--- a/src/HOL/UNITY/Mutex.ML Wed Aug 05 10:56:58 1998 +0200
+++ b/src/HOL/UNITY/Mutex.ML Wed Aug 05 10:57:25 1998 +0200
@@ -9,14 +9,14 @@
(*split_all_tac causes a big blow-up*)
claset_ref() := claset() delSWrapper "split_all_tac";
-val cmd_defs = [mutex_def,
+val cmd_defs = [Mprg_def,
cmd0U_def, cmd1U_def, cmd2U_def, cmd3U_def, cmd4U_def,
cmd0V_def, cmd1V_def, cmd2V_def, cmd3V_def, cmd4V_def];
-Goalw [mutex_def] "id : mutex";
+Goalw [Mprg_def] "id : Acts Mprg";
by (Simp_tac 1);
-qed "id_in_mutex";
-AddIffs [id_in_mutex];
+qed "id_in_Acts";
+AddIffs [id_in_Acts];
(*Simplification for records*)
@@ -30,30 +30,30 @@
Addsimps [invariantU_def, invariantV_def];
-Goalw [MInit_def] "invariant (MInit,mutex) invariantU";
+Goalw [Mprg_def] "invariant Mprg invariantU";
by (rtac invariantI 1);
by (constrains_tac cmd_defs 2);
by Auto_tac;
qed "invariantU";
-Goalw [MInit_def] "invariant (MInit,mutex) invariantV";
+Goalw [Mprg_def] "invariant Mprg invariantV";
by (rtac invariantI 1);
by (constrains_tac cmd_defs 2);
by Auto_tac;
qed "invariantV";
-val mutex_invariant = invariant_Int_rule [invariantU, invariantV];
+val invariantUV = invariant_Int_rule [invariantU, invariantV];
(*The safety property: mutual exclusion*)
-Goal "disjoint (reachable (MInit,mutex)) {s. MM s = 3 & NN s = 3}";
-by (cut_facts_tac [mutex_invariant RS invariant_includes_reachable] 1);
+Goal "(reachable Mprg) Int {s. MM s = 3 & NN s = 3} = {}";
+by (cut_facts_tac [invariantUV RS invariant_includes_reachable] 1);
by Auto_tac;
qed "mutual_exclusion";
(*The bad invariant FAILS in cmd1V*)
-Goalw [bad_invariantU_def] "stable mutex bad_invariantU";
+Goalw [bad_invariantU_def] "stable (Acts Mprg) bad_invariantU";
by (constrains_tac cmd_defs 1);
by (REPEAT (trans_tac 1));
by (safe_tac (claset() addSEs [le_SucE]));
@@ -67,49 +67,48 @@
(*** Progress for U ***)
-Goalw [unless_def] "unless mutex {s. MM s=2} {s. MM s=3}";
+Goalw [unless_def] "unless (Acts Mprg) {s. MM s=2} {s. MM s=3}";
by (constrains_tac cmd_defs 1);
qed "U_F0";
-Goal "LeadsTo(MInit,mutex) {s. MM s=1} {s. PP s = VV s & MM s = 2}";
+Goal "LeadsTo Mprg {s. MM s=1} {s. PP s = VV s & MM s = 2}";
by (ensures_tac cmd_defs "cmd1U" 1);
qed "U_F1";
-Goal "LeadsTo(MInit,mutex) {s. ~ PP s & MM s = 2} {s. MM s = 3}";
-by (cut_facts_tac [mutex_invariant] 1);
+Goal "LeadsTo Mprg {s. ~ PP s & MM s = 2} {s. MM s = 3}";
+by (cut_facts_tac [invariantUV] 1);
+bw Mprg_def;
by (ensures_tac cmd_defs "cmd2U" 1);
qed "U_F2";
-Goalw [mutex_def] "LeadsTo(MInit,mutex) {s. MM s = 3} {s. PP s}";
+Goal "LeadsTo Mprg {s. MM s = 3} {s. PP s}";
by (rtac leadsTo_imp_LeadsTo 1);
by (res_inst_tac [("B", "{s. MM s = 4}")] leadsTo_Trans 1);
by (ensures_tac cmd_defs "cmd4U" 2);
by (ensures_tac cmd_defs "cmd3U" 1);
qed "U_F3";
-Goal "LeadsTo(MInit,mutex) {s. MM s = 2} {s. PP s}";
+Goal "LeadsTo Mprg {s. MM s = 2} {s. PP s}";
by (rtac ([LeadsTo_weaken_L, subset_refl RS subset_imp_LeadsTo]
MRS LeadsTo_Diff) 1);
by (rtac ([U_F2, U_F3] MRS LeadsTo_Trans) 1);
by (auto_tac (claset() addSEs [less_SucE], simpset()));
val U_lemma2 = result();
-Goal "LeadsTo(MInit,mutex) {s. MM s = 1} {s. PP s}";
+Goal "LeadsTo Mprg {s. MM s = 1} {s. PP s}";
