[1952] | 1 | include "ASM/AssemblyProof.ma". |
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| 2 | include alias "arithmetics/nat.ma". |
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| 3 | include alias "basics/logic.ma". |
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| 4 | |
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[1966] | 5 | lemma set_arg_16_mk_Status_commutation: |
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| 6 | ∀M: Type[0]. |
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| 7 | ∀cm: M. |
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| 8 | ∀s: PreStatus M cm. |
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| 9 | ∀w: Word. |
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| 10 | ∀d: [[dptr]]. |
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| 11 | set_arg_16 M cm s w d = |
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| 12 | mk_PreStatus M cm |
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| 13 | (low_internal_ram … s) |
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| 14 | (high_internal_ram … s) |
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| 15 | (external_ram … s) |
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| 16 | (program_counter … s) |
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| 17 | (special_function_registers_8051 … (set_arg_16 M cm s w d)) |
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| 18 | (special_function_registers_8052 … s) |
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| 19 | (p1_latch … s) |
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| 20 | (p3_latch … s) |
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| 21 | (clock … s). |
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| 22 | #M #cm #s #w #d |
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| 23 | whd in match set_arg_16; normalize nodelta |
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| 24 | whd in match set_arg_16'; normalize nodelta |
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[2039] | 25 | @(subaddressing_mode_elim … d) |
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[2032] | 26 | cases (vsplit bool 8 8 w) #bu #bl normalize nodelta |
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[1966] | 27 | whd in match set_8051_sfr; normalize nodelta % |
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| 28 | qed. |
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[1963] | 29 | |
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[1966] | 30 | lemma set_program_counter_mk_Status_commutation: |
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| 31 | ∀M: Type[0]. |
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| 32 | ∀cm: M. |
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| 33 | ∀s: PreStatus M cm. |
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| 34 | ∀w: Word. |
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| 35 | set_program_counter M cm s w = |
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| 36 | mk_PreStatus M cm |
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| 37 | (low_internal_ram … s) |
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| 38 | (high_internal_ram … s) |
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| 39 | (external_ram … s) |
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| 40 | w |
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| 41 | (special_function_registers_8051 … s) |
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| 42 | (special_function_registers_8052 … s) |
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| 43 | (p1_latch … s) |
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| 44 | (p3_latch … s) |
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| 45 | (clock … s). |
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| 46 | // |
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[1983] | 47 | qed. |
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[1966] | 48 | |
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| 49 | lemma set_clock_mk_Status_commutation: |
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| 50 | ∀M: Type[0]. |
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| 51 | ∀cm: M. |
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| 52 | ∀s: PreStatus M cm. |
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| 53 | ∀c: nat. |
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| 54 | set_clock M cm s c = |
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| 55 | mk_PreStatus M cm |
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| 56 | (low_internal_ram … s) |
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| 57 | (high_internal_ram … s) |
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| 58 | (external_ram … s) |
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| 59 | (program_counter … s) |
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| 60 | (special_function_registers_8051 … s) |
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| 61 | (special_function_registers_8052 … s) |
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| 62 | (p1_latch … s) |
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| 63 | (p3_latch … s) |
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| 64 | c. |
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| 65 | // |
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| 66 | qed. |
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| 67 | |
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[1975] | 68 | lemma get_8051_sfr_set_clock: |
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| 69 | ∀M: Type[0]. |
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| 70 | ∀cm: M. |
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| 71 | ∀s: PreStatus M cm. |
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| 72 | ∀sfr: SFR8051. |
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| 73 | ∀t: Time. |
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| 74 | get_8051_sfr M cm (set_clock M cm s t) sfr = |
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| 75 | get_8051_sfr M cm s sfr. |
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| 76 | #M #cm #s #sfr #t % |
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| 77 | qed. |
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[1966] | 78 | |
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[2017] | 79 | lemma get_8051_sfr_set_program_counter: |
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| 80 | ∀M: Type[0]. |
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| 81 | ∀cm: M. |
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| 82 | ∀s: PreStatus M cm. |
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| 83 | ∀sfr: SFR8051. |
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| 84 | ∀pc: Word. |
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| 85 | get_8051_sfr M cm (set_program_counter M cm s pc) = |
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| 86 | get_8051_sfr M cm s. |
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| 87 | #M #cm #s #sfr #pc % |
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| 88 | qed. |
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| 89 | |
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[1966] | 90 | lemma special_function_registers_8051_set_arg_16: |
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| 91 | ∀M, M': Type[0]. |
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| 92 | ∀cm: M. |
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| 93 | ∀cm': M'. |
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| 94 | ∀s: PreStatus M cm. |
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| 95 | ∀s': PreStatus M' cm'. |
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| 96 | ∀w, w': Word. |
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| 97 | ∀d, d': [[dptr]]. |
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[1967] | 98 | special_function_registers_8051 ?? s = special_function_registers_8051 … s' → |
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| 99 | w = w' → |
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| 100 | special_function_registers_8051 ?? (set_arg_16 … s w d) = |
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| 101 | special_function_registers_8051 ?? (set_arg_16 M' cm' s' w' d'). |
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| 102 | #M #M' #cm #cm' #s #s' #w #w' |
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[2114] | 103 | #d @(subaddressing_mode_elim … d) |
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| 104 | #d' @(subaddressing_mode_elim … d') |
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[2032] | 105 | #EQ1 #EQ2 <EQ2 normalize cases (vsplit bool 8 8 w) #b1 #b2 normalize <EQ1 % |
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[1966] | 106 | qed. |
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| 107 | |
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[1984] | 108 | lemma program_counter_set_arg_1: |
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| 109 | ∀M: Type[0]. |
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| 110 | ∀cm: M. |
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| 111 | ∀s: PreStatus M cm. |
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| 112 | ∀addr: [[bit_addr; carry]]. |
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| 113 | ∀b: Bit. |
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| 114 | program_counter M cm (set_arg_1 M cm s addr b) = program_counter M cm s. |
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| 115 | #M #cm #s whd in match set_arg_1; whd in match set_arg_1'; normalize nodelta |
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| 116 | #addr #b |
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[2039] | 117 | @(subaddressing_mode_elim … addr) |
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[1984] | 118 | [1: |
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[2032] | 119 | #byte cases (vsplit ????) #nu #nl normalize nodelta |
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| 120 | cases (vsplit ????) #ignore #three_bits normalize nodelta |
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[1984] | 121 | cases (get_index_v bool ????) normalize nodelta |
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| 122 | [1: |
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| 123 | @program_counter_set_bit_addressable_sfr |
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| 124 | |2: |
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| 125 | @program_counter_set_low_internal_ram |
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| 126 | ] |
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| 127 | |2: |
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[2032] | 128 | cases (vsplit ????) // |
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[1984] | 129 | ] |
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| 130 | qed. |
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| 131 | |
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[2017] | 132 | lemma get_ov_flag_set_program_counter: |
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| 133 | ∀M: Type[0]. |
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| 134 | ∀cm: M. |
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| 135 | ∀s: PreStatus M cm. |
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| 136 | ∀pc: Word. |
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| 137 | get_ov_flag M cm (set_program_counter M cm s pc) = |
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| 138 | get_ov_flag M cm s. |
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| 139 | #M #cm #s #pc % |
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| 140 | qed. |
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| 141 | |
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| 142 | lemma external_ram_set_program_counter: |
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| 143 | ∀M: Type[0]. |
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| 144 | ∀cm: M. |
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| 145 | ∀s: PreStatus M cm. |
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| 146 | ∀pc: Word. |
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| 147 | external_ram M cm (set_program_counter M cm s pc) = |
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| 148 | external_ram M cm s. |
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| 149 | #M #cm #s #pc % |
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| 150 | qed. |
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| 151 | |
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| 152 | lemma low_internal_ram_set_program_counter: |
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| 153 | ∀M: Type[0]. |
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| 154 | ∀cm: M. |
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| 155 | ∀s: PreStatus M cm. |
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| 156 | ∀pc: Word. |
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| 157 | low_internal_ram M cm (set_program_counter M cm s pc) = |
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| 158 | low_internal_ram M cm s. |
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| 159 | #M #cm #s #pc % |
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| 160 | qed. |
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| 161 | |
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| 162 | lemma high_internal_ram_set_program_counter: |
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| 163 | ∀M: Type[0]. |
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| 164 | ∀cm: M. |
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| 165 | ∀s: PreStatus M cm. |
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| 166 | ∀pc: Word. |
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| 167 | high_internal_ram M cm (set_program_counter M cm s pc) = |
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| 168 | high_internal_ram M cm s. |
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| 169 | #M #cm #s #pc % |
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| 170 | qed. |
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| 171 | |
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| 172 | lemma get_arg_8_set_program_counter: |
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| 173 | ∀M: Type[0]. |
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| 174 | ∀cm: M. |
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| 175 | ∀s: PreStatus M cm. |
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| 176 | ∀flag: bool. |
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[2143] | 177 | ∀addr: [[direct; indirect; registr; acc_a; acc_b; data; acc_dptr; ext_indirect; ext_indirect_dptr]]. |
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[2017] | 178 | ∀pc: Word. |
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| 179 | get_arg_8 M cm (set_program_counter M cm s pc) flag addr = |
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| 180 | get_arg_8 M cm s flag addr. |
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[2143] | 181 | [2,3: |
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| 182 | cases addr #subaddressing_mode |
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| 183 | cases subaddressing_mode |
