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
54
55
56
57
58
59
60
61
62
63
64
65
66
67
|
(** The purpose of this file is to test functional properties of the
destructive patterns used in binders ([fun] and [forall]). *)
Definition swap {A B} '((x,y) : A*B) := (y,x).
(** Tests the use of patterns in [fun] and [Definition] *)
Section TestFun.
Variables A B : Type.
Goal forall (x:A) (y:B), swap (x,y) = (y,x).
Proof. reflexivity. Qed.
Goal forall u:A*B, swap (swap u) = u.
Proof. destruct u. reflexivity. Qed.
Goal @swap A B = fun '(x,y) => (y,x).
Proof. reflexivity. Qed.
End TestFun.
(** Tests the use of patterns in [forall] *)
Section TestForall.
Variables A B : Type.
Goal forall '((x,y) : A*B), swap (x,y) = (y,x).
Proof. intros [x y]. reflexivity. Qed.
Goal forall x0:A, exists '((x,y) : A*A), swap (x,y) = (x,y).
Proof.
intros x0.
exists (x0,x0).
reflexivity.
Qed.
End TestForall.
(** Tests the use of patterns in dependent definitions. *)
Section TestDependent.
Inductive Fin (n:nat) := Z : Fin n.
Definition F '(n,p) : Type := (Fin n * Fin p)%type.
Definition both_z '(n,p) : F (n,p) := (Z _,Z _).
End TestDependent.
(** Tests with a few other types just to make sure parsing is
robust. *)
Section TestExtra.
Definition proj_informative {A P} '(exist _ x _ : { x:A | P x }) : A := x.
Inductive Foo := Bar : nat -> bool -> unit -> nat -> Foo.
Definition foo '(Bar n b tt p) :=
if b then n+p else n-p.
End TestExtra.
|
