[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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| 103 | @list_addressing_mode_tags_elim_prop try % |
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| 104 | @list_addressing_mode_tags_elim_prop try % |
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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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[2047] | 172 | lemma pair_replace: |
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| 173 | ∀A,B,T:Type[0].∀P:T → Prop. ∀t. ∀a,b.∀c,c': A × B. c'=c → c ≃ 〈a,b〉 → |
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| 174 | P (t a b) → P (let 〈a',b'〉 ≝ c' in t a' b'). |
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| 175 | #A #B #T #P #t #a #b * #x #y * #x' #y' #H1 #H2 destruct // |
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| 176 | qed. |
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| 177 | |
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[2017] | 178 | lemma get_arg_8_set_program_counter: |
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| 179 | ∀M: Type[0]. |
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| 180 | ∀cm: M. |
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| 181 | ∀s: PreStatus M cm. |
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| 182 | ∀flag: bool. |
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| 183 | ∀addr. |
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| 184 | ∀pc: Word. |
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| 185 | get_arg_8 M cm (set_program_counter M cm s pc) flag addr = |
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| 186 | get_arg_8 M cm s flag addr. |
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| 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 #addr2 #absurd normalize in absurd; cases absurd @I) |
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| 191 | try (#addr1 #absurd normalize in absurd; cases absurd @I) |
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| 192 | try (#absurd normalize in absurd; cases absurd @I) |
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| 193 | try (#addr1 #addr2) try #addr1 |
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| 194 | normalize nodelta try % |
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| 195 | cases daemon (* XXX: rewrite not working but provable *) |
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| 196 | qed. |
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| 197 | |
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| 198 | lemma external_ram_set_flags: |
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| 199 | ∀M: Type[0]. |
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| 200 | ∀cm: M. |
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| 201 | ∀s: PreStatus M cm. |
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| 202 | ∀opt: option Bit. |
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| 203 | ∀bit1, bit2: Bit. |
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| 204 | external_ram M cm (set_flags M cm s bit1 opt bit2) = |
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| 205 | external_ram M cm s. |
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| 206 | #M #cm #s #opt #bit1 #bit2 % |
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| 207 | qed. |
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| 208 | |
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| 209 | lemma low_internal_ram_set_flags: |
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| 210 | ∀M: Type[0]. |
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| 211 | ∀cm: M. |
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| 212 | ∀s: PreStatus M cm. |
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| 213 | ∀opt: option Bit. |
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| 214 | ∀bit1, bit2: Bit. |
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| 215 | low_internal_ram M cm (set_flags M cm s bit1 opt bit2) = |
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| 216 | low_internal_ram M cm s. |
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| 217 | #M #cm #s #opt #bit1 #bit2 % |
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| 218 | qed. |
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| 219 | |
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| 220 | lemma high_internal_ram_set_flags: |
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| 221 | ∀M: Type[0]. |
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| 222 | ∀cm: M. |
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| 223 | ∀s: PreStatus M cm. |
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| 224 | ∀opt: option Bit. |
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| 225 | ∀bit1, bit2: Bit. |
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| 226 | high_internal_ram M cm (set_flags M cm s bit1 opt bit2) = |
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| 227 | high_internal_ram M cm s. |
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| 228 | #M #cm #s #opt #bit1 #bit2 % |
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| 229 | qed. |
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| 230 | |
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| 231 | lemma low_internal_ram_set_clock: |
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| 232 | ∀M: Type[0]. |
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| 233 | ∀cm: M. |
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| 234 | ∀s: PreStatus M cm. |
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| 235 | ∀t: Time. |
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| 236 | low_internal_ram M cm (set_clock M cm s t) = |
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| 237 | low_internal_ram M cm s. |
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| 238 | #M #cm #s #t % |
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| 239 | qed. |
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| 240 | |
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| 241 | lemma high_internal_ram_set_clock: |
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| 242 | ∀M: Type[0]. |
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| 243 | ∀cm: M. |
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| 244 | ∀s: PreStatus M cm. |
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| 245 | ∀t: Time. |
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| 246 | high_internal_ram M cm (set_clock M cm s t) = |
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| 247 | high_internal_ram M cm s. |
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| 248 | #M #cm #s #t % |
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| 249 | qed. |
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| 250 | |
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| 251 | lemma external_ram_set_clock: |
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| 252 | ∀M: Type[0]. |
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| 253 | ∀cm: M. |
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| 254 | ∀s: PreStatus M cm. |
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| 255 | ∀t: Time. |
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| 256 | external_ram M cm (set_clock M cm s t) = |
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| 257 | external_ram M cm s. |
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| 258 | #M #cm #s #t % |
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| 259 | qed. |
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| 260 | |
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| 261 | lemma set_8051_sfr_set_program_counter: |
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| 262 | ∀M: Type[0]. |
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| 263 | ∀cm: M. |
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| 264 | ∀s: PreStatus M cm. |
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| 265 | ∀pc: Word. |
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| 266 | ∀sfr: SFR8051. |
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| 267 | ∀v: Byte. |
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| 268 | set_8051_sfr M cm (set_program_counter M cm s pc) sfr v = |
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| 269 | set_program_counter M cm (set_8051_sfr M cm s sfr v) pc. |
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| 270 | #M #cm #s #pc #sfr #v % |
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| 271 | qed. |