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| 184 | try (#addr1 whd in ⊢ (% → %);) |
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| 185 | whd in ⊢ (% → %); // |
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| 186 | ] |
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[2017] | 187 | #M #cm #s #flag #addr #pc |
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| 188 | whd in match get_arg_8; normalize nodelta |
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| 189 | cases addr * |
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| 190 | try (#addr1 #absurd normalize in absurd; cases absurd @I) |
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| 191 | try (#absurd normalize in absurd; cases absurd @I) |
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| 192 | try (#addr1 #addr2) try #addr1 |
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[2143] | 193 | normalize nodelta % |
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[2017] | 194 | qed. |
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| 195 | |
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| 196 | lemma external_ram_set_flags: |
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| 197 | ∀M: Type[0]. |
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| 198 | ∀cm: M. |
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| 199 | ∀s: PreStatus M cm. |
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| 200 | ∀opt: option Bit. |
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| 201 | ∀bit1, bit2: Bit. |
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| 202 | external_ram M cm (set_flags M cm s bit1 opt bit2) = |
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| 203 | external_ram M cm s. |
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| 204 | #M #cm #s #opt #bit1 #bit2 % |
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| 205 | qed. |
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| 206 | |
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| 207 | lemma low_internal_ram_set_flags: |
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| 208 | ∀M: Type[0]. |
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| 209 | ∀cm: M. |
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| 210 | ∀s: PreStatus M cm. |
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| 211 | ∀opt: option Bit. |
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| 212 | ∀bit1, bit2: Bit. |
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| 213 | low_internal_ram M cm (set_flags M cm s bit1 opt bit2) = |
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| 214 | low_internal_ram M cm s. |
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| 215 | #M #cm #s #opt #bit1 #bit2 % |
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| 216 | qed. |
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| 217 | |
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| 218 | lemma high_internal_ram_set_flags: |
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| 219 | ∀M: Type[0]. |
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| 220 | ∀cm: M. |
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| 221 | ∀s: PreStatus M cm. |
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| 222 | ∀opt: option Bit. |
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| 223 | ∀bit1, bit2: Bit. |
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| 224 | high_internal_ram M cm (set_flags M cm s bit1 opt bit2) = |
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| 225 | high_internal_ram M cm s. |
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| 226 | #M #cm #s #opt #bit1 #bit2 % |
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| 227 | qed. |
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| 228 | |
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| 229 | lemma low_internal_ram_set_clock: |
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| 230 | ∀M: Type[0]. |
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| 231 | ∀cm: M. |
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| 232 | ∀s: PreStatus M cm. |
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| 233 | ∀t: Time. |
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| 234 | low_internal_ram M cm (set_clock M cm s t) = |
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| 235 | low_internal_ram M cm s. |
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| 236 | #M #cm #s #t % |
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| 237 | qed. |
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| 238 | |
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| 239 | lemma high_internal_ram_set_clock: |
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| 240 | ∀M: Type[0]. |
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| 241 | ∀cm: M. |
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| 242 | ∀s: PreStatus M cm. |
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| 243 | ∀t: Time. |
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| 244 | high_internal_ram M cm (set_clock M cm s t) = |
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| 245 | high_internal_ram M cm s. |
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| 246 | #M #cm #s #t % |
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| 247 | qed. |
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| 248 | |
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| 249 | lemma external_ram_set_clock: |
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| 250 | ∀M: Type[0]. |
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| 251 | ∀cm: M. |
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| 252 | ∀s: PreStatus M cm. |
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| 253 | ∀t: Time. |
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| 254 | external_ram M cm (set_clock M cm s t) = |
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| 255 | external_ram M cm s. |
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| 256 | #M #cm #s #t % |
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| 257 | qed. |
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| 258 | |
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| 259 | lemma set_8051_sfr_set_program_counter: |
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| 260 | ∀M: Type[0]. |
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| 261 | ∀cm: M. |
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| 262 | ∀s: PreStatus M cm. |
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| 263 | ∀pc: Word. |
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| 264 | ∀sfr: SFR8051. |
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| 265 | ∀v: Byte. |
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| 266 | set_8051_sfr M cm (set_program_counter M cm s pc) sfr v = |
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| 267 | set_program_counter M cm (set_8051_sfr M cm s sfr v) pc. |
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| 268 | #M #cm #s #pc #sfr #v % |
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| 269 | qed. |
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| 270 | |
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| 271 | lemma low_internal_ram_set_8051_sfr: |
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| 272 | ∀M: Type[0]. |
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| 273 | ∀cm: M. |
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| 274 | ∀s: PreStatus M cm. |
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| 275 | ∀sfr: SFR8051. |
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| 276 | ∀v: Byte. |
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| 277 | low_internal_ram M cm (set_8051_sfr M cm s sfr v) = |
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| 278 | low_internal_ram M cm s. |
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| 279 | #M #cm #s #sfr #v % |
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| 280 | qed. |
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| 281 | |
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| 282 | lemma high_internal_ram_set_8051_sfr: |
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| 283 | ∀M: Type[0]. |
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| 284 | ∀cm: M. |
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| 285 | ∀s: PreStatus M cm. |
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| 286 | ∀sfr: SFR8051. |
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| 287 | ∀v: Byte. |
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| 288 | high_internal_ram M cm (set_8051_sfr M cm s sfr v) = |
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| 289 | high_internal_ram M cm s. |
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| 290 | #M #cm #s #sfr #v % |
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| 291 | qed. |
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| 292 | |
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| 293 | lemma external_ram_set_8051_sfr: |
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| 294 | ∀M: Type[0]. |
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| 295 | ∀cm: M. |
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| 296 | ∀s: PreStatus M cm. |
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| 297 | ∀sfr: SFR8051. |
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| 298 | ∀v: Byte. |
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| 299 | external_ram M cm (set_8051_sfr M cm s sfr v) = |
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| 300 | external_ram M cm s. |
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| 301 | #M #cm #s #sfr #v % |
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| 302 | qed. |
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| 303 | |
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| 304 | lemma get_arg_8_set_clock: |
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| 305 | ∀M: Type[0]. |
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| 306 | ∀cm: M. |
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| 307 | ∀s: PreStatus M cm. |
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| 308 | ∀addr. |
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| 309 | ∀t: Time. |
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| 310 | get_arg_8 M cm (set_clock M cm s t) addr = |
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| 311 | get_arg_8 M cm s addr. |
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| 312 | #M #cm #s #addr #t % |
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| 313 | qed. |
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| 314 | |
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[2023] | 315 | lemma set_program_counter_set_program_counter: |
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| 316 | ∀M: Type[0]. |
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| 317 | ∀cm: M. |
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| 318 | ∀s: PreStatus M cm. |
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| 319 | ∀pc: Word. |
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| 320 | ∀pc': Word. |
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| 321 | set_program_counter M cm (set_program_counter M cm s pc) pc' = |
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| 322 | set_program_counter M cm s pc'. |
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| 323 | #M #cm #s #pc #pc' % |
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| 324 | qed. |
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| 325 | |
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[2143] | 326 | (* XXX: move elsewhere *) |
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| 327 | lemma bitvector_8_cases: |
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| 328 | ∀w: BitVector 8. |
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| 329 | ∃b0,b1,b2,b3,b4,b5,b6,b7: bool. |
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| 330 | w ≃ [[b0;b1;b2;b3;b4;b5;b6;b7]]. |
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| 331 | #w repeat (cases (BitVector_Sn … w) #b0 * #w0 #EQ0 >EQ0 %{b0} -w lapply w0 -w0 #w) |
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| 332 | >(BitVector_O … w) % |
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| 333 | qed. |
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| 334 | |
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| 335 | (* XXX: not true |
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| 336 | lemma p3_latch_set_arg_8: |
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| 337 | ∀M: Type[0]. |
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| 338 | ∀cm: M. |
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| 339 | ∀s: PreStatus M cm. |
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| 340 | ∀args. |
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| 341 | ∀v: Byte. |
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| 342 | p3_latch M cm (set_arg_8 M cm s args v) = |
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| 343 | p3_latch M cm s. |
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| 344 | #M #cm #s #args #v |
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| 345 | @(subaddressing_mode_elim … args) |
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| 346 | try #w try % |
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| 347 | whd in match set_arg_8; normalize nodelta |
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| 348 | whd in match set_arg_8'; normalize nodelta |
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| 349 | inversion (vsplit bool ???) #nu #nl #nu_nl_refl normalize nodelta |
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| 350 | inversion (vsplit bool ???) #ignore #three_bits #ignore_three_bits_refl normalize nodelta |
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| 351 | inversion (get_index_v bool ????) #get_index_v_refl normalize nodelta try % |
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| 352 | whd in match set_bit_addressable_sfr; normalize nodelta |
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| 353 | @(bitvector_8_elim_prop … w) |
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| 354 | *) |
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| 355 | |
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| 356 | lemma status_of_pseudo_status_does_not_change_8051_sfrs: |
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| 357 | ∀M: internal_pseudo_address_map. |
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| 358 | ∀cm: pseudo_assembly_program. |
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| 359 | ∀s: PreStatus pseudo_assembly_program cm. |
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| 360 | ∀sigma: Word → Word. |
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| 361 | ∀policy: Word → bool. |
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[2160] | 362 | \snd M = data → |
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[2143] | 363 | special_function_registers_8051 pseudo_assembly_program cm s = |
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| 364 | special_function_registers_8051 (BitVectorTrie Byte 16) |
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| 365 | (code_memory_of_pseudo_assembly_program cm sigma policy) |
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| 366 | (status_of_pseudo_status M cm s sigma policy). |
