1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
|
(************************************************************************)
(* * The Coq Proof Assistant / The Coq Development Team *)
(* v * Copyright INRIA, CNRS and contributors *)
(* <O___,, * (see version control and CREDITS file for authors & dates) *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(* Negative occurrence *)
Fail Inductive t : Type :=
c : (t -> nat) -> t.
(* Non-strictely positive occurrence *)
Fail Inductive t : Type :=
c : ((t -> nat) -> nat) -> t.
(* Self-nested type (no proof of
soundness yet *)
Fail Inductive t (A:Type) : Type :=
c : t (t A) -> t A.
(* Nested inductive types *)
Inductive pos (A:Type) :=
p : pos A -> pos A.
Inductive nnpos (A:Type) :=
nnp : ((A -> nat) -> nat) -> nnpos A.
Inductive neg (A:Type) :=
n : (A->neg A) -> neg A.
Inductive arg : Type -> Prop :=
a : forall A, arg A -> arg A.
(* Strictly covariant parameter: accepted. *)
Fail Fail Inductive t :=
c : pos t -> t.
(* Non-strictly covariant parameter: not
strictly positive. *)
Fail Inductive t :=
c : nnpos t -> t.
(* Contravariant parameter: not positive. *)
Fail Inductive t :=
c : neg t -> t.
(* Strict index: not positive. *)
Fail Inductive t :=
c : arg t -> t.
|
