Remove hack skipping comparison of algebraic universes in subtyping.

When inferring [u <= v+k] I replaced the exception and instead add
[u <= v]. This is trivially sound and it doesn't seem possible to have
the one without the other (except specially for [Set <= v+k] which was
already handled).

I don't know an example where this used to fail and now succeeds (the
point was to remove an anomaly, but the example
~~~
Module Type SG. Definition DG := Type. End SG.
Module MG : SG. Definition DG := Type : Type. Fail End MG.
~~~
now fails with universe inconsistency.

Fix #7695 (soundness bug!).

7 files changed, 25 insertions, 166 deletions

diff --git a/checker/subtyping.ml b/checker/subtyping.ml
index f4ae02084..9e9e94deb 100644
--- a/checker/subtyping.ml
+++ b/checker/subtyping.ml
@@ -9,7 +9,6 @@
 (************************************************************************)
 
 (*i*)
-open CErrors
 open Util
 open Names
 open Cic
@@ -132,40 +131,7 @@ let check_inductive  env mp1 l info1 mib2 spec2 subst1 subst2=
     check (eq_constr) (fun x -> x.proj_type);
     true
   in
-  let check_inductive_type t1 t2 =
-
-    (* Due to template polymorphism, the conclusions of
-       t1 and t2, if in Type, are generated as the least upper bounds
-       of the types of the constructors.
-
-       By monotonicity of the infered l.u.b.  wrt subtyping (i.e.  if X:U
-       |- T(X):s and |- M:U' and U'<=U then infer_type(T(M))<=s), each
-       universe in the conclusion of t1 has an bounding universe in
-       the conclusion of t2, so that we don't need to check the
-       subtyping of the conclusions of t1 and t2.
-
-       Even if we'd like to recheck it, the inference of constraints
-       is not designed to deal with algebraic constraints of the form
-       max-univ(u1..un) <= max-univ(u'1..u'n), so that it is not easy
-       to recheck it (in short, we would need the actual graph of
-       constraints as input while type checking is currently designed
-       to output a set of constraints instead) *)
-
-    (* So we cheat and replace the subtyping problem on algebraic
-       constraints of the form max-univ(u1..un) <= max-univ(u'1..u'n)
-       (that we know are necessary true) by trivial constraints that
-       the constraint generator knows how to deal with *)
-
-    let (ctx1,s1) = dest_arity env t1 in
-    let (ctx2,s2) = dest_arity env t2 in
-    let s1,s2 =
-      match s1, s2 with
-      | Type _, Type _ -> (* shortcut here *) Prop Null, Prop Null
-      | (Prop _, Type _) | (Type _,Prop _) -> error ()
-      | _ -> (s1, s2) in
-    check_conv conv_leq env
-      (mkArity (ctx1,s1)) (mkArity (ctx2,s2))
-  in
+  let check_inductive_type t1 t2 = check_conv conv_leq env t1 t2 in
 
