singletons-2.6 has been uploaded to Hackage, coming on the heels of GHC 8.8.1’s release. There are many interesting things to say about this particular version of singletons, and I invite you to check out the changelog if you want a quick overview.

What the changelog doesn’t contain is a story about how the singletons library nearly perished due to changes introduced in GHC 8.8. No, it wasn’t because GHC 8.8 introduced dependent types and made singletons obsolete. (Maybe some day…) Instead, GHC 8.8 nearly made it impossible to compile singletons at all! This is because GHC subtly changed the way it performs kind inference, and as a result, the code that singletons generates with Template Haskell broke in spectacular fashion, as it was not designed with this kind inference behavior in mind.

Fear not: the fact that singletons-2.6 was released means that the developers of singletons eventually found a solution to this problem. It took the developers (myself included) a surprising amount of time to figure out what the solution was, however! I think there is an interesting lesson to be learned from all this, so I wrote this post in the hopes of teaching such a lesson. This post is partly an amusing anecdote about living on the bleeding edge of software development, and partly a cautionary tale about how seemingly unnoticeable changes in a compiler can have unintended consequences.

The skinny on singletons

singletons is a library for emulating dependent types in GHC. Whether it is a convincing emulation of dependent types is somewhat up to personal interpretation, but regardless, I find it extremely useful for experimenting with dependently typed Haskell ideas. If you aren’t familiar with singletons, this series of blog posts is a great introduction that assumes no prior knowledge of dependent types. If you like reading papers, you may find this 2012 Haskell Symposium paper about singletons by Richard Eisenberg and Stephanie Weirich to be of interest.

One of singletons’ most impressive feats is Template Haskell functionality that takes function definitions as input and produces two things as output:

  • Type-level versions of the same functions (i.e., promoted functions)
  • “Dependently typed” versions of the same functions (i.e., singled functions)

For example, if you write the following code:

$(singletons [d|
  not :: Bool -> Bool
  not False = True
  not True  = False

Then singletons will automatically generate the following code as output:

type family Not (x :: Bool) :: Bool where
  Not False = True
  Not True  = False

sNot :: Sing x -> Sing (Not x)
sNot SFalse = STrue
sNot STrue  = SFalse

Now you have access to the promoted function Not, a type-level version of not, as well as the singled function sNot, which allows you to write dependently typed code that makes use of Not. I’m omitting quite a few details here, but that is the high-level view of how singletons’ Template Haskell machinery works.

One other important thing to know about singletons can require a lot of language extensions to use. So many language extensions, in fact, that the singletons README even includes an entire section about it. In this blog post, we are most concerned with the PolyKinds extension, as that is where things went awry in GHC 8.8.

The GHC commit that almost ruined everything

Let’s go back in time to August 2018. GHC 8.6.1 is on the cusp of being released, as a consequence, work on GHC 8.8 has just begun. Richard Eisenberg, the principal author of the singletons library, also happens to be a pretty big deal in the GHC developer community. Richard decided that August 21 was the day he would push through a commit named Remove decideKindGeneralisationPlan so that it could be included in a future 8.8 release.

On the surface, this commit seemed innocent enough. In fact, Richard even left a bold comment in the commit message (emphasis mine):

This commit fixes #15141. As it’s an internal refactor, there is no concrete test case for it.

Unfortunately, nothing could have been further from the truth. Although poor Richard didn’t intend to do so, he unwittingly opened a can of worms, as this commit ground singletons to a complete halt.

When internal refactors go wrong

Fortunately, I noticed that something was afoot very quickly, thanks to the amazing infrastructure the head.hackage repo offers for testing libraries against GHC HEAD. All of a sudden, the GHC HEAD configuration of singletons’ CI setup began to fail with this mysterious error:

    • Could not deduce (SSemigroup k) arising from a use of ‘%<>’
      from the context: SSemigroup a0
        bound by the class declaration for ‘SSemigroup’

Despite this rather strange-looking regression, I wasn’t worried yet. After all, it’s not unprecedented for libraries to stop compiling all of a sudden with GHC HEAD. This is simply because HEAD is a rapidly moving target, and on occasion a commit lands which introduces bugs. Under the assumption that this was a GHC bug, I went ahead and filed an issue.

To my surprise, however, Richard commented that he didn’t believe this to be a bug at all. Instead, he claimed that GHC was behaving correctly in this situation and that the code that singletons was generating actually should be rejected. Richard knows his stuff, so I reluctantly agreed with his assessment of the situation. Unfortunately, this meant that I would have to figure out how to patch singletons—which, if you can believe it, is sometimes more difficult than patching GHC itself. In any case, this definitely seemed like something that was possible to debug in an afternoon or two.

