| author | berghofe |
| Thu, 03 Apr 2008 17:50:50 +0200 | |
| changeset 26532 | 3fc9730403c1 |
| parent 26359 | 6d437bde2f1d |
| child 27361 | 24ec32bee347 |
| permissions | -rw-r--r-- |
| 6008 | 1 |
(* Title: HOL/IOA/example/Correctness.thy |
2 |
ID: $Id$ |
|
| 12218 | 3 |
Author: Olaf Müller |
| 6008 | 4 |
*) |
5 |
||
| 17244 | 6 |
header {* Correctness Proof *}
|
| 6008 | 7 |
|
| 17244 | 8 |
theory Correctness |
9 |
imports SimCorrectness Spec Impl |
|
10 |
begin |
|
| 6008 | 11 |
|
| 17244 | 12 |
defaultsort type |
| 6008 | 13 |
|
|
25131
2c8caac48ade
modernized specifications ('definition', 'abbreviation', 'notation');
wenzelm
parents:
19740
diff
changeset
|
14 |
definition |
|
2c8caac48ade
modernized specifications ('definition', 'abbreviation', 'notation');
wenzelm
parents:
19740
diff
changeset
|
15 |
sim_relation :: "((nat * bool) * (nat set * bool)) set" where |
|
2c8caac48ade
modernized specifications ('definition', 'abbreviation', 'notation');
wenzelm
parents:
19740
diff
changeset
|
16 |
"sim_relation = {qua. let c = fst qua; a = snd qua ;
|
|
2c8caac48ade
modernized specifications ('definition', 'abbreviation', 'notation');
wenzelm
parents:
19740
diff
changeset
|
17 |
k = fst c; b = snd c; |
|
2c8caac48ade
modernized specifications ('definition', 'abbreviation', 'notation');
wenzelm
parents:
19740
diff
changeset
|
18 |
used = fst a; c = snd a |
|
2c8caac48ade
modernized specifications ('definition', 'abbreviation', 'notation');
wenzelm
parents:
19740
diff
changeset
|
19 |
in |
|
2c8caac48ade
modernized specifications ('definition', 'abbreviation', 'notation');
wenzelm
parents:
19740
diff
changeset
|
20 |
(! l:used. l < k) & b=c}" |
| 6008 | 21 |
|
| 19740 | 22 |
declare split_paired_All [simp] |
23 |
declare split_paired_Ex [simp del] |
|
24 |
||
25 |
||
26 |
(* Idea: instead of impl_con_lemma do not rewrite impl_ioa, but derive |
|
27 |
simple lemmas asig_of impl_ioa = impl_sig, trans_of impl_ioa = impl_trans |
|
28 |
Idea: ?ex. move .. should be generally replaced by a step via a subst tac if desired, |
|
29 |
as this can be done globally *) |
|
30 |
||
31 |
lemma issimulation: |
|
32 |
"is_simulation sim_relation impl_ioa spec_ioa" |
|
33 |
apply (simp (no_asm) add: is_simulation_def) |
|
34 |
apply (rule conjI) |
|
35 |
txt {* start states *}
|
|
| 26359 | 36 |
apply (auto)[1] |
| 19740 | 37 |
apply (rule_tac x = " ({},False) " in exI)
|
38 |
apply (simp add: sim_relation_def starts_of_def Spec.ioa_def Impl.ioa_def) |
|
39 |
txt {* main-part *}
|
|
40 |
apply (rule allI)+ |
|
41 |
apply (rule imp_conj_lemma) |
|
42 |
apply (rename_tac k b used c k' b' a) |
|
43 |
apply (induct_tac "a") |
|
44 |
apply (simp_all (no_asm) add: sim_relation_def Impl.ioa_def Impl.trans_def trans_of_def) |
|
| 26359 | 45 |
apply auto |
| 19740 | 46 |
txt {* NEW *}
|
47 |
apply (rule_tac x = "(used,True)" in exI) |
|
48 |
apply simp |
|
49 |
apply (rule transition_is_ex) |
|
50 |
apply (simp (no_asm) add: Spec.ioa_def Spec.trans_def trans_of_def) |
|
51 |
txt {* LOC *}
|
|
52 |
apply (rule_tac x = " (used Un {k},False) " in exI)
|
|
53 |
apply (simp add: less_SucI) |
|
54 |
apply (rule transition_is_ex) |
|
55 |
apply (simp (no_asm) add: Spec.ioa_def Spec.trans_def trans_of_def) |
|
56 |
apply fast |
|
57 |
txt {* FREE *}
|
|
58 |
apply (rule_tac x = " (used - {nat},c) " in exI)
|
|
59 |
apply simp |
|
60 |
apply (rule transition_is_ex) |
|
61 |
apply (simp (no_asm) add: Spec.ioa_def Spec.trans_def trans_of_def) |
|
62 |
done |
|
63 |
||
64 |
||
65 |
lemma implementation: |
|
66 |
"impl_ioa =<| spec_ioa" |
|
67 |
apply (unfold ioa_implements_def) |
|
68 |
apply (rule conjI) |
|
69 |
apply (simp (no_asm) add: Impl.sig_def Spec.sig_def Impl.ioa_def Spec.ioa_def |
|
70 |
asig_outputs_def asig_of_def asig_inputs_def) |
|
71 |
apply (rule trace_inclusion_for_simulations) |
|
72 |
apply (simp (no_asm) add: Impl.sig_def Spec.sig_def Impl.ioa_def Spec.ioa_def |
|
73 |
externals_def asig_outputs_def asig_of_def asig_inputs_def) |
|
74 |
apply (rule issimulation) |
|
75 |
done |
|
| 17244 | 76 |
|
77 |
end |