Sometimes when I write PureScript code, I want to do something as easy as using row types with RowToList when dealing with normal ADTs, but I don't quite have as convenient of ways to work with ADTs: when I deal with (Polymorphic) Variants instead of sums, I can simply RowToList on the row type and work with the type level-list. Likewise, I when I deal with Record problems instead of products, I can simply RowToList again on the row type and work with the type-level list. But why not for normal ADT types' Generic Representations? Well, very well could!
One thing to keep in mind is that the Rep of a sum type will always be a non-empty list of at least two elements, as you can't have a left or right side otherwise. What do I mean? Consider a simple sum type:
data MySum = First | Second
derive instance genericMySum :: Generic MySum _Let's then see what the rep is by using a wildcard signature and expanding it:
from :: MySum -> _ -- expands to:
-- Sum
-- (Constructor "First" NoArguments)
-- (Constructor "Second" NoArguments)
from = GR.fromWe can see that the associated rep has two elements under the sum, and in the actual definition of Sum we can see that there are the Inl and Inr constructors for the rep:
data Sum a b = Inl a | Inr bFor my own uses though, I smashed this into a non-empty list of one, since I don't care to try to handle too many details at once. And so my SumList1 definition's type-level definition is as follows:
-- | a non-empty list made of a Generic Sum's type elements
foreign import kind SumList1
-- | the base element of a Generic Sum
foreign import data Sum1 :: Symbol -> Type -> SumList1
-- | the N-th element of a Generic Sum
foreign import data SumN :: Symbol -> Type -> SumList1 -> SumList1Where the Symbol is the name of the Constructor above and Type is the argument position type. Practically, this is the same as a Haskell GADT defined with constructor signatures (see https://en.wikibooks.org/wiki/Haskell/GADT#Summary):
-- this is Haskell GADTs, not PureScript
data List a where
Nil :: List a
Cons :: a -> List a -> List aNow, to be able to easily pass around this type-level information for the type class we're going to define and use, we need to define a Proxy:
-- | a Proxy for SumList1
data SLProxy (list :: SumList1) = SLProxyLet's define our class and its instances now. We know that this class will take the sum type in and produce our SumList1, and especially that we want our instances to be matched based on the sum type parameter (and that the list is determined by the sum type):
class SumToList sum (list :: SumList1) | sum -> listFrom here, one thing we can readily do is take advantage of the fact that sum type reps are always right-sided, so the left item will always be a constructor. With this knowledge, we don't need to bother with writing any append operation and can pop off items from the sum as a list readily:
instance sumSumToList ::
( SumToList b r
) => SumToList (Sum (Constructor name a) b) (SumN name a r)So for the Sum case, we take the name and type a from the left and create a N-th list item, then applying the rest of the list produced by running SumtoList further on the right side b.
Finally, the last item of the sum will also be a constructor, so the other instance we need is to then match Constructor and make a Sum1 element to finish the list:
instance conSumToList ::
SumToList (Constructor name a) (Sum1 name a)And these are the only instances we need to get going with simple sum types.
