choose between alternative computations, including their side effects.
 I know that Monad is supposed to be stronger than ArrowChoice, but I
have to ask, what exactly can Monad do that ArrowChoice can't do?


Monads are equivalent to ArrowApply, they allow you to use a computed *action*. 
For example:


getMissileLauncher :: IO (String - IO ())

notWithArrows = do
 launchMissiles - getMissleLauncher
 launchMissiles Russia

ArrowChoice is not enough to implement this function. But it is possible with 
ArrowApply, of which Kleisli IO is an instance.


Twan
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