--- a/src/HOLCF/IOA/meta_theory/Automata.ML Fri Sep 02 15:54:47 2005 +0200
+++ b/src/HOLCF/IOA/meta_theory/Automata.ML Fri Sep 02 17:23:59 2005 +0200
@@ -1,8 +1,6 @@
(* Title: HOLCF/IOA/meta_theory/Automata.ML
ID: $Id$
Author: Olaf Mueller, Tobias Nipkow, Konrad Slind
-
-The I/O automata of Lynch and Tuttle.
*)
(* this modification of the simpset is local to this file *)
@@ -37,14 +35,14 @@
qed "starts_of_par";
Goal
-"trans_of(A || B) = {tr. let s = fst(tr); a = fst(snd(tr)); t = snd(snd(tr)) \
+"trans_of(A || B) = {tr. let s = fst(tr); a = fst(snd(tr)); t = snd(snd(tr)) \
\ in (a:act A | a:act B) & \
-\ (if a:act A then \
-\ (fst(s),a,fst(t)):trans_of(A) \
-\ else fst(t) = fst(s)) \
-\ & \
-\ (if a:act B then \
-\ (snd(s),a,snd(t)):trans_of(B) \
+\ (if a:act A then \
+\ (fst(s),a,fst(t)):trans_of(A) \
+\ else fst(t) = fst(s)) \
+\ & \
+\ (if a:act B then \
+\ (snd(s),a,snd(t)):trans_of(B) \
\ else snd(t) = snd(s))}";
by (simp_tac (simpset() addsimps (par_def::ioa_projections)) 1);
@@ -56,7 +54,7 @@
section "actions and par";
-Goal
+Goal
"actions(asig_comp a b) = actions(a) Un actions(b)";
by (simp_tac (simpset() addsimps
([actions_def,asig_comp_def]@asig_projections)) 1);
@@ -73,24 +71,24 @@
\ (ext A1) Un (ext A2)";
by (asm_full_simp_tac (simpset() addsimps [externals_def,asig_of_par,asig_comp_def,
asig_inputs_def,asig_outputs_def,Un_def,set_diff_def]) 1);
-by (rtac set_ext 1);
+by (rtac set_ext 1);
by (fast_tac set_cs 1);
-qed"externals_of_par";
+qed"externals_of_par";
Goal "act (A1||A2) = \
\ (act A1) Un (act A2)";
by (asm_full_simp_tac (simpset() addsimps [actions_def,asig_of_par,asig_comp_def,
asig_inputs_def,asig_outputs_def,asig_internals_def,Un_def,set_diff_def]) 1);
-by (rtac set_ext 1);
+by (rtac set_ext 1);
by (fast_tac set_cs 1);
-qed"actions_of_par";
+qed"actions_of_par";
Goal "inp (A1||A2) =\
\ ((inp A1) Un (inp A2)) - ((out A1) Un (out A2))";
by (asm_full_simp_tac (simpset() addsimps [actions_def,asig_of_par,asig_comp_def,
asig_inputs_def,asig_outputs_def,Un_def,set_diff_def]) 1);
qed"inputs_of_par";
-
+
Goal "out (A1||A2) =\
\ (out A1) Un (out A2)";
by (asm_full_simp_tac (simpset() addsimps [actions_def,asig_of_par,asig_comp_def,
@@ -105,7 +103,7 @@
(* ------------------------------------------------------------------------ *)
-section "actions and compatibility";
+section "actions and compatibility";
Goal"compatible A B = compatible B A";
by (asm_full_simp_tac (simpset() addsimps [compatible_def,Int_commute]) 1);
@@ -158,13 +156,13 @@
(* ------------------------------------------------------------------------- *)
-section "input_enabledness and par";
+section "input_enabledness and par";
-(* ugly case distinctions. Heart of proof:
+(* ugly case distinctions. Heart of proof:
1. inpAAactB_is_inpBoroutB ie. internals are really hidden.
