blob: 1adcbd39a182449323e16a3166739ae43e346424 (
plain)
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
|
(* Check local definitions in context of inductive types *)
Inductive A (C D : Prop) (E:=C) (F:=D) (x y : E -> F) : E -> Set :=
I : forall z : E, A C D x y z.
Check
(fun C D : Prop =>
let E := C in
let F := D in
fun (x y : E -> F) (P : forall c : C, A C D x y c -> Type)
(f : forall z : C, P z (I C D x y z)) (y0 : C)
(a : A C D x y y0) =>
match a as a0 in (A _ _ _ _ y1) return (P y1 a0) with
| I x0 => f x0
end).
Record B (C D : Set) (E:=C) (F:=D) (x y : E -> F) : Set := {p : C; q : E}.
Check
(fun C D : Set =>
let E := C in
let F := D in
fun (x y : E -> F) (P : B C D x y -> Type)
(f : forall p0 q0 : C, P (Build_B C D x y p0 q0))
(b : B C D x y) =>
match b as b0 return (P b0) with
| Build_B x0 x1 => f x0 x1
end).
(* Check implicit parameters of inductive types (submitted by Pierre
Casteran and also implicit in #338) *)
Set Implicit Arguments.
Unset Strict Implicit.
CoInductive LList (A : Set) : Set :=
| LNil : LList A
| LCons : A -> LList A -> LList A.
Implicit Arguments LNil [A].
Inductive Finite (A : Set) : LList A -> Prop :=
| Finite_LNil : Finite LNil
| Finite_LCons :
forall (a : A) (l : LList A), Finite l -> Finite (LCons a l).
(* Check positivity modulo reduction (cf bug #983) *)
Record P:Type := {PA:Set; PB:Set}.
Definition F (p:P) := (PA p) -> (PB p).
Inductive I_F:Set := c : (F (Build_P nat I_F)) -> I_F.
|
