(* *)
(**************************************************************************)
-include "arithmetics/nat.ma".
+include "basics/pts.ma".
-(*BUG: kind signatures in type declarations*)
+inductive nat : Type[0] ≝ O: nat | S: nat → nat.
axiom test1: Type[1].
axiom test3: Prop → Type[1] → CProp[1] → Type[1] → Type[2].
-(* not in F_omega ? *)
axiom test4: ∀A:Type[1]. A → ∀B:Type[1]. B → ∀C:Prop. C → Type[1].
+axiom test4': ∀C:Prop. C → C.
+
+axiom test4'': ∀C:Prop. C → nat.
+
+axiom test4''': ∀C:Type[1]. C.
+
+axiom test4_5: (∀A:Type[0].A) → nat.
+
axiom test5: (Type[1] → Type[1]) → Type[1].
(* no content *)
definition dtest6: Type[1] ≝ dtest3 nat.
+inductive True : Prop ≝ I: True.
+
(* no content *)
definition dtest7: Prop ≝ True → True.
definition dtest10: Type[1] → Type[1] → Type[1] ≝ λX,Y.X.
-(*BUG: a' vs a''*)
definition dtest11: Type[1] → nat → Type[1] → Type[1] ≝ λ_:Type[1].λ_:nat.λX:Type[1]. X → nat → test1.
+
definition dtest12 ≝ λ_:Type[1].λ_:nat.λX:Type[1]. X → nat → test1.
definition dtest13 ≝ dtest3 nat → dtest3 True → dtest3 Prop → nat.
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 dtest20 ≝ test5 test2.
(*BUG: lambda-lift the inner declaration;
- to be traced, raises NotInFOmega; why? *)
-definition dtest21 ≝ test5 (λX:Type[1].X).
+ to be traced, raises NotInFOmega; why?
+definition dtest21 ≝ test5 (λX:Type[1].X).*)
definition ttest1 ≝ λx:nat.x.
(*BUG: clash of name due to capitalisation*)
-definition Ttest1 ≝ λx:nat.x.
+(*definition Ttest1 ≝ λx:nat.x.*)
+
+(*FEATURE: print binders in the l.h.s. without using lambda abstraction*)
+definition ttest2 ≝ λT:Type[1].λx:T.x.
+
+definition ttest3 ≝ λT:Type[1].λx:T.let y ≝ x in y.
+
+definition ttest4 ≝ λT:Type[1].let y ≝ T in λx:y.x.
+
+(*BUG IN HASKELL PRETTY PRINTING: all lets are let rec*)
+(*definition ttest5 ≝ λT:Type[1].λy:T.let y ≝ y in y.*)
+
+definition ttest6 ≝ ttest4 nat.
+
+definition ttest7 ≝ λf:∀X:Type[1].X. f (nat → nat) O.
+
+definition ttest8 ≝ λf:∀X:Type[1].X. f (True → True) I.
+
+definition ttest9 ≝ λf:∀X:Type[1].X. f (True → nat) I.
+
+definition ttest10 ≝ λf:∀X:Type[1].X. f (True → nat → nat) I O.
+
+definition ttest11_aux ≝ λS:Type[1]. S → nat.
+
+definition ttest11 ≝ λf:ttest11_aux True. f I.
+
+definition ttest12 ≝ λf:True → nat. f I.
+
+(*GENERAL BUG: name clashes when binders shadow each other in CIC*)
+
+(*BUG: for OCaml: cofixpoint not distinguished from fixpoints*)
+
+let rec rtest1 (n:nat) : nat ≝
+ match n with
+ [ O ⇒ O
+ | S m ⇒ rtest1 m ].
+
+let rec f (n:nat) : nat ≝
+ match n with
+ [ O ⇒ O
+ | S m ⇒ g m ]
+and g (n:nat) : nat ≝
+ match n with
+ [ O ⇒ O
+ | S m ⇒ f m ].
+
+(*BUG: pattern matching patterns when arguments have been deleted from
+ the constructor are wrong *)
+
+coinductive stream: Type[0] ≝ scons : nat → stream → stream.
+
+let corec div (n:nat) : stream ≝ scons n (div (S n)).
+
+axiom plus: nat → nat → nat.
+
+definition rtest2 : nat → stream → nat ≝
+ λm,s. match s with [ scons n l ⇒ plus m n ].
+
+(*
+let rec mkterm (n:nat) : nat ≝
+ match n with
+ [ O ⇒ O
+ | S m ⇒ mkterm m ]
+and mktyp (n:nat) : Type[0] ≝
+ match n with
+ [ O ⇒ nat
+ | S m ⇒ mktyp m ].*)
+
+inductive meee: Type[0] → Type[0] ≝ .
+
+inductive T1 : (Type[0] → Type[0]) → ∀B:Type[0]. nat → Type[0] → Type[0] ≝ .
+
+inductive T2 : (Type[0] → Type[0]) → ∀B:Type[0]. B → Type[0] → Type[0] ≝ .
+
+(* no content *)
+inductive T3 : (Type[0] → Type[0]) → CProp[2] ≝ .
+
+definition erase ≝ λX:Type[0].Type[0].
+
+axiom lt: nat → nat → Prop.
+
+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 False: Prop ≝ .
+
+inductive Empty: Type[0] ≝ .
+
+inductive bool: Type[0] ≝ true: bool | false:bool.
+
+inductive eq (A:Type[1]) (a:A) : A → Prop ≝ refl: eq A a a.
+
+(* requires coercion *)
+definition cast_bug1 ≝
+ λH:eq Type[0] bool nat. S (match H return λA:Type[0].λ_.A with [ refl ⇒ true ]).
-(*BUG: Failure nth*)
-definition ttest2 ≝ λT:Type[1].λx:T.x.
\ No newline at end of file
+(* 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.
+
+(*BUG: try singleton elimination with constructor arguments to show bug in
+ DeBrujin indexes *)
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