Thanks for the pointers! I don't quite know how to get to the form you recommend from the existing coercion, which is `Simple.NTCo:HasIf[0] <GHC.Types.Bool>_N`. (Note the `_N`.) I got that coercion in GHC 7.8.2 from the following code:

> class HasIf a where
>   ifThenElse :: Bool -> a -> a -> a
>
> instance HasIf Bool where
>   ifThenElse i t e = (i && t) || (not i && e)

With `--dump-tc`, I see

> TYPE SIGNATURES
> TYPE CONSTRUCTORS
>   HasIf :: * -> Constraint
>   class HasIf a
>     Roles: [nominal]
>     RecFlag NonRecursive
>     ifThenElse :: Bool -> a -> a -> a
> COERCION AXIOMS
>   axiom Main.NTCo:HasIf :: HasIf a = Bool -> a -> a -> a
> INSTANCES
>   instance HasIf Bool -- Defined at ../test/HasIf.hs:4:10

Do I need to convert the nominal coercion I got from GHC (`Simple.NTCo:HasIf[0] <GHC.Types.Bool>_N` in this case) to a representational one? If so, how?
My current formulation (tweaked to use `mkSubCo` and `mkAppCo`) is to apply `mkAppCo (mkSubCo (Refl Nominal ep))` to the given coercion, which then produces

> (LambdaCCC.Lambda.EP (Sym (Simple.NTCo:HasIf[0] <GHC.Types.Bool>_N)))_R

And still I get "Role incompatibility: expected nominal, got representational in `Sym (Simple.NTCo:HasIf[0] <GHC.Types.Bool>_N)`".

I also tried wrapping `mkSubCo` around the entire coercion (applying `mkSubCo . mkAppCo (Refl Nominal ep)`), and I see the same result:

> (LambdaCCC.Lambda.EP (Sym (Simple.NTCo:HasIf[0] <GHC.Types.Bool>_N)))_R

-- Conal


On Mon, Apr 14, 2014 at 4:39 AM, Richard Eisenberg <eir@cis.upenn.edu> wrote:
I agree with Simon, but just `Sub` the `<LambdaCCC.Lambda.EP>_N`, not the whole coercion.

There are actually two problems here. The one Simon identified, and also the fact that Simple.NTCo:HasIf[0] produces a representational coercion. How do I know? Because of the `NT` -- it's a newtype axiom and must produce representational coercions. Furthermore, unless the newtype definition is inferred to require a nominal parameter, the newtype would expect a representational coercion, not the nominal one you are passing. Check the dump (using -ddump-tc) of the newtype axiom to be sure.

Though putting a `Sub` on `<EP>` and changing the Refl constructor on `<Bool>` would work, you would then be violating an invariant of GHC's Coercion type: that we prefer `TyConAppCo tc ...` over `AppCo (Refl (TyConApp tc [])) ...`.

In sum, here is the coercion I think you want:

(LambdaCCC.Lambda.EP (Sym (Simple.NTCo:HasIf[0] <GHC.Types.Bool>_R)))_R

This is one of the problems with roles -- they are *very* fiddly within GHC, and it's hard for a non-expert in roles to get them right.

Have you seen docs/core-spec/core-spec.pdf? That is updated w.r.t. roles and may be of help.

Let me know if I can help further!
Richard

On Apr 14, 2014, at 5:45 AM, Simon Peyton Jones <simonpj@microsoft.com> wrote:

I think you need a ‘Sub’.
 
A cast  (e `cast` g) requires a representational coercion.  I think you have given it a (stronger) nominal one.  Sub gets from one to t’other.
 
Simon
 
From: Glasgow-haskell-users [mailto:glasgow-haskell-users-bounces@haskell.org] On Behalf Of Conal Elliott
Sent: 14 April 2014 06:00
To: ghc-devs@haskell.org; glasgow-haskell-users@haskell.org
Subject: Help with coercion & roles?
 

I’m working on a GHC plugin (as part of my Haskell-to-hardware work) and running into trouble with coercions & roles. Error message from Core Lint:

Warning: In the expression:

 
  LambdaCCC.Lambda.lamvP#
    @ (GHC.Types.Bool → GHC.Types.Bool → GHC.Types.Bool → GHC.Types.Bool)
    @ (Simple.HasIf GHC.Types.Bool)

    "tpl"#
    ((LambdaCCC.Lambda.varP#
        @ (GHC.Types.Bool → GHC.Types.Bool → GHC.Types.Bool → GHC.Types.Bool)
        "tpl"#)

     `cast` (<LambdaCCC.Lambda.EP>_N (Sym (Simple.NTCo:HasIf[0] <GHC.Types.Bool>_N))

             ∷ LambdaCCC.Lambda.EP
                  (GHC.Types.Bool

                   → GHC.Types.Bool → GHC.Types.Bool → GHC.Types.Bool)

                  ~#
                LambdaCCC.Lambda.EP (Simple.HasIf GHC.Types.Bool)))
 

Role incompatibility: expected nominal, got representational

in <LambdaCCC.Lambda.EP>_N (Sym (Simple.NTCo:HasIf[0] <GHC.Types.Bool>_N))

Do you see anything inconsistent/incompatible in the coercions or roles above? I constructed the nominal EP Refl coercion, and applied it (AppCo) an existing coercion of a simpler type.

Thanks,

-- Conal
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