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| 272 | |
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| 273 | lemma low_internal_ram_set_8051_sfr: |
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| 274 | ∀M: Type[0]. |
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| 275 | ∀cm: M. |
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| 276 | ∀s: PreStatus M cm. |
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| 277 | ∀sfr: SFR8051. |
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| 278 | ∀v: Byte. |
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| 279 | low_internal_ram M cm (set_8051_sfr M cm s sfr v) = |
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| 280 | low_internal_ram M cm s. |
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| 281 | #M #cm #s #sfr #v % |
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| 282 | qed. |
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| 283 | |
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| 284 | lemma high_internal_ram_set_8051_sfr: |
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| 285 | ∀M: Type[0]. |
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| 286 | ∀cm: M. |
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| 287 | ∀s: PreStatus M cm. |
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| 288 | ∀sfr: SFR8051. |
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| 289 | ∀v: Byte. |
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| 290 | high_internal_ram M cm (set_8051_sfr M cm s sfr v) = |
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| 291 | high_internal_ram M cm s. |
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| 292 | #M #cm #s #sfr #v % |
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| 293 | qed. |
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| 294 | |
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| 295 | lemma external_ram_set_8051_sfr: |
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| 296 | ∀M: Type[0]. |
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| 297 | ∀cm: M. |
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| 298 | ∀s: PreStatus M cm. |
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| 299 | ∀sfr: SFR8051. |
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| 300 | ∀v: Byte. |
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| 301 | external_ram M cm (set_8051_sfr M cm s sfr v) = |
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| 302 | external_ram M cm s. |
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| 303 | #M #cm #s #sfr #v % |
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| 304 | qed. |
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| 305 | |
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| 306 | lemma get_arg_8_set_clock: |
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| 307 | ∀M: Type[0]. |
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| 308 | ∀cm: M. |
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| 309 | ∀s: PreStatus M cm. |
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| 310 | ∀addr. |
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| 311 | ∀t: Time. |
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| 312 | get_arg_8 M cm (set_clock M cm s t) addr = |
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| 313 | get_arg_8 M cm s addr. |
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| 314 | #M #cm #s #addr #t % |
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| 315 | qed. |
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| 316 | |
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[2023] | 317 | lemma set_program_counter_set_program_counter: |
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| 318 | ∀M: Type[0]. |
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| 319 | ∀cm: M. |
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| 320 | ∀s: PreStatus M cm. |
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| 321 | ∀pc: Word. |
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| 322 | ∀pc': Word. |
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| 323 | set_program_counter M cm (set_program_counter M cm s pc) pc' = |
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| 324 | set_program_counter M cm s pc'. |
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| 325 | #M #cm #s #pc #pc' % |
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| 326 | qed. |
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| 327 | |
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[1969] | 328 | lemma None_Some_elim: ∀P:Prop. ∀A,a. None A = Some A a → P. |
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| 329 | #P #A #a #abs destruct |
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| 330 | qed. |
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[1966] | 331 | |
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[1971] | 332 | (* |
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| 333 | lemma pi1_let_commute: |
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| 334 | ∀A,B,C,P. ∀c:A × B. ∀t: Σc:C.P c. |
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| 335 | pi1 … (let 〈x1,y1〉 ≝ c in t) = (let 〈x1,y1〉 ≝ c in pi1 … t). |
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| 336 | #A #B #C #P * #a #b * // |
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| 337 | qed. |
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| 338 | |
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| 339 | lemma pi1_let_as_commute: |
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| 340 | ∀A,B,C,P. ∀c:A × B. ∀t: Σc:C.P c. |
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| 341 | pi1 … (let 〈x1,y1〉 as H ≝ c in t) = |
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| 342 | (let 〈x1,y1〉 as H ≝ c in pi1 … t). |
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| 343 | #A #B #C #P * #a #b * // |
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| 344 | qed. |
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| 345 | |
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| 346 | lemma tech_pi1_let_as_commute: |
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| 347 | ∀A,B,C,P. ∀f. ∀c,c':A × B. |
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| 348 | ∀t: ∀a,b. 〈a,b〉=c → Σc:C.P c. |
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| 349 | ∀t': ∀a,b. 〈a,b〉=c' → Σc:C.P c. |
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| 350 | c=c' → (∀x,y,H,H'.t x y H = f (pi1 … (t' x y H'))) → |
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| 351 | pi1 … (let 〈x1,y1〉 as H ≝ c in t x1 y1 H) = |
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| 352 | f (pi1 … (let 〈x1,y1〉 as H ≝ c' in t' x1 y1 H)). |
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| 353 | #A #B #C #P #f * #a #b * #a' #b' #t #t' #EQ1 destruct normalize /2/ |
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| 354 | qed. |
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[1975] | 355 | *) |
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[1971] | 356 | |
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| 357 | include alias "arithmetics/nat.ma". |
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| 358 | include alias "basics/logic.ma". |
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| 359 | include alias "ASM/BitVectorTrie.ma". |
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| 360 | |
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[1977] | 361 | lemma jmpair_as_replace: |
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| 362 | ∀A,B,T:Type[0].∀P:T → Prop. ∀a:A. ∀b:B.∀c,c': A × B. ∀t: ∀a,b. c' ≃ 〈a, b〉 → T. ∀EQc: c'= c. |
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| 363 | ∀EQ:c ≃ 〈a,b〉. |
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| 364 | P (t a b ?) → P ((let 〈a',b'〉 (*as H*) ≝ c' in λH. t a' b' H) (refl_jmeq ? c')). |
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[1975] | 365 | [2: |
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[1977] | 366 | >EQc @EQ |
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[1975] | 367 | |1: |
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[1977] | 368 | #A #B #T #P #a #b |
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[1979] | 369 | #c #c' #t #EQc >EQc in t; -c' normalize #f #EQ |
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| 370 | letin eta ≝ (? : ∀ab:A × B.∀P:A × B → Type[0]. P ab → P 〈\fst ab,\snd ab〉) [2: * // ] |
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| 371 | change with (eta 〈a,b〉 (λab.c ≃ ab) EQ) in match EQ; |