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| 367 | #M #cm #s #sigma #policy #None_proof cases s |
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| 368 | #H1 #H2 #H3 #H4 #H5 #H6 #H7 #H8 #H9 |
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| 369 | whd in match status_of_pseudo_status; normalize nodelta |
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| 370 | whd in match sfr_8051_of_pseudo_sfr_8051; normalize nodelta |
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| 371 | >None_proof % |
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| 372 | qed. |
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| 373 | |
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[2160] | 374 | lemma n_lt_19_elim_prop: |
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| 375 | ∀P: nat → Prop. |
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| 376 | P 0 → P 1 → P 2 → P 3 → P 4 → P 5 → P 6 → P 7 → P 8 → P 9 → |
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| 377 | P 10 → P 11 → P 12 → P 13 → P 14 → P 15 → P 16 → P 17 → P 18 → |
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| 378 | (∀n. n < 19 → P n). |
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| 379 | #P #H1 #H2 #H3 #H4 #H5 #H6 #H7 #H8 #H9 #H10 #H11 #H12 #H13 #H14 |
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| 380 | #H15 #H16 #H17 #H18 #H19 #n |
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| 381 | cases n [1: // ] |
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| 382 | #n' cases n' [1: // ] #n' cases n' [1: // ] #n' cases n' [1: // ] |
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| 383 | #n' cases n' [1: // ] #n' cases n' [1: // ] #n' cases n' [1: // ] |
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| 384 | #n' cases n' [1: // ] #n' cases n' [1: // ] #n' cases n' [1: // ] |
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| 385 | #n' cases n' [1: // ] #n' cases n' [1: // ] #n' cases n' [1: // ] |
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| 386 | #n' cases n' [1: // ] #n' cases n' [1: // ] #n' cases n' [1: // ] |
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| 387 | #n' cases n' [1: // ] #n' cases n' [1: // ] #n' cases n' [1: // ] |
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| 388 | #n' normalize in ⊢ (% → ?); |
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| 389 | #absurd repeat (lapply (le_S_S_to_le … absurd) #absurd) |
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| 390 | cases (lt_to_not_zero … absurd) |
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[2143] | 391 | qed. |
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| 392 | |
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[2160] | 393 | lemma get_index_v_set_index_miss: |
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| 394 | ∀T: Type[0]. |
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| 395 | ∀n, i, j: nat. |
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| 396 | ∀v: Vector T n. |
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| 397 | ∀b: T. |
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| 398 | ∀i_proof: i < n. |
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| 399 | ∀j_proof: j < n. |
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| 400 | i ≠ j → |
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| 401 | get_index_v T n (set_index T n v i b i_proof) j j_proof = |
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| 402 | get_index_v T n v j j_proof. |
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| 403 | #T #n #i #j #v lapply i lapply j elim v #i #j |
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[2143] | 404 | [1: |
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[2160] | 405 | #b #i_proof |
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| 406 | cases (lt_to_not_zero … i_proof) |
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[2143] | 407 | |2: |
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[2160] | 408 | #tl #inductive_hypothesis #j' #i' #b #i_proof #j_proof #i_neq_j |
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| 409 | lapply i_proof lapply i_neq_j cases i' |
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| 410 | [1: |
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| 411 | -i_neq_j #i_neq_j -i_proof #i_proof |
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| 412 | whd in match (set_index ??????); |
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| 413 | lapply j_proof lapply i_neq_j cases j' |
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| 414 | [1: |
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| 415 | #relevant @⊥ cases relevant -relevant #absurd @absurd % |
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| 416 | |2: |
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| 417 | #j' #_ -j_proof #j_proof % |
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[2143] | 418 | ] |
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[2160] | 419 | |2: |
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| 420 | #i' -i_neq_j #i_neq_j -i_proof #i_proof |
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| 421 | lapply j_proof lapply i_neq_j cases j' |
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| 422 | [1: |
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| 423 | #_ #j_proof % |
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| 424 | |2: |
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| 425 | #j' #i_neq_j #j_proof |
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| 426 | @inductive_hypothesis @nmk #relevant |
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| 427 | cases i_neq_j #absurd @absurd >relevant % |
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| 428 | ] |
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[2143] | 429 | ] |
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| 430 | ] |
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| 431 | qed. |
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| 432 | |
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[2160] | 433 | lemma get_index_v_special_function_registers_8051_not_acc_a: |
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| 434 | ∀M: internal_pseudo_address_map. |
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| 435 | ∀cm: pseudo_assembly_program. |
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| 436 | ∀s: PreStatus pseudo_assembly_program cm. |
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| 437 | ∀sigma: Word → Word. |
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| 438 | ∀policy: Word → bool. |
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| 439 | ∀n: nat. |
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| 440 | ∀proof: n < 19. |
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| 441 | n ≠ 17 → |
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| 442 | (get_index_v Byte 19 |
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| 443 | (special_function_registers_8051 pseudo_assembly_program cm s) n |
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| 444 | proof = |
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| 445 | get_index_v Byte 19 |
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| 446 | (special_function_registers_8051 (BitVectorTrie Byte 16) |
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| 447 | (code_memory_of_pseudo_assembly_program cm sigma policy) |
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| 448 | (status_of_pseudo_status M cm s sigma policy)) n |
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| 449 | proof). |
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| 450 | #M #cm #s #sigma #policy #n #proof lapply proof |
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| 451 | @(n_lt_19_elim_prop … proof) -proof #proof |
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| 452 | [18: |
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| 453 | #absurd @⊥ cases absurd -absurd #absurd @absurd % |
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| 454 | ] |
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| 455 | #_ cases s #H1 #H2 #H3 #H4 #H5 #H6 #H7 #H8 #H9 |
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| 456 | whd in match status_of_pseudo_status; normalize nodelta |
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| 457 | whd in match sfr_8051_of_pseudo_sfr_8051; normalize nodelta |
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| 458 | cases M #left #right cases right normalize nodelta try % |
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| 459 | -right * #address |
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| 460 | @pair_elim #high #low #high_low_refl normalize nodelta |
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| 461 | whd in match sfr_8051_index; normalize nodelta |
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| 462 | >get_index_v_set_index_miss try % |
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| 463 | #absurd destruct(absurd) |
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[1971] | 464 | qed. |
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| 465 | |
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| 466 | include alias "arithmetics/nat.ma". |
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| 467 | include alias "basics/logic.ma". |
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| 468 | include alias "ASM/BitVectorTrie.ma". |
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| 469 | |
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[1983] | 470 | lemma fetch_many_singleton: |
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| 471 | ∀code_memory: BitVectorTrie Byte 16. |
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| 472 | ∀final_pc, start_pc: Word. |
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| 473 | ∀i: instruction. |
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| 474 | fetch_many code_memory final_pc start_pc [i] → |
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| 475 | 〈i, final_pc, ticks_of_instruction i〉 = fetch code_memory start_pc. |
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[1984] | 476 | #code_memory #final_pc #start_pc #i * #new_pc |
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| 477 | #fetch_many_assm whd in fetch_many_assm; |
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[1983] | 478 | cases (eq_bv_eq … fetch_many_assm) assumption |
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| 479 | qed. |
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| 480 | |
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[2160] | 481 | (* XXX: this needs an extra invariant relating address and word that we look |
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| 482 | up! |
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| 483 | *) |
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| 484 | definition map_lower_internal_ram_address_using_pseudo_address_map: |
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| 485 | ∀M: internal_pseudo_address_map. (Word → Word) → Byte → Byte → Byte ≝ |
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| 486 | λM: internal_pseudo_address_map. |
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| 487 | λsigma: Word → Word. |
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| 488 | λaddress: Byte. |
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| 489 | λvalue: Byte. |
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| 490 | match assoc_list_lookup ?? address (eq_bv …) (\fst M) with |
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| 491 | [ None ⇒ value |
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| 492 | | Some upper_lower_word ⇒ |
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| 493 | let 〈upper_lower, word〉 ≝ upper_lower_word in |
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| 494 | let 〈high, low〉 ≝ vsplit bool 8 8 (sigma word) in |
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| 495 | if eq_upper_lower upper_lower upper then |
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| 496 | high |
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| 497 | else |
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| 498 | low |
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| 499 | ]. |
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| 500 | |
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| 501 | lemma get_8051_sfr_status_of_pseudo_status: |
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| 502 | ∀M. |
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| 503 | ∀cm, ps, sigma, policy. |
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| 504 | ∀sfr. |
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| 505 | (sfr = SFR_ACC_A → \snd M = data) → |
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| 506 | get_8051_sfr (BitVectorTrie Byte 16) |
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| 507 | (code_memory_of_pseudo_assembly_program cm sigma policy) |
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| 508 | (status_of_pseudo_status M cm ps sigma policy) sfr = |
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| 509 | get_8051_sfr pseudo_assembly_program cm ps sfr. |
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| 510 | #M #cm #ps #sigma #policy * cases M #fstM #sndM #relevant |
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| 511 | [18: |
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| 512 | >relevant % |
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| 513 | ] |
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| 514 | cases sndM try % * #address |
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| 515 | whd in match get_8051_sfr; |
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| 516 | whd in match status_of_pseudo_status; normalize nodelta |
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| 517 | whd in match sfr_8051_of_pseudo_sfr_8051; normalize nodelta |
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| 518 | @pair_elim #upper #lower #upper_lower_refl |
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| 519 | @get_index_v_set_index_miss @nmk #relevant |
---|
| 520 | normalize in relevant; destruct(relevant) |
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| 521 | qed. |
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| 522 | |
---|
| 523 | lemma bitvector_cases_hd_tl: |
---|
| 524 | ∀n: nat. |
---|
| 525 | ∀w: BitVector (S n). |
---|
| 526 | ∃hd: bool. ∃tl: BitVector n. |
---|
| 527 | w ≃ hd:::tl. |
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| 528 | #n #w cases (BitVector_Sn … w) #hd #relevant %{hd} @relevant |
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| 529 | qed. |
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| 530 | |
---|
| 531 | lemma external_ram_set_bit_addressable_sfr: |
---|
| 532 | ∀M: Type[0]. |
---|
| 533 | ∀cm: M. |
---|
| 534 | ∀ps. |
---|
| 535 | ∀w. |
---|
| 536 | ∀result: Byte. |
---|
| 537 | external_ram M cm |
---|
| 538 | (set_bit_addressable_sfr M cm ps w result) = |
---|
| 539 | external_ram M cm ps. |
---|
| 540 | #M #cm #ps #w #result cases daemon (* XXX: prove this with Russell in Status.ma! |
---|
| 541 | whd in match set_bit_addressable_sfr; normalize nodelta |
---|
| 542 | cases (eqb ??) normalize nodelta [1: cases not_implemented ] |
---|
| 543 | cases (eqb ??) normalize nodelta [1: % ] |
---|
| 544 | cases (eqb ??) normalize nodelta [1: cases not_implemented ] |
---|
| 545 | cases (eqb ??) normalize nodelta [1: % ] |
