Existential Haskell


The majority of software engineering literature portrays object-oriented programming as distinct from, and often irreconcilable with, functional programming. This is, of course, a false dichotomy, as the techniques encouraged by functional programming are applicable in even the most object-oriented languages. Yet object-orientation, being perhaps history’s most popular software paradigm, has popularized its tenets, and occasionally we can see them show up even in programming languages like Haskell, a language about as antithetical to the object-oriented philosophy as possible.

In this piece, I’ll describe a common example of information hiding in ALGOL-style languages like Java, then express that in terms compatible with Haskell. We’ll then use this technique to port a responder chain to Haskell, demonstrating how Haskell supports dynamic function dispatch in the presence of hidden type information. I write this not because I expect to break any new ground—all the techniques I use here are long-documented in the literature, and Haskell veterans will probably find little new in this postThose familiar with the care and feeding of existential types may wish to skip to the penultimate section, which contains a couple useful data types that I haven’t yet seen in the wild.

—but because the existing resources are scattered, perhaps oddly so given how central dynamic dispatch is to most programming languages that aren’t Haskell, and because exploring the edge cases in the design illustrates the compromises inherent in language and library design.

the “normal” way to do things

Most of the world’s statically-typed programming languages allow their users to write code resembling the following Java:

public static Comparable someFn() {
    return "a concrete String value";

Syntactically, this code is uncontroversial: it’s a function that returns a value. Its only interesting aspect lies in the function signature−even though the function body returns a value of type String, its return type is declared to be Comparable, which is not a concrete data type, but a Java interface. As such, we cannot treat the result of this function call as the String it actually is; we can only interact with it via the methods defined on the Comparable interface. This application of the rule of least power is a useful one, even in a strongly-typed language like Haskell: sometimes we want to hide the implementation details of a function’s return type.

We can try to write the same thing in Haskell:

someComparableValue :: Ord a => a
someComparableValue _ = "a concrete string value"

Because this is not semantically-valid Haskell, we get the following error:

<interactive>:3:27: error:
    • Couldn't match expected type ‘a’ with actual type ‘[Char]’
      ‘a’ is a rigid type variable bound by
        the type signature for:
          someComparableValue :: forall a. Ord a => Int -> a

Haskell’s typechecker looks at the body of this function and says “hey, man, you’re returning a concrete string value here, not ’any type that is Ord–erable.’” Though this is a valid notion in Java, it’s not valid in Haskell. Another perspective on this is that Java allows a value to have more than one type: we can treat a Java string literal as a value of type java.lang.String, or of typeeven though Comparable is an interface, not a concrete type

Comparable, or of its superclass java.lang.Object. However, since Haskell doesn’t support inheritance, Haskell treats its values as having one, and only one, type. Working around this takes a judicious application of an existential type.

quick, some definitions

In Haskell, an existential data type is one that is defined in terms not of a concrete type, but in terms of a quantified type variable, introduced on the right-hand side of the data declaration. This is, as is the case for so many Haskell concepts, not a particularly helpful definition in the abstract. It’s easier to show than to tell, so let’s take a look at one of the canonical examples of an existential type: a Showable type that wraps any type that implements the Show interface.

data Showable = forall a . Show a => Showable a

There are several interesting things about this data type. Firstly, it uses the forall keyword to introduce the a type variable: given that we’re dealing with exist-ential types, it threw me for a loop that there wasn’t an exists keyword.Scala reserves a forSome keyword for this purpose, which I think reads a little more accurately in terms of the intent of introducing this type variable: using the phrase “for all” is a bit inapposite given that the Showable constructor is applied to single values at a time.

Considering the constructor of Showable is perhaps more enlightening:

λ> :t Showable
Showable :: forall a . Show a => a -> Showable

We can read this as “Showable is a constructor that takes, for all types a such that a implements Show, an a value, and returns a value of type Showable, the internal a value of which is no longer visible to the world once it’s been applied.”

