10 |
10 |
11 |
11 |
12 (*** Machine specific ***) |
12 (*** Machine specific ***) |
13 |
13 |
14 Goal "!p. p<size(bs) --> maxreg(bs!p) < maxregs(bs)"; |
14 Goal "!p. p<size(bs) --> maxreg(bs!p) < maxregs(bs)"; |
15 by(induct_tac "bs" 1); |
15 by (induct_tac "bs" 1); |
16 by(auto_tac (claset(), simpset() addsimps [nth_Cons,less_max_iff_disj] |
16 by (auto_tac (claset(), simpset() addsimps [nth_Cons,less_max_iff_disj] |
17 addsplits [nat.split])); |
17 addsplits [nat.split])); |
18 qed_spec_mp "maxreg_less_maxregs"; |
18 qed_spec_mp "maxreg_less_maxregs"; |
19 |
19 |
20 Goalw [le_typ] "(t <= Ctyp) = (t = Ctyp)"; |
20 Goalw [le_typ] "(t <= Ctyp) = (t = Ctyp)"; |
21 by(Simp_tac 1); |
21 by (Simp_tac 1); |
22 qed "le_Ctyp_conv"; |
22 qed "le_Ctyp_conv"; |
23 |
23 |
24 Goalw [le_typ] "(t ~= Top) = (t = Atyp | t = Btyp | t = Ctyp)"; |
24 Goalw [le_typ] "(t ~= Top) = (t = Atyp | t = Btyp | t = Ctyp)"; |
25 by(induct_tac "t" 1); |
25 by (induct_tac "t" 1); |
26 by(ALLGOALS Simp_tac); |
26 by (ALLGOALS Simp_tac); |
27 qed "le_Top_conv"; |
27 qed "le_Top_conv"; |
28 |
28 |
29 Goalw [step_pres_type_def,listsn_def,exec_def,stype_def] |
29 Goalw [step_pres_type_def,listsn_def,exec_def,stype_def] |
30 "step_pres_type (%p. exec (bs!p)) (length bs) (stype bs)"; |
30 "step_pres_type (%p. exec (bs!p)) (length bs) (stype bs)"; |
31 by(force_tac (claset(), simpset() addsplits [instr.split_asm,split_if_asm]) 1); |
31 by (force_tac (claset(), simpset() addsplits [instr.split_asm,split_if_asm]) 1); |
32 qed "exec_pres_type"; |
32 qed "exec_pres_type"; |
33 |
33 |
34 Goalw [wti_is_fix_step_def,stable_def,wt_instr_def,exec_def,succs_def] |
34 Goalw [wti_is_fix_step_def,stable_def,wt_instr_def,exec_def,succs_def] |
35 "wti_is_fix_step (%p. exec (bs!p)) (%u. wt_instr (bs ! u) u) \ |
35 "wti_is_fix_step (%p. exec (bs!p)) (%u. wt_instr (bs ! u) u) \ |
36 \ (%p. succs (bs ! p) p) (length bs) (stype bs)"; |
36 \ (%p. succs (bs ! p) p) (length bs) (stype bs)"; |
37 by(force_tac (claset() addDs [maxreg_less_maxregs, |
37 by (force_tac (claset() addDs [maxreg_less_maxregs, |
38 le_Top_conv RS iffD1,le_Ctyp_conv RS iffD1], |
38 le_Top_conv RS iffD1,le_Ctyp_conv RS iffD1], |
39 simpset() addsplits [option.split,instr.split]) 1); |
39 simpset() addsplits [option.split,instr.split]) 1); |
40 qed "wt_instr_is_fix_exec"; |
40 qed "wt_instr_is_fix_exec"; |
41 |
41 |
42 |
42 |
43 Goalw [step_mono_None_def,exec_def,succs_def,le_list] |
43 Goalw [step_mono_None_def,exec_def,succs_def,le_list] |
44 "step_mono_None (%p. exec (bs!p)) (length bs) (stype bs)"; |
44 "step_mono_None (%p. exec (bs!p)) (length bs) (stype bs)"; |
45 by(Clarify_tac 1); |
45 by (Clarify_tac 1); |
46 by(forward_tac [maxreg_less_maxregs] 1); |
46 by (ftac maxreg_less_maxregs 1); |
47 by(split_asm_tac [instr.split_asm] 1); |
47 by (split_asm_tac [instr.split_asm] 1); |
48 |
48 |
49 by(ALLGOALS (asm_full_simp_tac (simpset() addsplits [split_if_asm]))); |
49 by (ALLGOALS (asm_full_simp_tac (simpset() addsplits [split_if_asm]))); |
50 |
50 |
51 by(rotate_tac 1 1); |
51 by (rotate_tac 1 1); |
52 by(Asm_full_simp_tac 1); |
52 by (Asm_full_simp_tac 1); |
53 by(blast_tac (claset() addIs [order_trans]) 1); |
53 by (blast_tac (claset() addIs [order_trans]) 1); |
54 |
54 |
55 by(rotate_tac 1 1); |
55 by (rotate_tac 1 1); |
56 by(Asm_full_simp_tac 1); |
56 by (Asm_full_simp_tac 1); |
57 by(blast_tac (claset() addIs [order_trans]) 1); |
57 by (blast_tac (claset() addIs [order_trans]) 1); |
58 |
58 |
59 by(rotate_tac 1 1); |
59 by (rotate_tac 1 1); |
60 by(Asm_full_simp_tac 1); |
60 by (Asm_full_simp_tac 1); |
61 by(blast_tac (claset() addIs [order_trans]) 1); |
61 by (blast_tac (claset() addIs [order_trans]) 1); |
