Dependent types in Haskell: Progress Report

It was drawn to my attention that there is an active Reddit thread about the future of dependent types in Haskell. (Thanks for the heads up, @thomie!) Instead of writing a long response inline in Reddit, it seems best to address the (very knowledgeable, respectful, and all around heartening) debate here.

When can we expect dependent types in GHC?

The short answer: GHC 8.4 (2018) at the very earliest. More likely 8.6 or 8.8 (2019-20).

Here is the schedule as I see it:

• GHC 8.2: Clean up some of the lingering issues with -XTypeInType. As I will be starting a new job (Asst. Prof. at Bryn Mawr College) this fall, I simply won’t have the opportunity to do more than some cleanup work for the next release. Also, quite frankly, I need a release cycle off from the challenge of putting in a large new feature. Polishing up -XTypeInType for release took probably an extra full month of unexpected work time! I don’t regret this in the slightest, but I could use a cycle off.

• GHC 8.4: This depends on what other research opportunities come up in the next year and how much more attention -XTypeInType needs. If all goes well this fall and I can get a few publications out in the next year (certainly possible – I have several in the works), then I could conceivably start primary implementation of -XDependentTypes next summer. The odds that it will be in a state to merge for 8.4 are slim, however.
• GHC 8.6: We’re now talking about a real possibility here. Assuming I start the implementation next summer, this would give me a year and a half to complete it. I desperately wish to avoid merging late in the cycle (which is what made -XTypeInType so stressful) so perhaps merging soon after GHC 8.4 comes out is a good goal. If this slips, GHC 8.8 seems like quite a likely candidate.

Regardless of the schedule, I have every intention of actually doing this work.

One major oversight in the schedule above: I have completely discounted the possibility of collaborators in coding this up. Do you wish to help make this a reality? If so, let’s talk. I’ll admit that there may be a bit of a hill for an outside collaborator to climb before I really start collaborating in earnest, so be prepared to show (or create!) evidence that you’re good at getting your hands dirty in the greasy wheels of GHC’s typechecker without very much oversight. I’ve encouraged several of you on Trac/Phab – you know who you are, I hope. For others who have not yet contributed to GHC: you’re likely best served starting smaller than implementing dependent types! But let’s talk anyway, if you’re interested.

What is the design of dependent types in Haskell?

I expect to hand in my dissertation in the next two weeks. While I am developing it in the public eye (and warmly welcome issues to be posted), there is no publicly available PDF build. Building instructions are in the README. I will post a built PDF when I hand in my draft to my thesis committee. I will be defending on September 1 and will likely make some revisions (as suggested by my committee) afterward.

Readers here will likely be most interested in Chapters 3 and 4. Chapter 3 will contain (I’m still writing it!) numerous examples of dependent types in Haskell and how they might be useful. Chapter 4 presents the design of dependent types in Haskell as a diff over current Haskell. This design is not yet up to the standard of the Haskell Reports, mostly because it is unimplemented and seems not worth the effort of formalization until we know it is implementable. For the overly curious, Chapter 5 contains a new intermediate language (to replace GHC Core) and Chapter 6 contains the type inference algorithm that will deal with dependent types. Happy summer reading!

Responses to particular comments on the Reddit thread

• @elucidatum: How radical of a change and how much of a challenge will it be to refactor existing codebases?

  No change is necessary. All code that currently compiles with -XTypeInType will compile with -XDependentTypes. (The only reason I have to set -XTypeInType as my baseline is because of the parsing annoyance around *, which must be imported to be used with -XTypeInType.) Any refactoring will be around how much you, as the Haskell author, wish to take advantage of dependent types.

• @jlimperg: Pervasive laziness in Haskell means that we like to use a lot of coinductive types. But this is really annoying for proof purposes because coinduction, despite the nice duality with induction, is a lot less pleasant to work with.

  Yes, this is true. My approach is, essentially, to pretend that types are inductive, not coinductive. One consequence of this decision is that proofs of type equality will have to be run. This means that including dependent types will slow down your running program. Sounds horrible, doesn’t it? It doesn’t have to, though.

