--- a/src/HOLCF/IOA/meta_theory/Automata.ML Mon Jun 22 17:12:27 1998 +0200
+++ b/src/HOLCF/IOA/meta_theory/Automata.ML Mon Jun 22 17:13:09 1998 +0200
@@ -19,7 +19,7 @@
section "asig_of, starts_of, trans_of";
-goal thy
+Goal
"((asig_of (x,y,z,w,s)) = x) & \
\ ((starts_of (x,y,z,w,s)) = y) & \
\ ((trans_of (x,y,z,w,s)) = z) & \
@@ -28,19 +28,19 @@
by (simp_tac (simpset() addsimps ioa_projections) 1);
qed "ioa_triple_proj";
-goalw thy [is_trans_of_def,actions_def, is_asig_def]
+Goalw [is_trans_of_def,actions_def, is_asig_def]
"!!A. [| is_trans_of A; (s1,a,s2):trans_of(A) |] ==> a:act A";
by (REPEAT(etac conjE 1));
by (EVERY1[etac allE, etac impE, atac]);
by (Asm_full_simp_tac 1);
qed "trans_in_actions";
-goal thy
+Goal
"starts_of(A || B) = {p. fst(p):starts_of(A) & snd(p):starts_of(B)}";
by (simp_tac (simpset() addsimps (par_def::ioa_projections)) 1);
qed "starts_of_par";
-goal thy
+Goal
"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 \
@@ -60,7 +60,7 @@
section "actions and par";
-goal thy
+Goal
"actions(asig_comp a b) = actions(a) Un actions(b)";
by (simp_tac (simpset() addsimps
([actions_def,asig_comp_def]@asig_projections)) 1);
@@ -68,12 +68,12 @@
qed "actions_asig_comp";
-goal thy "asig_of(A || B) = asig_comp (asig_of A) (asig_of B)";
+Goal "asig_of(A || B) = asig_comp (asig_of A) (asig_of B)";
by (simp_tac (simpset() addsimps (par_def::ioa_projections)) 1);
qed "asig_of_par";
-goal thy "ext (A1||A2) = \
+Goal "ext (A1||A2) = \
\ (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);
@@ -81,7 +81,7 @@
by (fast_tac set_cs 1);
qed"externals_of_par";
-goal thy "act (A1||A2) = \
+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);
@@ -89,19 +89,19 @@
by (fast_tac set_cs 1);
qed"actions_of_par";
-goal thy "inp (A1||A2) =\
+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 thy "out (A1||A2) =\
+Goal "out (A1||A2) =\
\ (out A1) Un (out A2)";
by (asm_full_simp_tac (simpset() addsimps [actions_def,asig_of_par,asig_comp_def,
asig_outputs_def,Un_def,set_diff_def]) 1);
qed"outputs_of_par";
-goal thy "int (A1||A2) =\
+Goal "int (A1||A2) =\
\ (int A1) Un (int 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);
@@ -111,19 +111,19 @@
section "actions and compatibility";
-goal thy"compatible A B = compatible B A";
+Goal"compatible A B = compatible B A";
by (asm_full_simp_tac (simpset() addsimps [compatible_def,Int_commute]) 1);
by Auto_tac;
qed"compat_commute";
-goalw thy [externals_def,actions_def,compatible_def]
+Goalw [externals_def,actions_def,compatible_def]
"!! a. [| compatible A1 A2; a:ext A1|] ==> a~:int A2";
by (Asm_full_simp_tac 1);
by (best_tac (set_cs addEs [equalityCE]) 1);
qed"ext1_is_not_int2";
(* just commuting the previous one: better commute compatible *)
-goalw thy [externals_def,actions_def,compatible_def]
+Goalw [externals_def,actions_def,compatible_def]
"!! a. [| compatible A2 A1 ; a:ext A1|] ==> a~:int A2";
by (Asm_full_simp_tac 1);
by (best_tac (set_cs addEs [equalityCE]) 1);
@@ -132,20 +132,20 @@
bind_thm("ext1_ext2_is_not_act2",ext1_is_not_int2 RS int_and_ext_is_act);
bind_thm("ext1_ext2_is_not_act1",ext2_is_not_int1 RS int_and_ext_is_act);
-goalw thy [externals_def,actions_def,compatible_def]
+Goalw [externals_def,actions_def,compatible_def]
"!! x. [| compatible A B; x:int A |] ==> x~:ext B";
by (Asm_full_simp_tac 1);
by (best_tac (set_cs addEs [equalityCE]) 1);
qed"intA_is_not_extB";
-goalw thy [externals_def,actions_def,compatible_def,is_asig_def,asig_of_def]
+Goalw [externals_def,actions_def,compatible_def,is_asig_def,asig_of_def]
"!! a. [| compatible A B; a:int A |] ==> a ~: act B";
by (Asm_full_simp_tac 1);
