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UnderstandingArrows


Arrows

?Arrows are a new abstract view of computation, defined by John Hughes [WWW](Hug00). They serve much the same purpose as Monads -- providing a common structure for libraries -- but are more general.

Also visit: http://haskell.cs.yale.edu/arrows/ and http://www.soi.city.ac.uk/~ross/papers/fop.html

Arrows can be used in ?FunctionalReactiveProgramming.

In [WWW]Control.Arrow, we see that an Arrow class has the following functions:

class Arrow a where
  arr :: (b -> c) -> a b c  -- the same as "pure"
  pure :: (b -> c) -> a b c -- the same as "arr"
  (>>>) :: a b c -> a c d -> a b d
  first :: a b c -> a (b, d) (c, d)
  second :: a b c -> a (d, b) (d, c)
  (***) :: a b c -> a b' c' -> a (b, b') (c, c')
  (&&&) :: a b c -> a b c' -> a b (c, c')


A description offered on the HaskellIrcChannel follows:

<kosmikus> well, it still is vague, but one can say that a monad represents "things"
           which can produce values of a type, whereas an arrow represents "things"
           that can consume values of one type and produce values of another ...
<kosmikus> shapr: as to syntax, the <- represents the "production" part
<kosmikus> whereas the "-<" represents the consumption ...
<kosmikus> that's why monad syntax just uses "<-", whereas arrow syntax uses both


By way of example, here's the add function lifted to arrows, and using ?RossPaterson's arrow syntax:

addA :: Arrow a => a b Int -> a b Int -> a b Int
addA f g = proc x -> do
                y <- f -< x
                z <- g -< x
                returnA -< y + z


How does one learn more about Arrows? Are there any tutorials? What are the best papers to read? Are there small examples using Control.Arrow like for StateMonad? I understand that there are some inconsistancies in the names of the functions which might cause confusion?

-- IsaacJones