   let check_packet p1 p2 =
     let check eq f = if not (eq (f p1) (f p2)) then error () in
@@ -251,52 +217,7 @@ let check_inductive  env mp1 l info1 mib2 spec2 subst1 subst2=
 let check_constant env mp1 l info1 cb2 spec2 subst1 subst2 =
   let error () = error_not_match l spec2 in
   let check_conv f = check_conv_error error f in
-  let check_type env t1 t2 =
-
-    (* If the type of a constant is generated, it may mention
-       non-variable algebraic universes that the general conversion
-       algorithm is not ready to handle. Anyway, generated types of
-       constants are functions of the body of the constant. If the
-       bodies are the same in environments that are subtypes one of
-       the other, the types are subtypes too (i.e. if Gamma <= Gamma',
-       Gamma |- A |> T, Gamma |- A' |> T' and Gamma |- A=A' then T <= T').
-       Hence they don't have to be checked again *)
-
-    let t1,t2 =
-      if isArity t2 then
-        let (ctx2,s2) = destArity t2 in
-        match s2 with
-        | Type v when not (Univ.is_univ_variable v) ->
-          (* The type in the interface is inferred and is made of algebraic
-             universes *)
-          begin try
-            let (ctx1,s1) = dest_arity env t1 in
-            match s1 with
-            | Type u when not (Univ.is_univ_variable u) ->
-              (* Both types are inferred, no need to recheck them. We
-                 cheat and collapse the types to Prop *)
-                mkArity (ctx1,Prop Null), mkArity (ctx2,Prop Null)
-            | Prop _ ->
-              (* The type in the interface is inferred, it may be the case
-                 that the type in the implementation is smaller because
-                 the body is more reduced. We safely collapse the upper
-                 type to Prop *)
-                mkArity (ctx1,Prop Null), mkArity (ctx2,Prop Null)
-            | Type _ ->
-              (* The type in the interface is inferred and the type in the
-                 implementation is not inferred or is inferred but from a
-                 more reduced body so that it is just a variable. Since
-                 constraints of the form "univ <= max(...)" are not
-                 expressible in the system of algebraic universes: we fail
-                 (the user has to use an explicit type in the interface *)
-                error ()
-          with UserError _ (* "not an arity" *) ->
-            error () end
-        | _ -> t1,t2
-      else
-        (t1,t2) in
-    check_conv conv_leq env t1 t2
-  in
+  let check_type env t1 t2 = check_conv conv_leq env t1 t2 in
     match info1 with
       | Constant cb1 ->
 	let cb1 = subst_const_body subst1 cb1 in
diff --git a/kernel/modops.ml b/kernel/modops.ml
index 22f523a9a..02bab581a 100644
--- a/kernel/modops.ml
+++ b/kernel/modops.ml
@@ -47,7 +47,6 @@ type signature_mismatch_error =
   | RecordFieldExpected of bool
   | RecordProjectionsExpected of Name.t list
   | NotEqualInductiveAliases
-  | NoTypeConstraintExpected
   | IncompatibleInstances
   | IncompatibleUniverses of Univ.univ_inconsistency
   | IncompatiblePolymorphism of env * types * types
diff --git a/kernel/modops.mli b/kernel/modops.mli
index ac76d28cf..8e7e618fc 100644
--- a/kernel/modops.mli
+++ b/kernel/modops.mli
@@ -106,7 +106,6 @@ type signature_mismatch_error =
   | RecordFieldExpected of bool
   | RecordProjectionsExpected of Name.t list
   | NotEqualInductiveAliases
-  | NoTypeConstraintExpected
   | IncompatibleInstances
   | IncompatibleUniverses of Univ.univ_inconsistency
   | IncompatiblePolymorphism of env * types * types
diff --git a/kernel/subtyping.ml b/kernel/subtyping.ml
index 8cf588c3e..2e9a33a91 100644
--- a/kernel/subtyping.ml
+++ b/kernel/subtyping.ml
@@ -17,7 +17,6 @@
 open Names
 open Univ
 open Util
-open Term
 open Constr
 open Declarations
 open Declareops
@@ -138,39 +137,8 @@ let check_inductive cst env mp1 l info1 mp2 mib2 spec2 subst1 subst2 reso1 reso2
   in
   let mib2 =  Declareops.subst_mind_body subst2 mib2 in
   let check_inductive_type cst name t1 t2 =
-
-    (* Due to template polymorphism, the conclusions of
-       t1 and t2, if in Type, are generated as the least upper bounds
-       of the types of the constructors.
-
-       By monotonicity of the infered l.u.b.  wrt subtyping (i.e.  if X:U
-       |- T(X):s and |- M:U' and U'<=U then infer_type(T(M))<=s), each
-       universe in the conclusion of t1 has an bounding universe in
-       the conclusion of t2, so that we don't need to check the
-       subtyping of the conclusions of t1 and t2.
-
-       Even if we'd like to recheck it, the inference of constraints
-       is not designed to deal with algebraic constraints of the form
-       max-univ(u1..un) <= max-univ(u'1..u'n), so that it is not easy
-       to recheck it (in short, we would need the actual graph of
-       constraints as input while type checking is currently designed
-       to output a set of constraints instead) *)
-
-    (* So we cheat and replace the subtyping problem on algebraic
-       constraints of the form max-univ(u1..un) <= max-univ(u'1..u'n)
-       (that we know are necessary true) by trivial constraints that
-       the constraint generator knows how to deal with *)
-
-    let (ctx1,s1) = dest_arity env t1 in
-    let (ctx2,s2) = dest_arity env t2 in
-    let s1,s2 =
-      match s1, s2 with
-      | Type _, Type _ -> (* shortcut here *) Sorts.prop, Sorts.prop
-      | (Prop _, Type _) | (Type _,Prop _) ->
-	error (NotConvertibleInductiveField name)
-      | _ -> (s1, s2) in
     check_conv (NotConvertibleInductiveField name)
-      cst (inductive_is_polymorphic mib1) infer_conv_leq env (mkArity (ctx1,s1)) (mkArity (ctx2,s2))
+      cst (inductive_is_polymorphic mib1) infer_conv_leq env t1 t2
   in
 
