Polymorphic variants for PureScript
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README.md

purescript-variant

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Polymorphic variants for PureScript.

Install

bower install purescript-variant

Documentation

Data.Variant is an implementation of polymorphic variants in PureScript. What are polymorphic variants? Before we get to that, lets look at the dual, which you are likely familiar with if you've been using PureScript: records.

Another name for records might be polymorphic products. A product is simply data that holds inhabitants for more than one type at a time, Tuple a b being the canonical product.

data Tuple a b = Tuple a b

If I have a Tuple Int String, then I have available some Int value paired with a String value (or Int * String, thus a product). For convenience, we often like to use records, especially for models in our shiny web apps.

type User =
  { name :: String
  , age :: Int
  , email :: Email
  }

And maybe use it like so:

addJrSuffix :: User -> User
addJrSuffix user = user { name = user.name <> ", Jr." }

However this type signature is needlessly specific. In fact, all it cares about is the name field. We can express this sort of structural typing in PureScript via row types:

addJrSuffix :: forall r. { name :: String | r } -> { name :: String | r }
addJrSuffix hasName = hasName { name = hasName.name <> ", Jr." }

Now I can pass in anything that merely has a name :: String.

addJrSuffix { name: "Bob" }
addJrSuffix { age: 42, name: "Gerald" }

So records, or polymorphic products, let us pass in anything as long as it has the structure we specify, and even get the same structure back after we are done with it.

Let's flip back around to sum types (or variants), Either a b being the canonical dual of Tuple a b.

data Either a b = Left a | Right b

Where Tuple a b says we have an a paired with a b, Either a b says we have either an a or a b via the Left and Right constructors. We'd handle the possibilities by pattern matching on it with case.

This library just uses the same structural row system that we use with records (products) and applies them to variants (sums). Voila!

We lift values into Variant with inj by specifying a tag.

someFoo :: forall v. Variant (foo :: Int | v)
someFoo = inj (SProxy :: SProxy "foo") 42

SProxy is just a way to tell the compiler what our tag is at the type level. I can stamp out a bunch of these with different labels:

someFoo :: forall v. Variant (foo :: Int | v)
someFoo = inj (SProxy :: SProxy "foo") 42

someBar :: forall v. Variant (bar :: Boolean | v)
someBar = inj (SProxy :: SProxy "bar") true

someBaz :: forall v. Variant (baz :: String | v)
someBaz = inj (SProxy :: SProxy "baz") "Baz"

We can try to extract a value from this via on, which takes a function to handle the inner value in case of success, and a function to handle the rest in case of failure.

fooToString :: forall v. Variant (foo :: Int | v) -> String
fooToString = on (SProxy :: SProxy "foo") show (\_ -> "not foo")

fooToString someFoo == "42"
fooToString someBar == "not foo"

We can chain usages of on and terminate it with case_ (for compiler-checked exhaustivity) or default (to provide a default value in case of failure).

_foo = SProxy :: SProxy "foo"
_bar = SProxy :: SProxy "bar"
_baz = SProxy :: SProxy "baz"

allToString :: Variant (foo :: Int, bar :: Boolean, baz :: String) -> String
allToString =
  case_
    # on _foo show
    # on _bar (if _ then "true" else "false")
    # on _baz (\str -> str)

someToString :: forall v. Variant (foo :: Int, bar :: Boolean | v) -> String
someToString =
  default "unknown"
    # on _foo show
    # on _bar (if _ then "true" else "false")

allToString someBaz == "Baz"
someToString someBaz == "unknown"

Handlers with on are also compositional! We can compose them together with function composition and reuse them in different contexts.

onFooOrBar :: forall v. (Variant v -> String) -> Variant (foo :: Int, bar :: Boolean | v) -> String
onFooOrBar = on _foo show >>> on _bar (if _ then "true" else "false")

allToString :: Variant (foo :: Int, bar :: Boolean, baz :: String) -> String
allToString =
  case_
    # onFooOrBar
    # on _baz (\str -> str)

Instead of chaining with just on, there is onMatch which adds record sugar.

onFooOrBar :: forall v. (Variant v -> String) -> Variant (foo :: Int, bar :: Boolean | v) -> String
onFooOrBar = onMatch
  { foo: show :: Int -> String
  , bar: if _ then "true" else "false"
  }

But note that polymorphic functions like show or id need to be either annotated or eta expanded due to record impredicativity.

onMatch can be used with case_ and default just like on, but there is also match for the common case of total matching.

allToString :: Variant (foo :: Int, bar :: Boolean, baz :: String) -> String
allToString = match
  { foo: \a -> show a
  , bar: \a -> if a then "true" else "false"
  , baz: \a -> a
  }

We can combine polymorphic variants with Functors as well using VariantF, which lives in Data.Functor.Variant. VariantF is just like Variant, except it's indexed by things of kind Type -> Type.

someFoo :: forall v. VariantF (foo :: FProxy Maybe | v) Int
someFoo = inj (SProxy :: SProxy "foo") (Just 42)

someBar :: forall v. VariantF (bar :: FProxy (Tuple String) | v) Int
someBar = inj (SProxy :: SProxy "bar") (Tuple "bar" 42)

someBaz :: forall v a. VariantF (baz :: FProxy (Either String) | v) a
someBaz = inj (SProxy :: SProxy "baz") (Left "Baz")

VariantF supports all the same combinators as Variant. We need to use FProxy in the types, however, because the row machinery in PuresScript is not poly-kinded. FProxy lets us talk about functors, but trick the type system into thinking they are the expected kind.