include "basics/pts.ma".
-(*FEATURE: kind signatures in type declarations*)
-
inductive nat : Type[0] ≝ O: nat | S: nat → nat.
axiom test1: Type[1].
definition dtest14 ≝ λX:Type[2]. X → X.
-(*FEATURE: type the forall bound variables*)
definition dtest15 ≝ ∀T:Type[1] → Type[1]. T nat → T nat.
definition dtest16 ≝ ∀T:Type[1]. T → nat.
definition ttest12 ≝ λf:True → nat. f I.
-(*GENERAL BUG: name clashes when binders shadow each other in CIC*)
+(*BUG: assertion failure here! difficult case for head application
+axiom ttest13_a: ∀T:Type[1]. T → nat.
+definition ttest13_b ≝ ttest13_a nat O.
+definition ttest13_c ≝ ttest13_a Prop True.*)
-(*BUG: mutual type definitions not handled correctly: the ref is computed in a
- wrong way *)
-
-(*BUG: multiple let-reced things are given the same (wrong) name*)
+(*GENERAL BUG: name clashes when binders shadow each other in CIC*)
(*BUG: for OCaml: cofixpoint not distinguished from fixpoints*)
(*BUG: pattern matching patterns when arguments have been deleted from
the constructor are wrong *)
-(*BUG: constructor names in pattern should be capitalised correctly;
- name clashes must be avoided*)
-
coinductive stream: Type[0] ≝ scons : nat → stream → stream.
let corec div (n:nat) : stream ≝ scons n (div (S n)).
inductive T2 : (Type[0] → Type[0]) → ∀B:Type[0]. B → Type[0] → Type[0] ≝ .
(* no content *)
-(*BUG: eliminators extracted anyway???*)
inductive T3 : (Type[0] → Type[0]) → CProp[2] ≝ .
definition erase ≝ λX:Type[0].Type[0].
axiom lt: nat → nat → Prop.
-(*BUG: elimination principles not extracted *)
inductive myvect (A: Type[0]) (b:nat) : nat → Type[0] ≝
myemptyv : myvect A b O
| mycons: ∀n. lt n b → A → myvect A b n → myvect A b (S n).
inductive eq (A:Type[1]) (a:A) : A → Prop ≝ refl: eq A a a.
-(* BUG: requires coercion *)
+(* requires coercion *)
definition cast_bug1 ≝
λH:eq Type[0] bool nat. S (match H return λA:Type[0].λ_.A with [ refl ⇒ true ]).
-(* BUG: requires top type *)
+(*
+(*BUG: Here we use eq_rect_Type0 in its poly-kinded form, but we only extracted
+ the one-kinded form. Require coercions *)
+definition cast_bug1' ≝
+ λH:eq Type[0] bool nat. S (eq_rect_Type0 Type[0] bool (λA:Type[0].λ_.A) true nat H).
+*)
+
+(* requires coercion in all branches *)
definition cast_bug2 ≝
- λb.
match true return λb.match b with [ true ⇒ nat → nat | false ⇒ bool ] with
[ true ⇒ S | false ⇒ false ]
O.