1 | include "ASM/Assembly.ma". |
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2 | include "ASM/Interpret.ma". |
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3 | |
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4 | let rec encoding_check (code_memory: BitVectorTrie Byte 16) (pc: Word) (final_pc: Word) |
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5 | (encoding: list Byte) on encoding: Prop ≝ |
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6 | match encoding with |
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7 | [ nil ⇒ final_pc = pc |
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8 | | cons hd tl ⇒ |
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9 | let 〈new_pc, byte〉 ≝ next code_memory pc in |
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10 | hd = byte ∧ encoding_check code_memory new_pc final_pc tl |
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11 | ]. |
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12 | |
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13 | definition assembly_specification: |
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14 | ∀sigma: Word → Word. ∀assembly_program: pseudo_assembly_program. |
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15 | ∀code_mem: BitVectorTrie Byte 16. Prop ≝ |
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16 | λsigma. |
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17 | λpseudo_assembly_program. |
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18 | λcode_mem. |
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19 | ∀pc: Word. |
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20 | let 〈preamble, instr_list〉 ≝ pseudo_assembly_program in |
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21 | let 〈pre_instr, pre_new_pc〉 ≝ fetch_pseudo_instruction instr_list pc in |
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22 | let address_of ≝ ? in |
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23 | let labels ≝ λx. sigma (address_of_word_labels_code_mem instr_list x) in |
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24 | let datalabels ≝ λx. sigma (lookup ? ? x (construct_datalabels preamble) (zero ?)) in |
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25 | let pre_assembled ≝ assembly_1_pseudoinstruction labels datalabels address_of 〈None ?, pre_instr〉 in |
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26 | encoding_check code_mem pc (sigma pre_new_pc) pre_assembled. |
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27 | cases not_implemented |
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28 | qed. |
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29 | |
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30 | axiom assembly_meets_specification: |
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31 | ∀pseudo_assembly_program. |
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32 | match assembly pseudo_assembly_program with |
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33 | [ None ⇒ True |
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34 | | Some code_mem_cost ⇒ |
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35 | let 〈code_mem, cost〉 ≝ code_mem_cost in |
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36 | assembly_specification ? pseudo_assembly_program (load_code_memory code_mem) |
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37 | ]. |
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38 | cases not_implemented (* |
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39 | # PROGRAM |
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40 | [ cases PROGRAM |
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41 | # PREAMBLE |
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42 | # INSTR_LIST |
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43 | elim INSTR_LIST |
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44 | [ whd |
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45 | whd in ⊢ (∀_. %) |
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46 | # PC |
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47 | whd |
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48 | | # INSTR |
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49 | # INSTR_LIST_TL |
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50 | # H |
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51 | whd |
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52 | normalize |
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53 | ] |
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54 | | cases not_implemented |
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55 | ] *) |
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56 | qed. |
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57 | |
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58 | axiom sigma: pseudo_assembly_program → Word → Word. |
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59 | |
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60 | definition status_of_pseudo_status: PseudoStatus → option Status ≝ |
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61 | λps. |
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62 | let pap ≝ code_memory … ps in |
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63 | match assembly pap with |
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64 | [ None ⇒ None … |
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65 | | Some p ⇒ |
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66 | let cm ≝ load_code_memory (\fst p) in |
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67 | let pc ≝ sigma pap (program_counter ? ps) in |
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68 | Some … |
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69 | (mk_PreStatus (BitVectorTrie Byte 16) |
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70 | cm |
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71 | (low_internal_ram … ps) |
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72 | (high_internal_ram … ps) |
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73 | (external_ram … ps) |
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74 | pc |
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75 | (special_function_registers_8051 … ps) |
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76 | (special_function_registers_8052 … ps) |
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77 | (p1_latch … ps) |
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78 | (p3_latch … ps) |
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79 | (clock … ps)) ]. |
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80 | |
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81 | |
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82 | lemma execute_code_memory_unchanged: |
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83 | ∀ticks_of,ps. code_memory ? ps = code_memory ? (execute_1_pseudo_instruction ticks_of ps). |
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84 | #ticks #ps whd in ⊢ (??? (??%)) |
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85 | cases (fetch_pseudo_instruction (\snd (code_memory pseudo_assembly_program ps)) |
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86 | (program_counter pseudo_assembly_program ps)) #instr #pc |
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87 | whd in ⊢ (??? (??%)) cases instr |
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88 | [ #pre cases pre |
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89 | [ #a1 #a2 whd in ⊢ (??? (??%)) cases (add_8_with_carry ???) #y1 #y2 whd in ⊢ (??? (??%)) |
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90 | cases (split ????) #z1 #z2 % |
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91 | | *: cases not_implemented |
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92 | ] |
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93 | | #comment % |
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94 | | #cost % |
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95 | | #label % |
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96 | | #label (* CSC: ??? *) |
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97 | | #dptr #label (* CSC: ??? *) |
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98 | ] |
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99 | cases not_implemented |
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100 | qed. |
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101 | |
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102 | lemma foo: |
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103 | ∀ticks_of. |
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104 | ∀ps: PseudoStatus. |
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105 | match status_of_pseudo_status ps with [ None ⇒ True | Some s ⇒ |
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106 | let ps' ≝ execute_1_pseudo_instruction ticks_of ps in |
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107 | match status_of_pseudo_status ps' with [ None ⇒ True | Some s'' ⇒ |
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108 | let s' ≝ execute_1 s in |
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109 | s = s'']]. |
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110 | #ticks_of #ps |
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111 | whd in ⊢ (match % with [ _ ⇒ ? | _ ⇒ ? ]) |
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112 | cases (assembly (code_memory pseudo_assembly_program ps)) [%] * #cm #costs whd |
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113 | whd in ⊢ (match % with [ _ ⇒ ? | _ ⇒ ? ]) |
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114 | cases (status_of_pseudo_status (execute_1_pseudo_instruction ticks_of ps)) [%] #s'' whd |
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