The Could not deduce (SSemigroup k) error message above was caused by singletons attempting to generate a singled version of the Semigroup type class, so I tried commenting it out in an attempt to get some subset of the library to compile on HEAD. What I could not have anticipated is how deep the rabbit hole went. Several other parts of singletons (which were not connected to Semigroup in any way) also mysteriously failed to typecheck for unknown reasons, and I only managed to get singletons to compile by commenting out a significant chunk of the library.

One thing had become clear: working around this issue would be no small feat.

To generalize or not to generalize

Up to this point, I’ve been rather vague about what exactly the underlying issue with singletons + GHC 8.8 was. Unfortunately, I’m going to continue to be vague for a little while yet. The reason is because diving right into the technical details of the bug would require some familiarity with the MonoLocalBinds language extension, which is not one of the more well known ones. I’ll take some time here to give a brief overview of MonoLocalBinds before going back to the main topic.


MonoLocalBinds is a very widely used language extension. This is not because people directly enable MonoLocalBinds in their code, but because enabling the use of GADTs or TypeFamilies implies MonoLocalBinds automatically. What does this MonoLocalBinds thing do? To explain this, consider the following code:

data R a where
  RBool :: R Bool

f :: a -> R a -> Bool
f x y = let g z = not x
        in case y of
             RBool -> g ()

Should f typecheck? One possible way to answer this question is: no, f should be rejected by the typechecker. Since not :: Bool -> Bool, calling not x would be tantamount to unifying the types a and Bool, which would be a type error.

Perhaps surprisingly, there is actually a way to typecheck f. One can infer the following type for g:

g :: forall b. (a ~ Bool) => b -> Bool

This type signature abstracts over the requirement that a be equal to Bool. Moreover, since g is a locally defined function, one only needs to provide evidence that a equals Bool at call sites for g, and nowhere else. The only call site for g is underneath an RBool pattern match, where we know precisely that a ~ Bool, so everything typechecks.

Although this works out, the resulting types are rather strange. The inferred type signature for g mentions a in an equality constraint, despite the fact that g is not polymorphic in a. If you find this a bit unsettling, you’re not alone. The paper Let Should not be Generalised argues that these sorts of types should not be inferred for local definitions. The authors claim that not only is this unintuitive from a programmer’s perspective, but this behavior can also be less efficient in advanced type inference engines like the one that GHC uses.

Let Should not be Generalised proposes that when inferring the type of a locally defined function, one should not abstract over constraints such as a ~ Bool. That is to say, locally defined types should not be generalized over [1]. The MonoLocalBinds extension is what controls this behavior in GHC; if enabled, the types of locally defined things are not generalized. Because GADTs-heavy and TypeFamilies-heavy code often make use of such constraints, both of these language extensions imply MonoLocalBinds.

Despite the name of the paper, MonoLocalBinds affects more than just let-bindings. Other “local” constructs in Haskell, such as where-clauses and case alternatives are also affected by MonoLocalBinds.

The kind generalization wrinkle

The PolyKinds extension adds another dimension to type signature generalization. To explain what I mean by this, let’s first define some helper types:

data Proxy (a :: k) = Proxy
type family Any :: k

Proxy is a simple data type that is isomorphic to (), but with an additional phantom type parameter with a polymorphic kind. Proxy does have some legitimate uses cases, but it is also valuable for being one of the simplest poly-kinded data types, which makes it extremely convenient for explaining the inner workings of PolyKinds. Any is a minimalist type family whose primary utility is being able to inhabit any kind. You can use Any :: Type, Any :: Bool, Any :: Maybe (Bool -> Type), etc., and those are all just dandy.

Now consider the following definition:

h :: Proxy Any
h = Proxy

What is the kind of Any in Proxy Any? Since Any is kind-polymorphic, it could be any kind under the sun. In this circumstance, GHC will choose to generalize over this kind, which makes h :: forall k. Proxy (Any :: k).

It is not guaranteed that GHC will always choose to kind-generalize, however. Take a look at this (somewhat contrived) example:

proxyAnyType :: Proxy (Any :: Type)
proxyAnyType = Proxy

foo :: forall x. x -> ()
foo x =
  let bar :: x -> Proxy Any
      bar _ = proxyAnyType
  in case bar x of Proxy -> ()

In particular, pay attention to the locally defined function bar. What is the full type of bar? It once again uses Proxy Any, so there is a choice to be made about what the kind of Any should be. Should the kind of Any be generalized here?

In this situation, GHC chooses not to generalize over the kind of Any. This is because (1) MonoLocalBinds is in effect (note that Any is a type family, and TypeFamilies implies MonoLocalBinds), and (2) bar is a locally defined function that falls under the purview of MonoLocalBinds. The net result is that kind generalization is switched off when inferring the type of bar, so GHC defaults the kind of Any to Type. In other words, the full inferred type of bar is forall x. x -> Proxy (Any :: Type).

