scopedSort and kind variable left-biasing

[Simon Peyton Jones]

See Note [Kind and type-variable binders] in RnTypes, and Note [Ordering of implicit variables].
And the data type FreeKiTyVars.

But NB: that in https://gitlab.haskell.org/ghc/ghc/merge_requests/361, I argue that with this patch we can sweep all this away.

If we did, we’d probably end up with [j,a,k,b].

Perhaps that’s an ergonomic reason for retaining the current rather cumbersome code.  (Maybe it could be simplified.)

Simon

From: ghc-devs <ghc-devs-bounces at haskell.org> On Behalf Of Ryan Scott
Sent: 14 February 2019 15:35
To: ghc-devs at haskell.org
Subject: scopedSort and kind variable left-biasing

Consider this function:

    f :: Proxy (a :: j) -> Proxy (b :: k)

If you just collect the free type variables of `f`'s type in left-to-right order, you'd be left with [a,j,b,k]. But the type of `f` is not `forall (a :: j) j (b :: k) k. Proxy a -> Proxy b`, as that would be ill scoped. `j` must come before `a`, since `j` appears in `a`'s kind, and similarly, `k` must come before `b`.

Fortunately, GHC is quite smart about sorting free variables such that they respect dependency order. If you ask GHCi what the type of `f` is (with -fprint-explicit-foralls enabled), it will tell you this:

    λ> :type +v f
    f :: forall j k (a :: j) (b :: k). Proxy a -> Proxy b

As expected, `j` appears before `a`, and `k` appears before `b`.

In a different context, I've been trying to implement a type variable sorting algorithm similar to the one that GHC is using. My previous understanding was that the entirely of this sorting algorithm was implemented in `Type.scopedSort`. To test my understanding, I decided to write a program using the GHC API which directly uses `scopedSort` on the example above:

    main :: IO ()
    main = do
      let tv :: String -> Int -> Type -> TyVar
          tv n uniq ty = mkTyVar (mkSystemName (mkUniqueGrimily uniq) (mkTyVarOcc n)) ty
          j = tv "j" 0 liftedTypeKind
          a = tv "a" 1 (TyVarTy j)
          k = tv "k" 2 liftedTypeKind
          b = tv "b" 3 (TyVarTy k)
          sorted = scopedSort [a, j, b, k]
      putStrLn $ showSDocUnsafe $ ppr sorted

To my surprise, however, running this program does /not/ give the answer [j,k,a,b], like what :type reported:

    λ> main
    [j_0, a_1, k_2, b_3]

Instead, it gives the answer [j,a,k,b]! Strictly speaking, this answer meets the specification of ScopedSort, since it respects dependency order and preserves the left-to-right ordering of variables that don't depend on each other (i.e., `j` appears to the left of `k`, and `a` appears to the left of `b`). But it's noticeably different that what :type reports. The order that :type reports, [j,k,a,b], appears to bias kind variables to the left such that all kind variables (`j` and `k`) appear before any type variables (`a` and `b`).

From what I can tell, scopedSort isn't the full story here. That is, something else appears to be left-biasing the kind variables. My question is: which part of GHC is doing this left-biasing?

Ryan S.
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