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Existential Types are the flip side of generics

Generic types, as can now be seen in all the major programming languages have a flip side that has yet to be widely appreciated: existential types.

Variables whose types are generic may not be modified within a generic function (or class): they can be kept in variables, they can be passed to other functions (provided they too have been supplied to the generic function), but other than that they are opaque. Again, when a generic function (or class) is used, then the actual type binding for the generic must be provided – although that type may also be generic, in which case the enclosing entity must also be generic.

Existential types are often motivated by modules. A module can be seen to be equivalent to a record with its included functions: except that modules also typically encapsulate types too. Abstract data types are a closely related topic that also naturally connect to existential types (there is an old but still very relevant and readable article on the topic Abstract types have existential type)

One way that I like to visualize existential types is that of a box with a type inside it. As a programmer using the box, you know there is a type in there, it has a name and it has a set of functions that reference the type but you know nothing about its actual realization.

Existsbox

Inside the box, you know what type foo is, and it can be any type so long as the other functions in the contract are implemented appropriately.

Outside the box you know nothing about the foo type. What this means is that any program text that uses the type from the box is strictly limited in what it can do: it is limited essentially to passing foo values around and to invoking other functions from the same box.

Thus, existentials and universals have a complementary role in programming: generics are used when the entity being defined must be general purpose. Existentials should be used when the use of the entity should be generic.

An excellent example of where this might be useful is in frameworks such as testing frameworks.

Existstest

Most test frameworks are pretty lame: you define a bunch of void functions with embedded assertions. A full test framework with existentials could be designed to test arbitrary functions and/or classes. All that the programmer would need to do to use such a framework to test her programs would be to invoke it!

A final note about existentials: they represent a neat way of characterizing system or built-in types. For example, the string type can be viewed as an existentially quantified type whose implementation belongs to the compiler. The difference here is that there is typically only one privileged instantiation of string; however, it would be very convenient for a language system to be able to support multiple kinds of string with different implementation characteristics.

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