by (rtac ([U_F1 RS LeadsTo_weaken_R, U_lemma2] MRS LeadsTo_Trans) 1);
by (Blast_tac 1);
val U_lemma1 = result();
-
-Goal "LeadsTo(MInit,mutex) {s. 1 <= MM s & MM s <= 3} {s. PP s}";
+Goal "LeadsTo Mprg {s. 1 <= MM s & MM s <= 3} {s. PP s}";
by (simp_tac (simpset() addsimps [le_Suc_eq, conj_disj_distribL]
addcongs [rev_conj_cong]) 1);
by (simp_tac (simpset() addsimps [Collect_disj_eq, LeadsTo_Un_distrib,
U_lemma1, U_lemma2, U_F3] ) 1);
val U_lemma123 = result();
-
(*Misra's F4*)
-Goal "LeadsTo(MInit,mutex) {s. UU s} {s. PP s}";
+Goal "LeadsTo Mprg {s. UU s} {s. PP s}";
by (rtac ([invariantU, U_lemma123] MRS invariant_LeadsTo_weaken) 1);
by Auto_tac;
qed "u_leadsto_p";
@@ -118,39 +117,39 @@
(*** Progress for V ***)
-Goalw [unless_def] "unless mutex {s. NN s=2} {s. NN s=3}";
+Goalw [unless_def] "unless (Acts Mprg) {s. NN s=2} {s. NN s=3}";
by (constrains_tac cmd_defs 1);
qed "V_F0";
-Goal "LeadsTo(MInit,mutex) {s. NN s=1} {s. PP s = (~ UU s) & NN s = 2}";
+Goal "LeadsTo Mprg {s. NN s=1} {s. PP s = (~ UU s) & NN s = 2}";
by (ensures_tac cmd_defs "cmd1V" 1);
qed "V_F1";
-Goal "LeadsTo(MInit,mutex) {s. PP s & NN s = 2} {s. NN s = 3}";
-by (cut_facts_tac [mutex_invariant] 1);
+Goal "LeadsTo Mprg {s. PP s & NN s = 2} {s. NN s = 3}";
+by (cut_facts_tac [invariantUV] 1);
by (ensures_tac cmd_defs "cmd2V" 1);
qed "V_F2";
-Goalw [mutex_def] "LeadsTo(MInit,mutex) {s. NN s = 3} {s. ~ PP s}";
+Goal "LeadsTo Mprg {s. NN s = 3} {s. ~ PP s}";
by (rtac leadsTo_imp_LeadsTo 1);
by (res_inst_tac [("B", "{s. NN s = 4}")] leadsTo_Trans 1);
by (ensures_tac cmd_defs "cmd4V" 2);
by (ensures_tac cmd_defs "cmd3V" 1);
qed "V_F3";
-Goal "LeadsTo(MInit,mutex) {s. NN s = 2} {s. ~ PP s}";
+Goal "LeadsTo Mprg {s. NN s = 2} {s. ~ PP s}";
by (rtac ([LeadsTo_weaken_L, subset_refl RS subset_imp_LeadsTo]
MRS LeadsTo_Diff) 1);
by (rtac ([V_F2, V_F3] MRS LeadsTo_Trans) 1);
by (auto_tac (claset() addSEs [less_SucE], simpset()));
val V_lemma2 = result();
-Goal "LeadsTo(MInit,mutex) {s. NN s = 1} {s. ~ PP s}";
+Goal "LeadsTo Mprg {s. NN s = 1} {s. ~ PP s}";
by (rtac ([V_F1 RS LeadsTo_weaken_R, V_lemma2] MRS LeadsTo_Trans) 1);
by (Blast_tac 1);
val V_lemma1 = result();
-Goal "LeadsTo(MInit,mutex) {s. 1 <= NN s & NN s <= 3} {s. ~ PP s}";
+Goal "LeadsTo Mprg {s. 1 <= NN s & NN s <= 3} {s. ~ PP s}";
by (simp_tac (simpset() addsimps [le_Suc_eq, conj_disj_distribL]
addcongs [rev_conj_cong]) 1);
by (simp_tac (simpset() addsimps [Collect_disj_eq, LeadsTo_Un_distrib,
@@ -159,7 +158,7 @@
(*Misra's F4*)
-Goal "LeadsTo(MInit,mutex) {s. VV s} {s. ~ PP s}";
+Goal "LeadsTo Mprg {s. VV s} {s. ~ PP s}";
by (rtac ([invariantV, V_lemma123] MRS invariant_LeadsTo_weaken) 1);
by Auto_tac;
qed "v_leadsto_not_p";
@@ -168,7 +167,7 @@
(** Absence of starvation **)
(*Misra's F6*)
-Goal "LeadsTo(MInit,mutex) {s. MM s = 1} {s. MM s = 3}";
+Goal "LeadsTo Mprg {s. MM s = 1} {s. MM s = 3}";
by (rtac LeadsTo_Un_duplicate 1);
by (rtac LeadsTo_cancel2 1);
by (rtac U_F2 2);
@@ -182,7 +181,7 @@
(*The same for V*)
-Goal "LeadsTo(MInit,mutex) {s. NN s = 1} {s. NN s = 3}";
+Goal "LeadsTo Mprg {s. NN s = 1} {s. NN s = 3}";
by (rtac LeadsTo_Un_duplicate 1);
by (rtac LeadsTo_cancel2 1);
by (rtac V_F2 2);