2. inputs_of_par: outputs are no longer inputs of par. This is important here *)
-Goalw [input_enabled_def]
+Goalw [input_enabled_def]
"[| compatible A B; input_enabled A; input_enabled B|] \
\ ==> input_enabled (A||B)";
by (asm_full_simp_tac (simpset()addsimps[Let_def,inputs_of_par,trans_of_par])1);
@@ -232,7 +230,7 @@
section "invariants";
-val [p1,p2] = goalw thy [invariant_def]
+val [p1,p2] = goalw (the_context ()) [invariant_def]
"[| !!s. s:starts_of(A) ==> P(s); \
\ !!s t a. [|reachable A s; P(s)|] ==> (s,a,t): trans_of(A) --> P(t) |] \
\ ==> invariant A P";
@@ -246,7 +244,7 @@
qed"invariantI";
-val [p1,p2] = goal thy
+val [p1,p2] = goal (the_context ())
"[| !!s. s : starts_of(A) ==> P(s); \
\ !!s t a. reachable A s ==> P(s) --> (s,a,t):trans_of(A) --> P(t) \
\ |] ==> invariant A P";
@@ -254,7 +252,7 @@
qed "invariantI1";
Goalw [invariant_def] "[| invariant A P; reachable A s |] ==> P(s)";
-by (Blast_tac 1);
+by (Blast_tac 1);
qed "invariantE";
(* ------------------------------------------------------------------------- *)
@@ -375,7 +373,7 @@
trans_B_proj2,trans_AB_proj];
-Goal
+Goal
"((s,a,t) : trans_of(A || B || C || D)) = \
\ ((a:actions(asig_of(A)) | a:actions(asig_of(B)) | a:actions(asig_of(C)) | \
\ a:actions(asig_of(D))) & \
@@ -397,24 +395,24 @@
(* ------------------------------------------------------------------------- *)
-section "proof obligation generator for IOA requirements";
+section "proof obligation generator for IOA requirements";
(* without assumptions on A and B because is_trans_of is also incorporated in ||def *)
Goalw [is_trans_of_def] "is_trans_of (A||B)";
by (simp_tac (simpset() addsimps [Let_def,actions_of_par,trans_of_par]) 1);
qed"is_trans_of_par";
-Goalw [is_trans_of_def]
+Goalw [is_trans_of_def]
"is_trans_of A ==> is_trans_of (restrict A acts)";
by (asm_simp_tac (simpset() addsimps [cancel_restrict,acts_restrict])1);
qed"is_trans_of_restrict";
-Goalw [is_trans_of_def,restrict_def,restrict_asig_def]
+Goalw [is_trans_of_def,restrict_def,restrict_asig_def]
"is_trans_of A ==> is_trans_of (rename A f)";
by (asm_full_simp_tac
(simpset() addsimps [Let_def,actions_def,trans_of_def, asig_internals_def,
- asig_outputs_def,asig_inputs_def,externals_def,
- asig_of_def,rename_def,rename_set_def]) 1);
+ asig_outputs_def,asig_inputs_def,externals_def,
+ asig_of_def,rename_def,rename_set_def]) 1);
by (Blast_tac 1);
qed"is_trans_of_rename";
@@ -428,7 +426,7 @@
qed"is_asig_of_par";
Goalw [is_asig_of_def,is_asig_def,asig_of_def,restrict_def,restrict_asig_def,
- asig_internals_def,asig_outputs_def,asig_inputs_def,externals_def,o_def]
+ asig_internals_def,asig_outputs_def,asig_inputs_def,externals_def,o_def]
"is_asig_of A ==> is_asig_of (restrict A f)";
by (Asm_full_simp_tac 1);
by Auto_tac;
@@ -438,7 +436,7 @@
by (asm_full_simp_tac (simpset() addsimps [is_asig_of_def,
rename_def,rename_set_def,asig_internals_def,asig_outputs_def,
asig_inputs_def,actions_def,is_asig_def,asig_of_def]) 1);
-by Auto_tac;
+by Auto_tac;
by (ALLGOALS(dres_inst_tac [("s","Some ?x")] sym THEN' Asm_full_simp_tac));
by (ALLGOALS(Blast_tac));
qed"is_asig_of_rename";
@@ -450,7 +448,7 @@
Goalw [compatible_def]
"[|compatible A B; compatible A C |]==> compatible A (B||C)";
-by (asm_full_simp_tac (simpset() addsimps [internals_of_par,
+by (asm_full_simp_tac (simpset() addsimps [internals_of_par,
outputs_of_par,actions_of_par]) 1);
by Auto_tac;
qed"compatible_par";
@@ -458,7 +456,7 @@
(* better derive by previous one and compat_commute *)
Goalw [compatible_def]
"[|compatible A C; compatible B C |]==> compatible (A||B) C";
-by (asm_full_simp_tac (simpset() addsimps [internals_of_par,
+by (asm_full_simp_tac (simpset() addsimps [internals_of_par,
outputs_of_par,actions_of_par]) 1);
by Auto_tac;
qed"compatible_par2";