内容简介:As I’m preparing a talk about refinement types I will be giving this Thursday at theIn the following sections, I will be providing examples and use cases for this typeclass to showcase why it would be great to have it in Haskell. Oh, yes… I love refinement
As I’m preparing a talk about refinement types I will be giving this Thursday at the Functional Tricity Meetup , and I’ve recently given a similar talk using the Scala language as well, I realized there is a missing typeclass in Haskell.
In the following sections, I will be providing examples and use cases for this typeclass to showcase why it would be great to have it in Haskell. Oh, yes… I love refinement types as well!
In Haskell, we have the refined library and other more complex tools such as Liquid Haskell .
Refinement types
Refinement types give us the ability to define validation rules, or more commonly called predicates , at the type level. This means we get compile-time validation whenever the values are known at compile-time.
Say we have the following predicates and datatype:
import Refined type Age = Refine (GreaterThan 17) Int type Name = Refine NonEmpty Text data Person = Person { personAge :: Age , personName :: Name } deriving Show
We can validate the creation of Person
at compile-time using Template Haskell:
me :: Person me = Person $$(refineTH 32) $$(refineTH "Gabriel")
If the age was a number under 18, or the name was an empty string, then our program wouldn’t compile. Isn’t that cool?
Though, most of the time, we need to validate incoming data from external services, meaning runtime validation . Refined gives us a bunch of useful functions to achieve this, effectively replacing smart constructors . The most common one is defined as follows:
refine :: Predicate p x => x -> Either RefineException (Refined p x)
We can then use this function to validate our input data.
mkPerson :: Int -> Text -> Either RefineException Person mkPerson a n = do age <- refine a name <- refine n return $ Person age name
However, the program above will short-circuit on the first error, as any other Monad will do. It would be nice if we could validate all our inputs in parallel and accumulates errors, wouldn’t it?
We can achieve this by converting our Either
values given by refine a
into Validation
, use Applicative
functions to compose the different parts, and finally converting back to Either
.
import Data.Validation mkPerson :: Int -> Text -> Either RefineException Person mkPerson a n = toEither $ Person <$> fromEither (refine a) <*> fromEither (refine n)
As we can see, it is a bit clunky, and this is a very repetitive task, which will only increase the amount of boilerplate in our codebase.
This seems to be the status quo
around validation in Haskell nowadays, and it was the same in Scala. So it’s kind of hard to realize we are missing what we don’t know: the Parallel
typeclass. I didn’t know it was such a game changer until I started using it everywhere.
This is exactly what this typeclass does for us in other languages, via its helpful functions and instances. Unfortunately, it doesn’t exist in Haskell, as far as I know… until now!
Parallel typeclass
Let me introduce you to the Parallel
typeclass, already present in PureScript
and Scala
:
import Control.Natural ((:~>)) class (Monad m, Applicative f) => Parallel f m | m -> f, f -> m where parallel :: m :~> f sequential :: f :~> m
It defines a relationship between a Monad
that can also be an Applicative
with “parallely” behavior. That is, an Applicative
instance that wouln’t pass the monadic laws.
The most common relationship is the one given by Either
and Validation
. These two types are isomorphic, with the difference being that Validation
has an Applicative
instance that accumulate errors instead of short-circuiting on the first error.
So we can represent this relationship via natural transformation
in a Parallel
instance:
instance Semigroup e => Parallel (Validation e) (Either e) where parallel = NT fromEither sequential = NT toEither
In the same way, we can represent the relationship between []
and ZipList
:
instance Parallel ZipList [] where parallel = NT ZipList sequential = NT getZipList
Now, all this ceremony only becomes useful if we define some functions based on Parallel
. One of the most common ones is parMapN
(or parMap2
in this case, but ideally, it should be abstracted over its arity).
parMapN :: (Applicative f, Monad m, Parallel f m) => m a0 -> m a1 -> (a0 -> a1 -> a) -> m a parMapN ma0 ma1 f = unwrapNT sequential (f <$> unwrapNT parallel ma0 <*> unwrapNT parallel ma1)
Before we get to see how we can leverage this function with refinement types and data validation, we will define a type alias for our effect type and a function ref
, which will convert RefineException
s into a [Text]
, since our error type needs to be a Semigroup
.
import Control.Arrow (left) import Data.Text (pack) import Refined type Eff a = Either [Text] a ref :: Predicate p x => x -> Eff (Refined p x) ref x = left (\e -> [pack $ show e]) (refine x)
In the example below, we can appreciate how this function can be used to create a Person
instance with validated input data (it’s a breeze):
mkPerson :: Int -> Text -> Eff Person mkPerson a n = parMapN (ref a) (ref n) Person
Our mkPerson
is now validating all our inputs in parallel via an implicit round-trip Either
/ Validation
given by our Parallel
instance.
We can also use parMapN
to use a different Applicative
instance for lists without manually wrapping / unwrapping ZipList
s.
n1 = [1..5] n2 = [6..10] n3 :: [Int] n3 = (+) <$> n1 <*> n2 n4 :: [Int] n4 = parMapN n1 n2 (+)
Without Parallel
’s simplicity, it would look as follows:
n4 :: [Int] n4 = getZipList $ (+) <$> ZipList n1 <*> ZipList n2
For convenience, here’s another function we can define in terms of parMapN
:
parTupled :: (Applicative f, Monad m, Parallel f m) => m a0 -> m a1 -> m (a0, a1) parTupled ma0 ma1 = parMapN ma0 ma1 (,)
In Scala, there’s also an instance for IO
and IO.Par
, a newtype that provides a different Applicative
instance, which allows us to use functions such as parMapN
with IO
computations to run them in parallel!
And this is only the beginning… There are so many other useful functions we could define!
For now, the code is presented in this Github repository together with some other examples. Should there be enough interest, I might polish it and ship it as a library.
Let me know your thoughts!
Gabriel.
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