blob: 12840f628810f3a949b7f17745286c2227c1a627 (
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
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
|
Require Import Coqlib Maps.
Require Import AST Integers Values Events Memory Globalenvs Smallstep.
Require Import RTL Op Registers OptionMonad BTL.
Require Import Errors Linking BTL_SEtheory.
(** External oracle *)
Axiom scheduler: BTL.function -> BTL.code.
Extract Constant scheduler => "BTLScheduleraux.btl_scheduler".
Definition equiv_input_regs (f1 f2: BTL.function): Prop :=
(forall pc, (fn_code f1)!pc = None <-> (fn_code f2)!pc = None)
/\ (forall pc ib1 ib2, (fn_code f1)!pc = Some ib1 -> (fn_code f2)!pc = Some ib2 -> ib1.(input_regs) = ib2.(input_regs)).
Lemma equiv_input_regs_union f1 f2:
equiv_input_regs f1 f2 -> forall tbl, union_inputs f1 tbl = union_inputs f2 tbl.
Proof.
intros (EQNone & EQSome). induction tbl as [|pc l']; simpl; auto.
generalize (EQNone pc) (EQSome pc); clear EQNone EQSome; intros EQN EQS.
do 2 autodestruct; intuition; try_simplify_someHyps.
intros; exploit EQS; eauto; clear EQS. congruence.
Qed.
Lemma equiv_input_regs_pre f1 f2 tbl or:
equiv_input_regs f1 f2 -> pre_inputs f1 tbl or = pre_inputs f2 tbl or.
Proof.
intros; unfold pre_inputs; erewrite equiv_input_regs_union; auto.
Qed.
Lemma equiv_input_regs_tr_inputs f1 f2 l oreg rs:
equiv_input_regs f1 f2 ->
tr_inputs f1 l oreg rs = tr_inputs f2 l oreg rs.
Proof.
intros; unfold tr_inputs; erewrite equiv_input_regs_pre; eauto.
Qed.
(* a specification of the verification to do on each function *)
Record match_function (f1 f2: BTL.function): Prop := {
preserv_fnsig: fn_sig f1 = fn_sig f2;
preserv_fnparams: fn_params f1 = fn_params f2;
preserv_fnstacksize: fn_stacksize f1 = fn_stacksize f2;
preserv_entrypoint: fn_entrypoint f1 = fn_entrypoint f2;
preserv_inputs: equiv_input_regs f1 f2;
symbolic_simu_ok: forall pc ib1, (fn_code f1)!pc = Some ib1 ->
exists ib2, (fn_code f2)!pc = Some ib2 /\ symbolic_simu f1 f2 (entry ib1) (entry ib2);
}.
Local Open Scope error_monad_scope.
Definition check_symbolic_simu (f tf: BTL.function): res unit := OK tt. (* TODO: fixme *)
Lemma check_symbolic_simu_input_equiv x f1 f2:
check_symbolic_simu f1 f2 = OK x -> equiv_input_regs f1 f2.
Proof.
Admitted.
Lemma check_symbolic_simu_correct x f1 f2:
check_symbolic_simu f1 f2 = OK x ->
forall pc ib1, (fn_code f1)!pc = Some ib1 ->
exists ib2, (fn_code f2)!pc = Some ib2 /\ symbolic_simu f1 f2 (entry ib1) (entry ib2).
Admitted.
Definition transf_function (f: BTL.function) :=
let tf := BTL.mkfunction (fn_sig f) (fn_params f) (fn_stacksize f) (scheduler f) (fn_entrypoint f) in
do _ <- check_symbolic_simu f tf;
OK tf.
Definition transf_fundef (f: fundef) : res fundef :=
transf_partial_fundef (fun f => transf_function f) f.
Definition transf_program (p: program) : res program :=
transform_partial_program transf_fundef p.
|
