From 7cfc4e5146be5666419451bdd516f1f3f264d24a Mon Sep 17 00:00:00 2001
From: Enrico Tassi <gareuselesinge@debian.org>
Date: Sun, 25 Jan 2015 14:42:51 +0100
Subject: Imported Upstream version 8.5~beta1+dfsg

---
 test-suite/success/polymorphism.v | 288 +++++++++++++++++++++++++++++++++++++-
 1 file changed, 285 insertions(+), 3 deletions(-)

(limited to 'test-suite/success/polymorphism.v')

diff --git a/test-suite/success/polymorphism.v b/test-suite/success/polymorphism.v
index 56cab0f6..9167c9fc 100644
--- a/test-suite/success/polymorphism.v
+++ b/test-suite/success/polymorphism.v
@@ -1,12 +1,294 @@
+Module withoutpoly.
+
+Inductive empty :=. 
+
+Inductive emptyt : Type :=. 
+Inductive singleton : Type :=
+  single.
+Inductive singletoninfo : Type :=
+  singleinfo : unit -> singletoninfo.
+Inductive singletonset : Set :=
+  singleset.
+
+Inductive singletonnoninfo : Type :=
+  singlenoninfo : empty -> singletonnoninfo.
+
+Inductive singletoninfononinfo : Prop :=
+  singleinfononinfo : unit -> singletoninfononinfo.
+
+Inductive bool : Type := 
+  | true | false.
+
+Inductive smashedbool : Prop := 
+  | trueP | falseP.
+End withoutpoly.
+
+Set Universe Polymorphism.
+
+Inductive empty :=. 
+Inductive emptyt : Type :=. 
+Inductive singleton : Type :=
+  single.
+Inductive singletoninfo : Type :=
+  singleinfo : unit -> singletoninfo.
+Inductive singletonset : Set :=
+  singleset.
+
+Inductive singletonnoninfo : Type :=
+  singlenoninfo : empty -> singletonnoninfo.
+
+Inductive singletoninfononinfo : Prop :=
+  singleinfononinfo : unit -> singletoninfononinfo.
+
+Inductive bool : Type := 
+  | true | false.
+
+Inductive smashedbool : Prop := 
+  | trueP | falseP.
+
+Section foo.
+  Let T := Type.
+  Inductive polybool : T := 
+  | trueT | falseT.
+End foo.
+
+Inductive list (A: Type) : Type := 
+| nil : list A
+| cons : A -> list A -> list A.
+
+Module ftypSetSet.
+Inductive ftyp : Type :=
+  | Funit : ftyp 
+  | Ffun : list ftyp -> ftyp 
+  | Fref : area -> ftyp
+with area : Type := 
+  | Stored : ftyp -> area        
+.
+End ftypSetSet.
+
+
+Module ftypSetProp.
+Inductive ftyp : Type :=
+  | Funit : ftyp 
+  | Ffun : list ftyp -> ftyp 
+  | Fref : area -> ftyp
+with area : Type := 
+  | Stored : (* ftyp ->  *)area        
+.
+End ftypSetProp.
+
+Module ftypSetSetForced.
+Inductive ftyp : Type :=
+  | Funit : ftyp 
+  | Ffun : list ftyp -> ftyp 
+  | Fref : area -> ftyp
+with area : Set (* Type *) := 
+  | Stored : (* ftyp ->  *)area        
+.
+End ftypSetSetForced.
+
+Unset Universe Polymorphism.
+
+Set Printing Universes.  
+Module Easy.
+
+  Polymorphic Inductive prod (A : Type) (B : Type) : Type :=
+    pair : A -> B -> prod A B.
+  
+  Check prod nat nat.
+  Print Universes.
+
+
+  Polymorphic Inductive sum (A B:Type) : Type :=
+  | inl : A -> sum A B
+  | inr : B -> sum A B.
+  Print sum.
+  Check (sum nat nat).
+
+End Easy.
+
+Section Hierarchy.
+
+Definition Type3 := Type.
+Definition Type2 := Type : Type3.
+Definition Type1 := Type : Type2.
+
+Definition id1 := ((forall A : Type1, A) : Type2).
+Definition id2 := ((forall A : Type2, A) : Type3).
+Definition id1' := ((forall A : Type1, A) : Type3).
+Fail Definition id1impred := ((forall A : Type1, A) : Type1).
+
+End Hierarchy.
+
+Section structures.
+
+Record hypo : Type := mkhypo {
+   hypo_type : Type;
+   hypo_proof : hypo_type
+ }.
+
+Definition typehypo (A : Type) : hypo := {| hypo_proof := A |}.
+
+Polymorphic Record dyn : Type := 
+  mkdyn {
+      dyn_type : Type;
+      dyn_proof : dyn_type
+    }.
+
+Definition monotypedyn (A : Type) : dyn := {| dyn_proof := A |}.
+Polymorphic Definition typedyn (A : Type) : dyn := {| dyn_proof := A |}.
+
+Definition atypedyn : dyn := typedyn Type.
+
+Definition projdyn := dyn_type atypedyn.
+
+Definition nested := {| dyn_type := dyn; dyn_proof := atypedyn |}.
+
