1 (* Title: HOL/BCV/Machine.ML |
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2 ID: $Id$ |
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3 Author: Tobias Nipkow |
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4 Copyright 1999 TUM |
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5 *) |
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6 |
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7 Addsimps [Let_def]; |
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8 |
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9 Addsimps [stype_def]; |
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10 |
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11 |
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12 (*** Machine specific ***) |
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13 |
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14 Goal "!p. p<size(bs) --> maxreg(bs!p) < maxregs(bs)"; |
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15 by (induct_tac "bs" 1); |
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16 by (auto_tac (claset(), simpset() addsimps [nth_Cons,less_max_iff_disj] |
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17 addsplits [nat.split])); |
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18 qed_spec_mp "maxreg_less_maxregs"; |
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19 |
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20 Goalw [le_typ] "(t <= Ctyp) = (t = Ctyp)"; |
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21 by (Simp_tac 1); |
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22 qed "le_Ctyp_conv"; |
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23 |
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24 Goalw [le_typ] "(t ~= Top) = (t = Atyp | t = Btyp | t = Ctyp)"; |
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25 by (induct_tac "t" 1); |
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26 by (ALLGOALS Simp_tac); |
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27 qed "le_Top_conv"; |
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28 |
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29 Goalw [step_pres_type_def,listsn_def,exec_def,stype_def] |
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30 "step_pres_type (%p. exec (bs!p)) (length bs) (stype bs)"; |
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31 by (force_tac (claset(), simpset() addsplits [instr.split_asm,split_if_asm]) 1); |
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32 qed "exec_pres_type"; |
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33 |
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34 Goalw [wti_is_fix_step_def,stable_def,wt_instr_def,exec_def,succs_def] |
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35 "wti_is_fix_step (%p. exec (bs!p)) (%u. wt_instr (bs ! u) u) \ |
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36 \ (%p. succs (bs ! p) p) (length bs) (stype bs)"; |
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37 by (force_tac (claset() addDs [maxreg_less_maxregs, |
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38 le_Top_conv RS iffD1,le_Ctyp_conv RS iffD1], |
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39 simpset() addsplits [option.split,instr.split]) 1); |
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40 qed "wt_instr_is_fix_exec"; |
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41 |
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42 |
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43 Goalw [step_mono_None_def,exec_def,succs_def,le_list] |
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44 "step_mono_None (%p. exec (bs!p)) (length bs) (stype bs)"; |
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45 by (Clarify_tac 1); |
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46 by (ftac maxreg_less_maxregs 1); |
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47 by (split_asm_tac [instr.split_asm] 1); |
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48 |
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49 by (ALLGOALS (asm_full_simp_tac (simpset() addsplits [split_if_asm]))); |
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50 |
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51 by (rotate_tac 1 1); |
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52 by (Asm_full_simp_tac 1); |
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53 by (blast_tac (claset() addIs [order_trans]) 1); |
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54 |
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55 by (rotate_tac 1 1); |
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56 by (Asm_full_simp_tac 1); |
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57 by (blast_tac (claset() addIs [order_trans]) 1); |
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58 |
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59 by (rotate_tac 1 1); |
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60 by (Asm_full_simp_tac 1); |
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61 by (blast_tac (claset() addIs [order_trans]) 1); |
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62 |
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63 by (rotate_tac 1 1); |
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64 by (Asm_full_simp_tac 1); |
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65 by (subgoal_tac "s!nat1 <= t!nat1" 1); |
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66 by (Blast_tac 2); |
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67 by (subgoal_tac "s!nat2 <= t!nat2" 1); |
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68 by (Blast_tac 2); |
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69 by (etac thin_rl 1); |
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70 by (asm_full_simp_tac (simpset() addsimps [le_typ])1); |
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71 by (case_tac "t!nat1" 1); |
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72 by (ALLGOALS Asm_full_simp_tac); |
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73 by (case_tac "t!nat2" 1); |
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74 by (ALLGOALS Asm_full_simp_tac); |
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75 by (case_tac "t!nat2" 1); |
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76 by (ALLGOALS Asm_full_simp_tac); |
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77 by (case_tac "s!nat1" 1); |
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78 by (ALLGOALS Asm_full_simp_tac); |
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79 by (case_tac "t!nat2" 1); |
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80 by (ALLGOALS Asm_full_simp_tac); |
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81 |
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82 qed "exec_mono_None"; |
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83 |
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84 Goalw [step_mono_def,exec_def,succs_def] |
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85 "step_mono (%p. exec (bs!p)) (length bs) (stype bs)"; |
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86 by (Clarify_tac 1); |
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87 by (ftac maxreg_less_maxregs 1); |
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88 by (split_asm_tac [instr.split_asm] 1); |
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89 by (ALLGOALS |
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90 (fast_tac (claset() addIs [list_update_le_cong,le_listD] |
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91 addss (simpset() addsplits [split_if_asm])))); |
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92 |
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93 qed_spec_mp "exec_mono_Some"; |
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94 |
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95 Goalw [stype_def] "semilat(stype bs)"; |
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96 by (Blast_tac 1); |
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97 qed "lat_stype"; |
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98 |
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99 Goalw [stype_def] "acc(stype bs)"; |
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100 by (Simp_tac 1); |
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101 qed "acc_stype"; |
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102 |
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103 Delsimps [stype_def]; |
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104 |
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105 Goal |
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106 "[| is_next next; \ |
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107 \ succs_bounded (%p. succs (bs!p) p) (size bs); \ |
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108 \ sos : listsn (size bs) (option(stype bs)) |] ==> \ |
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109 \ fix(next (%p. exec (bs!p)) (%p. succs (bs!p) p), sos) = \ |
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110 \ (? tos : listsn (size bs) (option(stype bs)). \ |
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111 \ sos <= tos & welltyping (%p. wt_instr (bs!p) p) tos)"; |
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112 by (simp_tac (simpset() delsimps [not_None_eq]) 1); |
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113 by (REPEAT(ares_tac [fix_next_iff_welltyping,exec_pres_type, |
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114 exec_mono_None,exec_mono_Some, |
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115 wt_instr_is_fix_exec,lat_stype,acc_stype] 1)); |
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116 |
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117 qed "fix_iff_welltyped"; |
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