Secondly, we can’t use a newtype to declare an existential. Attempting to write the following:

newtype Showable = forall a . Show a => Showable a

results in an error message:

• A newtype constructor cannot have a context in its type
  Showable :: forall a. Show a => a -> Showable
• In the definition of data constructor ‘Showable’
  In the newtype declaration for ‘Showable’

When we consider typeclasses as dictionaries, this restriction makes more sense: in GHC Core, this Show a constraint will be represented as a hypothetical ShowDict data type containing implementations for the show, showsPrec, and showList functions. In this light, we can see that Showable takes two parameters, not one: an a value to wrap, as well as the ShowDict dictionary associated with that value’s type. Newtypes exist to wrap single values, and here we’re wrapping both a datum and its associated Show dictionary: as a result, here we need a data declaration, even though the associated Showable constructor takes only one value (in Haskell surface syntax). This is an understandable limitation, though it would be cool if existential values of this sort could opt into the deriving mechanism in the manner of newtypes.

A third interesting thing: we can’t write a function that unwraps this data type. What might seem like an intuitive type for the function is rejected:

-- GHC will reject this.
unwrapShowable :: Showable -> (forall a . Show a => a)
unwrapShowable (Showable a) = a

We can see this explained a little more closely if we use the record selector syntax.

data Showable = forall a . Show a => Showable { getShowable :: a }

Attempting to use getShowable as a function that extracts some arbitrary Show–inhabiting type produces a well-explained error messages:

<interactive>:1:1: error:
    • Cannot use record selector ‘getShowable’ as a function due to escaped type variables
      Probable fix: use pattern-matching syntax instead
    • In the expression: getShowable

The mental model I use here is that applying a constructor of an existential type serves as a sort of event horizon for type information. In other languages we can assemble heterogenous lists natively; in Haskell, by contrast, we have to opt into it explicitly: applying the Showable constructor to a value swallows its type information. We can’t write a function, whether the hand-written unwrapShowable or descending from our getShowable record selector, that unwraps some arbitrary type out of an existential. All that is retained is the ability, given a proper case statement to unwrap the value within the existential, to Show the value contained therein: it cannot escape its scope, as the error message above explainsWe can, however, use the getShowable record selector to update the wrapped value present in a Showable.


We can, as I mentioned above, cross the event horizon with a case statement, binding the Show–conforming contents to a variable name:

let shown = case x of Showable val -> show val

Inside the right-hand-side of this case statement, we have a value x in scope. A quick inquiry with type holes reveals the type we expect:

• Relevant bindings include
    x :: a (bound at <interactive>:28:15)
  Constraints include Show a (from <interactive>:28:11-15)

All we know about this value x is that we can call Show on it. Other than passing it to the basic combinators (id and const), that’s all we can do with this value. Any bit of type information has been lost, replaced instead with capabilities, via typeclasses. Again, when we consider typeclasses as dictionary parameters, we can visualize how this works on a core-calculus level: we discard type information, including only the relevant dictionaries provided by the context of the forall.

A fourth and final interesting thing about this type is that you can write it, using the GADTs GHC extension, without an explicit forall keyword:

data Showable where
  Showable :: Show a => a -> Showable

This stems from the fact that GADTs allow us to introduce per-constructor type variables and associated constraints, even if the type variable is not visible externally. Another thing to note is that data declarations containing existential values don’t have to be limited to a single value: they can hold concrete values, or values expressed with more forall–introduced type variables.

casting around wildly

Being able to hide implementation details of a function’s return type is all well and good, but many users are going to need to convert (or attempt to convert) from an existential type back into a concrete type. Java provides this functionality with the instanceof operator and its cast syntax:

Comparable c = someFn();
if c instanceof String {
    System.out.println("Got a string: " + (String)c);
} else {
    System.out.println("Casting to a String here would raise a ClassCastException");