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| 372 | @(jmeq_elim ?? (λab.λH.P (f (\fst ab) (\snd ab) ?) → ?) ?? EQ) normalize -eta |
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| 373 | -EQ cases c in f; normalize // |
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| 374 | ] |
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[1975] | 375 | qed. |
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| 376 | |
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| 377 | lemma if_then_else_replace: |
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| 378 | ∀T: Type[0]. |
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| 379 | ∀P: T → Prop. |
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| 380 | ∀t1, t2: T. |
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| 381 | ∀c, c', c'': bool. |
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| 382 | c' = c → c ≃ c'' → P (if c'' then t1 else t2) → P (if c' then t1 else t2). |
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| 383 | #T #P #t1 #t2 #c #c' #c'' #c_refl #c_refl' destruct #assm |
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| 384 | assumption |
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| 385 | qed. |
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| 386 | |
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[1983] | 387 | lemma fetch_many_singleton: |
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| 388 | ∀code_memory: BitVectorTrie Byte 16. |
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| 389 | ∀final_pc, start_pc: Word. |
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| 390 | ∀i: instruction. |
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| 391 | fetch_many code_memory final_pc start_pc [i] → |
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| 392 | 〈i, final_pc, ticks_of_instruction i〉 = fetch code_memory start_pc. |
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[1984] | 393 | #code_memory #final_pc #start_pc #i * #new_pc |
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| 394 | #fetch_many_assm whd in fetch_many_assm; |
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[1983] | 395 | cases (eq_bv_eq … fetch_many_assm) assumption |
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| 396 | qed. |
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| 397 | |
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[2017] | 398 | lemma refl_to_jmrefl: |
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| 399 | ∀a: Type[0]. |
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| 400 | ∀l, r: a. |
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| 401 | l = r → l ≃ r. |
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| 402 | #a #l #r #refl destruct % |
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| 403 | qed. |
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| 404 | |
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| 405 | include alias "ASM/Vector.ma". |
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| 406 | |
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[2047] | 407 | axiom main_lemma_preinstruction: |
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| 408 | ∀M, M': internal_pseudo_address_map. |
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| 409 | ∀preamble: preamble. |
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| 410 | ∀instr_list: list labelled_instruction. |
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| 411 | ∀cm: pseudo_assembly_program. |
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| 412 | ∀EQcm: cm = 〈preamble, instr_list〉. |
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| 413 | ∀sigma: Word → Word. |
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| 414 | ∀policy: Word → bool. |
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| 415 | ∀sigma_policy_witness: sigma_policy_specification cm sigma policy. |
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| 416 | ∀ps: PseudoStatus cm. |
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| 417 | ∀ppc: Word. |
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| 418 | ∀EQppc: ppc = program_counter pseudo_assembly_program cm ps. |
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| 419 | ∀labels: label_map. |
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| 420 | ∀costs: BitVectorTrie costlabel 16. |
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| 421 | ∀create_label_cost_refl: create_label_cost_map instr_list = 〈labels, costs〉. |
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| 422 | ∀newppc: Word. |
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| 423 | ∀lookup_labels: Identifier → Word. |
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| 424 | ∀EQlookup_labels: lookup_labels = (λx:Identifier. address_of_word_labels_code_mem instr_list x). |
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| 425 | ∀lookup_datalabels: Identifier → Word. |
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| 426 | ∀EQlookup_datalabels: lookup_datalabels = (λx.lookup_def ASMTag Word (construct_datalabels preamble) x (zero 16)). |
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| 427 | ∀EQnewppc: newppc = add 16 ppc (bitvector_of_nat 16 1). |
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| 428 | ∀instr: preinstruction Identifier. |
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| 429 | ∀ticks: nat × nat. |
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| 430 | ∀EQticks: ticks = ticks_of0 〈preamble, instr_list〉 sigma policy ppc (Instruction instr). |
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| 431 | ∀addr_of: Identifier → PreStatus pseudo_assembly_program cm → BitVector 16. |
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| 432 | ∀EQaddr_of: addr_of = (λx:Identifier. λy:PreStatus pseudo_assembly_program cm. address_of_word_labels cm x). |
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| 433 | ∀s: PreStatus pseudo_assembly_program cm. |
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| 434 | ∀EQs: s = (set_program_counter pseudo_assembly_program cm ps (add 16 ppc (bitvector_of_nat 16 1))). |
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| 435 | ∀P: preinstruction Identifier → PseudoStatus cm → Prop. |
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| 436 | ∀EQP: P = (λinstr, s. sigma (add 16 ppc (bitvector_of_nat 16 1)) = add 16 (sigma ppc) |
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| 437 | (bitvector_of_nat 16 (\fst (assembly_1_pseudoinstruction lookup_labels sigma policy ppc |
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| 438 | lookup_datalabels (Instruction instr)))) → |
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| 439 | next_internal_pseudo_address_map0 pseudo_assembly_program (Instruction instr) M cm ps = Some internal_pseudo_address_map M' → |
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| 440 | 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)) |
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| 441 | (expand_pseudo_instruction lookup_labels sigma policy (program_counter pseudo_assembly_program cm ps) lookup_datalabels (Instruction instr)) → |
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| 442 | ∃n: nat. execute n (code_memory_of_pseudo_assembly_program cm sigma policy) (status_of_pseudo_status M cm ps sigma policy) = |
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| 443 | status_of_pseudo_status M' cm s sigma policy). |
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| 444 | P instr (execute_1_preinstruction ticks Identifier pseudo_assembly_program cm addr_of instr s). |
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| 445 | |
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| 446 | (* |
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[1971] | 447 | lemma main_lemma_preinstruction: |
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[2023] | 448 | ∀M, M': internal_pseudo_address_map. |
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| 449 | ∀preamble: preamble. |
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| 450 | ∀instr_list: list labelled_instruction. |
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| 451 | ∀cm: pseudo_assembly_program. |
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| 452 | ∀EQcm: cm = 〈preamble, instr_list〉. |
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| 453 | ∀sigma: Word → Word. |
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| 454 | ∀policy: Word → bool. |
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| 455 | ∀sigma_policy_witness: sigma_policy_specification cm sigma policy. |