---|
| 546 | cases (eqb ??) normalize nodelta [1: % ] |
---|
| 547 | cases (eqb ??) normalize nodelta [1: % ] |
---|
| 548 | cases (eqb ??) normalize nodelta [1: % ] |
---|
| 549 | cases (eqb ??) normalize nodelta [1: % ] |
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| 550 | cases (eqb ??) normalize nodelta [1: % ] |
---|
| 551 | cases (eqb ??) normalize nodelta [1: % ] |
---|
| 552 | cases (eqb ??) normalize nodelta [1: % ] |
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| 553 | cases (eqb ??) normalize nodelta [1: % ] |
---|
| 554 | cases (eqb ??) normalize nodelta [1: % ] |
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| 555 | cases (eqb ??) normalize nodelta [1: % ] |
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| 556 | cases (eqb ??) normalize nodelta [1: % ] |
---|
| 557 | cases (eqb ??) normalize nodelta [1: % ] |
---|
| 558 | cases (eqb ??) normalize nodelta [1: % ] |
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| 559 | cases (eqb ??) normalize nodelta [1: % ] |
---|
| 560 | cases (eqb ??) normalize nodelta [1: % ] |
---|
| 561 | cases (eqb ??) normalize nodelta [1: % ] |
---|
| 562 | cases (eqb ??) normalize nodelta [1: % ] |
---|
| 563 | cases (eqb ??) normalize nodelta [1: % ] |
---|
| 564 | cases (eqb ??) normalize nodelta [1: % ] |
---|
| 565 | cases (eqb ??) normalize nodelta [1: % ] |
---|
| 566 | cases (eqb ??) normalize nodelta [1: % ] |
---|
| 567 | cases (eqb ??) normalize nodelta [1: % ] |
---|
| 568 | cases not_implemented *) |
---|
| 569 | qed. |
---|
| 570 | |
---|
| 571 | lemma external_ram_set_arg_8: |
---|
| 572 | ∀M: Type[0]. |
---|
| 573 | ∀cm: M. |
---|
| 574 | ∀ps. |
---|
| 575 | ∀addr1: [[direct; indirect; registr; acc_a; acc_b ]]. |
---|
| 576 | ∀result. |
---|
| 577 | external_ram M cm (set_arg_8 M cm ps addr1 result) = |
---|
| 578 | external_ram M cm ps. |
---|
| 579 | [2: /2 by is_in_subvector_is_in_supervector, subaddressing_modein, I/ ] |
---|
| 580 | #M #cm #ps #addr1 #result |
---|
| 581 | @(subaddressing_mode_elim … addr1) try #w try % |
---|
| 582 | whd in ⊢ (??(???%)?); whd in ⊢ (??(???(???%))?); (* XXX: to be understood, slow match *) |
---|
| 583 | [1: |
---|
| 584 | cases (vsplit bool ???) #nu #nl normalize nodelta |
---|
| 585 | cases (vsplit bool ???) #ignore #three_bits normalize nodelta |
---|
| 586 | cases (get_index_v bool ????) normalize nodelta try % |
---|
| 587 | @external_ram_set_bit_addressable_sfr |
---|
| 588 | |2: |
---|
| 589 | cases (vsplit bool ???) #nu #nl normalize nodelta |
---|
| 590 | cases (vsplit bool ???) #ignore #three_bits normalize nodelta |
---|
| 591 | cases (get_index_v bool ????) normalize nodelta % |
---|
| 592 | ] |
---|
| 593 | qed. |
---|
| 594 | |
---|
| 595 | lemma special_function_registers_8051_set_clock: |
---|
| 596 | ∀M: Type[0]. |
---|
| 597 | ∀cm: M. |
---|
| 598 | ∀ps. |
---|
| 599 | ∀t. |
---|
| 600 | special_function_registers_8051 M cm (set_clock M cm ps t) = |
---|
| 601 | special_function_registers_8051 M cm ps. |
---|
| 602 | // |
---|
| 603 | qed. |
---|
| 604 | |
---|
| 605 | lemma get_arg_8_pseudo_addressing_mode_ok: |
---|
| 606 | ∀M: internal_pseudo_address_map. |
---|
| 607 | ∀cm: pseudo_assembly_program. |
---|
| 608 | ∀ps: PreStatus pseudo_assembly_program cm. |
---|
| 609 | ∀sigma: Word → Word. |
---|
| 610 | ∀policy: Word → bool. |
---|
| 611 | ∀addr1: [[registr; direct]]. |
---|
| 612 | addressing_mode_ok pseudo_assembly_program M cm ps addr1 = true → |
---|
| 613 | get_arg_8 (BitVectorTrie Byte 16) |
---|
| 614 | (code_memory_of_pseudo_assembly_program cm sigma policy) |
---|
| 615 | (status_of_pseudo_status M cm ps sigma policy) true addr1 = |
---|
| 616 | get_arg_8 pseudo_assembly_program cm ps true addr1. |
---|
| 617 | [2,3: /2 by is_in_subvector_is_in_supervector, subaddressing_modein, I/ ] |
---|
| 618 | #M #cm #ps #sigma #policy #addr1 |
---|
| 619 | @(subaddressing_mode_elim … addr1) #arg whd in ⊢ (? → ???%); |
---|
| 620 | [1: |
---|
| 621 | whd in ⊢ (??%? → ??%?); |
---|
| 622 | whd in match bit_address_of_register; normalize nodelta |
---|
| 623 | @pair_elim #un #ln #un_ln_refl |
---|
| 624 | lapply (refl_to_jmrefl ??? un_ln_refl) -un_ln_refl #un_ln_refl |
---|
| 625 | @(pair_replace ?????????? un_ln_refl) |
---|
| 626 | [1: |
---|
| 627 | whd in match get_8051_sfr; normalize nodelta |
---|
| 628 | whd in match sfr_8051_index; normalize nodelta |
---|
| 629 | @eq_f <get_index_v_special_function_registers_8051_not_acc_a |
---|
| 630 | try % #absurd destruct(absurd) |
---|
| 631 | |2: |
---|
| 632 | #assembly_mode_ok_refl |
---|
| 633 | >low_internal_ram_of_pseudo_internal_ram_miss |
---|
| 634 | [1: |
---|
| 635 | % |
---|
| 636 | |2: |
---|
| 637 | cases (assoc_list_exists ?????) in assembly_mode_ok_refl; normalize nodelta |
---|
| 638 | #absurd try % @sym_eq assumption |
---|
| 639 | ] |
---|
| 640 | ] |
---|
| 641 | |2: |
---|
| 642 | #addressing_mode_ok_refl whd in ⊢ (??%?); |
---|
| 643 | @pair_elim #nu #nl #nu_nl_refl normalize nodelta |
---|
| 644 | @pair_elim #ignore #three_bits #ignore_three_bits_refl normalize nodelta |
---|
| 645 | inversion (get_index_v bool ????) #get_index_v_refl normalize nodelta |
---|
| 646 | [1: |
---|
| 647 | whd in ⊢ (??%%); normalize nodelta |
---|
| 648 | cases (eqb ??) normalize nodelta [1: % ] |
---|
| 649 | cases (eqb ??) normalize nodelta [1: % ] |
---|
| 650 | cases (eqb ??) normalize nodelta [1: % ] |
---|
| 651 | cases (eqb ??) normalize nodelta [1: % ] |
---|
| 652 | cases (eqb ??) normalize nodelta [1: |
---|
| 653 | @get_8051_sfr_status_of_pseudo_status |
---|
| 654 | #absurd destruct(absurd) |
---|
| 655 | ] |
---|
| 656 | cases (eqb ??) normalize nodelta [1: |
---|
| 657 | @get_8051_sfr_status_of_pseudo_status |
---|
| 658 | #absurd destruct(absurd) |
---|
| 659 | ] |
---|
| 660 | cases (eqb ??) normalize nodelta [1: |
---|
| 661 | @get_8051_sfr_status_of_pseudo_status |
---|
| 662 | #absurd destruct(absurd) |
---|
| 663 | ] |
---|
| 664 | cases (eqb ??) normalize nodelta [1: |
---|
| 665 | @get_8051_sfr_status_of_pseudo_status |
---|
| 666 | #absurd destruct(absurd) |
---|
| 667 | ] |
---|
| 668 | cases (eqb ??) normalize nodelta [1: |
---|
| 669 | @get_8051_sfr_status_of_pseudo_status |
---|
| 670 | #absurd destruct(absurd) |
---|
| 671 | ] |
---|
| 672 | cases (eqb ??) normalize nodelta [1: % ] |
---|
| 673 | cases (eqb ??) normalize nodelta [1: % ] |
---|
| 674 | cases (eqb ??) normalize nodelta [1: % ] |
---|
| 675 | cases (eqb ??) normalize nodelta [1: % ] |
---|
| 676 | cases (eqb ??) normalize nodelta [1: % ] |
---|
| 677 | cases (eqb ??) normalize nodelta [1: |
---|
| 678 | @get_8051_sfr_status_of_pseudo_status |
---|
| 679 | #absurd destruct(absurd) |
---|
| 680 | ] |
---|
| 681 | cases (eqb ??) normalize nodelta [1: |
---|
| 682 | @get_8051_sfr_status_of_pseudo_status |
---|
| 683 | #absurd destruct(absurd) |
---|
| 684 | ] |
---|
| 685 | cases (eqb ??) normalize nodelta [1: |
---|
| 686 | @get_8051_sfr_status_of_pseudo_status |
---|
| 687 | #absurd destruct(absurd) |
---|
| 688 | ] |
---|
| 689 | cases (eqb ??) normalize nodelta [1: |
---|
| 690 | @get_8051_sfr_status_of_pseudo_status |
---|
| 691 | #absurd destruct(absurd) |
---|
| 692 | ] |
---|
| 693 | cases (eqb ??) normalize nodelta [1: |
---|
| 694 | @get_8051_sfr_status_of_pseudo_status |
---|
| 695 | #absurd destruct(absurd) |
---|
| 696 | ] |
---|
| 697 | cases (eqb ??) normalize nodelta [1: |
---|
| 698 | @get_8051_sfr_status_of_pseudo_status |
---|
| 699 | #absurd destruct(absurd) |
---|
| 700 | ] |
---|
| 701 | cases (eqb ??) normalize nodelta [1: |
---|
| 702 | @get_8051_sfr_status_of_pseudo_status |
---|
| 703 | #absurd destruct(absurd) |
---|
| 704 | ] |
---|
| 705 | cases (eqb ??) normalize nodelta [1: |
---|
| 706 | @get_8051_sfr_status_of_pseudo_status |
---|
| 707 | #absurd destruct(absurd) |
---|
| 708 | ] |
---|
| 709 | cases (eqb ??) normalize nodelta [1: |
---|
| 710 | @get_8051_sfr_status_of_pseudo_status |
---|
| 711 | #absurd destruct(absurd) |
---|
| 712 | ] |
---|
| 713 | cases (eqb ??) normalize nodelta [1: |
---|
| 714 | @get_8051_sfr_status_of_pseudo_status |
---|
| 715 | #absurd destruct(absurd) |
---|
| 716 | ] |
---|
| 717 | inversion (eqb ??) #eqb_refl normalize nodelta [1: |
---|
| 718 | @get_8051_sfr_status_of_pseudo_status lapply addressing_mode_ok_refl |
---|
| 719 | whd in ⊢ (??%? → ?); <(eqb_true_to_eq … eqb_refl) |
---|
| 720 | >bitvector_of_nat_inverse_nat_of_bitvector >eq_bv_refl normalize nodelta |
---|
| 721 | #assoc_list_assm cases (conjunction_true … assoc_list_assm) #_ |
---|
| 722 | #relevant #_ cases (eq_accumulator_address_map_entry_true_to_eq … relevant) % |
---|
| 723 | ] |
---|
| 724 | cases (eqb ??) normalize nodelta [1: |
---|
| 725 | @get_8051_sfr_status_of_pseudo_status |
---|
| 726 | #absurd destruct(absurd) |
---|
| 727 | ] % |
---|
| 728 | |2: |
---|
| 729 | lapply addressing_mode_ok_refl whd in ⊢ (??%? → ?); #relevant |
---|
| 730 | whd in match status_of_pseudo_status; normalize nodelta |
---|
| 731 | >low_internal_ram_of_pseudo_internal_ram_miss try % |
---|
| 732 | cut(arg = false:::(three_bits@@nl)) |
---|
| 733 | [1: |
---|
| 734 | <get_index_v_refl |
---|
| 735 | cut(nu=get_index_v bool 4 nu O (le_S_S O 3 (le_O_n 3)):::three_bits) |
---|
| 736 | [1: |
---|
| 737 | cut(ignore = [[get_index_v bool 4 nu 0 ?]]) |
---|
| 738 | [1: |
---|
| 739 | @le_S_S @le_O_n |
---|
| 740 | |2: |
---|
| 741 | cut(ignore = \fst (vsplit bool 1 3 nu)) |
---|
| 742 | [1: |
---|
| 743 | >ignore_three_bits_refl % |
---|
| 744 | |2: |
---|
| 745 | #ignore_refl >ignore_refl |
---|
| 746 | cases (bitvector_cases_hd_tl … nu) #hd * #tl #nu_refl |
---|
| 747 | >nu_refl % |
---|
| 748 | ] |
---|
| 749 | |3: |
---|
| 750 | #ignore_refl >ignore_refl in ignore_three_bits_refl; |
---|
| 751 | #relevant lapply (vsplit_ok ?????? (sym_eq … relevant)) |
---|
| 752 | #nu_refl <nu_refl % |
---|
| 753 | ] |
---|
| 754 | |2: |
---|
| 755 | #nu_refl change with (? = (?:::three_bits)@@?) <nu_refl |
---|
| 756 | @sym_eq @vsplit_ok >nu_nl_refl % |
---|
| 757 | ] |
---|
| 758 | |2: |
---|
| 759 | #arg_refl <arg_refl cases (assoc_list_exists ?????) in relevant; |
---|
| 760 | normalize nodelta |
---|
| 761 | [1: |
---|
| 762 | cases (eq_bv ???) normalize #absurd destruct(absurd) |
---|
| 763 | |2: |
---|
| 764 | #_ % |
---|
| 765 | ] |
---|
| 766 | ] |
---|
| 767 | ] |
---|
| 768 | ] |
---|
| 769 | qed. |
---|
| 770 | |
---|
| 771 | lemma special_function_registers_8051_set_program_counter: |
---|
| 772 | ∀M: Type[0]. |
---|
| 773 | ∀cm: M. |
---|
| 774 | ∀ps. |
---|
| 775 | ∀pc: Word. |
---|
| 776 | special_function_registers_8051 M cm (set_program_counter M cm ps pc) = |
---|
| 777 | special_function_registers_8051 M cm ps. |
---|
| 778 | // |
---|
| 779 | qed. |
---|
| 780 | |
---|
| 781 | lemma special_function_registers_8052_set_program_counter: |
---|
| 782 | ∀M: Type[0]. |
---|
| 783 | ∀cm: M. |
---|
| 784 | ∀ps. |
---|
| 785 | ∀pc: Word. |
---|
| 786 | special_function_registers_8052 M cm (set_program_counter M cm ps pc) = |
---|
| 787 | special_function_registers_8052 M cm ps. |
---|
| 788 | // |
---|
| 789 | qed. |
---|
| 790 | |
---|
| 791 | lemma set_index_set_index_commutation: |
---|
| 792 | ∀A: Type[0]. |
---|
| 793 | ∀n: nat. |
---|
| 794 | ∀v: Vector A n. |
---|
| 795 | ∀m, o: nat. |
---|
| 796 | ∀m_lt_proof: m < n. |
---|
| 797 | ∀o_lt_proof: o < n. |
---|
| 798 | ∀e, f: A. |
---|
| 799 | m ≠ o → |
---|
| 800 | set_index A n (set_index A n v o f o_lt_proof) m e m_lt_proof = |
---|
| 801 | set_index A n (set_index A n v m e m_lt_proof) o f o_lt_proof. |
---|
| 802 | #A #n #v elim v |
---|
| 803 | [1: |
---|
| 804 | #m #o #m_lt_proof |
---|
| 805 | normalize in m_lt_proof; cases (lt_to_not_zero … m_lt_proof) |
---|
| 806 | |2: |
---|
| 807 | #n' #hd #tl #inductive_hypothesis |
---|
| 808 | #m #o |
---|
| 809 | cases m cases o |
---|
| 810 | [1: |
---|
| 811 | #m_lt_proof #o_lt_proof #e #f #absurd @⊥ cases absurd #relevant |
---|
| 812 | @relevant % |
---|
| 813 | |2,3: |
---|
| 814 | #o' normalize // |
---|
| 815 | |4: |
---|
| 816 | #m' #o' #m_lt_proof #o_lt_proof #e #f #o_neq_m_assm |
---|
| 817 | normalize @eq_f @inductive_hypothesis @nmk #relevant |
---|
| 818 | >relevant in o_neq_m_assm; #relevant @(absurd ?? relevant) % |
---|
| 819 | ] |
---|
| 820 | ] |
---|
| 821 | qed. |
---|
| 822 | |
---|
| 823 | lemma special_function_registers_8051_sfr_8051_of_pseudo_sfr_8051: |
---|
| 824 | ∀M: internal_pseudo_address_map. |
---|
| 825 | ∀cm: pseudo_assembly_program. |
---|
| 826 | ∀ps. |
---|
| 827 | ∀sigma: Word → Word. |
---|
| 828 | ∀policy: Word → bool. |
---|
| 829 | ∀sfr. |
---|
| 830 | ∀result: Byte. |
---|
| 831 | eqb (sfr_8051_index sfr) (sfr_8051_index SFR_ACC_A) = false → |
---|
| 832 | special_function_registers_8051 (BitVectorTrie Byte 16) |
---|
| 833 | (code_memory_of_pseudo_assembly_program cm sigma policy) |
---|
| 834 | (set_8051_sfr (BitVectorTrie Byte 16) |
---|
| 835 | (code_memory_of_pseudo_assembly_program cm sigma policy) |
---|
| 836 | (status_of_pseudo_status M cm ps sigma policy) sfr result) = |
---|
| 837 | sfr_8051_of_pseudo_sfr_8051 M |
---|
| 838 | (special_function_registers_8051 pseudo_assembly_program cm |
---|
| 839 | (set_8051_sfr pseudo_assembly_program cm ps sfr result)) sigma. |
---|
| 840 | #M #cm #ps #sigma #policy #sfr #result #sfr_neq_assm |
---|
| 841 | whd in match (set_8051_sfr ?????); |
---|
| 842 | cases M #callM * try % #upper_lower #address |
---|
| 843 | whd in match (special_function_registers_8051 ???); |
---|
| 844 | whd in match (sfr_8051_of_pseudo_sfr_8051 ???); |
---|
| 845 | @pair_elim #high #low #high_low_refl normalize nodelta |
---|
| 846 | cases (eq_upper_lower ??) normalize nodelta |
---|
| 847 | whd in match (set_8051_sfr ?????); |
---|
| 848 | @set_index_set_index_commutation @nmk #relevant |
---|
| 849 | @(absurd ? relevant (eqb_false_to_not_eq ?? sfr_neq_assm)) |
---|
| 850 | qed. |
---|
| 851 | |
---|
| 852 | lemma special_function_registers_8051_set_arg_8: |
---|
| 853 | ∀M: internal_pseudo_address_map. |
---|
| 854 | ∀cm: pseudo_assembly_program. |
---|
| 855 | ∀ps. |
---|
| 856 | ∀sigma: Word → Word. |
---|
| 857 | ∀policy: Word → bool. |
---|
| 858 | ∀addr1: [[ registr; direct ]]. |
---|
| 859 | ∀result. |
---|
| 860 | addressing_mode_ok pseudo_assembly_program M cm ps addr1 = true → |
---|
| 861 | special_function_registers_8051 (BitVectorTrie Byte 16) |
---|
| 862 | (code_memory_of_pseudo_assembly_program cm sigma policy) |
---|
| 863 | (set_arg_8 (BitVectorTrie Byte 16) |
---|
| 864 | (code_memory_of_pseudo_assembly_program cm sigma policy) |
---|
| 865 | (status_of_pseudo_status M cm ps sigma policy) addr1 result) = |
---|
| 866 | sfr_8051_of_pseudo_sfr_8051 M |
---|
| 867 | (special_function_registers_8051 pseudo_assembly_program cm |
---|
| 868 | (set_arg_8 pseudo_assembly_program cm ps addr1 result)) sigma. |
---|
| 869 | cases daemon |
---|
| 870 | (* |
---|
| 871 | [2,3: /2 by is_in_subvector_is_in_supervector, subaddressing_modein, I/ ] |
---|
| 872 | #M #cm #ps #sigma #policy #addr1 #result |
---|
| 873 | @(subaddressing_mode_elim … addr1) #w #addressing_mode_ok_refl try % |
---|
| 874 | whd in match (set_arg_8 ?????); whd in ⊢ (??(???(???%))?); |
---|
| 875 | whd in match (set_arg_8 ?????) in ⊢ (???%); whd in ⊢ (???(??(???(???%))?)); |
---|
| 876 | cases (vsplit bool ???) #nu #nl normalize nodelta |
---|
| 877 | cases (vsplit bool ???) #ignore #three_bits normalize nodelta |
---|
| 878 | cases (get_index_v bool ????) normalize nodelta try % |
---|
| 879 | whd in match (set_bit_addressable_sfr ?????); whd in match (set_bit_addressable_sfr ?????) in ⊢ (???%); |