62 |
62 |
63 by(rotate_tac 1 1); |
63 by (rotate_tac 1 1); |
64 by(Asm_full_simp_tac 1); |
64 by (Asm_full_simp_tac 1); |
65 by(subgoal_tac "s!nat1 <= t!nat1" 1); |
65 by (subgoal_tac "s!nat1 <= t!nat1" 1); |
66 by(Blast_tac 2); |
66 by (Blast_tac 2); |
67 by(subgoal_tac "s!nat2 <= t!nat2" 1); |
67 by (subgoal_tac "s!nat2 <= t!nat2" 1); |
68 by(Blast_tac 2); |
68 by (Blast_tac 2); |
69 be thin_rl 1; |
69 by (etac thin_rl 1); |
70 by(asm_full_simp_tac (simpset() addsimps [le_typ])1); |
70 by (asm_full_simp_tac (simpset() addsimps [le_typ])1); |
71 by(exhaust_tac "t!nat1" 1); |
71 by (exhaust_tac "t!nat1" 1); |
72 by(ALLGOALS Asm_full_simp_tac); |
72 by (ALLGOALS Asm_full_simp_tac); |
73 by(exhaust_tac "t!nat2" 1); |
73 by (exhaust_tac "t!nat2" 1); |
74 by(ALLGOALS Asm_full_simp_tac); |
74 by (ALLGOALS Asm_full_simp_tac); |
75 by(exhaust_tac "t!nat2" 1); |
75 by (exhaust_tac "t!nat2" 1); |
76 by(ALLGOALS Asm_full_simp_tac); |
76 by (ALLGOALS Asm_full_simp_tac); |
77 by(exhaust_tac "s!nat1" 1); |
77 by (exhaust_tac "s!nat1" 1); |
78 by(ALLGOALS Asm_full_simp_tac); |
78 by (ALLGOALS Asm_full_simp_tac); |
79 by(exhaust_tac "t!nat2" 1); |
79 by (exhaust_tac "t!nat2" 1); |
80 by(ALLGOALS Asm_full_simp_tac); |
80 by (ALLGOALS Asm_full_simp_tac); |
81 |
81 |
82 qed "exec_mono_None"; |
82 qed "exec_mono_None"; |
83 |
83 |
84 Goalw [step_mono_def,exec_def,succs_def] |
84 Goalw [step_mono_def,exec_def,succs_def] |
85 "step_mono (%p. exec (bs!p)) (length bs) (stype bs)"; |
85 "step_mono (%p. exec (bs!p)) (length bs) (stype bs)"; |
86 by(Clarify_tac 1); |
86 by (Clarify_tac 1); |
87 by(forward_tac [maxreg_less_maxregs] 1); |
87 by (ftac maxreg_less_maxregs 1); |
88 by(split_asm_tac [instr.split_asm] 1); |
88 by (split_asm_tac [instr.split_asm] 1); |
89 by(ALLGOALS |
89 by (ALLGOALS |
90 (fast_tac (claset() addIs [list_update_le_cong,le_listD] |
90 (fast_tac (claset() addIs [list_update_le_cong,le_listD] |
91 addss (simpset() addsplits [split_if_asm])))); |
91 addss (simpset() addsplits [split_if_asm])))); |
92 |
92 |
93 qed_spec_mp "exec_mono_Some"; |
93 qed_spec_mp "exec_mono_Some"; |
94 |
94 |
95 Goalw [stype_def] "semilat(stype bs)"; |
95 Goalw [stype_def] "semilat(stype bs)"; |
96 by(Blast_tac 1); |
96 by (Blast_tac 1); |
97 qed "lat_stype"; |
97 qed "lat_stype"; |
98 |
98 |
99 Goalw [stype_def] "acc(stype bs)"; |
99 Goalw [stype_def] "acc(stype bs)"; |
100 by(Simp_tac 1); |
100 by (Simp_tac 1); |
101 qed "acc_stype"; |
101 qed "acc_stype"; |
102 |
102 |
103 Delsimps [stype_def]; |
103 Delsimps [stype_def]; |
104 |
104 |
105 Goal |
105 Goal |
107 \ succs_bounded (%p. succs (bs!p) p) (size bs); \ |
107 \ succs_bounded (%p. succs (bs!p) p) (size bs); \ |
108 \ sos : listsn (size bs) (option(stype bs)) |] ==> \ |
108 \ sos : listsn (size bs) (option(stype bs)) |] ==> \ |
109 \ fix(next (%p. exec (bs!p)) (%p. succs (bs!p) p), sos) = \ |
109 \ fix(next (%p. exec (bs!p)) (%p. succs (bs!p) p), sos) = \ |
110 \ (? tos : listsn (size bs) (option(stype bs)). \ |
110 \ (? tos : listsn (size bs) (option(stype bs)). \ |
111 \ sos <= tos & welltyping (%p. wt_instr (bs!p) p) tos)"; |
111 \ sos <= tos & welltyping (%p. wt_instr (bs!p) p) tos)"; |
112 by(simp_tac (simpset() delsimps [not_None_eq]) 1); |
112 by (simp_tac (simpset() delsimps [not_None_eq]) 1); |
113 by(REPEAT(ares_tac [fix_next_iff_welltyping,exec_pres_type, |
113 by (REPEAT(ares_tac [fix_next_iff_welltyping,exec_pres_type, |
114 exec_mono_None,exec_mono_Some, |
114 exec_mono_None,exec_mono_Some, |
115 wt_instr_is_fix_exec,lat_stype,acc_stype] 1)); |
115 wt_instr_is_fix_exec,lat_stype,acc_stype] 1)); |
116 |
116 |
117 qed "fix_iff_welltyped"; |
117 qed "fix_iff_welltyped"; |