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| 456 | ∀ps: PseudoStatus cm. |
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| 457 | ∀ppc: Word. |
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| 458 | ∀EQppc: ppc = program_counter pseudo_assembly_program cm ps. |
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| 459 | ∀labels: label_map. |
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| 460 | ∀costs: BitVectorTrie costlabel 16. |
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| 461 | ∀create_label_cost_refl: create_label_cost_map instr_list = 〈labels, costs〉. |
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| 462 | ∀newppc: Word. |
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| 463 | ∀lookup_labels: Identifier → Word. |
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| 464 | ∀EQlookup_labels: lookup_labels = (λx:Identifier. address_of_word_labels_code_mem instr_list x). |
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| 465 | ∀lookup_datalabels: Identifier → Word. |
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| 466 | ∀EQlookup_datalabels: lookup_datalabels = (λx.lookup_def ASMTag Word (construct_datalabels preamble) x (zero 16)). |
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| 467 | ∀EQnewppc: newppc = add 16 ppc (bitvector_of_nat 16 1). |
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| 468 | ∀instr: preinstruction Identifier. |
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| 469 | ∀ticks: nat × nat. |
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| 470 | ∀EQticks: ticks = ticks_of0 〈preamble, instr_list〉 sigma policy ppc (Instruction instr). |
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| 471 | ∀addr_of: Identifier → PreStatus pseudo_assembly_program cm → BitVector 16. |
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| 472 | ∀EQaddr_of: addr_of = (λx:Identifier. λy:PreStatus pseudo_assembly_program cm. address_of_word_labels cm x). |
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| 473 | ∀s: PreStatus pseudo_assembly_program cm. |
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| 474 | ∀EQs: s = (set_program_counter pseudo_assembly_program cm ps (add 16 ppc (bitvector_of_nat 16 1))). |
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| 475 | ∀P: preinstruction Identifier → PseudoStatus cm → Prop. |
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| 476 | ∀EQP: P = (λinstr, s. sigma (add 16 ppc (bitvector_of_nat 16 1)) = add 16 (sigma ppc) |
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| 477 | (bitvector_of_nat 16 (\fst (assembly_1_pseudoinstruction lookup_labels sigma policy ppc |
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| 478 | lookup_datalabels (Instruction instr)))) → |
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| 479 | next_internal_pseudo_address_map0 pseudo_assembly_program (Instruction instr) M cm ps = Some internal_pseudo_address_map M' → |
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| 480 | 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)) |
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| 481 | (expand_pseudo_instruction lookup_labels sigma policy (program_counter pseudo_assembly_program cm ps) lookup_datalabels (Instruction instr)) → |
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| 482 | ∃n: nat. execute n (code_memory_of_pseudo_assembly_program cm sigma policy) (status_of_pseudo_status M cm ps sigma policy) = |
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| 483 | status_of_pseudo_status M' cm s sigma policy). |
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| 484 | P instr (execute_1_preinstruction ticks Identifier pseudo_assembly_program cm addr_of instr s). |
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| 485 | #M #M' #preamble #instr_list #cm #EQcm #sigma #policy #sigma_policy_witness #ps #ppc #EQppc #labels |
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| 486 | #costs #create_label_cost_refl #newppc |
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| 487 | #lookup_labels #EQlookup_labels #lookup_datalabels #EQlookup_datalabels #EQnewppc #instr |
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| 488 | #ticks #EQticks #addr_of #EQaddr_of #s #EQs #P #EQP |
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| 489 | (*#sigma_increment_commutation #maps_assm #fetch_many_assm *) |
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| 490 | letin a ≝ Identifier letin m ≝ pseudo_assembly_program |
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| 491 | cut (Σxxx:PseudoStatus cm. P instr (execute_1_preinstruction ticks a m cm addr_of instr s)) |
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| 492 | [2: * // ] |
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| 493 | @( |
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[1971] | 494 | let add_ticks1 ≝ λs: PreStatus m cm. set_clock ?? s (\fst ticks + clock ?? s) in |
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| 495 | let add_ticks2 ≝ λs: PreStatus m cm. set_clock ?? s (\snd ticks + clock ?? s) in |
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| 496 | match instr in preinstruction return λx. x = instr → Σs'.? with |
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| 497 | [ ADD addr1 addr2 ⇒ λinstr_refl. |
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| 498 | let s ≝ add_ticks1 s in |
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| 499 | let 〈result, flags〉 ≝ add_8_with_carry (get_arg_8 … s false addr1) |
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| 500 | (get_arg_8 … s false addr2) false in |
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| 501 | let cy_flag ≝ get_index' ? O ? flags in |
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| 502 | let ac_flag ≝ get_index' ? 1 ? flags in |
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| 503 | let ov_flag ≝ get_index' ? 2 ? flags in |
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| 504 | let s ≝ set_arg_8 … s ACC_A result in |
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| 505 | set_flags … s cy_flag (Some Bit ac_flag) ov_flag |
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| 506 | | ADDC addr1 addr2 ⇒ λinstr_refl. |
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| 507 | let s ≝ add_ticks1 s in |
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| 508 | let old_cy_flag ≝ get_cy_flag ?? s in |
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| 509 | let 〈result, flags〉 ≝ add_8_with_carry (get_arg_8 … s false addr1) |
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| 510 | (get_arg_8 … s false addr2) old_cy_flag in |
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| 511 | let cy_flag ≝ get_index' ? O ? flags in |
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| 512 | let ac_flag ≝ get_index' ? 1 ? flags in |
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| 513 | let ov_flag ≝ get_index' ? 2 ? flags in |
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| 514 | let s ≝ set_arg_8 … s ACC_A result in |
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| 515 | set_flags … s cy_flag (Some Bit ac_flag) ov_flag |
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| 516 | | SUBB addr1 addr2 ⇒ λinstr_refl. |
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| 517 | let s ≝ add_ticks1 s in |
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| 518 | let old_cy_flag ≝ get_cy_flag ?? s in |
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| 519 | let 〈result, flags〉 ≝ sub_8_with_carry (get_arg_8 … s false addr1) |
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| 520 | (get_arg_8 … s false addr2) old_cy_flag in |
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| 521 | let cy_flag ≝ get_index' ? O ? flags in |
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| 522 | let ac_flag ≝ get_index' ? 1 ? flags in |
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| 523 | let ov_flag ≝ get_index' ? 2 ? flags in |
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| 524 | let s ≝ set_arg_8 … s ACC_A result in |
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| 525 | set_flags … s cy_flag (Some Bit ac_flag) ov_flag |
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| 526 | | ANL addr ⇒ λinstr_refl. |
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| 527 | let s ≝ add_ticks1 s in |
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| 528 | match addr with |
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| 529 | [ inl l ⇒ |
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| 530 | match l with |
