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Set Primitive Projections.
Record R A := mk { p : A -> A -> A }.
Arguments mk {_} _.
Arguments p {_} _ !_ !_.
(* using nat *)
Goal forall x, p (mk (fun _ _ => 2)) x x = 0.
Proof.
Fail progress cbn.
Abort.
Goal forall x, p (mk (fun _ _ => 2)) 3 x = 0.
Proof.
Fail progress cbn.
Abort.
Goal p (mk (fun _ _ => 2)) 3 4 = 0.
Proof.
progress cbn.
Abort.
Arguments p {_} _ !_ _.
Goal forall x, p (mk (fun _ _ => 2)) x x = 0.
Proof.
Fail progress cbn.
Abort.
Goal forall x, p (mk (fun _ _ => 2)) 3 x = 0.
Proof.
progress cbn.
Abort.
Goal forall x, p (mk (fun _ _ => 2)) x 4 = 0.
Proof.
Fail progress cbn.
Abort.
Goal p (mk (fun _ _ => 2)) 3 4 = 0.
Proof.
progress cbn.
Abort.
(* using prim int *)
Require Import PrimInt63.
Open Scope int63_scope.
Arguments p {_} _ !_ !_.
Goal forall x, p (mk (fun _ _ => 2)) x x = 0.
Proof.
intros x. Check x : int. (* sanity check that the scope is correct *)
Fail progress cbn.
Abort.
Goal forall x, p (mk (fun _ _ => 2)) 3 x = 0.
Proof.
Fail progress cbn.
Abort.
Goal p (mk (fun _ _ => 2)) 3 4 = 0.
Proof.
progress cbn.
Abort.
Arguments p {_} _ !_ _.
Goal forall x, p (mk (fun _ _ => 2)) x x = 0.
Proof.
Fail progress cbn.
Abort.
Goal forall x, p (mk (fun _ _ => 2)) 3 x = 0.
Proof.
progress cbn.
Abort.
Goal forall x, p (mk (fun _ _ => 2)) x 4 = 0.
Proof.
Fail progress cbn.
Abort.
Goal p (mk (fun _ _ => 2)) 3 4 = 0.
Proof.
progress cbn.
Abort.
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