---|
| 880 | cases (eqb ??) normalize nodelta [1: cases not_implemented ] |
---|
| 881 | cases (eqb ??) normalize nodelta [1: % ] |
---|
| 882 | cases (eqb ??) normalize nodelta [1: cases not_implemented ] |
---|
| 883 | cases (eqb ??) normalize nodelta [1: % ] |
---|
| 884 | cases (eqb ??) normalize nodelta [1: @special_function_registers_8051_sfr_8051_of_pseudo_sfr_8051 % ] |
---|
| 885 | cases (eqb ??) normalize nodelta [1: @special_function_registers_8051_sfr_8051_of_pseudo_sfr_8051 % ] |
---|
| 886 | cases (eqb ??) normalize nodelta [1: @special_function_registers_8051_sfr_8051_of_pseudo_sfr_8051 % ] |
---|
| 887 | cases (eqb ??) normalize nodelta [1: @special_function_registers_8051_sfr_8051_of_pseudo_sfr_8051 % ] |
---|
| 888 | cases (eqb ??) normalize nodelta [1: @special_function_registers_8051_sfr_8051_of_pseudo_sfr_8051 % ] |
---|
| 889 | cases (eqb ??) normalize nodelta [1: % ] |
---|
| 890 | cases (eqb ??) normalize nodelta [1: % ] |
---|
| 891 | cases (eqb ??) normalize nodelta [1: % ] |
---|
| 892 | cases (eqb ??) normalize nodelta [1: % ] |
---|
| 893 | cases (eqb ??) normalize nodelta [1: % ] |
---|
| 894 | cases (eqb ??) normalize nodelta [1: @special_function_registers_8051_sfr_8051_of_pseudo_sfr_8051 % ] |
---|
| 895 | cases (eqb ??) normalize nodelta [1: @special_function_registers_8051_sfr_8051_of_pseudo_sfr_8051 % ] |
---|
| 896 | cases (eqb ??) normalize nodelta [1: @special_function_registers_8051_sfr_8051_of_pseudo_sfr_8051 % ] |
---|
| 897 | cases (eqb ??) normalize nodelta [1: @special_function_registers_8051_sfr_8051_of_pseudo_sfr_8051 % ] |
---|
| 898 | cases (eqb ??) normalize nodelta [1: @special_function_registers_8051_sfr_8051_of_pseudo_sfr_8051 % ] |
---|
| 899 | cases (eqb ??) normalize nodelta [1: @special_function_registers_8051_sfr_8051_of_pseudo_sfr_8051 % ] |
---|
| 900 | cases (eqb ??) normalize nodelta [1: @special_function_registers_8051_sfr_8051_of_pseudo_sfr_8051 % ] |
---|
| 901 | cases (eqb ??) normalize nodelta [1: @special_function_registers_8051_sfr_8051_of_pseudo_sfr_8051 % ] |
---|
| 902 | cases (eqb ??) normalize nodelta [1: @special_function_registers_8051_sfr_8051_of_pseudo_sfr_8051 % ] |
---|
| 903 | cases (eqb ??) normalize nodelta [1: @special_function_registers_8051_sfr_8051_of_pseudo_sfr_8051 % ] |
---|
| 904 | inversion (eqb ??) #eqb_refl normalize nodelta [1: |
---|
| 905 | whd in addressing_mode_ok_refl:(??%?); <(eqb_true_to_eq … eqb_refl) in addressing_mode_ok_refl; |
---|
| 906 | >bitvector_of_nat_inverse_nat_of_bitvector >eq_bv_refl normalize nodelta |
---|
| 907 | #relevant cases (conjunction_true … relevant) #_ #eq_acc_assm |
---|
| 908 | whd in match (status_of_pseudo_status ?????); |
---|
| 909 | whd in match sfr_8051_of_pseudo_sfr_8051; normalize nodelta |
---|
| 910 | >(eq_accumulator_address_map_entry_true_to_eq … eq_acc_assm) normalize nodelta % |
---|
| 911 | ] |
---|
| 912 | cases (eqb ??) normalize nodelta [1: @special_function_registers_8051_sfr_8051_of_pseudo_sfr_8051 % ] |
---|
| 913 | cases not_implemented *) |
---|
| 914 | qed. |
---|
| 915 | |
---|
[2017] | 916 | include alias "ASM/Vector.ma". |
---|
| 917 | |
---|
[1971] | 918 | lemma main_lemma_preinstruction: |
---|
[2023] | 919 | ∀M, M': internal_pseudo_address_map. |
---|
| 920 | ∀preamble: preamble. |
---|
| 921 | ∀instr_list: list labelled_instruction. |
---|
| 922 | ∀cm: pseudo_assembly_program. |
---|
| 923 | ∀EQcm: cm = 〈preamble, instr_list〉. |
---|
[2139] | 924 | ∀is_well_labelled_witness: is_well_labelled_p instr_list. |
---|
[2023] | 925 | ∀sigma: Word → Word. |
---|
| 926 | ∀policy: Word → bool. |
---|
| 927 | ∀sigma_policy_witness: sigma_policy_specification cm sigma policy. |
---|
| 928 | ∀ps: PseudoStatus cm. |
---|
| 929 | ∀ppc: Word. |
---|
[2139] | 930 | ∀program_counter_in_bounds_witness: nat_of_bitvector … ppc < |instr_list|. |
---|
[2023] | 931 | ∀EQppc: ppc = program_counter pseudo_assembly_program cm ps. |
---|
| 932 | ∀labels: label_map. |
---|
| 933 | ∀costs: BitVectorTrie costlabel 16. |
---|
| 934 | ∀create_label_cost_refl: create_label_cost_map instr_list = 〈labels, costs〉. |
---|
| 935 | ∀newppc: Word. |
---|
| 936 | ∀lookup_labels: Identifier → Word. |
---|
[2131] | 937 | ∀EQlookup_labels: lookup_labels = (λx. bitvector_of_nat 16 (lookup_def … labels x 0)). |
---|
[2023] | 938 | ∀lookup_datalabels: Identifier → Word. |
---|
| 939 | ∀EQlookup_datalabels: lookup_datalabels = (λx.lookup_def ASMTag Word (construct_datalabels preamble) x (zero 16)). |
---|
| 940 | ∀EQnewppc: newppc = add 16 ppc (bitvector_of_nat 16 1). |
---|
| 941 | ∀instr: preinstruction Identifier. |
---|
[2139] | 942 | ∀fetch_pseudo_refl: \fst (fetch_pseudo_instruction instr_list ppc program_counter_in_bounds_witness) = Instruction instr. |
---|
[2023] | 943 | ∀ticks: nat × nat. |
---|
[2160] | 944 | ∀EQticks: ticks = ticks_of0 〈preamble, instr_list〉 lookup_datalabels sigma policy ppc (Instruction instr). |
---|
[2023] | 945 | ∀addr_of: Identifier → PreStatus pseudo_assembly_program cm → BitVector 16. |
---|
| 946 | ∀EQaddr_of: addr_of = (λx:Identifier. λy:PreStatus pseudo_assembly_program cm. address_of_word_labels cm x). |
---|
| 947 | ∀s: PreStatus pseudo_assembly_program cm. |
---|
| 948 | ∀EQs: s = (set_program_counter pseudo_assembly_program cm ps (add 16 ppc (bitvector_of_nat 16 1))). |
---|
| 949 | ∀P: preinstruction Identifier → PseudoStatus cm → Prop. |
---|
| 950 | ∀EQP: P = (λinstr, s. sigma (add 16 ppc (bitvector_of_nat 16 1)) = add 16 (sigma ppc) |
---|
| 951 | (bitvector_of_nat 16 (\fst (assembly_1_pseudoinstruction lookup_labels sigma policy ppc |
---|
| 952 | lookup_datalabels (Instruction instr)))) → |
---|
[2108] | 953 | next_internal_pseudo_address_map0 ? cm addr_of (Instruction instr) M ps = Some internal_pseudo_address_map M' → |
---|
[2023] | 954 | fetch_many (load_code_memory (\fst (pi1 … (assembly cm sigma policy)))) (sigma (add 16 ppc (bitvector_of_nat 16 1))) (sigma (program_counter pseudo_assembly_program cm ps)) |
---|
| 955 | (expand_pseudo_instruction lookup_labels sigma policy (program_counter pseudo_assembly_program cm ps) lookup_datalabels (Instruction instr)) → |
---|
| 956 | ∃n: nat. execute n (code_memory_of_pseudo_assembly_program cm sigma policy) (status_of_pseudo_status M cm ps sigma policy) = |
---|
| 957 | status_of_pseudo_status M' cm s sigma policy). |
---|
| 958 | P instr (execute_1_preinstruction ticks Identifier pseudo_assembly_program cm addr_of instr s). |
---|
[2140] | 959 | (* XXX: takes about 45 minutes to type check! *) |
---|
[2139] | 960 | #M #M' #preamble #instr_list #cm #EQcm #is_well_labelled_witness #sigma #policy |
---|
| 961 | #sigma_policy_witness #ps #ppc #ppc_in_bounds_witness #EQppc #labels |
---|
| 962 | #costs #create_label_cost_refl #newppc #lookup_labels #EQlookup_labels |
---|
| 963 | #lookup_datalabels #EQlookup_datalabels #EQnewppc #instr #fetch_pseudo_refl |
---|
[2023] | 964 | #ticks #EQticks #addr_of #EQaddr_of #s #EQs #P #EQP |
---|
| 965 | (*#sigma_increment_commutation #maps_assm #fetch_many_assm *) |
---|
| 966 | letin a ≝ Identifier letin m ≝ pseudo_assembly_program |
---|
| 967 | cut (Σxxx:PseudoStatus cm. P instr (execute_1_preinstruction ticks a m cm addr_of instr s)) |
---|
| 968 | [2: * // ] |
---|
| 969 | @( |
---|
[1971] | 970 | let add_ticks1 ≝ λs: PreStatus m cm. set_clock ?? s (\fst ticks + clock ?? s) in |
---|
| 971 | let add_ticks2 ≝ λs: PreStatus m cm. set_clock ?? s (\snd ticks + clock ?? s) in |
---|
| 972 | match instr in preinstruction return λx. x = instr → Σs'.? with |
---|
| 973 | [ ADD addr1 addr2 ⇒ λinstr_refl. |
---|
| 974 | let s ≝ add_ticks1 s in |
---|
| 975 | let 〈result, flags〉 ≝ add_8_with_carry (get_arg_8 … s false addr1) |
---|
| 976 | (get_arg_8 … s false addr2) false in |
---|
| 977 | let cy_flag ≝ get_index' ? O ? flags in |
---|
| 978 | let ac_flag ≝ get_index' ? 1 ? flags in |
---|
| 979 | let ov_flag ≝ get_index' ? 2 ? flags in |
---|
| 980 | let s ≝ set_arg_8 … s ACC_A result in |
---|
| 981 | set_flags … s cy_flag (Some Bit ac_flag) ov_flag |
---|
| 982 | | ADDC addr1 addr2 ⇒ λinstr_refl. |
---|
| 983 | let s ≝ add_ticks1 s in |
---|
| 984 | let old_cy_flag ≝ get_cy_flag ?? s in |
---|
| 985 | let 〈result, flags〉 ≝ add_8_with_carry (get_arg_8 … s false addr1) |
---|
| 986 | (get_arg_8 … s false addr2) old_cy_flag in |
---|
| 987 | let cy_flag ≝ get_index' ? O ? flags in |
---|
| 988 | let ac_flag ≝ get_index' ? 1 ? flags in |
---|
| 989 | let ov_flag ≝ get_index' ? 2 ? flags in |
---|
| 990 | let s ≝ set_arg_8 … s ACC_A result in |
---|
| 991 | set_flags … s cy_flag (Some Bit ac_flag) ov_flag |
---|
| 992 | | SUBB addr1 addr2 ⇒ λinstr_refl. |
---|
| 993 | let s ≝ add_ticks1 s in |
---|
| 994 | let old_cy_flag ≝ get_cy_flag ?? s in |
---|
| 995 | let 〈result, flags〉 ≝ sub_8_with_carry (get_arg_8 … s false addr1) |
---|
| 996 | (get_arg_8 … s false addr2) old_cy_flag in |
---|
| 997 | let cy_flag ≝ get_index' ? O ? flags in |
---|
| 998 | let ac_flag ≝ get_index' ? 1 ? flags in |
---|
| 999 | let ov_flag ≝ get_index' ? 2 ? flags in |
---|
| 1000 | let s ≝ set_arg_8 … s ACC_A result in |
---|
| 1001 | set_flags … s cy_flag (Some Bit ac_flag) ov_flag |
---|
| 1002 | | ANL addr ⇒ λinstr_refl. |
---|
| 1003 | let s ≝ add_ticks1 s in |
---|
| 1004 | match addr with |
---|
| 1005 | [ inl l ⇒ |
---|
| 1006 | match l with |
---|
| 1007 | [ inl l' ⇒ |
---|
| 1008 | let 〈addr1, addr2〉 ≝ l' in |
---|
| 1009 | let and_val ≝ conjunction_bv ? (get_arg_8 … s true addr1) (get_arg_8 … s true addr2) in |
---|
| 1010 | set_arg_8 … s addr1 and_val |
---|
| 1011 | | inr r ⇒ |
---|
| 1012 | let 〈addr1, addr2〉 ≝ r in |
---|
| 1013 | let and_val ≝ conjunction_bv ? (get_arg_8 … s true addr1) (get_arg_8 … s true addr2) in |
---|
| 1014 | set_arg_8 … s addr1 and_val |
---|
| 1015 | ] |
---|
| 1016 | | inr r ⇒ |
---|
| 1017 | let 〈addr1, addr2〉 ≝ r in |
---|
| 1018 | let and_val ≝ andb (get_cy_flag … s) (get_arg_1 … s addr2 true) in |
---|
| 1019 | set_flags … s and_val (None ?) (get_ov_flag ?? s) |
---|
| 1020 | ] |
---|
| 1021 | | ORL addr ⇒ λinstr_refl. |
---|
| 1022 | let s ≝ add_ticks1 s in |
---|
| 1023 | match addr with |
---|
| 1024 | [ inl l ⇒ |
---|
| 1025 | match l with |
---|
| 1026 | [ inl l' ⇒ |
---|
| 1027 | let 〈addr1, addr2〉 ≝ l' in |
---|
| 1028 | let or_val ≝ inclusive_disjunction_bv ? (get_arg_8 … s true addr1) (get_arg_8 … s true addr2) in |
---|
| 1029 | set_arg_8 … s addr1 or_val |
---|
| 1030 | | inr r ⇒ |
---|
| 1031 | let 〈addr1, addr2〉 ≝ r in |
---|
| 1032 | let or_val ≝ inclusive_disjunction_bv ? (get_arg_8 … s true addr1) (get_arg_8 … s true addr2) in |
---|
| 1033 | set_arg_8 … s addr1 or_val |
---|
| 1034 | ] |
---|
| 1035 | | inr r ⇒ |
---|
| 1036 | let 〈addr1, addr2〉 ≝ r in |
---|
| 1037 | let or_val ≝ (get_cy_flag … s) ∨ (get_arg_1 … s addr2 true) in |
---|
| 1038 | set_flags … s or_val (None ?) (get_ov_flag … s) |
---|
| 1039 | ] |
---|
| 1040 | | XRL addr ⇒ λinstr_refl. |
---|
| 1041 | let s ≝ add_ticks1 s in |
---|
| 1042 | match addr with |
---|
| 1043 | [ inl l' ⇒ |
---|
| 1044 | let 〈addr1, addr2〉 ≝ l' in |
---|
| 1045 | let xor_val ≝ exclusive_disjunction_bv ? (get_arg_8 … s true addr1) (get_arg_8 … s true addr2) in |
---|
| 1046 | set_arg_8 … s addr1 xor_val |
---|
| 1047 | | inr r ⇒ |
---|
| 1048 | let 〈addr1, addr2〉 ≝ r in |
---|
| 1049 | let xor_val ≝ exclusive_disjunction_bv ? (get_arg_8 … s true addr1) (get_arg_8 … s true addr2) in |
---|
| 1050 | set_arg_8 … s addr1 xor_val |
---|
| 1051 | ] |
---|
| 1052 | | INC addr ⇒ λinstr_refl. |
---|
[1975] | 1053 | match addr return λx. bool_to_Prop (is_in … [[ acc_a;registr;direct;indirect;dptr ]] x) → x = addr → Σs': PreStatus m cm. ? with |
---|
| 1054 | [ ACC_A ⇒ λacc_a: True. λEQaddr. |
---|
[1971] | 1055 | let s' ≝ add_ticks1 s in |
---|
| 1056 | let 〈 carry, result 〉 ≝ half_add ? (get_arg_8 … s' true ACC_A) (bitvector_of_nat 8 1) in |
---|
| 1057 | set_arg_8 … s' ACC_A result |
---|
[1975] | 1058 | | REGISTER r ⇒ λregister: True. λEQaddr. |
---|
[1971] | 1059 | let s' ≝ add_ticks1 s in |
---|
| 1060 | let 〈 carry, result 〉 ≝ half_add ? (get_arg_8 … s' true (REGISTER r)) (bitvector_of_nat 8 1) in |
---|
| 1061 | set_arg_8 … s' (REGISTER r) result |
---|
[1975] | 1062 | | DIRECT d ⇒ λdirect: True. λEQaddr. |
---|
[1971] | 1063 | let s' ≝ add_ticks1 s in |
---|
| 1064 | let 〈 carry, result 〉 ≝ half_add ? (get_arg_8 … s' true (DIRECT d)) (bitvector_of_nat 8 1) in |
---|
| 1065 | set_arg_8 … s' (DIRECT d) result |
---|
[1975] | 1066 | | INDIRECT i ⇒ λindirect: True. λEQaddr. |
---|
[1971] | 1067 | let s' ≝ add_ticks1 s in |
---|
| 1068 | let 〈 carry, result 〉 ≝ half_add ? (get_arg_8 … s' true (INDIRECT i)) (bitvector_of_nat 8 1) in |
---|
| 1069 | set_arg_8 … s' (INDIRECT i) result |
---|
[1975] | 1070 | | DPTR ⇒ λdptr: True. λEQaddr. |
---|
[1971] | 1071 | let s' ≝ add_ticks1 s in |
---|
| 1072 | let 〈 carry, bl 〉 ≝ half_add ? (get_8051_sfr … s' SFR_DPL) (bitvector_of_nat 8 1) in |
---|
| 1073 | let 〈 carry, bu 〉 ≝ full_add ? (get_8051_sfr … s' SFR_DPH) (zero 8) carry in |
---|
| 1074 | let s ≝ set_8051_sfr … s' SFR_DPL bl in |
---|
| 1075 | set_8051_sfr … s' SFR_DPH bu |
---|
| 1076 | | _ ⇒ λother: False. ⊥ |
---|
[1975] | 1077 | ] (subaddressing_modein … addr) (refl … (subaddressing_modeel … addr)) |
---|
[1971] | 1078 | | NOP ⇒ λinstr_refl. |
---|
| 1079 | let s ≝ add_ticks2 s in |
---|
| 1080 | s |
---|
| 1081 | | DEC addr ⇒ λinstr_refl. |
---|
| 1082 | let s ≝ add_ticks1 s in |
---|
| 1083 | let 〈 result, flags 〉 ≝ sub_8_with_carry (get_arg_8 … s true addr) (bitvector_of_nat 8 1) false in |
---|
| 1084 | set_arg_8 … s addr result |
---|
| 1085 | | MUL addr1 addr2 ⇒ λinstr_refl. |
---|
| 1086 | let s ≝ add_ticks1 s in |
---|
| 1087 | let acc_a_nat ≝ nat_of_bitvector 8 (get_8051_sfr … s SFR_ACC_A) in |
---|
| 1088 | let acc_b_nat ≝ nat_of_bitvector 8 (get_8051_sfr … s SFR_ACC_B) in |
---|
| 1089 | let product ≝ acc_a_nat * acc_b_nat in |
---|
| 1090 | let ov_flag ≝ product ≥ 256 in |
---|
| 1091 | let low ≝ bitvector_of_nat 8 (product mod 256) in |
---|
| 1092 | let high ≝ bitvector_of_nat 8 (product ÷ 256) in |
---|
| 1093 | let s ≝ set_8051_sfr … s SFR_ACC_A low in |
---|
| 1094 | set_8051_sfr … s SFR_ACC_B high |
---|
| 1095 | | DIV addr1 addr2 ⇒ λinstr_refl. |
---|
| 1096 | let s ≝ add_ticks1 s in |
---|
| 1097 | let acc_a_nat ≝ nat_of_bitvector 8 (get_8051_sfr … s SFR_ACC_A) in |
---|
| 1098 | let acc_b_nat ≝ nat_of_bitvector 8 (get_8051_sfr … s SFR_ACC_B) in |
---|
| 1099 | match acc_b_nat with |
---|
| 1100 | [ O ⇒ set_flags … s false (None Bit) true |
---|
| 1101 | | S o ⇒ |
---|
| 1102 | let q ≝ bitvector_of_nat 8 (acc_a_nat ÷ (S o)) in |
---|
| 1103 | let r ≝ bitvector_of_nat 8 (acc_a_nat mod 256) in |
---|
| 1104 | let s ≝ set_8051_sfr … s SFR_ACC_A q in |
---|
| 1105 | let s ≝ set_8051_sfr … s SFR_ACC_B r in |
---|
| 1106 | set_flags … s false (None Bit) false |
---|
| 1107 | ] |
---|
| 1108 | | DA addr ⇒ λinstr_refl. |
---|
| 1109 | let s ≝ add_ticks1 s in |
---|
[2032] | 1110 | let 〈acc_nu, acc_nl〉 ≝ vsplit ? 4 4 (get_8051_sfr … s SFR_ACC_A) in |
---|
[1971] | 1111 | if (gtb (nat_of_bitvector ? acc_nl) 9) ∨ (get_ac_flag … s) then |
---|
| 1112 | let 〈result, flags〉 ≝ add_8_with_carry (get_8051_sfr … s SFR_ACC_A) (bitvector_of_nat 8 6) false in |
---|
| 1113 | let cy_flag ≝ get_index' ? O ? flags in |
---|
[2032] | 1114 | let 〈acc_nu', acc_nl'〉 ≝ vsplit ? 4 4 result in |
---|
[1971] | 1115 | if (gtb (nat_of_bitvector ? acc_nu') 9) ∨ cy_flag then |
---|
| 1116 | let 〈 carry, nu 〉 ≝ half_add ? acc_nu' (bitvector_of_nat 4 6) in |
---|
| 1117 | let new_acc ≝ nu @@ acc_nl' in |
---|
| 1118 | let s ≝ set_8051_sfr … s SFR_ACC_A new_acc in |