GHC 8.8 just had to be difficult

I lied slightly in the previous paragraph. When I said “GHC chooses not to generalize over the kind of Any”, I really meant to say “up until GHC 8.6”. GHC 8.8, as it turns out, deviates from this convention slightly. If you try typechecking bar on GHC 8.8, you’ll actually get a type error!

    • Couldn't match type ‘k’ with ‘Type’
      ‘k’ is a rigid type variable bound by
        the type signature for:
          bar :: forall k. x -> Proxy Any

Eek! What on earth just happened?

The short answer is that generalization affects constraints and kinds in orthogonal ways, and one can perform kind generalization without needing to perform constraint generalization. In fact, this is exactly what GHC 8.8 does with MonoLocalBinds, while previous GHCs would avoid both forms of generalization for local things.

The long answer (or rather, the slightly less short answer) is that GHC 8.8 decided to more carefully examine which places MonoLocalBinds applied to. The examples in the Let Should not be Generalised paper that pose trouble for GHC’s type inference do not have direct equivalents at the kind level [2]. Therefore, Richard decided that having MonoLocalBinds disable kind generalization for locally defined things was needlessly conservative, so he opted to just always generalize in kinds.

As the example above proves, this isn’t a strictly backwards-compatible change, since there will now be programs that are rejected for being too kind polymorphic. If bar’s type is generalized to forall k. x -> Proxy (Any :: k), then using proxyAnyType to implement bar is no longer possible, since GHC cannot unify Type with k. In this small example, it’s quite possible to repair the damage, perhaps by explicitly writing bar :: x -> Proxy (Any :: Type).

Now back to your scheduled programming

Phew, that was quite a detour. Now that I’ve gone over the fundamentals of kind generalization and MonoLocalBinds, I can finally talk about the actual problem with singletons! Here is a stripped-down version of a piece of code from singletons that no longer typechecked on GHC 8.8:

$(singletons [d|
  class Foo a where
    bar :: a -> (a -> b) -> b
    baz :: a

  quux :: Foo a => a -> a
  quux x = x `bar` \_ -> baz

The error lies in the code that this generates with Template Haskell. I will reproduce the code below, but for the sake of your sanity, I would advise you not to read the actual code too closely, since it is needlessly convoluted, machine-generated goop. This sort of code is primarily meant for GHC’s eyes, not human eyes!

type family Case x arg where
  Case x arg = Baz

sQuux :: forall a (x :: a). SFoo a => Sing x -> Sing (Quux x :: a)
sQuux (sX :: Sing x)
  = sBar sX
      ((singFun1 @(LambdaSym1 x))
         (\ sArg
            -> case sArg of {
                 (_ :: Sing arg)
                   -> (case sArg of { _ -> sBaz }) ::
                        Sing (Case x arg) }))

This isn’t even the complete code (click here if you want the full, gory details), but fear not—you don’t need to see it all to understand the main point. This code will typecheck on GHC 8.6.5, but not with GHC 8.8.1, where it will fail with the following error:

    • Could not deduce (SFoo k) arising from a use of ‘sBaz’
    • In the expression: sBaz
      In a case alternative: _ -> sBaz
      In the expression:
          (case sArg of { _ -> sBaz }) :: Sing (Case x arg)

As it turns out, this all goes back to MonoLocalBinds. A case branch—such as the ... in case sArg of { (_ :: Sing arg) -> ... }— is considered “local” for the purposes of MonoLocalBinds. Moreover, Case is a poly-kinded type family definition. Since the :: Sing (Case x arg) kind annotation appears in a case branch, MonoLocalBinds kicks in on GHC 8.6.5 and prevents the return kind of Case x arg from being generalized over. As a consequence, the return kind of Case x arg is defaulted to a, and since there is an SFoo a constraint in scope, all is well.

On GHC 8.8, however, MonoLocalBinds is less constrictive, which means that the return kind of Case x arg is generalized over. This means that while the user wrote :: Sing (Case x arg), it is generalized to :: forall k. Sing (Case x arg :: k) during kind inference. Crucially, there is no SFoo k constraint in scope, which leads to the tumultuous error message witnessed above.

If it’s broke, why not just fix it?

At this point, you might be wondering what all the hullabaloo is about. Yes, GHC 8.8 infers more general kinds than it did in previous releases, but surely that’s not the end of the world? After all, you could make this program typecheck by simply adding an extra :: a kind annotation:

sQuux (sX :: Sing x)
  = sBar sX
      (({ ... :: Sing (Case x arg :: a) }))

Unfortunately, this is not as simple as it may seem. Recall that this code was generated automatically by Template Haskell, which means that in order to correctly insert this sort of kind annotation in the places that require it, the singletons library would need a way to systematically identify all such places. In general, this problem is tantamount to performing type inference, and trying to emulate type inference in Template Haskell is quite difficult.