This is a consequence of all Java objects descending from java.lang.Object, and the ability of the instanceof operator to query the type of an object at runtime. Though this style of programming isn’t hugely popular in Haskell, it’s not unheard of, and Haskell indeed supports it: this is where the Typeable typeclass comes in. It’s most prominently at work in base, under Control.Exception:

class (Typeable a, Show e) => Exception e

data SomeException = forall e . Exception e => SomeException e

This code begins with the declaration of a new typeclass, Exception, that inherits from both Typeable and Show. The fact that the Exception typeclass inherits from Typeable means that we can use cast, the fundamental Typeable primitive, to do safe casting to concrete values, accounting for the possibility of failure.

Let’s take an example, in the lowly (or perhaps mighty, depending on how you look at it) IO monad, of using Haskell’s dynamically-typed exception hierarchy:

cautiouslyPrint :: Show a => IO a -> IO ()
cautiouslyPrint go = Control.Exception.catch (go >>= print) handler
    handler :: SomeException -> IO ()
    handler (SomeException e) = case cast e of
      Just DivideByZero -> putStrLn "divide by zero"
      Nothing -> putStrLn ("Some other exception: " <> show e)

Here we use the catch function to evaluate the provided go argument, invoking handler should a runtime exception be thrown. We’re only handling one possible error type: DivideByZero, one of the constructors of ArithException. However, we are doing so via a checked cast, courtesy of the cast function, because we’re not recognizing ArithException values directly: handler will be invoked on any exception, because SomeException, to catch, means “this catch statement should handle any and all exceptions thrown by its body.” Looking at the type of cast can be illuminating:

cast :: (Typeable a, Typeable b) => a -> Maybe b

cast, perhaps unsurprisingly, is defined to return Just a value when the types a and b line up. This is done dynamically, at runtime, thanks to the Typeable class, which is a special typeclass indeed: it’s one of only two typeclasses that GHC explicitly prohibits any user-specified instances. Try it; you’ll get your hand slapped:

<interactive>:4:10: error:
    • Class ‘Typeable’ does not support user-specified instances
    • In the instance declaration for ‘Typeable Foo’

GHC is right to prohibit this: because Typeable is concerned with the internal representation of Haskell types in memory, it’s GHC’s responsibility to implement it for you. And indeed it does: all types implement Typeable, for free. Note that cast takes all type information into account, not just structure: in practice, this means that you can’t cast a Nothing value of type Maybe Int to a Nothing value of type Maybe Char, even though the standalone Nothing identifier can be implicitly cast to a value of Maybe Char, or Maybe Int, or Maybe String.

fluent dynamic dispatch

Let’s drop back to our prior example:

handler :: SomeException -> IO ()
handler (SomeException e) = case cast e of
  Just DivideByZero -> putStrLn "divide by zero"
  Nothing -> putStrLn ("Some other exception: " <> show e)

As I mentioned, we’re only handling one possible error case: though handler will be invoked for all exception types, our cast operation only handles DivideByZero exceptions (of type ArithException). We can add new ArithException cases without difficulty:

Just DivideByZero -> putStrLn "divide by zero"
Just Underflow -> putStrLn "floating point shenanigans"
Nothing -> putStrLn ("Some other exception: " <> show e)

However, the problem becomes thornier when we want to handle disjoint Exception-conformant types. A naïve encoding of the problem will not work, as in the followingNote that this syntax Just (e :: ArithException), in which we annotate a value with an indicated type without pattern matching on it, requires the ScopedTypeVariables extension to be enabled. ScopedTypeVariables should always be enabled: it does the right and obvious thing.