+Definition nested2 := {| dyn_type := dyn; dyn_proof := nested |}.
+
+Definition projnested2 := dyn_type nested2.
+
+Polymorphic Definition nest (d : dyn) := {| dyn_proof := d |}.
+
+Polymorphic Definition twoprojs (d : dyn) := dyn_proof d = dyn_proof d.
+
+End structures.
+
+Section cats.
+  Local Set Universe Polymorphism.
+  Require Import Utf8.
+  Definition fibration (A : Type) := A -> Type.
+  Definition Hom (A : Type) := A -> A -> Type.
+
+  Record sigma (A : Type) (P : fibration A) :=
+    { proj1 : A; proj2 : P proj1} .
+
+  Class Identity {A} (M : Hom A) :=
+    identity : ∀ x, M x x.
+  
+  Class Inverse {A} (M : Hom A) :=
+    inverse : ∀ x y:A, M x y -> M y x.
+  
+  Class Composition {A} (M : Hom A) :=
+    composition : ∀ {x y z:A}, M x y -> M y z -> M x z.
+  
+  Notation  "g ° f" := (composition f g) (at level 50). 
+  
+  Class Equivalence T (Eq : Hom T):= 
+    {
+      Equivalence_Identity :> Identity Eq ;
+      Equivalence_Inverse :> Inverse Eq ;
+      Equivalence_Composition :> Composition Eq 
+    }.
+
+  Class EquivalenceType (T : Type) : Type := 
+    {
+      m2: Hom T;
+      equiv_struct :> Equivalence T m2 }.
+  
+  Polymorphic Record cat (T : Type) := 
+    { cat_hom : Hom T;
+      cat_equiv : forall x y, EquivalenceType (cat_hom x y) }.
+
+  Definition catType := sigma Type cat.
+
+  Notation "[ T ]" := (proj1 T).
+
+  Require Import Program.
+
+  Program Definition small_cat : cat Empty_set :=
+    {| cat_hom x y := unit |}.
+  Next Obligation. 
+    refine ({|m2:=fun x y => True|}). 
+    constructor; red; intros; trivial.
+  Defined.
+
+  Record iso (T U : Set) := 
+    { f : T -> U;
+      g : U -> T }.
+
+  Program Definition Set_cat : cat Set :=
+    {| cat_hom := iso |}.
+  Next Obligation. 
+    refine ({|m2:=fun x y => True|}). 
+    constructor; red; intros; trivial.
+  Defined.
+
+  Record isoT (T U : Type) := 
+    { isoT_f : T -> U;
+      isoT_g : U -> T }.
+
+  Program Definition Type_cat : cat Type :=
+    {| cat_hom := isoT |}.
+  Next Obligation. 
+    refine ({|m2:=fun x y => True|}). 
+    constructor; red; intros; trivial.
+  Defined.
+    
+  Polymorphic Record cat1 (T : Type) := 
+    { cat1_car : Type;
+      cat1_hom : Hom cat1_car;
+      cat1_hom_cat : forall x y, cat (cat1_hom x y) }.
+End cats.  
+
+Polymorphic Definition id {A : Type} (a : A) : A := a.
+
+Definition typeid := (@id Type).
+
+
+Fail Check (Prop : Set).
+Fail Check (Set : Set).
+Check (Set : Type).
+Check (Prop : Type).
+Definition setType := $(let t := type of Set in exact t)$.
+
+Definition foo (A : Prop) := A.
+
+Fail Check foo Set.
+Check fun A => foo A.
+Fail Check fun A : Type => foo A.
+Check fun A : Prop => foo A.
+Fail Definition bar := fun A : Set => foo A.
+
+Fail Check (let A := Type in foo (id A)).
+
+Definition fooS (A : Set) := A.
+
+Check (let A := nat in fooS (id A)).
+Fail Check (let A := Set in fooS (id A)).
+Fail Check (let A := Prop in fooS (id A)).
+
 (* Some tests of sort-polymorphisme *)
 Section S.
-Variable A:Type.
+Polymorphic Variable A:Type.
 (*
 Definition f (B:Type) := (A * B)%type.
 *)
-Inductive I (B:Type) : Type := prod : A->B->I B.
+Polymorphic Inductive I (B:Type) : Type := prod : A->B->I B.
+
+Check I nat.
+
 End S.
 (*
 Check f nat nat : Set.
 *)
-Check I nat nat : Set.
\ No newline at end of file
+Definition foo' := I nat nat.
+Print Universes. Print foo. Set Printing Universes. Print foo.
+
+(* Polymorphic axioms: *)
+Polymorphic Axiom funext : forall (A B : Type) (f g : A -> B), 
+                 (forall x, f x = g x) -> f = g.
+
+(* Check @funext. *)
+(* Check funext. *)
+
+Polymorphic Definition fun_ext (A B : Type) := 
+  forall (f g : A -> B), 
+    (forall x, f x = g x) -> f = g.
+
+Polymorphic Class Funext A B := extensional : fun_ext A B.
+
+Section foo2. 
+  Context `{forall A B, Funext A B}.
+  Print Universes.
+End foo2.
-- 
cgit v1.2.3