by (best_tac (set_cs addEs [equalityCE]) 1);
qed"intA_is_not_actB";
(* the only one that needs disjointness of outputs and of internals and _all_ acts *)
-goalw thy [asig_outputs_def,asig_internals_def,actions_def,asig_inputs_def,
+Goalw [asig_outputs_def,asig_internals_def,actions_def,asig_inputs_def,
compatible_def,is_asig_def,asig_of_def]
"!! a. [| compatible A B; a:out A ;a:act B|] ==> a : inp B";
by (Asm_full_simp_tac 1);
@@ -153,7 +153,7 @@
qed"outAactB_is_inpB";
(* needed for propagation of input_enabledness from A,B to A||B *)
-goalw thy [asig_outputs_def,asig_internals_def,actions_def,asig_inputs_def,
+Goalw [asig_outputs_def,asig_internals_def,actions_def,asig_inputs_def,
compatible_def,is_asig_def,asig_of_def]
"!! a. [| compatible A B; a:inp A ;a:act B|] ==> a : inp B | a: out B";
by (Asm_full_simp_tac 1);
@@ -168,7 +168,7 @@
(* 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 thy [input_enabled_def]
+Goalw [input_enabled_def]
"!!A. [| 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);
@@ -267,12 +267,12 @@
section "restrict";
-goal thy "starts_of(restrict ioa acts) = starts_of(ioa) & \
+Goal "starts_of(restrict ioa acts) = starts_of(ioa) & \
\ trans_of(restrict ioa acts) = trans_of(ioa)";
by (simp_tac (simpset() addsimps ([restrict_def]@ioa_projections)) 1);
qed "cancel_restrict_a";
-goal thy "reachable (restrict ioa acts) s = reachable ioa s";
+Goal "reachable (restrict ioa acts) s = reachable ioa s";
by (rtac iffI 1);
by (etac reachable.induct 1);
by (asm_full_simp_tac (simpset() addsimps [cancel_restrict_a,reachable_0]) 1);
@@ -286,14 +286,14 @@
by (asm_full_simp_tac (simpset() addsimps [cancel_restrict_a]) 1);
qed "cancel_restrict_b";
-goal thy "act (restrict A acts) = act A";
+Goal "act (restrict A acts) = act A";
by (simp_tac (simpset() addsimps [actions_def,asig_internals_def,
asig_outputs_def,asig_inputs_def,externals_def,asig_of_def,restrict_def,
restrict_asig_def]) 1);
by Auto_tac;
qed"acts_restrict";
-goal thy "starts_of(restrict ioa acts) = starts_of(ioa) & \
+Goal "starts_of(restrict ioa acts) = starts_of(ioa) & \
\ trans_of(restrict ioa acts) = trans_of(ioa) & \
\ reachable (restrict ioa acts) s = reachable ioa s & \
\ act (restrict A acts) = act A";
@@ -306,12 +306,12 @@
-goal thy "!!f. s -a--(rename C f)-> t ==> (? x. Some(x) = f(a) & s -x--C-> t)";
+Goal "!!f. s -a--(rename C f)-> t ==> (? x. Some(x) = f(a) & s -x--C-> t)";
by (asm_full_simp_tac (simpset() addsimps [Let_def,rename_def,trans_of_def]) 1);
qed"trans_rename";
-goal thy "!!s.[| reachable (rename C g) s |] ==> reachable C s";
+Goal "!!s.[| reachable (rename C g) s |] ==> reachable C s";
by (etac reachable.induct 1);
by (rtac reachable_0 1);
by (asm_full_simp_tac (simpset() addsimps [rename_def]@ioa_projections) 1);
@@ -329,44 +329,44 @@
section "trans_of(A||B)";
-goal thy "!!A.[|(s,a,t):trans_of (A||B); a:act A|] \
+Goal "!!A.[|(s,a,t):trans_of (A||B); a:act A|] \
\ ==> (fst s,a,fst t):trans_of A";
by (asm_full_simp_tac (simpset() addsimps [Let_def,par_def,trans_of_def]) 1);
qed"trans_A_proj";
-goal thy "!!A.[|(s,a,t):trans_of (A||B); a:act B|] \
+Goal "!!A.[|(s,a,t):trans_of (A||B); a:act B|] \
\ ==> (snd s,a,snd t):trans_of B";
by (asm_full_simp_tac (simpset() addsimps [Let_def,par_def,trans_of_def]) 1);
qed"trans_B_proj";
-goal thy "!!A.[|(s,a,t):trans_of (A||B); a~:act A|]\
+Goal "!!A.[|(s,a,t):trans_of (A||B); a~:act A|]\
\ ==> fst s = fst t";
by (asm_full_simp_tac (simpset() addsimps [Let_def,par_def,trans_of_def]) 1);
qed"trans_A_proj2";
-goal thy "!!A.[|(s,a,t):trans_of (A||B); a~:act B|]\
+Goal "!!A.[|(s,a,t):trans_of (A||B); a~:act B|]\
