Fix bug #5019 (looping zify on dependent types)

This fixes [bug #5019](https://coq.inria.fr/bugs/show_bug.cgi?id=5019),
"[zify] loops on dependent types"; before, we would see a `Z.of_nat (S
?k)` which could not be turned into `Z.succ (Z.of_nat k)`, add a
hypothesis of the shape `0 <= Z.of_nat (S k)`, turn that into a
hypothesis of the shape `0 <= Z.succ (Z.of_nat k)`, and loop forever on
this.

This may not be the "right" fix (there may be cases where `zify` should
succeed where it still fails with this change), but this is a pure
bugfix in the sense that the only places where it changes the behavior
of `zify` are the places where, previously, `zify` looped forever.

1 files changed, 6 insertions, 1 deletions

diff --git a/plugins/omega/PreOmega.v b/plugins/omega/PreOmega.v
index 5f5f548f8..6c0e2d776 100644
--- a/plugins/omega/PreOmega.v
+++ b/plugins/omega/PreOmega.v
@@ -174,12 +174,18 @@ Ltac zify_nat_op :=
      match isnat with
       | true => simpl (Z.of_nat (S a)) in H
       | _ => rewrite (Nat2Z.inj_succ a) in H
+      | _ => (* if the [rewrite] fails (most likely a dependent occurence of [Z.of_nat (S a)]),
+                hide [Z.of_nat (S a)] in this one hypothesis *)
+        change (Z.of_nat (S a)) with (Z_of_nat' (S a)) in H
      end
   | |- context [ Z.of_nat (S ?a) ] =>
      let isnat := isnatcst a in
      match isnat with
       | true => simpl (Z.of_nat (S a))
       | _ => rewrite (Nat2Z.inj_succ a)
+      | _ => (* if the [rewrite] fails (most likely a dependent occurence of [Z.of_nat (S a)]),
+                hide [Z.of_nat (S a)] in the goal *)
+        change (Z.of_nat (S a)) with (Z_of_nat' (S a))
      end
 
   (* atoms of type nat : we add a positivity condition (if not already there) *)
@@ -401,4 +407,3 @@ Ltac zify_N := repeat zify_N_rel; repeat zify_N_op; unfold Z_of_N' in *.
 (** The complete Z-ification tactic *)
 
 Ltac zify := repeat (zify_nat; zify_positive; zify_N); zify_op.
-