As a general rule, we try to keep the Template Haskell code in singletons dumb but predictable. Trying to cram some ad hoc form of type inference into the Template Haskell machinery would fall afoul of this principle, in my opinion, so I avoided pursuing this line of thought. Some other ideas that I did ponder, but ultimately rejected, include:

Use fewer kind annotations

The original problem arose because of the use of an explicit :: Sing (Case x arg) kind annotation. Would the problem be fixed if we just avoiding generating that annotation entirely? Alas, the answer is “no”, because there are other programs which require them in order to typecheck. (See here for one example.)

Tell MonoLocalBinds to get bent

Since the problem appears to involve MonoLocalBinds, what happens if we explicitly disable it with NoMonoLocalBinds? Unfortunately, that doesn’t have any effect. GHC 8.8 will generalize the kinds of local things with or without the presence of MonoLocalBinds, so we’re pretty much stuck with it…

Use visible type applications

…or are we stuck with it? I was getting pretty desperate until Richard pointed out to me an obscure piece of GHC trivia. There is, in fact, one place where local kind generalization does not happen: within the @(...) part of a visible type application. Here is an example to better illustrate this trivium:

{-# LANGUAGE TypeApplications #-}

idProxy :: Proxy (Any :: Type)
idProxy = id @(Proxy Any) proxyAnyType

You might worry that the @(Proxy Any) part of this program would kind-generalize to @(forall k. Proxy (Any :: k)), leading to kind mismatches like the ones observed earlier. Luckily, this won’t happen, since the arguments of visible type applications are simply not kind-generalized! As a result, the kind of Any in @(Proxy Any) simply defaults to Type, and all is well.

This trick ends up being a convenient escape hatch from the clutches of kind generalization. Recall that our woes started because of singletons’ use of explicit kind annotations of the form ... :: Sing (Case x arg). Instead of using kind annotations, which always trigger kind generalization in GHC 8.8, we can instead use id @(Sing (Case x arg)) ...:

sQuux (sX :: Sing x)
  = sBar sX
      (({ id @(Sing (Case x arg)) ... }))

Now we get the benefits of having the extra Sing (Case x arg) kind information, with none of the drawbacks of kind generalization! Now the kind of Case x arg defaults to a, and the typechecker continues humming along happily. Yay!

Fixing up singletons

Using the lessons that I learned during this ordeal, I committed a patch to singletons that restored its ability to build on GHC 8.8. The main trick was taking the bit of Template Haskell code that generates explicit kind annotations in case branches and rewriting it to produce equivalent id @(...) code instead.

Besides the problematic case branches, there were also a handful of other local definitions whose kinds generalized too much, such as in the following example:

replicateM_ :: (Applicative m) => Nat -> m a -> m ()
replicateM_ cnt0 f =
    loop cnt0
    loop cnt
        | cnt <= 0  = pure ()
        | otherwise = f *> loop (cnt - 1)

The singled version of the loop function kind generalizes more in GHC 8.8 than it did in previous releases, resulting in error messages mentioning SNum k1. Luckily, in this situation there is a very simple, non-invasive way to fix it up: just add a type signature.

-replicateM_       :: (Applicative m) => Nat -> m a -> m ()
+replicateM_       :: forall m a. (Applicative m) => Nat -> m a -> m ()
 replicateM_ cnt0 f =
     loop cnt0
+    loop :: Nat -> m ()
     loop cnt
         | cnt <= 0  = pure ()
         | otherwise = f *> loop (cnt - 1)

This works well enough that I decided not to pursue further hackery to try and allow the original program without the type signature. I conjecture that this won’t be that big of a deal in practice, since I only discovered three functions in all of singletons (including replicateM_) that needed extra typing information of this sort to compile.


In the end, we were able to save singletons from imploding, thanks in no small part to Richard’s clever ideas. (Seriously, how does he think of this stuff?) If there’s one lesson to be learned from all this, it’s that small changes to the way type inference works can sometimes have big impacts. Or, to put it another way, make sure that your “internal refactors” don’t leak to the outside world.

If you can believe it, the id @(...) trick wasn’t the only crazy hack I had to use in order to make the most recent singletons release happen. I think I’ll save discussion of these other hacks for future blog posts.

  1. Yes, I’m aware of the fact that I’m using both the American and British English spellings of generalization/generalisation in this post. I’m too stubborn to use one spelling consistently. 

  2. This is my attempt at paraphrasing the commit message in this commit, which implemented the kind generalization change in GHC 8.8. Any misrepresentations are mine.