\ ==> snd s = snd t";
by (asm_full_simp_tac (simpset() addsimps [Let_def,par_def,trans_of_def]) 1);
qed"trans_B_proj2";
-goal thy "!!A.(s,a,t):trans_of (A||B) \
+Goal "!!A.(s,a,t):trans_of (A||B) \
\ ==> a :act A | a :act B";
by (asm_full_simp_tac (simpset() addsimps [Let_def,par_def,trans_of_def]) 1);
qed"trans_AB_proj";
-goal thy "!!A. [|a:act A;a:act B;\
+Goal "!!A. [|a:act A;a:act B;\
\ (fst s,a,fst t):trans_of A;(snd s,a,snd t):trans_of B|]\
\ ==> (s,a,t):trans_of (A||B)";
by (asm_full_simp_tac (simpset() addsimps [Let_def,par_def,trans_of_def]) 1);
qed"trans_AB";
-goal thy "!!A. [|a:act A;a~:act B;\
+Goal "!!A. [|a:act A;a~:act B;\
\ (fst s,a,fst t):trans_of A;snd s=snd t|]\
\ ==> (s,a,t):trans_of (A||B)";
by (asm_full_simp_tac (simpset() addsimps [Let_def,par_def,trans_of_def]) 1);
qed"trans_A_notB";
-goal thy "!!A. [|a~:act A;a:act B;\
+Goal "!!A. [|a~:act A;a:act B;\
\ (snd s,a,snd t):trans_of B;fst s=fst t|]\
\ ==> (s,a,t):trans_of (A||B)";
by (asm_full_simp_tac (simpset() addsimps [Let_def,par_def,trans_of_def]) 1);
@@ -377,7 +377,7 @@
trans_B_proj2,trans_AB_proj];
-goal thy
+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))) & \
@@ -402,16 +402,16 @@
section "proof obligation generator for IOA requirements";
(* without assumptions on A and B because is_trans_of is also incorporated in ||def *)
-goalw thy [is_trans_of_def] "is_trans_of (A||B)";
+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 thy [is_trans_of_def]
+Goalw [is_trans_of_def]
"!!A. 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 thy [is_trans_of_def,restrict_def,restrict_asig_def]
+Goalw [is_trans_of_def,restrict_def,restrict_asig_def]
"!!A. 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,
@@ -420,7 +420,7 @@
by (Blast_tac 1);
qed"is_trans_of_rename";
-goal thy "!! A. [| is_asig_of A; is_asig_of B; compatible A B|] \
+Goal "!! A. [| is_asig_of A; is_asig_of B; compatible A B|] \
\ ==> is_asig_of (A||B)";
by (asm_full_simp_tac (simpset() addsimps [is_asig_of_def,asig_of_par,
asig_comp_def,compatible_def,asig_internals_def,asig_outputs_def,
@@ -430,7 +430,7 @@
by (REPEAT (best_tac (set_cs addEs [equalityCE]) 1));
qed"is_asig_of_par";
-goalw thy [is_asig_of_def,is_asig_def,asig_of_def,restrict_def,restrict_asig_def,
+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]
"!! A. is_asig_of A ==> is_asig_of (restrict A f)";
by (Asm_full_simp_tac 1);
@@ -438,7 +438,7 @@
by (REPEAT (best_tac (set_cs addEs [equalityCE]) 1));
qed"is_asig_of_restrict";
-goal thy "!! A. is_asig_of A ==> is_asig_of (rename A f)";
+Goal "!! A. is_asig_of A ==> is_asig_of (rename A f)";
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);
@@ -452,7 +452,7 @@
is_trans_of_par,is_trans_of_restrict,is_trans_of_rename];
-goalw thy [compatible_def]
+Goalw [compatible_def]
"!! A. [|compatible A B; compatible A C |]==> compatible A (B||C)";
by (asm_full_simp_tac (simpset() addsimps [internals_of_par,
outputs_of_par,actions_of_par]) 1);
@@ -461,7 +461,7 @@
qed"compatible_par";
(* FIX: better derive by previous one and compat_commute *)
-goalw thy [compatible_def]
+Goalw [compatible_def]
"!! A. [|compatible A C; compatible B C |]==> compatible (A||B) C";
by (asm_full_simp_tac (simpset() addsimps [internals_of_par,
outputs_of_par,actions_of_par]) 1);
@@ -469,7 +469,7 @@
by (REPEAT (best_tac (set_cs addEs [equalityCE]) 1));
qed"compatible_par2";
-goalw thy [compatible_def]
+Goalw [compatible_def]
"!! A. [| compatible A B; (ext B - S) Int ext A = {}|] \
\ ==> compatible A (restrict B S)";
by (asm_full_simp_tac (simpset() addsimps [ioa_triple_proj,asig_triple_proj,