Home/ Questions/Q 6342959
In Process

The Archive Base Latest Questions

Editorial Team
  • 0
Asked: 2026-05-24T20:20:41+00:00

This is a bit esoteric, but maddening. In an answer to another question ,

  • 0

This is a bit esoteric, but maddening. In an answer to another question, I noted that in this entirely valid program

poo :: String -> a -> a
poo _ = id

qoo :: (a -> a) -> String
qoo _ = ""

roo :: String -> String
roo = qoo . poo

the type variable a is neither solved nor generalized in the process of checking roo. I’m wondering what happens in the translation to GHC’s core language, a Church-style variant of System F. Let me spell things out longhand, with explicit type lambdas /\ and type applications @.

poo :: forall a. [Char] -> a -> a
poo = /\ a -> \ s x -> id @ a

qoo :: forall a. (a -> a) -> [Char]
qoo = /\ a -> \ f -> [] @ Char

roo :: [Char] -> [Char]
roo = (.) @ [Char] @ (? -> ?) @ [Char] (qoo @ ?) (poo @ ?)

What on earth goes in the ? places? How does roo become a valid core term? Or do we really get a mysterious vacuous quantifier, despite what the type signature says?

roo :: forall a. [Char] -> [Char]
roo = /\ a -> ...

I’ve just checked that

roo :: forall . String -> String
roo = qoo . poo

goes through ok, which may or may not mean that the thing typechecks with no extra quantification.

What’s happening down there?

Share

Leave an answer

You must login to add an answer.

Need An Account,

1 Answer

  1. Editorial Team

    Here’s the core generated by GHC (after adding some NOINLINE pragmas).

    qoo_rbu :: forall a_abz. (a_abz -> a_abz) -> GHC.Base.String
[GblId, Arity=1, Caf=NoCafRefs]
qoo_rbu = \ (@ a_abN) _ -> GHC.Types.[] @ GHC.Types.Char

poo_rbs :: forall a_abA. GHC.Base.String -> a_abA -> a_abA
[GblId, Arity=1]
poo_rbs = \ (@ a_abP) _ -> GHC.Base.id @ a_abP

roo_rbw :: GHC.Base.String -> GHC.Base.String
[GblId]
roo_rbw =
  GHC.Base..
    @ (GHC.Prim.Any -> GHC.Prim.Any)
    @ GHC.Base.String
    @ GHC.Base.String
    (qoo_rbu @ GHC.Prim.Any)
    (poo_rbs @ GHC.Prim.Any)

    It seems GHC.Prim.Any is used for the polymorphic type.

    From the docs (emphasis mine):

    The type constructor Any is type to which you can unsafely coerce any
    lifted type, and back.

    • It is lifted, and hence represented by a pointer
    • It does not claim to
      be a data type, and that’s important for the code generator, because
      the code gen may enter a data value but never enters a function value.

    It’s also used to instantiate un-constrained type variables after type
    checking.

    It makes sense to have such a type to insert in place of un-constrained types, as otherwise trivial expressions like length [] would cause an ambiguous type error.

    • 0