Make kernel parametric on the lowest universe and fix #9294

This could be Prop (for compat with usual Coq), Set (for HoTT),
 or actually an arbitrary "i".

Take lower bound of universes into account in pretyping/engine

Reinstate proper elaboration of SProp <= l constraints:

replacing is_small with equality with lbound is _not_ semantics preserving!

lbound = Set

Elaborate template polymorphic inductives with lower bound Prop

This will make more constraints explicit

Check univ constraints with Prop as lower bound for template inductives

Restrict template polymorphic universes to those not bounded from below

Fixes #9294

fix suggested by Matthieu

Try second fix suggested by Matthieu

Take care of modifying elaboration for record declarations as well.

Rebase and export functions for debug

Remove exported functions used while debugging

Add a new typing flag "check_template" and option "-no-template-checl"

This parameterizes the new criterion on template polymorphic inductives
to allow bypassing it (necessary for backward compatibility).

Update checker to the new typing flags structure

Switch on the new template_check flag to allow old unsafe behavior in
indTyping.

This is the only change of code really impacting the kernel, together
with the commit implementing unbounded from below and parameterization
by the lower bound on universes.

Add deprecated option `Unset Template Check` allowing to make proof
scripts work with both 8.9 and 8.10 for a while

Fix `Template Check` option name and test it

Add `Unset Template Check` to Coq89.v

Cooking of inductives and template-check tests

Cleanup test-suite file for template check / universes(template) flags

cookind tests

Move test of `Unset Template Check` to the failure/ dir, but comment it
for now

Template test-suite test explanation

Overlays for PR 9918

Overlay for paramcoq

Add overlay for fiat_parsers (-no-template-check)

Add overlay for fiat_crypto_legacy

Update fiat-crypto legacy overlay

Now it points at the version that I plan on merging; I am hoping that doing this will guard against mistakes by adding an extra check that the target tested by Coq's CI on this branch works with the change I made.

Remove overlay that should no longer be necessary

The setting in the compat file should handle it

Remove now-merged fiat-crypto-legacy overlay

Update `Print Assumptions` to reflect the typing flag for template checking

Fix About and Print Assumptions for template poly, giving info on which
variables are actually polymorphic

Fix pretty printing to print global universe levels properly

Fix printing of template polymorphic universes

Fix pretty printing for template polymorphism on no universe

Fix interaction of template check and universes(template) flag

Fix indTyping to really check if there is any point in polymorphism: the
conclusion sort should be parameterized over at least one local universe

Indtyping fixes for template polymorphic Props

Allow explicit template polymorphism again

Adapt to new indTyping interface

Handle the case of template-polymorphic on no universes
correctly (morally Type0m univ represented as Prop).

Fix check of meaningfullness of template polymorphism in the kernel.

It is now done w.r.t the min_univ, the minimal universe inferred for the
inductive/record type, independently of the user-written annotation
which must only be larger than min_univ. This preserves compatibility
with UniMath and template-polymorphism as it has been implemented up-to
now.

Comment on identity non-template-polymorphism

Remove incorrect universes(template) attributes from ssr

simpl_fun can be meaningfully template-poly, as well as
pred_key (although the use is debatable: it could just
as well be in Prop).

Move `fun_of_simpl` coercion declaration out of section to respect
uniform inheritance

Remove incorrect uses of #[universes(template)] from the stdlib

Extraction of micromega changes due to moving an ind decl out of a section

Remove incorrect uses of #[universes(template)] from plugins

Fix test-suite files, removing incorrect #[universes(template)] attributes

Remove incorrect #[universes(template)] attributes in test-suite

Fix test-suite

Remove overlays as they have been merged upstream.

6 files changed, 1 insertions, 9 deletions

diff --git a/plugins/setoid_ring/Field_theory.v b/plugins/setoid_ring/Field_theory.v
index b4300da4d5..3736bc47a5 100644
--- a/plugins/setoid_ring/Field_theory.v
+++ b/plugins/setoid_ring/Field_theory.v
@@ -730,7 +730,6 @@ Qed.
 