The product type case is largely the same, but starts with a Constructor that then has the following arguments as a Product:
data MyProduct = MyConstructor Int String
derive instance genericMyProduct :: Generic MyProduct _
from :: MyProduct -> _ -- expands to
-- Constructor
-- "MyConstructor"
-- (Product
-- (Argument Int)
-- (Argument String))
from = GR.fromIn this case, since the arguments will be normal types, we won't have a name parameter:
-- | a non-empty list made of a Generic Product's type elements
foreign import kind ProductList1
-- | the base element of a Generic Product
foreign import data Product1 :: Type -> ProductList1
-- | the N-th element of a Generic Product
foreign import data ProductN :: Type -> ProductList1 -> ProductList1
-- | a Proxy for ProductList1
data PLProxy (list :: ProductList1) = PLProxyJust to unwrap the constructor, I made a convenience class with a single instance to extract out the rep to the name and the actual list:
-- | convenience class to apply ProductToList on a data type directly
class ToProductList product (name :: Symbol) (list :: ProductList1) | product -> name list
instance toProductList ::
( ProductToList product list
) => ToProductList (Constructor name product) name listLike before, the Product rep is right-sided, so we can take items from the head and create the N-th list item with this, and then match Argument to make the last list item:
class ProductToList product (list :: ProductList1) | product -> list
instance productProductToList ::
( ProductToList b r
) => ProductToList (Product a b) (ProductN a r)
instance argProductToList ::
ProductToList (Argument a) (Product1 (Argument a))Like with any class using RowList, we write a class to the list and handle the base and increment cases. The main diference with typical RowToList classes is that since we have a non-empty list, our base repeats the increment case actions, and we can return the results as a NonEmptyList for a class such as SumNames:
class SumNames (list :: SumList1) where
sumNames :: SLProxy list -> NonEmptyList String
instance zSumNames ::
( IsSymbol sumName
) => SumNames (Sum1 sumName ty) where
sumNames _ = pure $ reflectSymbol (SProxy :: SProxy sumName)
instance sSumNames ::
( IsSymbol sumName
, SumNames tail
) => SumNames (SumN sumName ty tail) where
sumNames _ = head <> rest
where
head = pure $ reflectSymbol (SProxy :: SProxy sumName)
rest = sumNames (SLProxy :: SLProxy tail)We can then apply this to a sum type that derives a Generics-Rep instance accordingly:
data Fruit
= Apple
| Banana
| Cherry
derive instance genericFruit :: Generic Fruit _
availableFruits :: NonEmptyList String
availableFruits = availableFruits'
where
availableFruits'
:: forall rep list
. Generic Fruit rep
=> SumToList rep list
=> SumNames list
=> NonEmptyList String
availableFruits' = sumNames (SLProxy :: SLProxy list)So while we need to apply the classes with quantified variables, these are fully solved and the actual exposed value does not have any free variables.
And as expected:
test "SumToList works" do
Assert.equal
"Apple, Banana, Cherry"
(intercalate ", " availableFruits)Similarly, we can define a class for the actual ProductList1 and handle the split information of the constructor name and the actual types.
-- so we can get the type names of the arguments
class TypeName a where
typeName :: Proxy a -> String
instance intTypeName :: TypeName (Argument Int) where
typeName _ = "Int"
instance stringTypeName :: TypeName (Argument String) where
typeName _ = "String"
-- normal list class like before
class ProductNames (list :: ProductList1) where
productNames :: PLProxy list -> NonEmptyList String
instance zProductNames ::
( TypeName ty
) => ProductNames (Product1 ty) where
productNames _ = pure $ typeName (Proxy :: Proxy ty)
instance sProductNames ::
( TypeName ty
, ProductNames tail
) => ProductNames (ProductN ty tail) where
productNames _ = head <> rest
where
head = pure $ typeName (Proxy :: Proxy ty)
rest = productNames (PLProxy :: PLProxy tail)Then, we can apply the classes as before to prepare the actual static value:
thingNames :: NonEmptyList String
thingNames = thingNames'
where
thingNames'
:: forall rep name list
. Generic Thing rep
=> ToProductList rep name list
=> IsSymbol name
=> ProductNames list
=> NonEmptyList String
thingNames' =
head <> productNames (PLProxy :: PLProxy list)
where
head = pure $ reflectSymbol (SProxy :: SProxy name)Coming together:
test "ToProductList/ProductToList works" do
Assert.equal
"Thing Int String Int"
(intercalate " " thingNames)Hopefully this has shown you that you can readily transform these generics-rep types into other type-level structures as you wish, so you can write instances that require a lot less work than if you tried to work with the original types directly. In addition, you can control which reps you want to actually handle by only writing instances for them -- the SumToList does not attempt to transform Product reps into SumList1, rightly so.