   let check_packet cst p1 p2 =
@@ -259,53 +227,8 @@ let check_constant cst env mp1 l info1 cb2 spec2 subst1 subst2 =
   let error why = error_signature_mismatch l spec2 why in
   let check_conv cst poly f = check_conv_error error cst poly f in
   let check_type poly cst env t1 t2 =
-
     let err = NotConvertibleTypeField (env, t1, t2) in
-
-    (* If the type of a constant is generated, it may mention
-       non-variable algebraic universes that the general conversion
-       algorithm is not ready to handle. Anyway, generated types of
-       constants are functions of the body of the constant. If the
-       bodies are the same in environments that are subtypes one of
-       the other, the types are subtypes too (i.e. if Gamma <= Gamma',
-       Gamma |- A |> T, Gamma |- A' |> T' and Gamma |- A=A' then T <= T').
-       Hence they don't have to be checked again *)
-
-    let t1,t2 =
-      if isArity t2 then
-        let (ctx2,s2) = destArity t2 in
-        match s2 with
-        | Type v when not (is_univ_variable v) ->
-          (* The type in the interface is inferred and is made of algebraic
-             universes *)
-          begin try
-            let (ctx1,s1) = dest_arity env t1 in
-            match s1 with
-            | Type u when not (is_univ_variable u) ->
-              (* Both types are inferred, no need to recheck them. We
-                 cheat and collapse the types to Prop *)
-                mkArity (ctx1,Sorts.prop), mkArity (ctx2,Sorts.prop)
-            | Prop _ ->
-              (* The type in the interface is inferred, it may be the case
-                 that the type in the implementation is smaller because
-                 the body is more reduced. We safely collapse the upper
-                 type to Prop *)
-                mkArity (ctx1,Sorts.prop), mkArity (ctx2,Sorts.prop)
-            | Type _ ->
-              (* The type in the interface is inferred and the type in the
-                 implementation is not inferred or is inferred but from a
-                 more reduced body so that it is just a variable. Since
-                 constraints of the form "univ <= max(...)" are not
-                 expressible in the system of algebraic universes: we fail
-                 (the user has to use an explicit type in the interface *)
-                error NoTypeConstraintExpected
-          with NotArity ->
-            error err end
-        | _ ->
-	  t1,t2
-      else
-        (t1,t2) in
-      check_conv err cst poly infer_conv_leq env t1 t2
+    check_conv err cst poly infer_conv_leq env t1 t2
   in
   match info1 with
     | Constant cb1 ->
diff --git a/kernel/univ.ml b/kernel/univ.ml
index 2b4a1c50c..311477dac 100644
--- a/kernel/univ.ml
+++ b/kernel/univ.ml
@@ -666,7 +666,7 @@ let constraint_add_leq v u c =
       else (* j >= 1 *) (* m = n + k, u <= v+k *)
 	if Level.equal x y then c (* u <= u+k, trivial *)
 	else if Level.is_small x then c (* Prop,Set <= u+S k, trivial *)
-	else anomaly (Pp.str"Unable to handle arbitrary u <= v+k constraints.")
+        else Constraint.add (x,Le,y) c (* u <= v implies u <= v+k *)
 	  
 let check_univ_leq_one u v = Universe.exists (Expr.leq u) v
 
diff --git a/test-suite/bugs/closed/7695.v b/test-suite/bugs/closed/7695.v
new file mode 100644
index 000000000..42bdb076b
--- /dev/null
+++ b/test-suite/bugs/closed/7695.v
@@ -0,0 +1,20 @@
+Require Import Hurkens.
+
+Universes i j k.
+Module Type T.
+  Parameter T1 : Type@{i+1}.
+  Parameter e : Type@{j} = T1 : Type@{k}.
+End T.
+
+Module M.
+  Definition T1 := Type@{j}.
+  Definition e : Type@{j} = T1 : Type@{k} := eq_refl.
+End M.
+
+Module F (A:T).
+  Definition bad := TypeNeqSmallType.paradox _ A.e.
+End F.
+
+Set Printing Universes.
+Fail Module X := F M.
+(* Universe inconsistency. Cannot enforce j <= i because i < Coq.Logic.Hurkens.105 = j. *)
diff --git a/vernac/himsg.ml b/vernac/himsg.ml
index 5d671ef52..534e58f9c 100644
--- a/vernac/himsg.ml
+++ b/vernac/himsg.ml
@@ -871,9 +871,6 @@ let explain_not_match_error = function
     pr_enum (function Name id -> Id.print id | _ -> str "_") nal
   | NotEqualInductiveAliases ->
     str "Aliases to inductive types do not match"
-  | NoTypeConstraintExpected ->
-    strbrk "a definition whose type is constrained can only be subtype " ++
-    strbrk "of a definition whose type is itself constrained"
   | CumulativeStatusExpected b ->
     let status b = if b then str"cumulative" else str"non-cumulative" in
       str "a " ++ status b ++ str" declaration was expected, but a " ++