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README
pardual
The PureScript language defines a Parallel typeclass in the parallel
package. Quoting its documentation:
The
Parallel
class abstracts over monads which support parallel composition via some relatedApplicative
.
The same typeclass is defined in the Scala language, as part of the Cats library.
This typeclass has been controversial, in a sense, for not having strong laws. However, it has been proven to be actually useful in realworld applications.
The idea of this package is to bring this power over to the Haskell language while exploring the design space to identify and define stronger laws (if possible).
Originally, this idea has been described in this blogpost.
ParDual
Here's the definition of the same typeclass in Haskell:
class (Monad m, Applicative f) => ParDual f m  m > f, f > m where
parallel :: forall a . m a > f a
sequential :: forall a . f a > m a
I decided to call it ParDual
instead of Parallel
, because this duality doesn't always define a sequential
and parallel
relationship. Such is the case between []
and ZipList
, as we will soon discover.
It defines two functions, which are natural transformations between a Monad m
and an Applicative f
. It could also be seen as a typeclass version of an isomorphism such as forall a . Iso (f a) (m a)
.
The most common and useful relationships are both Either
/ Validation
and IO
/ Concurrently
.
instance Semigroup e => ParDual (Validation e) (Either e) where
parallel = fromEither
sequential = toEither
instance ParDual Concurrently IO where
parallel = Concurrently
sequential = runConcurrently
Validation
comes from the validators package, whereas Concurrently
comes from the async package.
Additionally, we can define a lot of powerful functions solely in terms of Applicative
, Monad
, and ParDual
. A few other functions might require extra requirements, such as Traversable
.
parMapN
The parMapN
set of functions are analogue to combining <$>
and <*>
, for any dual Applicative
.
parMap2
:: (Applicative f, Monad m, ParDual f m)
=> m a0
> m a1
> (a0 > a1 > a)
> m a
In this case, parMap2
takes only two computations and a function, but you can find other versions up to parMap6
. If there is demand, we can consider abstracting over its arity, in order to compose an arbitrary number of computations.
For example, if we define a Person
datatype with two fields:
type Name = Refined NonEmpty String
type Age = Refined (GreaterThan 17) Int
data Person = Person
{ personAge :: Age
, personName :: Name
} deriving Show
We can then validate different inputs, while accumulating errors on the left side, even when our type is Either [String] Person
.
mkPerson :: Int > String > Either [String] Person
mkPerson a n = parMap2 (ref a) (ref n) Person
Where ref
is a generic function that converts RefineException
s to [String]
:
ref :: Predicate p x => x > Either [String] (Refined p x)
ref x = left (\e > [show e]) (refine x)
In case of two invalid inputs, we will get as a result a list of validation errors:
mkPerson 10 "" == Left ["error 1", "error 2"]
If parMapN
didn't exist, we could do the same by manually converting between Either
and Validation
(which is exactly what parMapN
does via the ParDual
class).
mkPerson :: Int > String > Either [String] Person
mkPerson a n = toEither $ Person <$> fromEither (ref a) <*> fromEither (ref n)
Though, we can see how cumbersome and boilerplatey it gets.
parTraverse
Another great application of the ParDual
class is the definition of a traverse
function that takes a Monad
and a Traversable t
, but that operates over its dual Applicative
, and at the end it converts back to this Monad
.
parTraverse
:: (Traversable t, Applicative f, Monad m, ParDual f m)
=> (a > m b)
> t a
> m (t b)
The type signature is exactly the same as traverse
, except the constraints are different.
We can appreciate its usability by looking at some examples. Here's one with Either
:
f :: Int > Either [String] Int
f n = Left [show n]
traverse f [1..5] == Left ["1"]
parTraverse f [1..5] == Left ["1","2","3","4","5"]
Below there is another one with IO
:
randomDelay :: IO ()
randomDelay = do
r < randomRIO (1, 10)
threadDelay (r * 500000)
traverseIO :: IO ()
traverseIO = traverse_ (\n > randomDelay >> print n) [1 .. 10]
parTraverseIO :: IO ()
parTraverseIO = parTraverse_ (\n > randomDelay >> print n) [1 .. 10]
The traverse
version prints out numbers from 1 to 10 in sequence, while waiting for every random delay. So the output is pretty much 1 2 3 4 5 6 7 8 9 10
.
The parTraverse
version has a nondeterministic output, since it goes through Concurrently
(IO
's dual). It is exactly what you would expect while using mapConcurrently. One possible output is 5 10 6 1 3 2 9 4 7 8
.
ZipList
The dual Applicative
instance of []
is the one defined by ZipList
, which doesn't have anything to do with parallelism.
instance ParDual ZipList [] where
parallel = ZipList
sequential = getZipList
Let's have a look at the examples shown below.
((+) <$> [1..5] <*> [6..10]) == [7,8,9,10,11,8,9,10,11,12,9,10,11,12,13,10,11,12,13,14,11,12,13,14,15]
parMap2 [1..5] [6..10] (+) == [7,9,11,13,15]
The standard version iterates over both lists "sequentially". That is, it iterates over the first one, and then over the second one, returning the cartesian product of both lists.
Conversely, ZipList
s only return the sum of the current elements of both lists such as 1 + 6
, 2 + 7
, and so on. It iterates over both lists in "parallel", effectively traversing both at once.
parBitraverse
Operates over any Bitraversable
such as Either
or (,,)
.
res1 = [("ba",'2','T'),("ba",'2','r'),("ba",'2','u'),("ba",'2','e'),("ba",'4','T'),("ba",'4','r'),("ba",'4','u'),("ba",'4','e')]
(bitraverse show show ("ba", 24, True)) == res1
The standard bitraverse
for (String, Int, Bool)
traverses over the second value and then over the third value, combining the results on each iteration.
(parBitraverse show show ("ba", 24, True)) == [("ba",'2','T'),("ba",'4','r')]
The dual variant traverses all the values at the same time, terminating as soon as either value is empty.
Test suite
The test suite propertychecks the functions defined in ParDual
applied to different types of values.
$ nixshell run 'cabal newrun pardualtests'
━━━ Main ━━━
✓ prop_parMap2_on_success passed 100 tests.
✓ prop_parMap2_accumulates_errors passed 100 tests.
✓ prop_parTraverse_accumulates_errors passed 100 tests.
✓ prop_parTraverse_io_is_concurrent passed 10 tests.
✓ prop_parMap2_on_lists passed 100 tests.
✓ prop_parBitraverse passed 100 tests.
✓ 6 succeeded.
Publishing
Generating documentation and tarball file to upload.
$ cabal newhaddock haddockforhackage enabledoc
$ cabal upload d distnewstyle/pardual0.1.0.0docs.tar.gz
$ cabal newsdist