, where we try to handle ArithExceptions and ArrayExceptions:

Just (arith :: ArithException) -> putStrLn ("arithmetic: " <> show arith)
Just (array :: ArrayException) -> putStrLn ("array: " <> show array)

This will produce a compiler error, because all the values on the left-hand-sides of a case statement’s branches must have the same type! A corrected version might read:

handler (SomeException e) = case cast e of
  Just (arith :: ArithException) -> putStrLn ("arith: " <> show arith)
  Nothing -> case cast e of
    Just (array :: ArrayException) -> putStrLn ("array: " <> show array)
    Nothing -> putStrLn ("Some other exception: " <> show e)

To work around the fact that the first cast expression limits its result type to values of type ArithException, we have to call cast again: this time, the Typeable value is pinned to ArrayException, which lets us handle successful casts in the Just clause and failure in the Nothing clause.

There is a grave issue with the above pattern: it’s clunky as hell with only two cases, and gets even clunkier as you add more possible types. A more modern approach is to use GHC’s MultiwayIf, in a manner that can be surprising for newcomers. if statements are usually concerned with boolean values, but this one won’t be: instead, we’re going to call cast, using the guard syntax to discriminate between cases. By guarding (with |) on Just values returned from cast, we can have something akin to a polytypic case statement:

  | Just (arith :: ArithException) <- cast e -> putStrLn ("arith: " <> show arith)
  | Just (array :: ArrayException) <- cast e -> putStrLn ("array: " <> show array)
  | otherwise -> putStrLn ("Something else: " <> show e)

This is arguably a bastardization of the spirit of MultiWayIf, which is ostensibly about simplifying large systems of boolean equations. Here, the only Bool value involved is otherwise, defined by the Prelude to be True. Because True is always, well, True, its position as the last branch will mean that it is always matched, unless matched by a previous case (that is, a successful Just value). Yet the otherwise is readable in context, and the code’s intent is clear.

Though this kind of runtime polymorphism isn’t enormously common in Haskell–we usually resolve polymorphism at compile-time—it’s not unheard of, and, as mentioned above, is provided as part of the Control.Exception interface to GHC’s hierarchy of exceptions. This Haskell design pattern—an existential data type that inherits from Typeable—is as close to dynamic dispatch as Haskell gets. Though it’s not common, neither is it invalid: sometimes what’s needed is an event horizon, that hides the concrete representation of a datum but provides, via polymorphism, the chance to reconstitute itself into a concrete type with Typeable.

let’s build a responder chain

Essential to most GUI programming is the notion of what macOS and iOS call the responder chain. The responder chain is responsible for passing events—key presses, mouse clicks, device motions—through the hierarchy of a user interface. For example, shaking one’s device in iOS produces an undo event, if the user has a text field selected. The responder chain is responsible for passing shake events down the window hierarchy, eventually settling on the text field; were it not selected, the rest of the UI would have a chance to intercept and interpret this event.

Implementing a responder chain is fairly straightforward in an object-oriented view of the world: there is some superclass that all user interface elements extend, and this interface provides a lingua franca for events to be dynamically dispatched. It becomes somewhat more intricate, at least on the face of it, in a strongly-typed world sans subtyping. Indeed, this was one of the qualms expressed by the Objective-C community in response to the emergence of Swift. While Swift is perfectly capable of expressing a fluent, idiomatic responder chain, the lesson is more broadly applicable. Indeed, we can envision a UI framework that implemented this behavior in Haskell:

data Response a where
  Accept :: a -> Response a
  Finish :: a -> Response a
  Defer :: Response a

class (Typeable a, Show a) => Responder a where
  respond :: Event -> a -> Response a

data SomeResponder = forall a . Responder a => SomeResponder a

newtype Chain = Chain [SomeResponder]