---|
| 1119 | set_flags … s cy_flag (Some ? (get_ac_flag … s)) (get_ov_flag … s) |
---|
| 1120 | else |
---|
| 1121 | s |
---|
| 1122 | else |
---|
| 1123 | s |
---|
| 1124 | | CLR addr ⇒ λinstr_refl. |
---|
[1975] | 1125 | match addr return λx. bool_to_Prop (is_in … [[ acc_a; carry; bit_addr ]] x) → x = addr → Σs': PreStatus m cm. ? with |
---|
| 1126 | [ ACC_A ⇒ λacc_a: True. λEQaddr. |
---|
[1971] | 1127 | let s ≝ add_ticks1 s in |
---|
| 1128 | set_arg_8 … s ACC_A (zero 8) |
---|
[1975] | 1129 | | CARRY ⇒ λcarry: True. λEQaddr. |
---|
[1971] | 1130 | let s ≝ add_ticks1 s in |
---|
| 1131 | set_arg_1 … s CARRY false |
---|
[1975] | 1132 | | BIT_ADDR b ⇒ λbit_addr: True. λEQaddr. |
---|
[1971] | 1133 | let s ≝ add_ticks1 s in |
---|
| 1134 | set_arg_1 … s (BIT_ADDR b) false |
---|
| 1135 | | _ ⇒ λother: False. ⊥ |
---|
[1975] | 1136 | ] (subaddressing_modein … addr) (refl … (subaddressing_modeel … addr)) |
---|
[1971] | 1137 | | CPL addr ⇒ λinstr_refl. |
---|
[1975] | 1138 | match addr return λx. bool_to_Prop (is_in … [[ acc_a; carry; bit_addr ]] x) → x = addr → Σs': PreStatus m cm. ? with |
---|
| 1139 | [ ACC_A ⇒ λacc_a: True. λEQaddr. |
---|
[1971] | 1140 | let s ≝ add_ticks1 s in |
---|
| 1141 | let old_acc ≝ get_8051_sfr … s SFR_ACC_A in |
---|
| 1142 | let new_acc ≝ negation_bv ? old_acc in |
---|
| 1143 | set_8051_sfr … s SFR_ACC_A new_acc |
---|
[1975] | 1144 | | CARRY ⇒ λcarry: True. λEQaddr. |
---|
[1971] | 1145 | let s ≝ add_ticks1 s in |
---|
| 1146 | let old_cy_flag ≝ get_arg_1 … s CARRY true in |
---|
| 1147 | let new_cy_flag ≝ ¬old_cy_flag in |
---|
| 1148 | set_arg_1 … s CARRY new_cy_flag |
---|
[1975] | 1149 | | BIT_ADDR b ⇒ λbit_addr: True. λEQaddr. |
---|
[1971] | 1150 | let s ≝ add_ticks1 s in |
---|
| 1151 | let old_bit ≝ get_arg_1 … s (BIT_ADDR b) true in |
---|
| 1152 | let new_bit ≝ ¬old_bit in |
---|
| 1153 | set_arg_1 … s (BIT_ADDR b) new_bit |
---|
| 1154 | | _ ⇒ λother: False. ? |
---|
[1975] | 1155 | ] (subaddressing_modein … addr) (refl … (subaddressing_modeel … addr)) |
---|
[1971] | 1156 | | SETB b ⇒ λinstr_refl. |
---|
| 1157 | let s ≝ add_ticks1 s in |
---|
| 1158 | set_arg_1 … s b false |
---|
| 1159 | | RL _ ⇒ λinstr_refl. (* DPM: always ACC_A *) |
---|
| 1160 | let s ≝ add_ticks1 s in |
---|
| 1161 | let old_acc ≝ get_8051_sfr … s SFR_ACC_A in |
---|
| 1162 | let new_acc ≝ rotate_left … 1 old_acc in |
---|
| 1163 | set_8051_sfr … s SFR_ACC_A new_acc |
---|
| 1164 | | RR _ ⇒ λinstr_refl. (* DPM: always ACC_A *) |
---|
| 1165 | let s ≝ add_ticks1 s in |
---|
| 1166 | let old_acc ≝ get_8051_sfr … s SFR_ACC_A in |
---|
| 1167 | let new_acc ≝ rotate_right … 1 old_acc in |
---|
| 1168 | set_8051_sfr … s SFR_ACC_A new_acc |
---|
| 1169 | | RLC _ ⇒ λinstr_refl. (* DPM: always ACC_A *) |
---|
| 1170 | let s ≝ add_ticks1 s in |
---|
| 1171 | let old_cy_flag ≝ get_cy_flag ?? s in |
---|
| 1172 | let old_acc ≝ get_8051_sfr … s SFR_ACC_A in |
---|
| 1173 | let new_cy_flag ≝ get_index' ? O ? old_acc in |
---|
| 1174 | let new_acc ≝ shift_left … 1 old_acc old_cy_flag in |
---|
| 1175 | let s ≝ set_arg_1 … s CARRY new_cy_flag in |
---|
| 1176 | set_8051_sfr … s SFR_ACC_A new_acc |
---|
| 1177 | | RRC _ ⇒ λinstr_refl. (* DPM: always ACC_A *) |
---|
| 1178 | let s ≝ add_ticks1 s in |
---|
| 1179 | let old_cy_flag ≝ get_cy_flag ?? s in |
---|
| 1180 | let old_acc ≝ get_8051_sfr … s SFR_ACC_A in |
---|
| 1181 | let new_cy_flag ≝ get_index' ? 7 ? old_acc in |
---|
| 1182 | let new_acc ≝ shift_right … 1 old_acc old_cy_flag in |
---|
| 1183 | let s ≝ set_arg_1 … s CARRY new_cy_flag in |
---|
| 1184 | set_8051_sfr … s SFR_ACC_A new_acc |
---|
| 1185 | | SWAP _ ⇒ λinstr_refl. (* DPM: always ACC_A *) |
---|
| 1186 | let s ≝ add_ticks1 s in |
---|
| 1187 | let old_acc ≝ get_8051_sfr … s SFR_ACC_A in |
---|
[2032] | 1188 | let 〈nu,nl〉 ≝ vsplit ? 4 4 old_acc in |
---|
[1971] | 1189 | let new_acc ≝ nl @@ nu in |
---|
| 1190 | set_8051_sfr … s SFR_ACC_A new_acc |
---|
| 1191 | | PUSH addr ⇒ λinstr_refl. |
---|
[1975] | 1192 | match addr return λx. bool_to_Prop (is_in … [[ direct ]] x) → x = addr → Σs': PreStatus m cm. ? with |
---|
| 1193 | [ DIRECT d ⇒ λdirect: True. λEQaddr. |
---|
[1971] | 1194 | let s ≝ add_ticks1 s in |
---|
| 1195 | let 〈carry, new_sp〉 ≝ half_add ? (get_8051_sfr … s SFR_SP) (bitvector_of_nat 8 1) in |
---|
| 1196 | let s ≝ set_8051_sfr … s SFR_SP new_sp in |
---|
| 1197 | write_at_stack_pointer … s d |
---|
| 1198 | | _ ⇒ λother: False. ⊥ |
---|
[1975] | 1199 | ] (subaddressing_modein … addr) (refl … (subaddressing_modeel … addr)) |
---|
[1971] | 1200 | | POP addr ⇒ λinstr_refl. |
---|
| 1201 | let s ≝ add_ticks1 s in |
---|
| 1202 | let contents ≝ read_at_stack_pointer ?? s in |
---|
| 1203 | let 〈new_sp, flags〉 ≝ sub_8_with_carry (get_8051_sfr … s SFR_SP) (bitvector_of_nat 8 1) false in |
---|
| 1204 | let s ≝ set_8051_sfr … s SFR_SP new_sp in |
---|
| 1205 | set_arg_8 … s addr contents |
---|
| 1206 | | XCH addr1 addr2 ⇒ λinstr_refl. |
---|
| 1207 | let s ≝ add_ticks1 s in |
---|
| 1208 | let old_addr ≝ get_arg_8 … s false addr2 in |
---|
| 1209 | let old_acc ≝ get_8051_sfr … s SFR_ACC_A in |
---|
| 1210 | let s ≝ set_8051_sfr … s SFR_ACC_A old_addr in |
---|
| 1211 | set_arg_8 … s addr2 old_acc |
---|
| 1212 | | XCHD addr1 addr2 ⇒ λinstr_refl. |
---|
| 1213 | let s ≝ add_ticks1 s in |
---|
[2032] | 1214 | let 〈acc_nu, acc_nl〉 ≝ vsplit … 4 4 (get_8051_sfr … s SFR_ACC_A) in |
---|
| 1215 | let 〈arg_nu, arg_nl〉 ≝ vsplit … 4 4 (get_arg_8 … s false addr2) in |
---|
[1971] | 1216 | let new_acc ≝ acc_nu @@ arg_nl in |
---|
| 1217 | let new_arg ≝ arg_nu @@ acc_nl in |
---|
| 1218 | let s ≝ set_8051_sfr ?? s SFR_ACC_A new_acc in |
---|
| 1219 | set_arg_8 … s addr2 new_arg |
---|
| 1220 | | RET ⇒ λinstr_refl. |
---|
| 1221 | let s ≝ add_ticks1 s in |
---|
| 1222 | let high_bits ≝ read_at_stack_pointer ?? s in |
---|
| 1223 | let 〈new_sp, flags〉 ≝ sub_8_with_carry (get_8051_sfr … s SFR_SP) (bitvector_of_nat 8 1) false in |
---|
| 1224 | let s ≝ set_8051_sfr … s SFR_SP new_sp in |
---|
| 1225 | let low_bits ≝ read_at_stack_pointer ?? s in |
---|
| 1226 | let 〈new_sp, flags〉 ≝ sub_8_with_carry (get_8051_sfr … s SFR_SP) (bitvector_of_nat 8 1) false in |
---|
| 1227 | let s ≝ set_8051_sfr … s SFR_SP new_sp in |
---|
| 1228 | let new_pc ≝ high_bits @@ low_bits in |
---|
| 1229 | set_program_counter … s new_pc |
---|
| 1230 | | RETI ⇒ λinstr_refl. |
---|
| 1231 | let s ≝ add_ticks1 s in |
---|
| 1232 | let high_bits ≝ read_at_stack_pointer ?? s in |
---|
| 1233 | let 〈new_sp, flags〉 ≝ sub_8_with_carry (get_8051_sfr … s SFR_SP) (bitvector_of_nat 8 1) false in |
---|
| 1234 | let s ≝ set_8051_sfr … s SFR_SP new_sp in |
---|
| 1235 | let low_bits ≝ read_at_stack_pointer ?? s in |
---|
| 1236 | let 〈new_sp, flags〉 ≝ sub_8_with_carry (get_8051_sfr … s SFR_SP) (bitvector_of_nat 8 1) false in |
---|
| 1237 | let s ≝ set_8051_sfr … s SFR_SP new_sp in |
---|
| 1238 | let new_pc ≝ high_bits @@ low_bits in |
---|
| 1239 | set_program_counter … s new_pc |
---|
| 1240 | | MOVX addr ⇒ λinstr_refl. |
---|
| 1241 | let s ≝ add_ticks1 s in |
---|
| 1242 | (* DPM: only copies --- doesn't affect I/O *) |
---|
| 1243 | match addr with |
---|
| 1244 | [ inl l ⇒ |
---|
| 1245 | let 〈addr1, addr2〉 ≝ l in |
---|
| 1246 | set_arg_8 … s addr1 (get_arg_8 … s false addr2) |
---|
| 1247 | | inr r ⇒ |
---|
| 1248 | let 〈addr1, addr2〉 ≝ r in |
---|
| 1249 | set_arg_8 … s addr1 (get_arg_8 … s false addr2) |
---|
| 1250 | ] |
---|
| 1251 | | MOV addr ⇒ λinstr_refl. |
---|
| 1252 | let s ≝ add_ticks1 s in |
---|
| 1253 | match addr with |
---|
| 1254 | [ inl l ⇒ |
---|
| 1255 | match l with |
---|
| 1256 | [ inl l' ⇒ |
---|
| 1257 | match l' with |
---|
| 1258 | [ inl l'' ⇒ |
---|
| 1259 | match l'' with |
---|
| 1260 | [ inl l''' ⇒ |
---|
| 1261 | match l''' with |
---|
| 1262 | [ inl l'''' ⇒ |
---|
| 1263 | let 〈addr1, addr2〉 ≝ l'''' in |
---|
| 1264 | set_arg_8 … s addr1 (get_arg_8 … s false addr2) |
---|
| 1265 | | inr r'''' ⇒ |
---|
| 1266 | let 〈addr1, addr2〉 ≝ r'''' in |
---|
| 1267 | set_arg_8 … s addr1 (get_arg_8 … s false addr2) |
---|
| 1268 | ] |
---|
| 1269 | | inr r''' ⇒ |
---|
| 1270 | let 〈addr1, addr2〉 ≝ r''' in |
---|
| 1271 | set_arg_8 … s addr1 (get_arg_8 … s false addr2) |
---|
| 1272 | ] |
---|
| 1273 | | inr r'' ⇒ |
---|
| 1274 | let 〈addr1, addr2〉 ≝ r'' in |
---|
| 1275 | set_arg_16 … s (get_arg_16 … s addr2) addr1 |
---|
| 1276 | ] |
---|
| 1277 | | inr r ⇒ |
---|
| 1278 | let 〈addr1, addr2〉 ≝ r in |
---|
| 1279 | set_arg_1 … s addr1 (get_arg_1 … s addr2 false) |
---|
| 1280 | ] |
---|
| 1281 | | inr r ⇒ |
---|
| 1282 | let 〈addr1, addr2〉 ≝ r in |
---|
| 1283 | set_arg_1 … s addr1 (get_arg_1 … s addr2 false) |
---|
| 1284 | ] |
---|
| 1285 | | JC addr ⇒ λinstr_refl. |
---|
| 1286 | if get_cy_flag ?? s then |
---|
| 1287 | let s ≝ add_ticks1 s in |
---|
| 1288 | set_program_counter … s (addr_of addr s) |
---|
| 1289 | else |
---|
| 1290 | let s ≝ add_ticks2 s in |
---|
| 1291 | s |
---|
| 1292 | | JNC addr ⇒ λinstr_refl. |
---|
| 1293 | if ¬(get_cy_flag ?? s) then |
---|
| 1294 | let s ≝ add_ticks1 s in |
---|
| 1295 | set_program_counter … s (addr_of addr s) |
---|
| 1296 | else |
---|
| 1297 | let s ≝ add_ticks2 s in |
---|
| 1298 | s |
---|
| 1299 | | JB addr1 addr2 ⇒ λinstr_refl. |
---|
| 1300 | if get_arg_1 … s addr1 false then |
---|
| 1301 | let s ≝ add_ticks1 s in |
---|
| 1302 | set_program_counter … s (addr_of addr2 s) |
---|
| 1303 | else |
---|
| 1304 | let s ≝ add_ticks2 s in |
---|
| 1305 | s |
---|
| 1306 | | JNB addr1 addr2 ⇒ λinstr_refl. |
---|
| 1307 | if ¬(get_arg_1 … s addr1 false) then |
---|
| 1308 | let s ≝ add_ticks1 s in |
---|
| 1309 | set_program_counter … s (addr_of addr2 s) |
---|
| 1310 | else |
---|
| 1311 | let s ≝ add_ticks2 s in |
---|
| 1312 | s |
---|
| 1313 | | JBC addr1 addr2 ⇒ λinstr_refl. |
---|
| 1314 | let s ≝ set_arg_1 … s addr1 false in |
---|
| 1315 | if get_arg_1 … s addr1 false then |
---|
| 1316 | let s ≝ add_ticks1 s in |
---|
| 1317 | set_program_counter … s (addr_of addr2 s) |
---|
| 1318 | else |
---|
| 1319 | let s ≝ add_ticks2 s in |
---|
| 1320 | s |
---|
| 1321 | | JZ addr ⇒ λinstr_refl. |
---|
| 1322 | if eq_bv ? (get_8051_sfr … s SFR_ACC_A) (zero 8) then |
---|
| 1323 | let s ≝ add_ticks1 s in |
---|
| 1324 | set_program_counter … s (addr_of addr s) |
---|
| 1325 | else |
---|
| 1326 | let s ≝ add_ticks2 s in |
---|
| 1327 | s |
---|
| 1328 | | JNZ addr ⇒ λinstr_refl. |
---|
| 1329 | if ¬(eq_bv ? (get_8051_sfr … s SFR_ACC_A) (zero 8)) then |
---|
| 1330 | let s ≝ add_ticks1 s in |
---|
| 1331 | set_program_counter … s (addr_of addr s) |
---|
| 1332 | else |
---|
| 1333 | let s ≝ add_ticks2 s in |
---|
| 1334 | s |
---|
| 1335 | | CJNE addr1 addr2 ⇒ λinstr_refl. |
---|
| 1336 | match addr1 with |
---|
| 1337 | [ inl l ⇒ |
---|
| 1338 | let 〈addr1, addr2'〉 ≝ l in |
---|
| 1339 | let new_cy ≝ ltb (nat_of_bitvector ? (get_arg_8 … s false addr1)) |
---|
| 1340 | (nat_of_bitvector ? (get_arg_8 … s false addr2')) in |
---|
| 1341 | if ¬(eq_bv ? (get_arg_8 … s false addr1) (get_arg_8 … s false addr2')) then |
---|
| 1342 | let s ≝ add_ticks1 s in |
---|
| 1343 | let s ≝ set_program_counter … s (addr_of addr2 s) in |
---|
| 1344 | set_flags … s new_cy (None ?) (get_ov_flag ?? s) |
---|
| 1345 | else |
---|
| 1346 | let s ≝ add_ticks2 s in |
---|
| 1347 | set_flags … s new_cy (None ?) (get_ov_flag ?? s) |
---|
| 1348 | | inr r' ⇒ |
---|
| 1349 | let 〈addr1, addr2'〉 ≝ r' in |
---|
| 1350 | let new_cy ≝ ltb (nat_of_bitvector ? (get_arg_8 … s false addr1)) |
---|
| 1351 | (nat_of_bitvector ? (get_arg_8 … s false addr2')) in |
---|
| 1352 | if ¬(eq_bv ? (get_arg_8 … s false addr1) (get_arg_8 … s false addr2')) then |
---|
| 1353 | let s ≝ add_ticks1 s in |
---|
| 1354 | let s ≝ set_program_counter … s (addr_of addr2 s) in |
---|
| 1355 | set_flags … s new_cy (None ?) (get_ov_flag ?? s) |
---|
| 1356 | else |
---|
| 1357 | let s ≝ add_ticks2 s in |
---|
| 1358 | set_flags … s new_cy (None ?) (get_ov_flag ?? s) |
---|
| 1359 | ] |
---|
| 1360 | | DJNZ addr1 addr2 ⇒ λinstr_refl. |
---|
| 1361 | let 〈result, flags〉 ≝ sub_8_with_carry (get_arg_8 … s true addr1) (bitvector_of_nat 8 1) false in |
---|
| 1362 | let s ≝ set_arg_8 … s addr1 result in |
---|
| 1363 | if ¬(eq_bv ? result (zero 8)) then |
---|
| 1364 | let s ≝ add_ticks1 s in |
---|
| 1365 | set_program_counter … s (addr_of addr2 s) |
---|
| 1366 | else |
---|
| 1367 | let s ≝ add_ticks2 s in |
---|
| 1368 | s |
---|
| 1369 | ] (refl … instr)) |
---|
[2160] | 1370 | try cases other |
---|
[2017] | 1371 | try assumption (*20s*) |
---|
| 1372 | try (% @False) (*6s*) (* Bug exploited here to implement solve :-*) |
---|
| 1373 | try (@(execute_1_technical … (subaddressing_modein …)) @I) (*66s*) |
---|
| 1374 | whd in match execute_1_preinstruction; normalize nodelta |
---|
[2023] | 1375 | [31,32: (* DJNZ *) |
---|
[1984] | 1376 | (* XXX: work on the right hand side *) |
---|
[2108] | 1377 | >p normalize nodelta >p1 normalize nodelta |
---|
[2020] | 1378 | (* XXX: switch to the left hand side *) |
---|
[2143] | 1379 | >EQP -P normalize nodelta |
---|
[2020] | 1380 | #sigma_increment_commutation #maps_assm #fetch_many_assm |
---|
| 1381 | whd in match (expand_pseudo_instruction ??????) in fetch_many_assm; |
---|
| 1382 | <EQppc in fetch_many_assm; |
---|
[2108] | 1383 | whd in match (short_jump_cond ??); |
---|
| 1384 | @pair_elim #sj_possible #disp |
---|
[2020] | 1385 | @pair_elim #result #flags #sub16_refl |
---|
[2032] | 1386 | @pair_elim #upper #lower #vsplit_refl |
---|
[2108] | 1387 | inversion (get_index' bool ???) #get_index_refl' normalize nodelta |
---|
| 1388 | #sj_possible_pair destruct(sj_possible_pair) |
---|
| 1389 | >p1 normalize nodelta |
---|
[2023] | 1390 | [1,3: |
---|
[2020] | 1391 | >EQppc in ⊢ (% → ?); #fetch_many_assm %{1} |
---|
[2108] | 1392 | >(sub16_with_carry_overflow … sub16_refl vsplit_refl get_index_refl') in fetch_many_assm; |
---|
| 1393 | normalize nodelta in ⊢ (% → ?); #fetch_many_assm |
---|
[2160] | 1394 | whd in ⊢ (??%?); |
---|
[2020] | 1395 | <(fetch_many_singleton … fetch_many_assm) -fetch_many_assm whd in ⊢ (??%?); |
---|
[2160] | 1396 | lapply maps_assm whd in ⊢ (??%? → ?); |
---|
| 1397 | inversion (addressing_mode_ok ?????) #addressing_mode_ok_refl normalize nodelta |
---|
| 1398 | [2,4: #absurd destruct(absurd) ] @Some_Some_elim #Mrefl <Mrefl -M' |
---|
[2020] | 1399 | (* XXX: work on the left hand side *) |
---|
| 1400 | @(pair_replace ?????????? p) normalize nodelta |
---|
[2023] | 1401 | [1,3: |
---|
[2160] | 1402 | >EQs @eq_f3 [2,3,5,6: % ] >(get_arg_8_set_program_counter … true addr1) |
---|
| 1403 | [2,4: /2 by is_in_subvector_is_in_supervector, subaddressing_modein, I/ ] |
---|
| 1404 | >(get_arg_8_set_program_counter … true addr1) |
---|
| 1405 | [2,4: /2 by is_in_subvector_is_in_supervector, subaddressing_modein, I/ ] |
---|
| 1406 | @get_arg_8_pseudo_addressing_mode_ok assumption |
---|
| 1407 | |2,4: |
---|
| 1408 | >p1 normalize nodelta >EQs |
---|
| 1409 | alias id "set_program_counter_status_of_pseudo_status" = "cic:/matita/cerco/ASM/Test/set_program_counter_status_of_pseudo_status.def(26)". |
---|
| 1410 | >set_program_counter_status_of_pseudo_status |
---|
| 1411 | whd in ⊢ (??%%); |
---|
| 1412 | @split_eq_status |
---|
| 1413 | [1,10: |
---|
| 1414 | whd in ⊢ (??%%); >set_arg_8_set_program_counter |
---|
| 1415 | [2,4: /2 by is_in_subvector_is_in_supervector, subaddressing_modein, I/ ] |
---|
| 1416 | >low_internal_ram_set_program_counter |
---|
| 1417 | [1: |
---|
| 1418 | >low_internal_ram_set_program_counter |
---|
| 1419 | (* XXX: ??? *) |
---|
| 1420 | |2: |
---|
