-
Notifications
You must be signed in to change notification settings - Fork 0
/
Constructors.v
72 lines (58 loc) · 1.77 KB
/
Constructors.v
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
68
69
70
71
From Elo Require Import Core.
From Elo Require Import Definitions.
From Elo Require Import Inversions.
(* ------------------------------------------------------------------------- *)
(* not-access constructors *)
(* ------------------------------------------------------------------------- *)
Local Ltac solve_nacc_construction :=
intros ** ?; invc_acc; contradiction.
Lemma nacc_unit : forall m ad,
~ access ad m <{unit}>.
Proof.
intros ** ?. inv_acc.
Qed.
Lemma nacc_num : forall m ad n,
~ access ad m <{N n}>.
Proof. solve_nacc_construction. Qed.
Lemma nacc_ref : forall m ad ad' T,
ad <> ad' ->
~ access ad m m[ad'].tm ->
~ access ad m <{&ad' :: T}>.
Proof. solve_nacc_construction. Qed.
Lemma nacc_new : forall m t ad T,
~ access ad m t ->
~ access ad m <{new T t}>.
Proof. solve_nacc_construction. Qed.
Lemma nacc_load : forall m t ad,
~ access ad m t ->
~ access ad m <{*t}>.
Proof. solve_nacc_construction. Qed.
Lemma nacc_asg : forall m t1 t2 ad,
~ access ad m t1 ->
~ access ad m t2 ->
~ access ad m <{t1 = t2}>.
Proof. solve_nacc_construction. Qed.
Lemma nacc_fun : forall m x Tx t ad,
~ access ad m t ->
~ access ad m <{fn x Tx t}>.
Proof. solve_nacc_construction. Qed.
Lemma nacc_call : forall m t1 t2 ad,
~ access ad m t1 ->
~ access ad m t2 ->
~ access ad m <{call t1 t2}>.
Proof. solve_nacc_construction. Qed.
Lemma nacc_seq : forall m t1 t2 ad,
~ access ad m t1 ->
~ access ad m t2 ->
~ access ad m <{t1; t2}>.
Proof. solve_nacc_construction. Qed.
Lemma nacc_spawn : forall m t ad,
~ access ad m <{spawn t}>.
Proof. solve_nacc_construction. Qed.
#[export] Hint Resolve
nacc_unit nacc_num
nacc_ref nacc_new nacc_load nacc_asg
nacc_fun nacc_call
nacc_seq
nacc_spawn
: acc.