Friday, June 15, 2007

Objects are Existential Packages

There's a long-running debate on the power of functional languages over object-oriented languages. In truth, now that C# has full generics, aka parametric polymorphism, it's almost equivalent in typing power to most typical statically typed functional languages. In fact, in terms of typing power, generic objects are universal and existential types, and can be used for all the fancy static typing trickery that those entail (see my previous reference to the GADTs in C# to see what I mean).

As a prior post explained, C#'s type system still lacks some of the flexible constraint refinement available in more powerful functional type systems, but in general C# is powerful enough to encode most interesting functional abstractions.

And I started a new project to demonstrate this: FP#. It provides a number of widely used functional abstractions, like the option type, a lazy type, lists, lazy lists, etc. and map, filter, and fold over all the collection types, including the standard .NET collections API. Each of these abstractions will be available as a separate DLL, so instead of linking to a large library, you can just pick those abstractions you're interested in using.

Besides more flexible typing as in GADTs, expressiveness is the only advantage functional languages still have over C#. Compare the verbosity of the C# option type:
//T is the type variable
public abstract class Option<T> { }
public sealed class None<T> : Option<T> { }
public sealed class Some<T> : Option<T>
  T value;
  public Some(T v) { value = v; }

  public T Value
    get { return value; }
as compared to an O'Caml definition:
type 'a option = None | Some of 'a    (* 'a is the type variable *)
This contrast highlights my previous argument in favour of expressiveness; just think of it as 1 line of O'Caml generating 12 lines of C#, since the efficiency of both definitions is equivalent.

To demonstrate the power of existential packages and universal types in C#, I'll be including a number of statically typed abstractions that have only been found in O'Caml and Haskell to date; types like statically sized lists and arrays, number-parameterized types, and other type wizardry resulting in strong partial correctness properties (see: Lightweight Static Capabilities).

It will be particularly interesting to compare the efficiency of a sized type, like a list, to its unsized counterpart, because .NET does not erase types like Java and O'Caml do.