From 9043add656177eeac1491a73d2f3ab92bec0013c Mon Sep 17 00:00:00 2001
From: Benjamin Barenblat <bbaren@debian.org>
Date: Sat, 29 Dec 2018 14:31:27 -0500
Subject: Imported Upstream version 8.8.2

---
 test-suite/output/UnivBinders.v | 154 ++++++++++++++++++++++++++++++++++++++++
 1 file changed, 154 insertions(+)
 create mode 100644 test-suite/output/UnivBinders.v

(limited to 'test-suite/output/UnivBinders.v')

diff --git a/test-suite/output/UnivBinders.v b/test-suite/output/UnivBinders.v
new file mode 100644
index 00000000..f806a9f4
--- /dev/null
+++ b/test-suite/output/UnivBinders.v
@@ -0,0 +1,154 @@
+Set Universe Polymorphism.
+Set Printing Universes.
+(* Unset Strict Universe Declaration. *)
+
+(* universe binders on inductive types and record projections *)
+Inductive Empty@{u} : Type@{u} := .
+Print Empty.
+
+Set Primitive Projections.
+Record PWrap@{u} (A:Type@{u}) := pwrap { punwrap : A }.
+Print PWrap.
+Print punwrap.
+
+Unset Primitive Projections.
+Record RWrap@{u} (A:Type@{u}) := rwrap { runwrap : A }.
+Print RWrap.
+Print runwrap.
+
+(* universe binders also go on the constants for operational typeclasses. *)
+Class Wrap@{u} (A:Type@{u}) := wrap : A.
+Print Wrap.
+Print wrap.
+
+(* Instance in lemma mode used to ignore the binders. *)
+Instance bar@{u} : Wrap@{u} Set. Proof. exact nat. Qed.
+Print bar.
+
+Unset Strict Universe Declaration.
+(* The universes in the binder come first, then the extra universes in
+   order of appearance. *)
+Definition foo@{u +} := Type -> Type@{v} -> Type@{u}.
+Print foo.
+
+Check Type@{i} -> Type@{j}.
+
+Eval cbv in Type@{i} -> Type@{j}.
+
+Set Strict Universe Declaration.
+
+(* Binders even work with monomorphic definitions! *)
+Monomorphic Definition mono@{u} := Type@{u}.
+Print mono.
+Check mono.
+Check Type@{mono.u}.
+
+Module mono.
+  Fail Monomorphic Universe u.
+  Monomorphic Universe MONOU.
+
+  Monomorphic Definition monomono := Type@{MONOU}.
+  Check monomono.
+
+  Monomorphic Inductive monoind@{i} : Type@{i} := .
+  Monomorphic Record monorecord@{i} : Type@{i} := mkmonorecord {}.
+End mono.
+Check mono.monomono. (* qualified MONOU *)
+Import mono.
+Check monomono. (* unqualified MONOU *)
+Check mono. (* still qualified mono.u *)
+
+Monomorphic Constraint Set < Top.mono.u.
+
+Module mono2.
+  Monomorphic Universe u.
+End mono2.
+
+Fail Monomorphic Definition mono2@{u} := Type@{u}.
+
+Module SecLet.
+  Unset Universe Polymorphism.
+  Section foo.
+    (* Fail Let foo@{} := Type@{u}. (* doesn't parse: Let foo@{...} doesn't exist *) *)
+    Unset Strict Universe Declaration.
+    Let tt : Type@{u} := Type@{v}. (* names disappear in the ether *)
+    Let ff : Type@{u}. Proof. exact Type@{v}. Qed. (* if Set Universe Polymorphism: universes are named ff.u and ff.v. Otherwise names disappear into space *)
+    Definition bobmorane := tt -> ff.
+  End foo.
+  Print bobmorane. (*
+                     bobmorane@{Top.15 Top.16 ff.u ff.v} =
+                     let tt := Type@{Top.16} in let ff := Type@{ff.v} in tt -> ff
+                     : Type@{max(Top.15,ff.u)}
+                     (* Top.15 Top.16 ff.u ff.v |= Top.16 < Top.15
+                     ff.v < ff.u
+                    *)
+
+                    bobmorane is universe polymorphic
+                    *)
+End SecLet.
+
+(* fun x x => foo is nonsense with local binders *)
+Fail Definition fo@{u u} := Type@{u}.
+
+(* Using local binders for printing. *)
+Print foo@{E M N}.
+(* Underscores discard the name if there's one. *)
+Print foo@{_ _ _}.
+
+(* Also works for inductives and records. *)
+Print Empty@{E}.
+Print PWrap@{E}.
+
+(* Also works for About. *)
+About punwrap@{K}.
+
+(* Instance length check. *)
+Fail Print foo@{E}.
+Fail Print mono@{E}.
+
+(* Not everything can be printed with custom universe names. *)
+Fail Print Coq.Init.Logic@{E}.
+
+(* Nice error when constraints are impossible. *)
+Monomorphic Universes gU gV. Monomorphic Constraint gU < gV.
+Fail Lemma foo@{u v|u < gU, gV < v, v < u} : nat.
+
+(* Universe binders survive through compilation, sections and modules. *)
+Require TestSuite.bind_univs.
+Print bind_univs.mono.
+Print bind_univs.poly.
+
+Section SomeSec.
+  Universe u.
+  Definition insec@{v} := Type@{u} -> Type@{v}.
+  Print insec.
+End SomeSec.
+Print insec.
+
+Module SomeMod.
+  Definition inmod@{u} := Type@{u}.
+  Print inmod.
+End SomeMod.
+Print SomeMod.inmod.
+Import SomeMod.
+Print inmod.
+
+Module Type SomeTyp. Definition inmod := Type. End SomeTyp.
+Module SomeFunct (In : SomeTyp).
+  Definition infunct@{u v} := In.inmod@{u} -> Type@{v}.
+End SomeFunct.
+Module Applied := SomeFunct(SomeMod).
+Print Applied.infunct.
+
+(* Multi-axiom declaration
+
+   In polymorphic mode the domain Type gets separate universes for the
+   different axioms, but all axioms have to declare all universes. In
+   polymorphic mode they get the same universes, ie the type is only
+   interpd once. *)
+Axiom axfoo@{i+} axbar : Type -> Type@{i}.
+Monomorphic Axiom axfoo'@{i+} axbar' : Type -> Type@{i}.
+
+About axfoo. About axbar. About axfoo'. About axbar'.
+
+Fail Axiom failfoo failbar@{i} : Type.
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