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| 531 | [ inl l' ⇒ |
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| 532 | let 〈addr1, addr2〉 ≝ l' in |
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| 533 | let and_val ≝ conjunction_bv ? (get_arg_8 … s true addr1) (get_arg_8 … s true addr2) in |
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| 534 | set_arg_8 … s addr1 and_val |
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| 535 | | inr r ⇒ |
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| 536 | let 〈addr1, addr2〉 ≝ r in |
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| 537 | let and_val ≝ conjunction_bv ? (get_arg_8 … s true addr1) (get_arg_8 … s true addr2) in |
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| 538 | set_arg_8 … s addr1 and_val |
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| 539 | ] |
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| 540 | | inr r ⇒ |
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| 541 | let 〈addr1, addr2〉 ≝ r in |
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| 542 | let and_val ≝ andb (get_cy_flag … s) (get_arg_1 … s addr2 true) in |
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| 543 | set_flags … s and_val (None ?) (get_ov_flag ?? s) |
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| 544 | ] |
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| 545 | | ORL addr ⇒ λinstr_refl. |
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| 546 | let s ≝ add_ticks1 s in |
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| 547 | match addr with |
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| 548 | [ inl l ⇒ |
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| 549 | match l with |
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| 550 | [ inl l' ⇒ |
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| 551 | let 〈addr1, addr2〉 ≝ l' in |
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| 552 | let or_val ≝ inclusive_disjunction_bv ? (get_arg_8 … s true addr1) (get_arg_8 … s true addr2) in |
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| 553 | set_arg_8 … s addr1 or_val |
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| 554 | | inr r ⇒ |
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| 555 | let 〈addr1, addr2〉 ≝ r in |
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| 556 | let or_val ≝ inclusive_disjunction_bv ? (get_arg_8 … s true addr1) (get_arg_8 … s true addr2) in |
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| 557 | set_arg_8 … s addr1 or_val |
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| 558 | ] |
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| 559 | | inr r ⇒ |
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| 560 | let 〈addr1, addr2〉 ≝ r in |
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| 561 | let or_val ≝ (get_cy_flag … s) ∨ (get_arg_1 … s addr2 true) in |
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| 562 | set_flags … s or_val (None ?) (get_ov_flag … s) |
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| 563 | ] |
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| 564 | | XRL addr ⇒ λinstr_refl. |
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| 565 | let s ≝ add_ticks1 s in |
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| 566 | match addr with |
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| 567 | [ inl l' ⇒ |
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| 568 | let 〈addr1, addr2〉 ≝ l' in |
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| 569 | let xor_val ≝ exclusive_disjunction_bv ? (get_arg_8 … s true addr1) (get_arg_8 … s true addr2) in |
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| 570 | set_arg_8 … s addr1 xor_val |
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| 571 | | inr r ⇒ |
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| 572 | let 〈addr1, addr2〉 ≝ r in |
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| 573 | let xor_val ≝ exclusive_disjunction_bv ? (get_arg_8 … s true addr1) (get_arg_8 … s true addr2) in |
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| 574 | set_arg_8 … s addr1 xor_val |
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| 575 | ] |
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| 576 | | INC addr ⇒ λinstr_refl. |
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[1975] | 577 | match addr return λx. bool_to_Prop (is_in … [[ acc_a;registr;direct;indirect;dptr ]] x) → x = addr → Σs': PreStatus m cm. ? with |
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| 578 | [ ACC_A ⇒ λacc_a: True. λEQaddr. |
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[1971] | 579 | let s' ≝ add_ticks1 s in |
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| 580 | let 〈 carry, result 〉 ≝ half_add ? (get_arg_8 … s' true ACC_A) (bitvector_of_nat 8 1) in |
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| 581 | set_arg_8 … s' ACC_A result |
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[1975] | 582 | | REGISTER r ⇒ λregister: True. λEQaddr. |
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[1971] | 583 | let s' ≝ add_ticks1 s in |
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| 584 | let 〈 carry, result 〉 ≝ half_add ? (get_arg_8 … s' true (REGISTER r)) (bitvector_of_nat 8 1) in |
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| 585 | set_arg_8 … s' (REGISTER r) result |
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[1975] | 586 | | DIRECT d ⇒ λdirect: True. λEQaddr. |
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[1971] | 587 | let s' ≝ add_ticks1 s in |
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| 588 | let 〈 carry, result 〉 ≝ half_add ? (get_arg_8 … s' true (DIRECT d)) (bitvector_of_nat 8 1) in |
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| 589 | set_arg_8 … s' (DIRECT d) result |
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[1975] | 590 | | INDIRECT i ⇒ λindirect: True. λEQaddr. |
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[1971] | 591 | let s' ≝ add_ticks1 s in |
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| 592 | let 〈 carry, result 〉 ≝ half_add ? (get_arg_8 … s' true (INDIRECT i)) (bitvector_of_nat 8 1) in |
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| 593 | set_arg_8 … s' (INDIRECT i) result |
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[1975] | 594 | | DPTR ⇒ λdptr: True. λEQaddr. |
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[1971] | 595 | let s' ≝ add_ticks1 s in |
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| 596 | let 〈 carry, bl 〉 ≝ half_add ? (get_8051_sfr … s' SFR_DPL) (bitvector_of_nat 8 1) in |
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| 597 | let 〈 carry, bu 〉 ≝ full_add ? (get_8051_sfr … s' SFR_DPH) (zero 8) carry in |
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| 598 | let s ≝ set_8051_sfr … s' SFR_DPL bl in |
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| 599 | set_8051_sfr … s' SFR_DPH bu |
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| 600 | | _ ⇒ λother: False. ⊥ |
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[1975] | 601 | ] (subaddressing_modein … addr) (refl … (subaddressing_modeel … addr)) |
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[1971] | 602 | | NOP ⇒ λinstr_refl. |
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| 603 | let s ≝ add_ticks2 s in |
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| 604 | s |
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| 605 | | DEC addr ⇒ λinstr_refl. |
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| 606 | let s ≝ add_ticks1 s in |
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| 607 | let 〈 result, flags 〉 ≝ sub_8_with_carry (get_arg_8 … s true addr) (bitvector_of_nat 8 1) false in |
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| 608 | set_arg_8 … s addr result |
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| 609 | | MUL addr1 addr2 ⇒ λinstr_refl. |
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| 610 | let s ≝ add_ticks1 s in |
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| 611 | let acc_a_nat ≝ nat_of_bitvector 8 (get_8051_sfr … s SFR_ACC_A) in |
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| 612 | let acc_b_nat ≝ nat_of_bitvector 8 (get_8051_sfr … s SFR_ACC_B) in |
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| 613 | let product ≝ acc_a_nat * acc_b_nat in |
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| 614 | let ov_flag ≝ product ≥ 256 in |
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| 615 | let low ≝ bitvector_of_nat 8 (product mod 256) in |