  Suppose you have a function proof :: ... -> a :~: b. The function proof provides a proof that type a equals type b. If this function terminates at all, it will always produce Refl. Thus, if we knew that the function terminated, then we wouldn’t have to run it. We can’t know whether it terminates. But you, the programmer, can assert that it terminates, like this: {-# RULES "proof" proof ... = unsafeCoerce Refl #-} Now, GHC will replace any use of proof with Refl directly. Note that GHC still type-checks your proof. All this RULE does is assert termination.

  “But,” you say, “I don’t want to have to merely assert termination! If I wanted to assert correctness instead of prove it, I wouldn’t use dependent types.” My response: “Touché.” Haskell indeed is less powerful than those other dependently typed languages in this regard. Nevertheless, by using dependent types in Haskell, you still get a whole lot more compile-time guarantees than you get without dependent types. You just don’t get termination. You thus have a choice: “prove” termination at runtime by actually running your proofs, or assert it at compile time and keep your dependently typed program efficient, and still with lots of guarantees. Recall that we Haskellers have never proved termination of anything, ever, so not proving termination of a function named proof shouldn’t be all that alarming.

  Note: If RULES such as the one above become pervasive, perhaps a compiler flag can make them automatic, effectively (and concisely) assuming termination for all proofs in a module.

• @jlimperg: Proving is hard

  Yes, it is. Typechecker plugins may help here. It is easy enough, however, to implement dependent types without this advanced support. As we work through the consequences of dependent types in Haskell, I’m confident the community (including me) will come up with ways to make it easier.

• @jlimperg: As is well-known, a dependent type system is inconsistent (i.e. everything can be proven) unless all computations terminate, which is obviously not the case for general Haskell.

  Yes, this is true. Dependent types in Haskell will be inconsistent, when we view Haskell as a logic. Dependent types will still remain type-safe however. (This is because we run the proofs!) I just wish to point out here that @jlimperg suggests a syntactic check for termination: this, sadly, will not work. Haskell has too many ways for a computation to diverge, and a syntactic check can rule out only general recursion and partial pattern matches. Haskell also has infinite data types, non-strictly-positive datatypes, TypeRep (which can be abused to cause a loop), Type :: Type, and likely more back doors. I’d love to see a termination checker for Haskell, but I’m not holding my breath.

• @jlimperg: This point is very speculative, but I strongly dislike the current flavour of ‘almost-dependent’ type-level programming in Haskell.

  So do I. Singletons are an abomination. I hate them. These are gone with my design for dependent types, and I think the resulting language has the niceties we all want in a dependently typed language (modulo termination checking).

• @dogodel: I think it will take a while for the change to percolate into better design. … I think the most immediate benefit will be for (no surprise) expressive DSL, which are actually quite common in any modest codebase, but maybe not the “core” of the project.

  Agreed completely. It will take time for us to figure out the best way to use dependent types.

• @sinyesdo: The best summary I can offer is that “totality” is really really important for DT languages

  This is true for those other dependently typed languages, but not for Haskell. See my response to the first of @jlimperg’s points quoted here.

• @ccasin: The main reasons to care that your programming language is total are to make the type system consistent as a logic and to make type checking decidable. But we’ve already given up both these things in Haskell, and it’s possible to have dependent types without them.

  Agreed in full, and with @ccasin’s full post.

• @jmite: If you want fully Dependent-Type types, why not use Idris, Agda, Coq, or F*?

  I’m in broad agreement with the responses to this point on Reddit: basically, that none of these languages have Haskell’s ecosystem or optimizing compiler. See also Section 3.3 of my dissertation.

• @tactics: What does “fully dependent types” even mean for something like Haskell? You would have to rework the core language entirely.

  Yes, precisely. This is Chapter 5 of my dissertation.

Conclusion

I hope this information helps. Do keep an eye out for my finished dissertation sometime in the next few months. And, as always, this is all a work in progress and no one should take anything as set in stone. If there’s a design decision you disagree with, please speak up!

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