purescript-ajnsit-typeable

Reified types for Purescript

This is an implementation of indexed typereps for Purescript, similar to the corresponding implementation in Haskell.

Slides for a talk about Purescript-Typeable, presented at the Purescript semi-monthly meetup on 18 January 2021, are available.

TypeReps are values that represent types (i.e. they reify types). When they are indexed they have the type itself as a parameter.

data TypeRep a -- A *value* that represents the type 'a'

All typeable things have typereps -

class Typeable a where
  typeRep :: TypeRep a

Instances are provided for common data types.

We can recover the unindexed representation by making it existential -

data SomeTypeRep

We can also test any two typereps for equality -

eqTypeRep :: forall a b. TypeRep a -> TypeRep b -> Boolean

We can compare two typeReps and extract a witness for type equality.

eqT :: forall a b. TypeRep a -> TypeRep b -> Maybe (a ~ b)

It's extremely easy. You just need to create a mechanical Taggable class instance for your datatype. The instance will always use the provided makeTag function. There is no other possible way to create an instance.

For example -

data Person = Person {name::String, age::Int}

instance Taggable Person where tag = makeTag unit

This is valid even for data types that take parameters. For example -

data Optional a = Some a | None

instance Taggable Optional where tag = makeTag unit

Don't worry about getting it wrong since the type system will prevent you from writing an invalid instance.

CAVEAT

Do not add any extra constraints to the instances. For example don't do Foo => Taggable Person. This currently cannot be caught by the type checker, but will break typerep comparisons for your data type.

And that's it! You are done! Now your datatype will have a Typeable instance.

Note that you will have Typeable instances even for unsaturated types. For example, with the tagTOptional instance above, you have instances for TypeRep (Optional a) as well as for TypeRep Optional.

We can have dynamic values which holds a value a in a context t and forgets the type of a

data Dynamic t

We can wrap a value into a dynamic

dynamic :: forall a t. Typeable a => t a -> Dynamic t

We can recover the value from a dynamic if supply the type we expect to find in the Dynamic

unwrapDynamic :: forall a. TypeRep a -> Dynamic t -> Maybe a

This is an implementation of the Data class Purescript, similar to the corresponding implementation of Data in Haskell. Check the documentation there for more information on the API. A brief overview is provided below.

class Typeable a <= Data a where
  dataDict :: DataDict a

Where DataDict is a manually reified dictionary because PureScript has trouble with constraints inside records.

Common instances are provided for Data. You can define Data instances for your own datatypes though it is slightly involved due to the dictionary reification.

When you cut through the dictionary reification noise, the definition of Data looks like the following -

class Typeable a => Data a where
  gmapT :: (forall b. Data b => b -> b) -> a -> a

Basically Data encodes a traversal through the structure of the data.

Let's say you have the following data structure -

data Foo = Foo Bar Baz

You would define a Data instance for Foo like the following -

instance Data Foo where
  gmapT k (Foo a b) = Foo (k a) (k b)

i.e. You apply the supplied function to the immediate children of the top level structure.

Now because of the dictionary reification in PureScript, you can't directly write the instance that way. You need to do the following instead -

instance Data Foo where
  dataDict = DataDict \k z (Foo a b) -> z Foo `k` a `k` b

i.e. You are doing the same traversal, but start with the z, and intersperse all the immediate children of the data structure with k.

If your data structure has multiple branches, for example -

data Foo = Bar Baz | Buzz Int

Simply handle the branches separately, for example -

instance Data Foo where
  dataDict = DataDict \k z foo -> case foo of
    Bar b -> z Bar `k` b
    Buzz i -> z Buzz `k` i

Once you have a Data instance for your datatype, you can use gmapT, and functions that depend on gmapT, such as everywhere.

For example, to apply a function f :: forall a. Typeable a => a -> a to all leaves of your data structure, you can do everywhere f. Inside f, you can use the Typeable instance to decide when to change the data structure. For example, if you want the function to increment all integers, but leave all other data intact, use -

f :: forall a. Typeable a => a -> a
f a =
  -- Check if `a` is an int
  case (typeRep :: _ a) `eqT` (typeRep :: _ Int) of
    -- Return unmodified if `a` is not an int
    Nothing -> a
    Just witness -> do
      -- If `a` is an int, we get access to bidirectional conversion functions
      let aToI = coerce witness
      let iToA = coerce (symm witness)
      -- Increment and return
      iToA (aToI a + 1)