-- Dirt-simple imperative implementation with the ST monad.
-- An implementation with a fold could do this all purely
-- but the accumulator is a little fiddly
propagate :: Event -> Chain -> Chain
propagate evt (Chain c) = runST do
  -- We need a signaling variable in case something in the chain
  -- wants to abort the traversal.
  abort <- newSTRef False
  -- Iterate through the responder chain...
  result <- for c \(SomeResponder item) -> do
    -- attempting to apply the function at each item
    let given = respond evt item
    -- but first checking to see if we've aborted in prior iterations
    done <- readSTRef abort
    -- shortcut for rewrapping and returning a SomeResponder
    let wrap = pure . SomeResponder
      -- A prior Finish result means we no-op
      | done -> wrap item
      -- Return a new value while writing to the signal variable.
      | Finish a <- given -> writeSTRef abort True *> wrap a
      -- Just return the new value.
      | Accept a <- given -> wrap a
      -- No match? Continue onward
      | Defer -> wrap item
  pure (Chain result)

Similarly to the Exception class, we define a Responder typeclass that implements the interface common to all UI elements that can respond to some hypothetical Event type. This inherits both from Show and from Typeable, in order to admit the cast operation on the contents of a concrete SomeResponder wrapper. From this definition, we can describe a responder chain as a list of existentially-wrapped UI elements, the capabilities of which are described by the Responder class; the process of propagating an event down a chain involves a for loop over the elements, asking each item in turn how it handles a given Event. This is profoundly imperative code, but that’s okay: sometimes imperative code is what’s needed, even in a functional language like Haskell.

We can also define a function similar to the above, yet simpler and less imperative; it’ll apply the provided fn parameter everywhere possible, being treated as a no-op if not.

applying :: Responder a => (a -> a) -> Chain -> Chain
applying f (Chain c) = Chain (map go c)
    go (SomeResponder r) = maybe (SomeResponder r) (SomeResponder . f) (cast r)

one polytypic existential to rule them all

You, the reader, might at this point be turning up your nose at the idea of having to write a forall-based existential type for every concievable typeclass that you might need to wrap. This is indeed a valid observation. Luckily, GHC Haskell gives us sufficient tools to write a data type that is polymorphic not just in terms of a hidden value it wraps, but in terms of the typeclass it uses!

data Some (c :: Type -> Constraint) where
  Some :: c a => a -> Some c

With the TypeApplications and ConstraintKinds extensions, we can specify that the type variable passed to Some is not of kind Type, or Type -> Type; instead, it takes a Type and returns a Constraint. This means that we can pass in Show, Eq, Ord, or any other unary typeclass, using a type application:

let wrappedInt = Some @Show (5 :: Int)

This seems like a broadly applicable data type, but it’s not present in the standard library or any widely-used libraries (though the inimitable Rob Rix tells me that he’s defined it many times, at which I bear zero surprise, because Rob is a maestro).

We can extend this to types composed out of other types, like [Int] or Vector String: this Some1 constructor is polymorphic in two type variables, both of which take arguments and return Constraint kinds.

data Some1 c d where
  Some1 ::
    forall k
      (c :: (k -> Type) -> Constraint)
      (d :: k -> Constraint)
      (f :: k -> Type)
      (a :: k) .
    (c f, d a)
    => f a
    -> Some1 c d

The built-in ~ syntax, included with the GADTs extension, provides us a method to establish that type variables must be equal: the present of an a ~ Int constraint ensures that the a type variable must unify with (read: be equal to) the Int type. By partially applying this constraint, we can speak of useful types with remarkable brevity, such as the following type representing “some Functor containing Int values”:

someFunctorOfInts :: Some1 Functor ((~) Int)
someFunctorOfInts = Some1 [1, 2, 3]

I dunno, draw your own conclusions

Haskell is a language where we like concrete, inferable types and type variables. Yet sometimes the Right Thing to do is to hide the details of heterogenous data types behind an existential wrapper—you can see this in action in Semantic, where we hide the fact that different languages’ AST types are disjoint behind a SomeParser wrapper. And though existentials in Haskell are a little odd, at least when compared to standard data types, they’re nonetheless profoundly useful, both in the abstract and when dealing with the nitty-gritty of data manipulation.

Thanks to Ayman Nadeem, Rob Rix, and Peter Berger for reviewing drafts of this post.