Add more regression tests for univ poly/prim proj

hese regression tests are aggregated from the various bugs I (and
others) have reported on https://github.com/HoTT/coq/issues relating to
universe polymorphism, primitive projections, and eta for records.

These are the tests that trunk currently fails.

I'm not sure about the naming scheme (HoTT_coq_###.v, where ### is the
number of the issue in GitHub), but I couldn't think of a better one.

1 files changed, 75 insertions, 0 deletions

diff --git a/test-suite/bugs/closed/HoTT_coq_027.v b/test-suite/bugs/closed/HoTT_coq_027.v
new file mode 100644
index 000000000..8132f51d2
--- /dev/null
+++ b/test-suite/bugs/closed/HoTT_coq_027.v
@@ -0,0 +1,75 @@
+Set Implicit Arguments.
+Generalizable All Variables.
+Set Asymmetric Patterns.
+Set Universe Polymorphism.
+
+Record Category (obj : Type) := { Morphism : obj -> obj -> Type }.
+
+Record Functor `(C : Category objC) `(D : Category objD) :=
+  { ObjectOf :> objC -> objD;
+    MorphismOf : forall s d, C.(Morphism) s d -> D.(Morphism) (ObjectOf s) (ObjectOf d) }.
+
+Definition TypeCat : @Category Type := @Build_Category Type (fun s d => s -> d).
+Definition SetCat : @Category Set := @Build_Category Set (fun s d => s -> d).
+
+Definition FunctorToSet `(C : @Category objC) := Functor C SetCat.
+Definition FunctorToType `(C : @Category objC) := Functor C TypeCat.
+
+(* Removing the following line, as well as the [Definition] and [Identity Coercion] immediately following it, makes the file go through *)
+Identity Coercion FunctorToType_Id : FunctorToType >-> Functor.
+
+Definition FunctorTo_Set2Type `(C : @Category objC) (F : FunctorToSet C)
+: FunctorToType C.
+  refine (@Build_Functor _ C _ TypeCat
+                         (fun x => F.(ObjectOf) x)
+                         (fun s d m => F.(MorphismOf) _ _ m)).
+Defined. (* Toplevel input, characters 0-8:
+Error:
+The term
+ "fun (objC : Type) (C : Category objC) (F : FunctorToSet C) =>
+  {|
+  ObjectOf := fun x : objC => F x;
+  MorphismOf := fun (s d : objC) (m : Morphism C s d) => MorphismOf F s d m |}"
+has type
+ "forall (objC : Type) (C : Category objC),
+  FunctorToSet C -> Functor C TypeCat" while it is expected to have type
+ "forall (objC : Type) (C : Category objC), FunctorToSet C -> FunctorToType C".
+ *)
+
+Coercion FunctorTo_Set2Type : FunctorToSet >-> FunctorToType.
+
+Record GrothendieckPair `(C : @Category objC) (F : Functor C TypeCat) :=
+  { GrothendieckC : objC;
+    GrothendieckX : F GrothendieckC }.
+
+Record SetGrothendieckPair `(C : @Category objC) (F' : Functor C SetCat) :=
+  { SetGrothendieckC : objC;
+    SetGrothendieckX : F' SetGrothendieckC }.
+
+Section SetGrothendieckCoercion.
+  Context `(C : @Category objC).
+  Variable F : Functor C SetCat.
+  Let F' := (F : FunctorToSet _) : FunctorToType _.
+
+  Set Printing Universes.
+  Definition SetGrothendieck2Grothendieck (G : SetGrothendieckPair F) : GrothendieckPair F'
+    := {| GrothendieckC := G.(SetGrothendieckC); GrothendieckX := G.(SetGrothendieckX) : F' _ |}.
+  (* Toplevel input, characters 0-187:
+Error: Illegal application:
+The term "ObjectOf (* Top.8375 Top.8376 Top.8379 Set *)" of type
+ "forall (objC : Type (* Top.8375 *))
+    (C : Category (* Top.8375 Top.8376 *) objC) (objD : Type (* Top.8379 *))
+    (D : Category (* Top.8379 Set *) objD),
+  Functor (* Top.8375 Top.8376 Top.8379 Set *) C D -> objC -> objD"
+cannot be applied to the terms
+ "objC" : "Type (* Top.8375 *)"
+ "C" : "Category (* Top.8375 Top.8376 *) objC"
+ "Type (* Set *)" : "Type (* Set+1 *)"
+ "TypeCat (* Top.8379 Set *)" : "Category (* Top.8379 Set *) Set"
+ "F'" : "FunctorToType (* Top.8375 Top.8376 Top.8379 Set *) C"
+ "SetGrothendieckC (* Top.8375 Top.8376 Top.8379 *) G" : "objC"
+The 5th term has type "FunctorToType (* Top.8375 Top.8376 Top.8379 Set *) C"
+which should be coercible to
+ "Functor (* Top.8375 Top.8376 Top.8379 Set *) C TypeCat (* Top.8379 Set *)".
+ *)
+End SetGrothendieckCoercion.