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| 616 | let high ≝ bitvector_of_nat 8 (product ÷ 256) in |
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| 617 | let s ≝ set_8051_sfr … s SFR_ACC_A low in |
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| 618 | set_8051_sfr … s SFR_ACC_B high |
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| 619 | | DIV addr1 addr2 ⇒ λinstr_refl. |
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| 620 | let s ≝ add_ticks1 s in |
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| 621 | let acc_a_nat ≝ nat_of_bitvector 8 (get_8051_sfr … s SFR_ACC_A) in |
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| 622 | let acc_b_nat ≝ nat_of_bitvector 8 (get_8051_sfr … s SFR_ACC_B) in |
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| 623 | match acc_b_nat with |
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| 624 | [ O ⇒ set_flags … s false (None Bit) true |
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| 625 | | S o ⇒ |
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| 626 | let q ≝ bitvector_of_nat 8 (acc_a_nat ÷ (S o)) in |
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| 627 | let r ≝ bitvector_of_nat 8 (acc_a_nat mod 256) in |
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| 628 | let s ≝ set_8051_sfr … s SFR_ACC_A q in |
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| 629 | let s ≝ set_8051_sfr … s SFR_ACC_B r in |
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| 630 | set_flags … s false (None Bit) false |
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| 631 | ] |
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| 632 | | DA addr ⇒ λinstr_refl. |
---|
| 633 | let s ≝ add_ticks1 s in |
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[2032] | 634 | let 〈acc_nu, acc_nl〉 ≝ vsplit ? 4 4 (get_8051_sfr … s SFR_ACC_A) in |
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[1971] | 635 | if (gtb (nat_of_bitvector ? acc_nl) 9) ∨ (get_ac_flag … s) then |
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| 636 | let 〈result, flags〉 ≝ add_8_with_carry (get_8051_sfr … s SFR_ACC_A) (bitvector_of_nat 8 6) false in |
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| 637 | let cy_flag ≝ get_index' ? O ? flags in |
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[2032] | 638 | let 〈acc_nu', acc_nl'〉 ≝ vsplit ? 4 4 result in |
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[1971] | 639 | if (gtb (nat_of_bitvector ? acc_nu') 9) ∨ cy_flag then |
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| 640 | let 〈 carry, nu 〉 ≝ half_add ? acc_nu' (bitvector_of_nat 4 6) in |
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| 641 | let new_acc ≝ nu @@ acc_nl' in |
---|
| 642 | let s ≝ set_8051_sfr … s SFR_ACC_A new_acc in |
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| 643 | set_flags … s cy_flag (Some ? (get_ac_flag … s)) (get_ov_flag … s) |
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| 644 | else |
---|
| 645 | s |
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| 646 | else |
---|
| 647 | s |
---|
| 648 | | CLR addr ⇒ λinstr_refl. |
---|
[1975] | 649 | match addr return λx. bool_to_Prop (is_in … [[ acc_a; carry; bit_addr ]] x) → x = addr → Σs': PreStatus m cm. ? with |
---|
| 650 | [ ACC_A ⇒ λacc_a: True. λEQaddr. |
---|
[1971] | 651 | let s ≝ add_ticks1 s in |
---|
| 652 | set_arg_8 … s ACC_A (zero 8) |
---|
[1975] | 653 | | CARRY ⇒ λcarry: True. λEQaddr. |
---|
[1971] | 654 | let s ≝ add_ticks1 s in |
---|
| 655 | set_arg_1 … s CARRY false |
---|
[1975] | 656 | | BIT_ADDR b ⇒ λbit_addr: True. λEQaddr. |
---|
[1971] | 657 | let s ≝ add_ticks1 s in |
---|
| 658 | set_arg_1 … s (BIT_ADDR b) false |
---|
| 659 | | _ ⇒ λother: False. ⊥ |
---|
[1975] | 660 | ] (subaddressing_modein … addr) (refl … (subaddressing_modeel … addr)) |
---|
[1971] | 661 | | CPL addr ⇒ λinstr_refl. |
---|
[1975] | 662 | match addr return λx. bool_to_Prop (is_in … [[ acc_a; carry; bit_addr ]] x) → x = addr → Σs': PreStatus m cm. ? with |
---|
| 663 | [ ACC_A ⇒ λacc_a: True. λEQaddr. |
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[1971] | 664 | let s ≝ add_ticks1 s in |
---|
| 665 | let old_acc ≝ get_8051_sfr … s SFR_ACC_A in |
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| 666 | let new_acc ≝ negation_bv ? old_acc in |
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| 667 | set_8051_sfr … s SFR_ACC_A new_acc |
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[1975] | 668 | | CARRY ⇒ λcarry: True. λEQaddr. |
---|
[1971] | 669 | let s ≝ add_ticks1 s in |
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| 670 | let old_cy_flag ≝ get_arg_1 … s CARRY true in |
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| 671 | let new_cy_flag ≝ ¬old_cy_flag in |
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| 672 | set_arg_1 … s CARRY new_cy_flag |
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[1975] | 673 | | BIT_ADDR b ⇒ λbit_addr: True. λEQaddr. |
---|
[1971] | 674 | let s ≝ add_ticks1 s in |
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| 675 | let old_bit ≝ get_arg_1 … s (BIT_ADDR b) true in |
---|
| 676 | let new_bit ≝ ¬old_bit in |
---|
| 677 | set_arg_1 … s (BIT_ADDR b) new_bit |
---|
| 678 | | _ ⇒ λother: False. ? |
---|
[1975] | 679 | ] (subaddressing_modein … addr) (refl … (subaddressing_modeel … addr)) |
---|
[1971] | 680 | | SETB b ⇒ λinstr_refl. |
---|
| 681 | let s ≝ add_ticks1 s in |
---|
| 682 | set_arg_1 … s b false |
---|
| 683 | | RL _ ⇒ λinstr_refl. (* DPM: always ACC_A *) |
---|
| 684 | let s ≝ add_ticks1 s in |
---|
| 685 | let old_acc ≝ get_8051_sfr … s SFR_ACC_A in |
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| 686 | let new_acc ≝ rotate_left … 1 old_acc in |
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| 687 | set_8051_sfr … s SFR_ACC_A new_acc |
---|
| 688 | | RR _ ⇒ λinstr_refl. (* DPM: always ACC_A *) |
---|
| 689 | let s ≝ add_ticks1 s in |
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| 690 | let old_acc ≝ get_8051_sfr … s SFR_ACC_A in |
---|
| 691 | let new_acc ≝ rotate_right … 1 old_acc in |
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| 692 | set_8051_sfr … s SFR_ACC_A new_acc |
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| 693 | | RLC _ ⇒ λinstr_refl. (* DPM: always ACC_A *) |
---|
| 694 | let s ≝ add_ticks1 s in |
---|
| 695 | let old_cy_flag ≝ get_cy_flag ?? s in |
---|
| 696 | let old_acc ≝ get_8051_sfr … s SFR_ACC_A in |
---|
| 697 | let new_cy_flag ≝ get_index' ? O ? old_acc in |
---|
| 698 | let new_acc ≝ shift_left … 1 old_acc old_cy_flag in |
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| 699 | let s ≝ set_arg_1 … s CARRY new_cy_flag in |
---|
| 700 | set_8051_sfr … s SFR_ACC_A new_acc |
---|
| 701 | | RRC _ ⇒ λinstr_refl. (* DPM: always ACC_A *) |
---|
| 702 | let s ≝ add_ticks1 s in |
---|
| 703 | let old_cy_flag ≝ get_cy_flag ?? s in |
---|
| 704 | let old_acc ≝ get_8051_sfr … s SFR_ACC_A in |
---|
| 705 | let new_cy_flag ≝ get_index' ? 7 ? old_acc in |
---|
| 706 | let new_acc ≝ shift_right … 1 old_acc old_cy_flag in |
---|
| 707 | let s ≝ set_arg_1 … s CARRY new_cy_flag in |
---|
| 708 | set_8051_sfr … s SFR_ACC_A new_acc |
---|
| 709 | | SWAP _ ⇒ λinstr_refl. (* DPM: always ACC_A *) |
---|
| 710 | let s ≝ add_ticks1 s in |
---|
| 711 | let old_acc ≝ get_8051_sfr … s SFR_ACC_A in |
---|
[2032] | 712 | let 〈nu,nl〉 ≝ vsplit ? 4 4 old_acc in |
---|
[1971] | 713 | let new_acc ≝ nl @@ nu in |
---|
| 714 | set_8051_sfr … s SFR_ACC_A new_acc |
---|
| 715 | | PUSH addr ⇒ λinstr_refl. |
---|
[1975] | 716 | match addr return λx. bool_to_Prop (is_in … [[ direct ]] x) → x = addr → Σs': PreStatus m cm. ? with |
---|
| 717 | [ DIRECT d ⇒ λdirect: True. λEQaddr. |
---|
[1971] | 718 | let s ≝ add_ticks1 s in |
---|
| 719 | let 〈carry, new_sp〉 ≝ half_add ? (get_8051_sfr … s SFR_SP) (bitvector_of_nat 8 1) in |
---|
| 720 | let s ≝ set_8051_sfr … s SFR_SP new_sp in |
---|
| 721 | write_at_stack_pointer … s d |
---|
| 722 | | _ ⇒ λother: False. ⊥ |
---|
[1975] | 723 | ] (subaddressing_modein … addr) (refl … (subaddressing_modeel … addr)) |
---|
[1971] | 724 | | POP addr ⇒ λinstr_refl. |
---|
| 725 | let s ≝ add_ticks1 s in |
---|
| 726 | let contents ≝ read_at_stack_pointer ?? s in |
---|
| 727 | let 〈new_sp, flags〉 ≝ sub_8_with_carry (get_8051_sfr … s SFR_SP) (bitvector_of_nat 8 1) false in |
---|
| 728 | let s ≝ set_8051_sfr … s SFR_SP new_sp in |
---|
| 729 | set_arg_8 … s addr contents |
---|
| 730 | | XCH addr1 addr2 ⇒ λinstr_refl. |
---|
| 731 | let s ≝ add_ticks1 s in |
---|
| 732 | let old_addr ≝ get_arg_8 … s false addr2 in |
---|
| 733 | let old_acc ≝ get_8051_sfr … s SFR_ACC_A in |
