(* *)
(**************************************************************************)
-include "arithmetics/nat.ma".
+include "basics/pts.ma".
-(*FEATURE: kind signatures in type declarations*)
-
-axiom Nat: Type[0].
-axiom S: Nat → Nat.
-axiom O: Nat.
+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:Prop. C → nat.
axiom test4''': ∀C:Type[1]. C.
-axiom test4_5: (∀A:Type[0].A) → Nat.
+axiom test4_5: (∀A:Type[0].A) → nat.
axiom test5: (Type[1] → Type[1]) → Type[1].
(* no content *)
axiom test6: Type[1] → Prop.
-definition dtest1: Type[1] ≝ Nat → Nat.
+definition dtest1: Type[1] ≝ nat → nat.
definition dtest2: Type[2] ≝ ∀A:Type[1]. A → A.
definition dtest5: Type[1] → Type[1] ≝ dtest3.
-definition dtest6: Type[1] ≝ dtest3 Nat.
+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.
-definition dtest11: Type[1] → Nat → Type[1] → Type[1] ≝ λ_:Type[1].λ_:Nat.λX:Type[1]. X → Nat → test1.
+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 dtest12 ≝ λ_:Type[1].λ_:nat.λX:Type[1]. X → nat → test1.
-definition dtest13 ≝ dtest3 Nat → dtest3 True → dtest3 Prop → Nat.
+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 dtest15 ≝ ∀T:Type[1] → Type[1]. T nat → T nat.
-definition dtest16 ≝ ∀T:Type[1]. T → Nat.
+definition dtest16 ≝ ∀T:Type[1]. T → nat.
-definition dtest17 ≝ ∀T:dtest14 Type[1]. T Nat → dtest14 Nat → dtest14 Nat.
+definition dtest17 ≝ ∀T:dtest14 Type[1]. T nat → dtest14 nat → dtest14 nat.
-definition dtest18 ≝ λA,B:Type[0].λn:Nat.λC:Type[0].A.
+definition dtest18 ≝ λA,B:Type[0].λn:nat.λC:Type[0].A.
-definition dtest19 ≝ dtest18 Nat True O Nat → dtest18 Nat Nat O Nat.
+definition dtest19 ≝ dtest18 nat True O nat → dtest18 nat nat O 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.
+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.
(*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 ttest6 ≝ ttest4 nat.
-definition ttest7 ≝ λf:∀X:Type[1].X. f (Nat → Nat) O.
+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 ttest9 ≝ λf:∀X:Type[1].X. f (True → nat) I.
-definition ttest10 ≝ λf:∀X:Type[1].X. f (True → Nat → Nat) I O.
+definition ttest10 ≝ λf:∀X:Type[1].X. f (True → nat → nat) I O.
-definition ttest11_aux ≝ λS:Type[1]. S → Nat.
+definition ttest11_aux ≝ λS:Type[1]. S → nat.
definition ttest11 ≝ λf:ttest11_aux True. f I.
-definition ttest12 ≝ λf:True → Nat. f I.
+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)).
+axiom plus: nat → nat → nat.
+
definition rtest2 : nat → stream → nat ≝
- λm,s. match s with [ scons n l ⇒ m + n ].
+ λm,s. match s with [ scons n l ⇒ plus m n ].
(*
let rec mkterm (n:nat) : nat ≝
[ O ⇒ nat
| S m ⇒ mktyp m ].*)
-inductive mynat : Type[0] ≝ myzero: mynat | mysucc: mynat → mynat.
+inductive meee: Type[0] → Type[0] ≝ .
-(*FEATURE: print kind signatures*)
-inductive T1 : (Type[0] → Type[0]) → ∀B:Type[0]. mynat → Type[0] → Type[0] ≝ .
+inductive T1 : (Type[0] → Type[0]) → ∀B:Type[0]. nat → Type[0] → Type[0] ≝ .
-(*Not in F_omega *)
inductive T2 : (Type[0] → Type[0]) → ∀B:Type[0]. B → Type[0] → Type[0] ≝ .
(* no content *)
inductive T3 : (Type[0] → Type[0]) → CProp[2] ≝ .
-(*BUG: elimination principles not extracted *)
+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 0
- | mycons: ∀n. n < b → A → myvect A b n → myvect A b (S n).
\ No newline at end of file
+ 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: 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 ≝
+ 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 *)
\ No newline at end of file
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