| 1421 | >low_internal_ram_set_clock |
---|
| 1422 | (* XXX: ??? *) |
---|
[2143] | 1423 | ] |
---|
[2160] | 1424 | |2,11: |
---|
| 1425 | whd in ⊢ (??%%); >set_arg_8_set_program_counter |
---|
| 1426 | [2,4: /2 by is_in_subvector_is_in_supervector, subaddressing_modein, I/ ] |
---|
| 1427 | >high_internal_ram_set_program_counter |
---|
| 1428 | [1: |
---|
| 1429 | >high_internal_ram_set_program_counter |
---|
| 1430 | (* XXX: ??? *) |
---|
| 1431 | |2: |
---|
| 1432 | >high_internal_ram_set_clock |
---|
| 1433 | (* XXX: ??? *) |
---|
[2143] | 1434 | ] |
---|
[2160] | 1435 | |3,12: |
---|
| 1436 | whd in ⊢ (??%%); >(external_ram_set_arg_8 ??? addr1) in ⊢ (???%); |
---|
| 1437 | [2,4: /2 by is_in_subvector_is_in_supervector, subaddressing_modein, I/ ] |
---|
| 1438 | >(external_ram_set_arg_8 ??? addr1) |
---|
| 1439 | [2,4: /2 by is_in_subvector_is_in_supervector, subaddressing_modein, I/ ] % |
---|
| 1440 | |4,13: |
---|
| 1441 | whd in ⊢ (??%%); >EQaddr_of normalize nodelta |
---|
| 1442 | [1: |
---|
| 1443 | >program_counter_set_program_counter |
---|
| 1444 | >set_arg_8_set_program_counter |
---|
| 1445 | [2: /2 by is_in_subvector_is_in_supervector, subaddressing_modein, I/ ] |
---|
| 1446 | >set_clock_set_program_counter >program_counter_set_program_counter |
---|
| 1447 | change with (add ??? = ?) |
---|
| 1448 | (* XXX: ??? *) |
---|
| 1449 | |2: |
---|
| 1450 | >set_arg_8_set_program_counter |
---|
| 1451 | [2: /2 by is_in_subvector_is_in_supervector, subaddressing_modein, I/ ] |
---|
| 1452 | >program_counter_set_program_counter |
---|
| 1453 | >set_arg_8_set_program_counter |
---|
| 1454 | [2: /2 by is_in_subvector_is_in_supervector, subaddressing_modein, I/ ] |
---|
| 1455 | >set_clock_set_program_counter >program_counter_set_program_counter |
---|
| 1456 | >sigma_increment_commutation <EQppc |
---|
| 1457 | whd in match (assembly_1_pseudoinstruction ??????); |
---|
| 1458 | whd in match (expand_pseudo_instruction ??????); |
---|
| 1459 | (* XXX: ??? *) |
---|
| 1460 | ] |
---|
| 1461 | |5,14: |
---|
| 1462 | whd in match (special_function_registers_8051 ???); |
---|
| 1463 | [1: |
---|
| 1464 | >special_function_registers_8051_set_program_counter |
---|
| 1465 | >special_function_registers_8051_set_clock |
---|
| 1466 | >set_arg_8_set_program_counter in ⊢ (???%); |
---|
| 1467 | [2: /2 by is_in_subvector_is_in_supervector, subaddressing_modein, I/ ] |
---|
| 1468 | >special_function_registers_8051_set_program_counter |
---|
| 1469 | >set_arg_8_set_program_counter |
---|
| 1470 | [2: /2 by is_in_subvector_is_in_supervector, subaddressing_modein, I/ ] |
---|
| 1471 | >special_function_registers_8051_set_program_counter |
---|
| 1472 | @special_function_registers_8051_set_arg_8 assumption |
---|
| 1473 | |2: |
---|
| 1474 | >special_function_registers_8051_set_clock |
---|
| 1475 | >set_arg_8_set_program_counter |
---|
| 1476 | [2: /2 by is_in_subvector_is_in_supervector, subaddressing_modein, I/ ] |
---|
| 1477 | >set_arg_8_set_program_counter |
---|
| 1478 | [2: /2 by is_in_subvector_is_in_supervector, subaddressing_modein, I/ ] |
---|
| 1479 | >special_function_registers_8051_set_program_counter |
---|
| 1480 | >special_function_registers_8051_set_program_counter |
---|
| 1481 | @special_function_registers_8051_set_arg_8 assumption |
---|
| 1482 | ] |
---|
| 1483 | |6,15: |
---|
| 1484 | whd in match (special_function_registers_8052 ???); |
---|
| 1485 | whd in match (special_function_registers_8052 ???) in ⊢ (???%); |
---|
| 1486 | [1: |
---|
| 1487 | >set_arg_8_set_program_counter |
---|
| 1488 | [2: /2 by is_in_subvector_is_in_supervector, subaddressing_modein, I/ ] |
---|
| 1489 | >set_arg_8_set_program_counter |
---|
| 1490 | [2: /2 by is_in_subvector_is_in_supervector, subaddressing_modein, I/ ] |
---|
| 1491 | >special_function_registers_8052_set_program_counter |
---|
| 1492 | >special_function_registers_8052_set_program_counter |
---|
| 1493 | @special_function_registers_8052_set_arg_8 assumption |
---|
| 1494 | |2: |
---|
| 1495 | whd in ⊢ (??%%); |
---|
| 1496 | >special_function_registers_8052_set_arg_8 in ⊢ (??%?); assumption |
---|
| 1497 | ] |
---|
| 1498 | (* XXX: we need special_function_registers_8052_set_arg_8 *) |
---|
| 1499 | |7,16: |
---|
| 1500 | whd in match (p1_latch ???); |
---|
| 1501 | whd in match (p1_latch ???) in ⊢ (???%); |
---|
| 1502 | (* XXX: we need p1_latch_8052_set_arg_8 *) |
---|
| 1503 | |8,17: |
---|
| 1504 | whd in match (p3_latch ???); |
---|
| 1505 | whd in match (p3_latch ???) in ⊢ (???%); |
---|
| 1506 | (* XXX: we need p3_latch_8052_set_arg_8 *) |
---|
| 1507 | |9: |
---|
| 1508 | >clock_set_clock |
---|
| 1509 | >clock_set_program_counter in ⊢ (???%); >clock_set_clock |
---|
| 1510 | >EQticks <instr_refl @eq_f2 |
---|
| 1511 | [1: |
---|
| 1512 | whd in ⊢ (??%%); whd in match (ticks_of0 ??????); |
---|
| 1513 | |2: |
---|
| 1514 | (* XXX: we need clock_set_arg_8 *) |
---|
| 1515 | ] |
---|
| 1516 | |18: |
---|
[2143] | 1517 | ] |
---|
[2020] | 1518 | ] |
---|
| 1519 | (* XXX: switch to the right hand side *) |
---|
| 1520 | normalize nodelta >EQs -s >EQticks -ticks |
---|
| 1521 | cases (¬ eq_bv ???) normalize nodelta |
---|
| 1522 | whd in ⊢ (??%%); |
---|
| 1523 | (* XXX: finally, prove the equality using sigma commutation *) |
---|
| 1524 | @split_eq_status try % |
---|
[2143] | 1525 | [1,2,3,19,20,21,28,29,30: |
---|
| 1526 | cases daemon (* XXX: axioms as above *) |
---|
| 1527 | |4,13,22,31: |
---|
| 1528 | |5,14,23,32: |
---|
| 1529 | |6,15,24,33: |
---|
| 1530 | |7,16,25,34: |
---|
| 1531 | |8,17,26,35: |
---|
[2160] | 1532 | whd in ⊢ (??%%);maps_assm |
---|
[2143] | 1533 | |
---|
| 1534 | |9,18,27,36: |
---|
| 1535 | whd in ⊢ (??%%); |
---|
| 1536 | whd in match (ticks_of_instruction ?); <instr_refl |
---|
| 1537 | cases daemon (* XXX: daemon in ticks_of0 stopping progression *) |
---|
| 1538 | ] |
---|
[2023] | 1539 | |2,4: |
---|
[2109] | 1540 | >(? : eq_v bool 9 eq_b upper (zero 9) = false) |
---|
| 1541 | [2, 4: |
---|
| 1542 | cases daemon (* XXX: !!! *) |
---|
| 1543 | ] |
---|
| 1544 | normalize nodelta >EQppc |
---|
[2020] | 1545 | * @(pose … (add 16 ??)) #intermediate_pc #EQintermediate_pc #fetch_refl |
---|
| 1546 | * @(pose … (add 16 ??)) #intermediate_pc' #EQintermediate_pc' #fetch_refl' |
---|
| 1547 | * @(pose … (add 16 ??)) #intermediate_pc'' #EQintermediate_pc'' #fetch_refl'' |
---|
| 1548 | #fetch_many_assm whd in fetch_many_assm; %{2} |
---|
| 1549 | change with (execute_1 ?? = ?) |
---|
| 1550 | @(pose … (execute_1 ? (status_of_pseudo_status …))) |
---|
| 1551 | #status_after_1 #EQstatus_after_1 |
---|
| 1552 | <(?: ? = status_after_1) |
---|
[2023] | 1553 | [3,6: |
---|
[2020] | 1554 | >EQstatus_after_1 in ⊢ (???%); |
---|
| 1555 | whd in ⊢ (???%); |
---|
[2109] | 1556 | [1: |
---|
[2023] | 1557 | <fetch_refl in ⊢ (???%); |
---|
| 1558 | |2: |
---|
| 1559 | <fetch_refl in ⊢ (???%); |
---|
| 1560 | ] |
---|
[2020] | 1561 | whd in ⊢ (???%); |
---|
| 1562 | @(pair_replace ?????????? p) |
---|
[2023] | 1563 | [1,3: |
---|
[2020] | 1564 | cases daemon |
---|
[2023] | 1565 | |2,4: |
---|
[2020] | 1566 | normalize nodelta |
---|
| 1567 | whd in match (addr_of_relative ????); |
---|
| 1568 | cases (¬ eq_bv ???) normalize nodelta |
---|
| 1569 | >set_clock_mk_Status_commutation |
---|
| 1570 | whd in ⊢ (???%); |
---|
| 1571 | change with (add ???) in match (\snd (half_add ???)); |
---|
| 1572 | >set_arg_8_set_program_counter in ⊢ (???%); |
---|
[2114] | 1573 | [2,4,6,8: /2 by is_in_subvector_is_in_supervector, subaddressing_modein, I/ ] |
---|
[2020] | 1574 | >program_counter_set_program_counter in ⊢ (???%); |
---|
| 1575 | >(?: add ? intermediate_pc (sign_extension (bitvector_of_nat ? 2)) = intermediate_pc') |
---|
[2023] | 1576 | [2,4,6,8: |
---|
[2020] | 1577 | >bitvector_of_nat_sign_extension_equivalence |
---|
[2023] | 1578 | [1,3,5,7: |
---|
[2020] | 1579 | >EQintermediate_pc' % |
---|
| 1580 | |*: |
---|
| 1581 | repeat @le_S_S @le_O_n |
---|
| 1582 | ] |
---|
| 1583 | ] |
---|
[2023] | 1584 | [1,3: % ] |
---|
[2020] | 1585 | ] |
---|
[2023] | 1586 | |1,4: |
---|
[2020] | 1587 | skip |
---|
| 1588 | ] |
---|
[2023] | 1589 | [3,4: |
---|
[2020] | 1590 | -status_after_1 |
---|
| 1591 | @(pose … (execute_1 ? (mk_PreStatus …))) |
---|
| 1592 | #status_after_1 #EQstatus_after_1 |
---|
| 1593 | <(?: ? = status_after_1) |
---|
[2023] | 1594 | [3,6: |
---|
[2020] | 1595 | >EQstatus_after_1 in ⊢ (???%); |
---|
| 1596 | whd in ⊢ (???%); |
---|
| 1597 | (* XXX: matita bug with patterns across multiple goals *) |
---|
[2023] | 1598 | [1: |
---|
| 1599 | <fetch_refl'' in ⊢ (???%); |
---|
| 1600 | |2: |
---|
| 1601 | <fetch_refl'' in ⊢ (???%); |
---|
| 1602 | ] |
---|
| 1603 | [2: % |1: whd in ⊢ (???%); % ] |
---|
| 1604 | |1,4: |
---|
| 1605 | skip |
---|
| 1606 | ] |
---|
| 1607 | -status_after_1 whd in ⊢ (??%?); |
---|
| 1608 | (* XXX: switch to the right hand side *) |
---|
| 1609 | normalize nodelta >EQs -s >EQticks -ticks |
---|
[2109] | 1610 | normalize nodelta whd in ⊢ (??%%); |
---|
[2020] | 1611 | ] |
---|
[2023] | 1612 | (* XXX: finally, prove the equality using sigma commutation *) |
---|
| 1613 | @split_eq_status try % |
---|
[2020] | 1614 | whd in ⊢ (??%%); |
---|
[2023] | 1615 | cases daemon |
---|
[2020] | 1616 | ] |
---|
| 1617 | |30: (* CJNE *) |
---|
| 1618 | (* XXX: work on the right hand side *) |
---|
[2018] | 1619 | cases addr1 -addr1 #addr1 normalize nodelta |
---|
| 1620 | cases addr1 -addr1 #addr1_l #addr1_r normalize nodelta |
---|
| 1621 | (* XXX: switch to the left hand side *) |
---|
| 1622 | >EQP -P normalize nodelta |
---|
| 1623 | #sigma_increment_commutation #maps_assm #fetch_many_assm |
---|
| 1624 | |
---|
| 1625 | whd in match (expand_pseudo_instruction ??????) in fetch_many_assm; |
---|
| 1626 | <EQppc in fetch_many_assm; |
---|
[2109] | 1627 | whd in match (short_jump_cond ??); |
---|
| 1628 | @pair_elim #sj_possible #disp |
---|
[2018] | 1629 | @pair_elim #result #flags #sub16_refl |
---|
[2032] | 1630 | @pair_elim #upper #lower #vsplit_refl |
---|
[2109] | 1631 | inversion (get_index' bool ???) #get_index_refl' normalize nodelta |
---|
| 1632 | #sj_possible_pair destruct(sj_possible_pair) normalize nodelta |
---|
[2018] | 1633 | [1,3: |
---|
| 1634 | >EQppc in ⊢ (% → ?); #fetch_many_assm %{1} |
---|
[2109] | 1635 | >(sub16_with_carry_overflow … sub16_refl vsplit_refl get_index_refl') in fetch_many_assm; |
---|
| 1636 | normalize nodelta in ⊢ (% → ?); #fetch_many_assm |
---|
[2018] | 1637 | whd in ⊢ (??%?); |
---|
| 1638 | <(fetch_many_singleton … fetch_many_assm) -fetch_many_assm whd in ⊢ (??%?); |
---|
| 1639 | inversion (¬ (eq_bv ???)) in ⊢ (???%); #eq_bv_refl normalize nodelta |
---|
| 1640 | lapply (refl_to_jmrefl ??? eq_bv_refl) -eq_bv_refl #eq_bv_refl |
---|
| 1641 | @(if_then_else_replace ???????? eq_bv_refl) |
---|
| 1642 | [1,3,5,7: |
---|
| 1643 | cases daemon |
---|
| 1644 | |2,4,6,8: |
---|
| 1645 | (* XXX: switch to the right hand side *) |
---|
| 1646 | normalize nodelta >EQs -s >EQticks -ticks |
---|
| 1647 | whd in ⊢ (??%%); |
---|
| 1648 | (* XXX: finally, prove the equality using sigma commutation *) |
---|
| 1649 | @split_eq_status try % |
---|
| 1650 | [3,7,11,15: |
---|
| 1651 | whd in ⊢ (??%?); |
---|
| 1652 | [1,3: |
---|
| 1653 | cases daemon |
---|
| 1654 | |2,4: |
---|
| 1655 | cases daemon |
---|
| 1656 | ] |
---|
| 1657 | ] |
---|
| 1658 | cases daemon (* XXX *) |
---|
| 1659 | ] |
---|
| 1660 | |2,4: |
---|
[2109] | 1661 | >(? : eq_v bool 9 eq_b upper (zero 9) = false) |
---|
| 1662 | [2, 4: |
---|
| 1663 | cases daemon (* XXX: !!! *) |
---|
| 1664 | ] |
---|
| 1665 | normalize nodelta >EQppc |
---|
[2018] | 1666 | * @(pose … (add 16 ??)) #intermediate_pc #EQintermediate_pc #fetch_refl |
---|
| 1667 | * @(pose … (add 16 ??)) #intermediate_pc' #EQintermediate_pc' #fetch_refl' |
---|
| 1668 | * @(pose … (add 16 ??)) #intermediate_pc'' #EQintermediate_pc'' #fetch_refl'' |
---|
| 1669 | #fetch_many_assm whd in fetch_many_assm; %{2} |
---|
| 1670 | change with (execute_1 ?? = ?) |
---|
| 1671 | @(pose … (execute_1 ? (status_of_pseudo_status …))) |
---|
| 1672 | #status_after_1 #EQstatus_after_1 |
---|
| 1673 | <(?: ? = status_after_1) |
---|
[2020] | 1674 | [2,5: |
---|
| 1675 | inversion (¬ (eq_bv ???)) #eq_bv_refl normalize nodelta |
---|
| 1676 | |3,6: |
---|
[2018] | 1677 | >EQstatus_after_1 in ⊢ (???%); |
---|
| 1678 | whd in ⊢ (???%); |
---|
| 1679 | [1: <fetch_refl in ⊢ (???%); |
---|
| 1680 | |2: <fetch_refl in ⊢ (???%); |
---|
| 1681 | ] |
---|
| 1682 | whd in ⊢ (???%); |
---|
| 1683 | inversion (¬ (eq_bv ???)) in ⊢ (???%); #eq_bv_refl normalize nodelta |
---|
| 1684 | whd in ⊢ (???%); |
---|
| 1685 | whd in match (addr_of_relative ????); |
---|
| 1686 | change with (add ???) in match (\snd (half_add ???)); |
---|
| 1687 | >set_clock_set_program_counter in ⊢ (???%); |
---|
| 1688 | >program_counter_set_program_counter in ⊢ (???%); |
---|
| 1689 | >(?: add ? intermediate_pc (sign_extension (bitvector_of_nat ? 2)) = intermediate_pc') |
---|
| 1690 | [2,4,6,8: |
---|
| 1691 | >bitvector_of_nat_sign_extension_equivalence |
---|
| 1692 | [1,3,5,7: |
---|
| 1693 | >EQintermediate_pc' % |
---|
| 1694 | |*: |
---|
| 1695 | repeat @le_S_S @le_O_n |
---|
| 1696 | ] |
---|
[2020] | 1697 | |1,5: |
---|
| 1698 | % |
---|
[2018] | 1699 | ] |
---|
[2020] | 1700 | |1,4: skip |
---|
[2018] | 1701 | ] |
---|
[2020] | 1702 | [1,2,3,4: |
---|
| 1703 | -status_after_1 |
---|
| 1704 | @(pose … (execute_1 ? (mk_PreStatus …))) |
---|
| 1705 | #status_after_1 #EQstatus_after_1 |
---|
| 1706 | <(?: ? = status_after_1) |
---|
| 1707 | [3,6,9,12: |
---|
| 1708 | >EQstatus_after_1 in ⊢ (???%); |
---|
| 1709 | whd in ⊢ (???%); |
---|
| 1710 | (* XXX: matita bug with patterns across multiple goals *) |
---|
| 1711 | [1: <fetch_refl'' in ⊢ (???%); |
---|
| 1712 | |2: <fetch_refl'' in ⊢ (???%); |
---|
| 1713 | |3: <fetch_refl'' in ⊢ (???%); |
---|
| 1714 | |4: <fetch_refl'' in ⊢ (???%); |
---|
| 1715 | ] % |
---|
| 1716 | |1,4,7,10: |
---|
| 1717 | skip |
---|
| 1718 | ] |
---|
| 1719 | -status_after_1 whd in ⊢ (??%?); |
---|
| 1720 | (* XXX: switch to the right hand side *) |
---|
| 1721 | normalize nodelta >EQs -s >EQticks -ticks |
---|
| 1722 | whd in ⊢ (??%%); |
---|
| 1723 | ] |
---|
| 1724 | (* XXX: finally, prove the equality using sigma commutation *) |
---|
| 1725 | @split_eq_status try % |
---|
[2023] | 1726 | cases daemon |
---|
[2018] | 1727 | ] |
---|
| 1728 | |17,19,21,23,25,27,29,16,18,20,22,24,26,28: (* JC, JNC, JB, JNB, JBC, JZ, JNZ (true cases last) *) |
---|
| 1729 | (* XXX: work on the right hand side *) |
---|
| 1730 | >p normalize nodelta |
---|
| 1731 | (* XXX: switch to the left hand side *) |
---|
[2139] | 1732 | >EQP -P normalize nodelta |
---|
[2018] | 1733 | #sigma_increment_commutation #maps_assm #fetch_many_assm |
---|
| 1734 | |
---|
| 1735 | whd in match (expand_pseudo_instruction ??????) in fetch_many_assm; |
---|
| 1736 | <EQppc in fetch_many_assm; |
---|
[2109] | 1737 | whd in match (short_jump_cond ??); |
---|
| 1738 | @pair_elim #sj_possible #disp |
---|
[2018] | 1739 | @pair_elim #result #flags #sub16_refl |
---|
[2032] | 1740 | @pair_elim #upper #lower #vsplit_refl |
---|
[2109] | 1741 | inversion (get_index' bool ???) #get_index_refl' normalize nodelta |
---|
| 1742 | #sj_possible_pair destruct(sj_possible_pair) normalize nodelta |
---|
[2018] | 1743 | [1,3,5,7,9,11,13,15,17,19,21,23,25,27: |
---|
| 1744 | >EQppc in ⊢ (% → ?); #fetch_many_assm %{1} |
---|
[2109] | 1745 | >(sub16_with_carry_overflow … sub16_refl vsplit_refl get_index_refl') in fetch_many_assm; |
---|
| 1746 | normalize nodelta in ⊢ (% → ?); #fetch_many_assm |