---|
| 734 | let s ≝ set_8051_sfr … s SFR_ACC_A old_addr in |
---|
| 735 | set_arg_8 … s addr2 old_acc |
---|
| 736 | | XCHD addr1 addr2 ⇒ λinstr_refl. |
---|
| 737 | let s ≝ add_ticks1 s in |
---|
[2032] | 738 | let 〈acc_nu, acc_nl〉 ≝ vsplit … 4 4 (get_8051_sfr … s SFR_ACC_A) in |
---|
| 739 | let 〈arg_nu, arg_nl〉 ≝ vsplit … 4 4 (get_arg_8 … s false addr2) in |
---|
[1971] | 740 | let new_acc ≝ acc_nu @@ arg_nl in |
---|
| 741 | let new_arg ≝ arg_nu @@ acc_nl in |
---|
| 742 | let s ≝ set_8051_sfr ?? s SFR_ACC_A new_acc in |
---|
| 743 | set_arg_8 … s addr2 new_arg |
---|
| 744 | | RET ⇒ λinstr_refl. |
---|
| 745 | let s ≝ add_ticks1 s in |
---|
| 746 | let high_bits ≝ read_at_stack_pointer ?? s in |
---|
| 747 | let 〈new_sp, flags〉 ≝ sub_8_with_carry (get_8051_sfr … s SFR_SP) (bitvector_of_nat 8 1) false in |
---|
| 748 | let s ≝ set_8051_sfr … s SFR_SP new_sp in |
---|
| 749 | let low_bits ≝ read_at_stack_pointer ?? s in |
---|
| 750 | let 〈new_sp, flags〉 ≝ sub_8_with_carry (get_8051_sfr … s SFR_SP) (bitvector_of_nat 8 1) false in |
---|
| 751 | let s ≝ set_8051_sfr … s SFR_SP new_sp in |
---|
| 752 | let new_pc ≝ high_bits @@ low_bits in |
---|
| 753 | set_program_counter … s new_pc |
---|
| 754 | | RETI ⇒ λinstr_refl. |
---|
| 755 | let s ≝ add_ticks1 s in |
---|
| 756 | let high_bits ≝ read_at_stack_pointer ?? s in |
---|
| 757 | let 〈new_sp, flags〉 ≝ sub_8_with_carry (get_8051_sfr … s SFR_SP) (bitvector_of_nat 8 1) false in |
---|
| 758 | let s ≝ set_8051_sfr … s SFR_SP new_sp in |
---|
| 759 | let low_bits ≝ read_at_stack_pointer ?? s in |
---|
| 760 | let 〈new_sp, flags〉 ≝ sub_8_with_carry (get_8051_sfr … s SFR_SP) (bitvector_of_nat 8 1) false in |
---|
| 761 | let s ≝ set_8051_sfr … s SFR_SP new_sp in |
---|
| 762 | let new_pc ≝ high_bits @@ low_bits in |
---|
| 763 | set_program_counter … s new_pc |
---|
| 764 | | MOVX addr ⇒ λinstr_refl. |
---|
| 765 | let s ≝ add_ticks1 s in |
---|
| 766 | (* DPM: only copies --- doesn't affect I/O *) |
---|
| 767 | match addr with |
---|
| 768 | [ inl l ⇒ |
---|
| 769 | let 〈addr1, addr2〉 ≝ l in |
---|
| 770 | set_arg_8 … s addr1 (get_arg_8 … s false addr2) |
---|
| 771 | | inr r ⇒ |
---|
| 772 | let 〈addr1, addr2〉 ≝ r in |
---|
| 773 | set_arg_8 … s addr1 (get_arg_8 … s false addr2) |
---|
| 774 | ] |
---|
| 775 | | MOV addr ⇒ λinstr_refl. |
---|
| 776 | let s ≝ add_ticks1 s in |
---|
| 777 | match addr with |
---|
| 778 | [ inl l ⇒ |
---|
| 779 | match l with |
---|
| 780 | [ inl l' ⇒ |
---|
| 781 | match l' with |
---|
| 782 | [ inl l'' ⇒ |
---|
| 783 | match l'' with |
---|
| 784 | [ inl l''' ⇒ |
---|
| 785 | match l''' with |
---|
| 786 | [ inl l'''' ⇒ |
---|
| 787 | let 〈addr1, addr2〉 ≝ l'''' in |
---|
| 788 | set_arg_8 … s addr1 (get_arg_8 … s false addr2) |
---|
| 789 | | inr r'''' ⇒ |
---|
| 790 | let 〈addr1, addr2〉 ≝ r'''' in |
---|
| 791 | set_arg_8 … s addr1 (get_arg_8 … s false addr2) |
---|
| 792 | ] |
---|
| 793 | | inr r''' ⇒ |
---|
| 794 | let 〈addr1, addr2〉 ≝ r''' in |
---|
| 795 | set_arg_8 … s addr1 (get_arg_8 … s false addr2) |
---|
| 796 | ] |
---|
| 797 | | inr r'' ⇒ |
---|
| 798 | let 〈addr1, addr2〉 ≝ r'' in |
---|
| 799 | set_arg_16 … s (get_arg_16 … s addr2) addr1 |
---|
| 800 | ] |
---|
| 801 | | inr r ⇒ |
---|
| 802 | let 〈addr1, addr2〉 ≝ r in |
---|
| 803 | set_arg_1 … s addr1 (get_arg_1 … s addr2 false) |
---|
| 804 | ] |
---|
| 805 | | inr r ⇒ |
---|
| 806 | let 〈addr1, addr2〉 ≝ r in |
---|
| 807 | set_arg_1 … s addr1 (get_arg_1 … s addr2 false) |
---|
| 808 | ] |
---|
| 809 | | JC addr ⇒ λinstr_refl. |
---|
| 810 | if get_cy_flag ?? s then |
---|
| 811 | let s ≝ add_ticks1 s in |
---|
| 812 | set_program_counter … s (addr_of addr s) |
---|
| 813 | else |
---|
| 814 | let s ≝ add_ticks2 s in |
---|
| 815 | s |
---|
| 816 | | JNC addr ⇒ λinstr_refl. |
---|
| 817 | if ¬(get_cy_flag ?? s) then |
---|
| 818 | let s ≝ add_ticks1 s in |
---|
| 819 | set_program_counter … s (addr_of addr s) |
---|
| 820 | else |
---|
| 821 | let s ≝ add_ticks2 s in |
---|
| 822 | s |
---|
| 823 | | JB addr1 addr2 ⇒ λinstr_refl. |
---|
| 824 | if get_arg_1 … s addr1 false then |
---|
| 825 | let s ≝ add_ticks1 s in |
---|
| 826 | set_program_counter … s (addr_of addr2 s) |
---|
| 827 | else |
---|
| 828 | let s ≝ add_ticks2 s in |
---|
| 829 | s |
---|
| 830 | | JNB addr1 addr2 ⇒ λinstr_refl. |
---|
| 831 | if ¬(get_arg_1 … s addr1 false) then |
---|
| 832 | let s ≝ add_ticks1 s in |
---|
| 833 | set_program_counter … s (addr_of addr2 s) |
---|
| 834 | else |
---|
| 835 | let s ≝ add_ticks2 s in |
---|
| 836 | s |
---|
| 837 | | JBC addr1 addr2 ⇒ λinstr_refl. |
---|
| 838 | let s ≝ set_arg_1 … s addr1 false in |
---|
| 839 | if get_arg_1 … s addr1 false then |
---|
| 840 | let s ≝ add_ticks1 s in |
---|
| 841 | set_program_counter … s (addr_of addr2 s) |
---|
| 842 | else |
---|
| 843 | let s ≝ add_ticks2 s in |
---|
| 844 | s |
---|
| 845 | | JZ addr ⇒ λinstr_refl. |
---|
| 846 | if eq_bv ? (get_8051_sfr … s SFR_ACC_A) (zero 8) then |
---|
| 847 | let s ≝ add_ticks1 s in |
---|
| 848 | set_program_counter … s (addr_of addr s) |
---|
| 849 | else |
---|
| 850 | let s ≝ add_ticks2 s in |
---|
| 851 | s |
---|
| 852 | | JNZ addr ⇒ λinstr_refl. |
---|
| 853 | if ¬(eq_bv ? (get_8051_sfr … s SFR_ACC_A) (zero 8)) then |
---|
| 854 | let s ≝ add_ticks1 s in |
---|
| 855 | set_program_counter … s (addr_of addr s) |
---|
| 856 | else |
---|
| 857 | let s ≝ add_ticks2 s in |
---|
| 858 | s |
---|
| 859 | | CJNE addr1 addr2 ⇒ λinstr_refl. |
---|
| 860 | match addr1 with |
---|
| 861 | [ inl l ⇒ |
---|
| 862 | let 〈addr1, addr2'〉 ≝ l in |
---|
| 863 | let new_cy ≝ ltb (nat_of_bitvector ? (get_arg_8 … s false addr1)) |
---|
| 864 | (nat_of_bitvector ? (get_arg_8 … s false addr2')) in |
---|
| 865 | if ¬(eq_bv ? (get_arg_8 … s false addr1) (get_arg_8 … s false addr2')) then |
---|
| 866 | let s ≝ add_ticks1 s in |
---|
| 867 | let s ≝ set_program_counter … s (addr_of addr2 s) in |
---|
| 868 | set_flags … s new_cy (None ?) (get_ov_flag ?? s) |
---|
| 869 | else |
---|
| 870 | let s ≝ add_ticks2 s in |
---|
| 871 | set_flags … s new_cy (None ?) (get_ov_flag ?? s) |
---|
| 872 | | inr r' ⇒ |
---|
| 873 | let 〈addr1, addr2'〉 ≝ r' in |
---|
| 874 | let new_cy ≝ ltb (nat_of_bitvector ? (get_arg_8 … s false addr1)) |
---|
| 875 | (nat_of_bitvector ? (get_arg_8 … s false addr2')) in |
---|
| 876 | if ¬(eq_bv ? (get_arg_8 … s false addr1) (get_arg_8 … s false addr2')) then |
---|
| 877 | let s ≝ add_ticks1 s in |
---|
| 878 | let s ≝ set_program_counter … s (addr_of addr2 s) in |
---|
| 879 | set_flags … s new_cy (None ?) (get_ov_flag ?? s) |
---|
| 880 | else |
---|
| 881 | let s ≝ add_ticks2 s in |
---|
| 882 | set_flags … s new_cy (None ?) (get_ov_flag ?? s) |
---|
| 883 | ] |
---|
| 884 | | DJNZ addr1 addr2 ⇒ λinstr_refl. |
---|
| 885 | let 〈result, flags〉 ≝ sub_8_with_carry (get_arg_8 … s true addr1) (bitvector_of_nat 8 1) false in |
---|
| 886 | let s ≝ set_arg_8 … s addr1 result in |
---|
| 887 | if ¬(eq_bv ? result (zero 8)) then |
---|
| 888 | let s ≝ add_ticks1 s in |
---|
| 889 | set_program_counter … s (addr_of addr2 s) |
---|
| 890 | else |
---|
| 891 | let s ≝ add_ticks2 s in |
---|
| 892 | s |
---|
| 893 | ] (refl … instr)) |
---|
[2017] | 894 | try (cases(other)) |
---|
| 895 | try assumption (*20s*) |
---|
| 896 | try (% @False) (*6s*) (* Bug exploited here to implement solve :-*) |
---|
| 897 | try (@(execute_1_technical … (subaddressing_modein …)) @I) (*66s*) |
---|
| 898 | whd in match execute_1_preinstruction; normalize nodelta |
---|
[2023] | 899 | [31,32: (* DJNZ *) |
---|
[1984] | 900 | (* XXX: work on the right hand side *) |
---|
[2020] | 901 | >p normalize nodelta |
---|
| 902 | (* XXX: switch to the left hand side *) |
---|
| 903 | -instr_refl >EQP -P normalize nodelta |
---|
| 904 | #sigma_increment_commutation #maps_assm #fetch_many_assm |
---|
| 905 | whd in match (expand_pseudo_instruction ??????) in fetch_many_assm; |
---|
| 906 | whd in match (expand_relative_jump ????); |
---|
| 907 | <EQppc in fetch_many_assm; |
---|
| 908 | @pair_elim #result #flags #sub16_refl |
---|
[2032] | 909 | @pair_elim #upper #lower #vsplit_refl |
---|
[2020] | 910 | cases (eq_bv ???) normalize nodelta |
---|
[2023] | 911 | [1,3: |
---|
[2020] | 912 | >EQppc in ⊢ (% → ?); #fetch_many_assm %{1} |
---|
| 913 | whd in ⊢ (??%?); |
---|
| 914 | <(fetch_many_singleton … fetch_many_assm) -fetch_many_assm whd in ⊢ (??%?); |
---|
| 915 | (* XXX: work on the left hand side *) |
---|
| 916 | @(pair_replace ?????????? p) normalize nodelta |
---|
[2023] | 917 | [1,3: |
---|
[2047] | 918 | >get_arg_8_set_program_counter |
---|
[2020] | 919 | cases daemon |
---|
| 920 | ] |
---|
