If SML.NET had functors why can't F#?

Question

This question started out from

1. My translating of "ML for the Working Programmer" (WorldCat) by L. C. PAULSON to F# which uses functors for the examples.
2. Eventual desire to translate "Purely Functional Data Structures" (WorldCat) by Chris Okasaki which uses functors.
3. Reading "CATEGORIES TYPES AND STRUCTURES - An Introduction to Category Theory for the working computer scientist" (WorldCat) by Andrea Asperti and Giuseppe Longo.
4. Not understanding it all, mostly the category theory.

SML.NET can do functors and worked with Microsoft .NET.
* See: SML.NET User Guide Section 4.8.2 Class types and functors?

I keep seeing that F# cannot do true functors because of some limitation in Microsoft .NET.
* Can ML functors be fully encoded in .NET (C#/F#)?
* Any workaround for functor?

So if SML.NET could do functors on .NET then why can't F#? What did SML.NET do that F# can't?

The more I learn about functors coming from category theory, the more I see the beauty of them and desire to have them in F#.

EDIT

In a pursuit to better understand the relation between category theory and functional programming see these Q&A at CS:StackExchange.

Answer 1

There's no fundamental limitation of .NET that stops functors from being implemented in F#. True, they can't be represented directly in .NET metadata, but neither can other F# language features like union types. Compilers for languages with functors (e.g., Standard ML, OCaml) have a pass called defunctorize; it works just like C++ template expansion, in that it "flattens" the functors by specializing them into normal modules.

The F# compiler could do the same thing, but you then have to ask: how will this be exposed to other .NET languages? Since functors can't be directly encoded in the .NET type system, you'd need to come up with some way to represent them; and if that representation is difficult/impossible to use from C# or VB.NET, would it still make sense to include F# functors? A non-trivial part of F#'s success comes from it's ability to easily interop (in both directions) with C# and VB.NET.

EDIT: Don't get me wrong -- I'd love to have functors in F#, they'd be really useful to handle a few cases which are currently painful and/or impossible to implement without them. I'm just pointing out that the main reason the language doesn't yet (and maybe won't ever) have functors is that the interop issue hasn't been solved; the metadata-encoding issue is actually the easy part.

EDIT 2: Code for the defunctorize pass of MLton: defunctorize.fun

Update: I had a thought about how functors actually could be expressed within the .NET type system, so I put together a little experiment. It isn't pretty, but it works -- so now we know it's at least plausible that F# could one day support functors. In practice, the complexity you see in my experimental code would all be hidden by the compiler/language. If you want to check it out: experimental-functors