The Glasgow Haskell Compiler User's Guide, Version 4.06
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6.7. Existentially quantified data constructors

The idea of using existential quantification in data type declarations was suggested by Laufer (I believe, thought doubtless someone will correct me), and implemented in Hope+. It's been in Lennart Augustsson's hbc Haskell compiler for several years, and proved very useful. Here's the idea. Consider the declaration:

data Foo = forall a. MkFoo a (a -> Bool) | Nil

The data type Foo has two constructors with types:

MkFoo :: forall a. a -> (a -> Bool) -> Foo Nil :: Foo

Notice that the type variable a in the type of MkFoo does not appear in the data type itself, which is plain Foo. For example, the following expression is fine:

[MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]

Here, (MkFoo 3 even) packages an integer with a function even that maps an integer to Bool; and MkFoo 'c' isUpper packages a character with a compatible function. These two things are each of type Foo and can be put in a list.

What can we do with a value of type Foo?. In particular, what happens when we pattern-match on MkFoo?

f (MkFoo val fn) = ???

Since all we know about val and fn is that they are compatible, the only (useful) thing we can do with them is to apply fn to val to get a boolean. For example:

f :: Foo -> Bool f (MkFoo val fn) = fn val

What this allows us to do is to package heterogenous values together with a bunch of functions that manipulate them, and then treat that collection of packages in a uniform manner. You can express quite a bit of object-oriented-like programming this way.

6.7.1. Why existential?

What has this to do with existential quantification? Simply that MkFoo has the (nearly) isomorphic type

MkFoo :: (exists a . (a, a -> Bool)) -> Foo

But Haskell programmers can safely think of the ordinary universally quantified type given above, thereby avoiding adding a new existential quantification construct.

6.7.2. Type classes

An easy extension (implemented in hbc) is to allow arbitrary contexts before the constructor. For example:

data Baz = forall a. Eq a => Baz1 a a | forall b. Show b => Baz2 b (b -> b)

The two constructors have the types you'd expect:

Baz1 :: forall a. Eq a => a -> a -> Baz Baz2 :: forall b. Show b => b -> (b -> b) -> Baz

But when pattern matching on Baz1 the matched values can be compared for equality, and when pattern matching on Baz2 the first matched value can be converted to a string (as well as applying the function to it). So this program is legal:

f :: Baz -> String f (Baz1 p q) | p == q = "Yes" | otherwise = "No" f (Baz1 v fn) = show (fn v)

Operationally, in a dictionary-passing implementation, the constructors Baz1 and Baz2 must store the dictionaries for Eq and Show respectively, and extract it on pattern matching.

Notice the way that the syntax fits smoothly with that used for universal quantification earlier.

6.7.3. Restrictions

There are several restrictions on the ways in which existentially-quantified constructors can be use.

When pattern matching, each pattern match introduces a new, distinct, type for each existential type variable. These types cannot be unified with any other type, nor can they escape from the scope of the pattern match. For example, these fragments are incorrect:
f1 (MkFoo a f) = a
Here, the type bound by MkFoo "escapes", because a is the result of f1. One way to see why this is wrong is to ask what type f1 has:
f1 :: Foo -> a -- Weird!
What is this "a" in the result type? Clearly we don't mean this:
f1 :: forall a. Foo -> a -- Wrong!
The original program is just plain wrong. Here's another sort of error
f2 (Baz1 a b) (Baz1 p q) = a==q
It's ok to say a==b or p==q, but a==q is wrong because it equates the two distinct types arising from the two Baz1 constructors.
You can't pattern-match on an existentially quantified constructor in a let or where group of bindings. So this is illegal:
f3 x = a==b where { Baz1 a b = x }
You can only pattern-match on an existentially-quantified constructor in a case expression or in the patterns of a function definition. The reason for this restriction is really an implementation one. Type-checking binding groups is already a nightmare without existentials complicating the picture. Also an existential pattern binding at the top level of a module doesn't make sense, because it's not clear how to prevent the existentially-quantified type "escaping". So for now, there's a simple-to-state restriction. We'll see how annoying it is.
You can't use existential quantification for newtype declarations. So this is illegal:
newtype T = forall a. Ord a => MkT a
Reason: a value of type T must be represented as a pair of a dictionary for Ord t and a value of type t. That contradicts the idea that newtype should have no concrete representation. You can get just the same efficiency and effect by using data instead of newtype. If there is no overloading involved, then there is more of a case for allowing an existentially-quantified newtype, because the data because the data version does carry an implementation cost, but single-field existentially quantified constructors aren't much use. So the simple restriction (no existential stuff on newtype) stands, unless there are convincing reasons to change it.
You can't use deriving to define instances of a data type with existentially quantified data constructors. Reason: in most cases it would not make sense. For example:#
data T = forall a. MkT [a] deriving( Eq )
To derive Eq in the standard way we would need to have equality between the single component of two MkT constructors:
instance Eq T where (MkT a) == (MkT b) = ???
But a and b have distinct types, and so can't be compared. It's just about possible to imagine examples in which the derived instance would make sense, but it seems altogether simpler simply to prohibit such declarations. Define your own instances!