---|
[2018] | 1747 | whd in ⊢ (??%?); |
---|
| 1748 | <(fetch_many_singleton … fetch_many_assm) -fetch_many_assm whd in ⊢ (??%?); |
---|
| 1749 | (* XXX: work on the left hand side *) |
---|
| 1750 | @(if_then_else_replace ???????? p) normalize nodelta |
---|
| 1751 | [1,3,5,7,9,11,13,15,17,19,21,23,25,27: |
---|
| 1752 | cases daemon |
---|
| 1753 | ] |
---|
| 1754 | (* XXX: switch to the right hand side *) |
---|
| 1755 | normalize nodelta >EQs -s >EQticks -ticks |
---|
| 1756 | whd in ⊢ (??%%); |
---|
| 1757 | (* XXX: finally, prove the equality using sigma commutation *) |
---|
| 1758 | @split_eq_status try % |
---|
| 1759 | cases daemon |
---|
| 1760 | |2,4,6,8,10,12,14,16,18,20,22,24,26,28: |
---|
[2109] | 1761 | >(? : eq_v bool 9 eq_b upper (zero 9) = false) |
---|
| 1762 | [2,4,6,8,10,12,14,16,18,20,22,24,26,28: |
---|
| 1763 | cases daemon (* XXX: !!! *) |
---|
| 1764 | ] |
---|
| 1765 | normalize nodelta >EQppc |
---|
[2018] | 1766 | * @(pose … (add 16 ??)) #intermediate_pc #EQintermediate_pc #fetch_refl |
---|
| 1767 | * @(pose … (add 16 ??)) #intermediate_pc' #EQintermediate_pc' #fetch_refl' |
---|
| 1768 | * @(pose … (add 16 ??)) #intermediate_pc'' #EQintermediate_pc'' #fetch_refl'' |
---|
| 1769 | #fetch_many_assm whd in fetch_many_assm; %{2} |
---|
| 1770 | change with (execute_1 ?? = ?) |
---|
| 1771 | @(pose … (execute_1 ? (status_of_pseudo_status …))) |
---|
| 1772 | #status_after_1 #EQstatus_after_1 |
---|
| 1773 | <(?: ? = status_after_1) |
---|
| 1774 | [3,6,9,12,15,18,21,24,27,30,33,36,39,42: |
---|
| 1775 | >EQstatus_after_1 in ⊢ (???%); |
---|
| 1776 | whd in ⊢ (???%); |
---|
| 1777 | [1: <fetch_refl in ⊢ (???%); |
---|
| 1778 | |2: <fetch_refl in ⊢ (???%); |
---|
| 1779 | |3: <fetch_refl in ⊢ (???%); |
---|
| 1780 | |4: <fetch_refl in ⊢ (???%); |
---|
| 1781 | |5: <fetch_refl in ⊢ (???%); |
---|
| 1782 | |6: <fetch_refl in ⊢ (???%); |
---|
| 1783 | |7: <fetch_refl in ⊢ (???%); |
---|
| 1784 | |8: <fetch_refl in ⊢ (???%); |
---|
| 1785 | |9: <fetch_refl in ⊢ (???%); |
---|
| 1786 | |10: <fetch_refl in ⊢ (???%); |
---|
| 1787 | |11: <fetch_refl in ⊢ (???%); |
---|
| 1788 | |12: <fetch_refl in ⊢ (???%); |
---|
| 1789 | |13: <fetch_refl in ⊢ (???%); |
---|
| 1790 | |14: <fetch_refl in ⊢ (???%); |
---|
| 1791 | ] |
---|
| 1792 | whd in ⊢ (???%); |
---|
| 1793 | @(if_then_else_replace ???????? p) |
---|
| 1794 | [1,3,5,7,9,11,13,15,17,19,21,23,25,27: |
---|
| 1795 | cases daemon |
---|
| 1796 | |2,4,6,8,10,12,14,16,18,20,22,24,26,28: |
---|
| 1797 | normalize nodelta |
---|
| 1798 | whd in match (addr_of_relative ????); |
---|
| 1799 | >set_clock_mk_Status_commutation |
---|
| 1800 | [9,10: |
---|
| 1801 | (* XXX: demodulation not working in this case *) |
---|
| 1802 | >program_counter_set_arg_1 in ⊢ (???%); |
---|
| 1803 | >program_counter_set_program_counter in ⊢ (???%); |
---|
| 1804 | |*: |
---|
| 1805 | /demod/ |
---|
| 1806 | ] |
---|
| 1807 | whd in ⊢ (???%); |
---|
| 1808 | change with (add ???) in match (\snd (half_add ???)); |
---|
| 1809 | >(?: add ? intermediate_pc (sign_extension (bitvector_of_nat ? 2)) = intermediate_pc') |
---|
| 1810 | [2,4,6,8,10,12,14,16,18,20,22,24,26,28: |
---|
| 1811 | >bitvector_of_nat_sign_extension_equivalence |
---|
| 1812 | [1,3,5,7,9,11,13,15,17,19,21,23,25,27: |
---|
| 1813 | >EQintermediate_pc' % |
---|
| 1814 | |*: |
---|
| 1815 | repeat @le_S_S @le_O_n |
---|
| 1816 | ] |
---|
| 1817 | ] |
---|
| 1818 | % |
---|
| 1819 | ] |
---|
| 1820 | |1,4,7,10,13,16,19,22,25,28,31,34,37,40: |
---|
| 1821 | skip |
---|
| 1822 | ] |
---|
| 1823 | -status_after_1 |
---|
| 1824 | @(pose … (execute_1 ? (mk_PreStatus …))) |
---|
| 1825 | #status_after_1 #EQstatus_after_1 |
---|
| 1826 | <(?: ? = status_after_1) |
---|
| 1827 | [3,6,9,12,15,18,21,24,27,30,33,36,39,42: |
---|
| 1828 | >EQstatus_after_1 in ⊢ (???%); |
---|
| 1829 | whd in ⊢ (???%); |
---|
| 1830 | (* XXX: matita bug with patterns across multiple goals *) |
---|
| 1831 | [1: <fetch_refl'' in ⊢ (???%); |
---|
| 1832 | |2: <fetch_refl' in ⊢ (???%); |
---|
| 1833 | |3: <fetch_refl'' in ⊢ (???%); |
---|
| 1834 | |4: <fetch_refl' in ⊢ (???%); |
---|
| 1835 | |5: <fetch_refl'' in ⊢ (???%); |
---|
| 1836 | |6: <fetch_refl' in ⊢ (???%); |
---|
| 1837 | |7: <fetch_refl'' in ⊢ (???%); |
---|
| 1838 | |8: <fetch_refl' in ⊢ (???%); |
---|
| 1839 | |9: <fetch_refl'' in ⊢ (???%); |
---|
| 1840 | |10: <fetch_refl' in ⊢ (???%); |
---|
| 1841 | |11: <fetch_refl'' in ⊢ (???%); |
---|
| 1842 | |12: <fetch_refl' in ⊢ (???%); |
---|
| 1843 | |13: <fetch_refl'' in ⊢ (???%); |
---|
| 1844 | |14: <fetch_refl' in ⊢ (???%); |
---|
| 1845 | ] |
---|
| 1846 | whd in ⊢ (???%); |
---|
| 1847 | [9,10: |
---|
| 1848 | |*: |
---|
| 1849 | /demod/ |
---|
| 1850 | ] % |
---|
| 1851 | |1,4,7,10,13,16,19,22,25,28,31,34,37,40: |
---|
| 1852 | skip |
---|
| 1853 | ] |
---|
| 1854 | -status_after_1 whd in ⊢ (??%?); |
---|
| 1855 | (* XXX: switch to the right hand side *) |
---|
| 1856 | normalize nodelta >EQs -s >EQticks -ticks |
---|
| 1857 | whd in ⊢ (??%%); |
---|
| 1858 | (* XXX: finally, prove the equality using sigma commutation *) |
---|
| 1859 | @split_eq_status try % |
---|
| 1860 | [3,11,19,27,36,53,61: |
---|
| 1861 | >program_counter_set_program_counter >set_clock_mk_Status_commutation |
---|
| 1862 | [5: >program_counter_set_program_counter ] |
---|
| 1863 | >EQaddr_of normalize nodelta |
---|
| 1864 | whd in ⊢ (??%?); >EQlookup_labels normalize nodelta |
---|
[2139] | 1865 | >EQcm change with (address_of_word_labels_code_mem ??) in match (address_of_word_labels ??); |
---|
| 1866 | @eq_f lapply (create_label_cost_map_ok 〈preamble, instr_list〉) |
---|
| 1867 | >create_label_cost_refl normalize nodelta #relevant @relevant |
---|
| 1868 | whd in is_well_labelled_witness; @(is_well_labelled_witness … ppc … (Instruction … instr)) |
---|
| 1869 | try assumption whd in match instruction_has_label; normalize nodelta |
---|
| 1870 | <instr_refl normalize nodelta % |
---|
[2018] | 1871 | |7,15,23,31,45,57,65: |
---|
| 1872 | >set_clock_mk_Status_commutation >program_counter_set_program_counter |
---|
| 1873 | whd in ⊢ (??%?); normalize nodelta |
---|
| 1874 | >EQppc in fetch_many_assm; #fetch_many_assm |
---|
| 1875 | [5: |
---|
| 1876 | >program_counter_set_arg_1 >program_counter_set_program_counter |
---|
| 1877 | ] |
---|
| 1878 | <(eq_bv_eq … fetch_many_assm) >EQintermediate_pc'' |
---|
| 1879 | <bitvector_of_nat_sign_extension_equivalence |
---|
| 1880 | [1,3,5,7,9,11,13: |
---|
| 1881 | whd in ⊢ (???%); cases (half_add ???) normalize // |
---|
| 1882 | |2,4,6,8,10,12,14: |
---|
| 1883 | @assembly1_lt_128 |
---|
| 1884 | @le_S_S @le_O_n |
---|
| 1885 | ] |
---|
| 1886 | |*: |
---|
| 1887 | cases daemon |
---|
| 1888 | ] |
---|
| 1889 | ] |
---|
| 1890 | |4,5,6,7,8,36,37,38,39,40,41,50: (* INC, CLR, CPL, PUSH *) |
---|
| 1891 | (* XXX: work on the right hand side *) |
---|
[1975] | 1892 | lapply (subaddressing_modein ???) |
---|
| 1893 | <EQaddr normalize nodelta #irrelevant |
---|
| 1894 | try (>p normalize nodelta) |
---|
| 1895 | try (>p1 normalize nodelta) |
---|
[1984] | 1896 | (* XXX: switch to the left hand side *) |
---|
[2017] | 1897 | >EQP -P normalize nodelta |
---|
[1984] | 1898 | #sigma_increment_commutation #maps_assm #fetch_many_assm %{1} |
---|
| 1899 | whd in ⊢ (??%?); |
---|
[2109] | 1900 | whd in match (expand_pseudo_instruction ??????) in fetch_many_assm; |
---|
[1984] | 1901 | <(fetch_many_singleton … fetch_many_assm) -fetch_many_assm whd in ⊢ (??%?); |
---|
| 1902 | (* XXX: work on the left hand side *) |
---|
[1975] | 1903 | [1,2,3,4,5: |
---|
| 1904 | generalize in ⊢ (??(???(?%))?); |
---|
| 1905 | |6,7,8,9,10,11: |
---|
| 1906 | generalize in ⊢ (??(???(?%))?); |
---|
| 1907 | |12: |
---|
| 1908 | generalize in ⊢ (??(???(?%))?); |
---|
| 1909 | ] |
---|
| 1910 | <EQaddr normalize nodelta #irrelevant |
---|
[1977] | 1911 | try @(jmpair_as_replace ?????????? p) |
---|
| 1912 | [10: normalize nodelta try @(jmpair_as_replace ?????????? p1) ] |
---|
[1984] | 1913 | (* XXX: switch to the right hand side *) |
---|
| 1914 | normalize nodelta >EQs -s >EQticks -ticks |
---|
[1975] | 1915 | whd in ⊢ (??%%); |
---|
[1984] | 1916 | (* XXX: finally, prove the equality using sigma commutation *) |
---|
[2017] | 1917 | try @split_eq_status try % whd in ⊢ (??%%); |
---|
[2023] | 1918 | cases daemon |
---|
[2017] | 1919 | |1,2,3,9,46,51,53,54,55: (* ADD, ADDC, SUBB, DEC, SWAP, POP, XCHD, RET, RETI *) |
---|
[1984] | 1920 | (* XXX: work on the right hand side *) |
---|
[1971] | 1921 | >p normalize nodelta |
---|
[1975] | 1922 | try (>p1 normalize nodelta) |
---|
[1984] | 1923 | (* XXX: switch to the left hand side *) |
---|
| 1924 | -instr_refl >EQP -P normalize nodelta |
---|
| 1925 | #sigma_increment_commutation #maps_assm #fetch_many_assm %{1} |
---|
| 1926 | whd in ⊢ (??%?); |
---|
| 1927 | <(fetch_many_singleton … fetch_many_assm) -fetch_many_assm whd in ⊢ (??%?); |
---|
| 1928 | (* XXX: work on the left hand side *) |
---|
[1971] | 1929 | @(pair_replace ?????????? p) |
---|
[1978] | 1930 | [1,3,5,7,9,11,13,15,17: |
---|
[2017] | 1931 | >set_clock_set_program_counter >set_clock_mk_Status_commutation |
---|
| 1932 | >set_program_counter_mk_Status_commutation >clock_set_program_counter |
---|
[1975] | 1933 | cases daemon |
---|
[1978] | 1934 | |14,16,18: |
---|
[1975] | 1935 | normalize nodelta |
---|
| 1936 | @(pair_replace ?????????? p1) |
---|
[2017] | 1937 | [1,3,5: |
---|
| 1938 | >set_clock_mk_Status_commutation |
---|
| 1939 | cases daemon |
---|
| 1940 | ] |
---|
[1975] | 1941 | ] |
---|
[1984] | 1942 | (* XXX: switch to the right hand side *) |
---|
| 1943 | normalize nodelta >EQs -s >EQticks -ticks |
---|
[1975] | 1944 | whd in ⊢ (??%%); |
---|
[1984] | 1945 | (* XXX: finally, prove the equality using sigma commutation *) |
---|
[2017] | 1946 | try @split_eq_status try % |
---|
[2023] | 1947 | cases daemon |
---|
[2017] | 1948 | |10,42,43,44,45,49,52,56: (* MUL *) |
---|
[1984] | 1949 | (* XXX: work on the right hand side *) |
---|
| 1950 | (* XXX: switch to the left hand side *) |
---|
| 1951 | -instr_refl >EQP -P normalize nodelta |
---|
| 1952 | #sigma_increment_commutation #maps_assm #fetch_many_assm %{1} |
---|
| 1953 | whd in ⊢ (??%?); |
---|
| 1954 | <(fetch_many_singleton … fetch_many_assm) -fetch_many_assm whd in ⊢ (??%?); |
---|
| 1955 | (* XXX: work on the left hand side *) |
---|
| 1956 | (* XXX: switch to the right hand side *) |
---|
| 1957 | normalize nodelta >EQs -s >EQticks -ticks |
---|
[1975] | 1958 | whd in ⊢ (??%%); |
---|
[1984] | 1959 | (* XXX: finally, prove the equality using sigma commutation *) |
---|
[1975] | 1960 | cases daemon |
---|
[2017] | 1961 | |11,12: (* DIV *) |
---|
[1984] | 1962 | (* XXX: work on the right hand side *) |
---|
[1975] | 1963 | normalize nodelta in p; |
---|
| 1964 | >p normalize nodelta |
---|
[1984] | 1965 | (* XXX: switch to the left hand side *) |
---|
| 1966 | -instr_refl >EQP -P normalize nodelta |
---|
| 1967 | #sigma_increment_commutation #maps_assm #fetch_many_assm %{1} |
---|
| 1968 | whd in ⊢ (??%?); |
---|
| 1969 | <(fetch_many_singleton … fetch_many_assm) -fetch_many_assm whd in ⊢ (??%?); |
---|
[1975] | 1970 | @(pose … (nat_of_bitvector 8 ?)) #pose_assm #pose_refl |
---|
[1984] | 1971 | >(?: pose_assm = 0) normalize nodelta |
---|
[1975] | 1972 | [2,4: |
---|
| 1973 | <p >pose_refl |
---|
| 1974 | cases daemon |
---|
| 1975 | |1,3: |
---|
[1984] | 1976 | (* XXX: switch to the right hand side *) |
---|
| 1977 | >EQs -s >EQticks -ticks |
---|
[1975] | 1978 | whd in ⊢ (??%%); |
---|
[1984] | 1979 | (* XXX: finally, prove the equality using sigma commutation *) |
---|
[1975] | 1980 | @split_eq_status try % |
---|
| 1981 | cases daemon |
---|
| 1982 | ] |
---|
[2017] | 1983 | |13,14,15: (* DA *) |
---|
[1984] | 1984 | (* XXX: work on the right hand side *) |
---|
[1975] | 1985 | >p normalize nodelta |
---|
| 1986 | >p1 normalize nodelta |
---|
| 1987 | try (>p2 normalize nodelta |
---|
| 1988 | try (>p3 normalize nodelta |
---|
| 1989 | try (>p4 normalize nodelta |
---|
| 1990 | try (>p5 normalize nodelta)))) |
---|
[1984] | 1991 | (* XXX: switch to the left hand side *) |
---|
| 1992 | -instr_refl >EQP -P normalize nodelta |
---|
| 1993 | #sigma_increment_commutation #maps_assm #fetch_many_assm %{1} |
---|
| 1994 | whd in ⊢ (??%?); |
---|
| 1995 | <(fetch_many_singleton … fetch_many_assm) -fetch_many_assm whd in ⊢ (??%?); |
---|
| 1996 | (* XXX: work on the left hand side *) |
---|
[1975] | 1997 | @(pair_replace ?????????? p) |
---|
| 1998 | [1,3,5: |
---|
[2017] | 1999 | /demod/ |
---|
[1975] | 2000 | cases daemon |
---|
| 2001 | |2,4,6: |
---|
| 2002 | @(if_then_else_replace ???????? p1) |
---|
| 2003 | [1,3,5: |
---|
| 2004 | cases daemon |
---|
| 2005 | |2,4: |
---|
| 2006 | normalize nodelta |
---|
| 2007 | @(pair_replace ?????????? p2) |
---|
| 2008 | [1,3: |
---|
| 2009 | cases daemon |
---|
| 2010 | |2,4: |
---|
| 2011 | normalize nodelta >p3 normalize nodelta |
---|
| 2012 | >p4 normalize nodelta try >p5 |
---|
| 2013 | ] |
---|
| 2014 | ] |
---|
[1984] | 2015 | (* XXX: switch to the right hand side *) |
---|
| 2016 | normalize nodelta >EQs -s >EQticks -ticks |
---|
| 2017 | whd in ⊢ (??%%); |
---|
| 2018 | (* XXX: finally, prove the equality using sigma commutation *) |
---|
| 2019 | @split_eq_status try % |
---|
| 2020 | cases daemon |
---|
[1975] | 2021 | ] |
---|
[2017] | 2022 | |33,34,35,48: (* ANL, ORL, XRL, MOVX *) |
---|
[1984] | 2023 | (* XXX: work on the right hand side *) |
---|
| 2024 | cases addr #addr' normalize nodelta |
---|
[1978] | 2025 | [1,3: |
---|
[1984] | 2026 | cases addr' #addr'' normalize nodelta |
---|
[1975] | 2027 | ] |
---|
[1984] | 2028 | @pair_elim #lft #rgt #lft_rgt_refl >lft_rgt_refl normalize nodelta |
---|
| 2029 | (* XXX: switch to the left hand side *) |
---|
| 2030 | -instr_refl >EQP -P normalize nodelta |
---|
| 2031 | #sigma_increment_commutation #maps_assm #fetch_many_assm %{1} |
---|
| 2032 | whd in ⊢ (??%?); |
---|
| 2033 | <(fetch_many_singleton … fetch_many_assm) -fetch_many_assm whd in ⊢ (??%?); |
---|
| 2034 | (* XXX: work on the left hand side *) |
---|
| 2035 | (* XXX: switch to the right hand side *) |
---|
| 2036 | normalize nodelta >EQs -s >EQticks -ticks |
---|
[1975] | 2037 | whd in ⊢ (??%%); |
---|
[1984] | 2038 | (* XXX: finally, prove the equality using sigma commutation *) |
---|
[1975] | 2039 | cases daemon |
---|
[2017] | 2040 | |47: (* MOV *) |
---|
[1984] | 2041 | (* XXX: work on the right hand side *) |
---|
| 2042 | cases addr -addr #addr normalize nodelta |
---|
| 2043 | [1: |
---|
| 2044 | cases addr #addr normalize nodelta |
---|
| 2045 | [1: |
---|
| 2046 | cases addr #addr normalize nodelta |
---|
| 2047 | [1: |
---|
| 2048 | cases addr #addr normalize nodelta |
---|
| 2049 | [1: |
---|
| 2050 | cases addr #addr normalize nodelta |
---|
| 2051 | ] |
---|
| 2052 | ] |
---|
| 2053 | ] |
---|
| 2054 | ] |
---|
| 2055 | cases addr #lft #rgt normalize nodelta |
---|
| 2056 | (* XXX: switch to the left hand side *) |
---|
| 2057 | >EQP -P normalize nodelta |
---|
| 2058 | #sigma_increment_commutation #maps_assm #fetch_many_assm %{1} |
---|
| 2059 | whd in ⊢ (??%?); |
---|
| 2060 | <(fetch_many_singleton … fetch_many_assm) -fetch_many_assm whd in ⊢ (??%?); |
---|
| 2061 | (* XXX: work on the left hand side *) |
---|
| 2062 | (* XXX: switch to the right hand side *) |
---|
| 2063 | normalize nodelta >EQs -s >EQticks -ticks |
---|
| 2064 | whd in ⊢ (??%%); |
---|
| 2065 | (* XXX: finally, prove the equality using sigma commutation *) |
---|
| 2066 | cases daemon |
---|
[2131] | 2067 | ] |
---|
| 2068 | qed. |
---|