I’m encoding a HOAS in Coq, but my coercions are not working well.

Here is a MWE:

From Coq Require Import ZArith String.

Variant tag := A | B.
Variant const := Unit | Int : Z -> const.

Inductive expr : tag -> Type :=
  | Const {tag} (c : const) : expr tag
  | Var {tag} (x : string) : expr tag
  | AB (e : expr A) : expr B.

Open Scope Z_scope.
Open Scope string_scope.

Declare Custom Entry syntax.
Notation "'<{' e '}>'" := e (e custom syntax at level 99).
Notation "x" := x (in custom syntax at level 0, x constr at level 0).

Notation "'()'" := (Const Unit) (in custom syntax at level 0).
Coercion Int : Z >-> const.
Coercion Const : const >-> expr.
Coercion Var : string >-> expr.

Notation "'!' e" := (AB e) (right associativity, in custom syntax at level 1).

Set Printing Coercions.
Check <{ !"x" }>.

which works quite well:

<{ ! (Var "x") }>
     : expr B

But my Const and Var coercions give warnings, e.g.,

Var does not respect the uniform inheritance condition.
[uniform-inheritance,coercions,default]

Var is now a coercion

I believe it is due to the tag input, but I’m not sure how to resolve this warning.

Thanks!