 (* The input: syntax of a field expression *)
 
-#[universes(template)]
 Inductive FExpr : Type :=
  | FEO : FExpr
  | FEI : FExpr
@@ -763,7 +762,6 @@ Strategy expand [FEeval].
 
 (* The result of the normalisation *)
 
-#[universes(template)]
 Record linear : Type := mk_linear {
    num : PExpr C;
    denum : PExpr C;
@@ -946,7 +944,6 @@ induction e2; intros p1 p2;
   now rewrite <- PEpow_mul_r.
 Qed.
 
-#[universes(template)]
 Record rsplit : Type := mk_rsplit {
    rsplit_left : PExpr C;
    rsplit_common : PExpr C;
diff --git a/plugins/setoid_ring/InitialRing.v b/plugins/setoid_ring/InitialRing.v
index b024f65988..a98a963207 100644
--- a/plugins/setoid_ring/InitialRing.v
+++ b/plugins/setoid_ring/InitialRing.v
@@ -740,7 +740,6 @@ Ltac abstract_ring_morphism set ext rspec :=
   | _ => fail 1 "bad ring structure"
   end.
 
-#[universes(template)]
 Record hypo : Type := mkhypo {
    hypo_type : Type;
    hypo_proof : hypo_type
diff --git a/plugins/setoid_ring/Ncring_polynom.v b/plugins/setoid_ring/Ncring_polynom.v
index 6a8c514a7b..048c8eecf9 100644
--- a/plugins/setoid_ring/Ncring_polynom.v
+++ b/plugins/setoid_ring/Ncring_polynom.v
@@ -32,7 +32,6 @@ Variable phiCR_comm: forall (c:C)(x:R), x * [c] == [c] * x.
    with coefficients in C :
  *)
 
-#[universes(template)]
  Inductive Pol : Type :=
   | Pc : C -> Pol
   | PX : Pol -> positive -> positive -> Pol -> Pol. 
diff --git a/plugins/setoid_ring/Ring_polynom.v b/plugins/setoid_ring/Ring_polynom.v
index 9d56084fd4..092114ff0b 100644
--- a/plugins/setoid_ring/Ring_polynom.v
+++ b/plugins/setoid_ring/Ring_polynom.v
@@ -121,7 +121,6 @@ Section MakeRingPol.
     - (Pinj i (Pc c)) is (Pc c)
  *)
 
- #[universes(template)]
  Inductive Pol : Type :=
   | Pc : C -> Pol
   | Pinj : positive -> Pol -> Pol
@@ -909,7 +908,6 @@ Section MakeRingPol.
 
  (** Definition of polynomial expressions *)
 
- #[universes(template)]
  Inductive PExpr : Type :=
   | PEO : PExpr
   | PEI : PExpr            
diff --git a/plugins/setoid_ring/Ring_theory.v b/plugins/setoid_ring/Ring_theory.v
index 8f24b281c6..dc45853458 100644
--- a/plugins/setoid_ring/Ring_theory.v
+++ b/plugins/setoid_ring/Ring_theory.v
@@ -540,7 +540,6 @@ Section AddRing.
  Variable (rO rI : R) (radd rmul rsub: R->R->R) (ropp : R -> R).
  Variable req : R -> R -> Prop. *)
 
-#[universes(template)]
 Inductive ring_kind : Type :=
 | Abstract
 | Computational
diff --git a/plugins/setoid_ring/newring.ml b/plugins/setoid_ring/newring.ml
index eb75fca0a1..b456d2eed2 100644
--- a/plugins/setoid_ring/newring.ml
+++ b/plugins/setoid_ring/newring.ml
@@ -151,7 +151,7 @@ let ic_unsafe c = (*FIXME remove *)
 let decl_constant na univs c =
   let open Constr in
   let vars = CVars.universes_of_constr c in
-  let univs = UState.restrict_universe_context univs vars in
+  let univs = UState.restrict_universe_context ~lbound:(Global.universes_lbound ()) univs vars in
   let () = Declare.declare_universe_context ~poly:false univs in
   let types = (Typeops.infer (Global.env ()) c).uj_type in
   let univs = Monomorphic_entry Univ.ContextSet.empty in