| 921 | (* XXX: switch to the right hand side *) |
---|
| 922 | normalize nodelta >EQs -s >EQticks -ticks |
---|
| 923 | cases (¬ eq_bv ???) normalize nodelta |
---|
| 924 | whd in ⊢ (??%%); |
---|
| 925 | (* XXX: finally, prove the equality using sigma commutation *) |
---|
| 926 | @split_eq_status try % |
---|
| 927 | cases daemon |
---|
[2023] | 928 | |2,4: |
---|
[2020] | 929 | >EQppc |
---|
| 930 | * @(pose … (add 16 ??)) #intermediate_pc #EQintermediate_pc #fetch_refl |
---|
| 931 | * @(pose … (add 16 ??)) #intermediate_pc' #EQintermediate_pc' #fetch_refl' |
---|
| 932 | * @(pose … (add 16 ??)) #intermediate_pc'' #EQintermediate_pc'' #fetch_refl'' |
---|
| 933 | #fetch_many_assm whd in fetch_many_assm; %{2} |
---|
| 934 | change with (execute_1 ?? = ?) |
---|
| 935 | @(pose … (execute_1 ? (status_of_pseudo_status …))) |
---|
| 936 | #status_after_1 #EQstatus_after_1 |
---|
| 937 | <(?: ? = status_after_1) |
---|
[2023] | 938 | [3,6: |
---|
[2020] | 939 | >EQstatus_after_1 in ⊢ (???%); |
---|
| 940 | whd in ⊢ (???%); |
---|
[2047] | 941 | [1:exists_labelled_instruction id instr_list → |
---|
[2023] | 942 | <fetch_refl in ⊢ (???%); |
---|
| 943 | |2: |
---|
| 944 | <fetch_refl in ⊢ (???%); |
---|
| 945 | ] |
---|
[2020] | 946 | whd in ⊢ (???%); |
---|
| 947 | @(pair_replace ?????????? p) |
---|
[2023] | 948 | [1,3: |
---|
[2020] | 949 | cases daemon |
---|
[2023] | 950 | |2,4: |
---|
[2020] | 951 | normalize nodelta |
---|
| 952 | whd in match (addr_of_relative ????); |
---|
| 953 | cases (¬ eq_bv ???) normalize nodelta |
---|
| 954 | >set_clock_mk_Status_commutation |
---|
| 955 | whd in ⊢ (???%); |
---|
| 956 | change with (add ???) in match (\snd (half_add ???)); |
---|
| 957 | >set_arg_8_set_program_counter in ⊢ (???%); |
---|
[2047] | 958 | [2,4,6,8: /2/ ] |
---|
[2020] | 959 | >program_counter_set_program_counter in ⊢ (???%); |
---|
| 960 | >(?: add ? intermediate_pc (sign_extension (bitvector_of_nat ? 2)) = intermediate_pc') |
---|
[2023] | 961 | [2,4,6,8: |
---|
[2020] | 962 | >bitvector_of_nat_sign_extension_equivalence |
---|
[2023] | 963 | [1,3,5,7: |
---|
[2020] | 964 | >EQintermediate_pc' % |
---|
| 965 | |*: |
---|
| 966 | repeat @le_S_S @le_O_n |
---|
| 967 | ] |
---|
| 968 | ] |
---|
[2023] | 969 | [1,3: % ] |
---|
[2020] | 970 | ] |
---|
[2023] | 971 | |1,4: |
---|
[2020] | 972 | skip |
---|
| 973 | ] |
---|
[2023] | 974 | [3,4: |
---|
[2020] | 975 | -status_after_1 |
---|
| 976 | @(pose … (execute_1 ? (mk_PreStatus …))) |
---|
| 977 | #status_after_1 #EQstatus_after_1 |
---|
| 978 | <(?: ? = status_after_1) |
---|
[2023] | 979 | [3,6: |
---|
[2020] | 980 | >EQstatus_after_1 in ⊢ (???%); |
---|
| 981 | whd in ⊢ (???%); |
---|
| 982 | (* XXX: matita bug with patterns across multiple goals *) |
---|
[2023] | 983 | [1: |
---|
| 984 | <fetch_refl'' in ⊢ (???%); |
---|
| 985 | |2: |
---|
| 986 | <fetch_refl'' in ⊢ (???%); |
---|
| 987 | ] |
---|
| 988 | [2: % |1: whd in ⊢ (???%); % ] |
---|
| 989 | |1,4: |
---|
| 990 | skip |
---|
| 991 | ] |
---|
| 992 | -status_after_1 whd in ⊢ (??%?); |
---|
| 993 | (* XXX: switch to the right hand side *) |
---|
| 994 | normalize nodelta >EQs -s >EQticks -ticks |
---|
| 995 | cases (¬ eq_bv ???) normalize nodelta |
---|
| 996 | whd in ⊢ (??%%); |
---|
[2020] | 997 | ] |
---|
[2023] | 998 | (* XXX: finally, prove the equality using sigma commutation *) |
---|
| 999 | @split_eq_status try % |
---|
[2020] | 1000 | whd in ⊢ (??%%); |
---|
[2023] | 1001 | cases daemon |
---|
[2020] | 1002 | ] |
---|
| 1003 | |30: (* CJNE *) |
---|
| 1004 | (* XXX: work on the right hand side *) |
---|
[2018] | 1005 | cases addr1 -addr1 #addr1 normalize nodelta |
---|
| 1006 | cases addr1 -addr1 #addr1_l #addr1_r normalize nodelta |
---|
| 1007 | (* XXX: switch to the left hand side *) |
---|
| 1008 | >EQP -P normalize nodelta |
---|
| 1009 | #sigma_increment_commutation #maps_assm #fetch_many_assm |
---|
| 1010 | |
---|
| 1011 | whd in match (expand_pseudo_instruction ??????) in fetch_many_assm; |
---|
| 1012 | whd in match (expand_relative_jump ????); |
---|
| 1013 | <EQppc in fetch_many_assm; |
---|
| 1014 | @pair_elim #result #flags #sub16_refl |
---|
[2032] | 1015 | @pair_elim #upper #lower #vsplit_refl |
---|
| 1016 | inversion (eq_bv ???) #upper_vsplit_refl normalize nodelta |
---|
[2018] | 1017 | [1,3: |
---|
| 1018 | >EQppc in ⊢ (% → ?); #fetch_many_assm %{1} |
---|
| 1019 | whd in ⊢ (??%?); |
---|
| 1020 | <(fetch_many_singleton … fetch_many_assm) -fetch_many_assm whd in ⊢ (??%?); |
---|
| 1021 | inversion (¬ (eq_bv ???)) in ⊢ (???%); #eq_bv_refl normalize nodelta |
---|
| 1022 | lapply (refl_to_jmrefl ??? eq_bv_refl) -eq_bv_refl #eq_bv_refl |
---|
| 1023 | @(if_then_else_replace ???????? eq_bv_refl) |
---|
| 1024 | [1,3,5,7: |
---|
| 1025 | cases daemon |
---|
| 1026 | |2,4,6,8: |
---|
| 1027 | (* XXX: switch to the right hand side *) |
---|
| 1028 | normalize nodelta >EQs -s >EQticks -ticks |
---|
| 1029 | whd in ⊢ (??%%); |
---|
| 1030 | (* XXX: finally, prove the equality using sigma commutation *) |
---|
| 1031 | @split_eq_status try % |
---|
| 1032 | [3,7,11,15: |
---|
| 1033 | whd in ⊢ (??%?); |
---|
| 1034 | [1,3: |
---|
| 1035 | cases daemon |
---|
| 1036 | |2,4: |
---|
| 1037 | cases daemon |
---|
| 1038 | ] |
---|
| 1039 | ] |
---|
| 1040 | cases daemon (* XXX *) |
---|
| 1041 | ] |
---|
| 1042 | |2,4: |
---|
| 1043 | >EQppc |
---|
| 1044 | * @(pose … (add 16 ??)) #intermediate_pc #EQintermediate_pc #fetch_refl |
---|
| 1045 | * @(pose … (add 16 ??)) #intermediate_pc' #EQintermediate_pc' #fetch_refl' |
---|
| 1046 | * @(pose … (add 16 ??)) #intermediate_pc'' #EQintermediate_pc'' #fetch_refl'' |
---|
| 1047 | #fetch_many_assm whd in fetch_many_assm; %{2} |
---|
| 1048 | change with (execute_1 ?? = ?) |
---|
| 1049 | @(pose … (execute_1 ? (status_of_pseudo_status …))) |
---|
| 1050 | #status_after_1 #EQstatus_after_1 |
---|
| 1051 | <(?: ? = status_after_1) |
---|
[2020] | 1052 | [2,5: |
---|
| 1053 | inversion (¬ (eq_bv ???)) #eq_bv_refl normalize nodelta |
---|
| 1054 | |3,6: |
---|
[2018] | 1055 | >EQstatus_after_1 in ⊢ (???%); |
---|
| 1056 | whd in ⊢ (???%); |
---|
| 1057 | [1: <fetch_refl in ⊢ (???%); |
---|
| 1058 | |2: <fetch_refl in ⊢ (???%); |
---|
| 1059 | ] |
---|
| 1060 | whd in ⊢ (???%); |
---|
| 1061 | inversion (¬ (eq_bv ???)) in ⊢ (???%); #eq_bv_refl normalize nodelta |
---|
| 1062 | whd in ⊢ (???%); |
---|
| 1063 | whd in match (addr_of_relative ????); |
---|
| 1064 | change with (add ???) in match (\snd (half_add ???)); |
---|
| 1065 | >set_clock_set_program_counter in ⊢ (???%); |
---|
| 1066 | >program_counter_set_program_counter in ⊢ (???%); |
---|
| 1067 | >(?: add ? intermediate_pc (sign_extension (bitvector_of_nat ? 2)) = intermediate_pc') |
---|
| 1068 | [2,4,6,8: |
---|
| 1069 | >bitvector_of_nat_sign_extension_equivalence |
---|
| 1070 | [1,3,5,7: |
---|
| 1071 | >EQintermediate_pc' % |
---|
| 1072 | |*: |
---|
| 1073 | repeat @le_S_S @le_O_n |
---|
| 1074 | ] |
---|
[2020] | 1075 | |1,5: |
---|
| 1076 | % |
---|
[2018] | 1077 | ] |
---|
[2020] | 1078 | |1,4: skip |
---|
[2018] | 1079 | ] |
---|
[2020] | 1080 | [1,2,3,4: |
---|
| 1081 | -status_after_1 |
---|
| 1082 | @(pose … (execute_1 ? (mk_PreStatus …))) |
---|
| 1083 | #status_after_1 #EQstatus_after_1 |
---|
| 1084 | <(?: ? = status_after_1) |
---|
| 1085 | [3,6,9,12: |
---|
| 1086 | >EQstatus_after_1 in ⊢ (???%); |
---|
| 1087 | whd in ⊢ (???%); |
---|
| 1088 | (* XXX: matita bug with patterns across multiple goals *) |
---|
| 1089 | [1: <fetch_refl'' in ⊢ (???%); |
---|
| 1090 | |2: <fetch_refl'' in ⊢ (???%); |
---|
| 1091 | |3: <fetch_refl'' in ⊢ (???%); |
---|
| 1092 | |4: <fetch_refl'' in ⊢ (???%); |
---|
| 1093 | ] % |
---|
| 1094 | |1,4,7,10: |
---|
| 1095 | skip |
---|
| 1096 | ] |
---|
| 1097 | -status_after_1 whd in ⊢ (??%?); |
---|
| 1098 | (* XXX: switch to the right hand side *) |
---|
| 1099 | normalize nodelta >EQs -s >EQticks -ticks |
---|
| 1100 | whd in ⊢ (??%%); |
---|
| 1101 | ] |
---|
| 1102 | (* XXX: finally, prove the equality using sigma commutation *) |
---|
| 1103 | @split_eq_status try % |
---|
[2023] | 1104 | cases daemon |
---|
[2018] | 1105 | ] |
---|
| 1106 | |17,19,21,23,25,27,29,16,18,20,22,24,26,28: (* JC, JNC, JB, JNB, JBC, JZ, JNZ (true cases last) *) |
---|
| 1107 | (* XXX: work on the right hand side *) |
---|
| 1108 | >p normalize nodelta |
---|
| 1109 | (* XXX: switch to the left hand side *) |
---|
| 1110 | -instr_refl >EQP -P normalize nodelta |
---|
| 1111 | #sigma_increment_commutation #maps_assm #fetch_many_assm |
---|
| 1112 | |
---|
| 1113 | whd in match (expand_pseudo_instruction ??????) in fetch_many_assm; |
---|
| 1114 | whd in match (expand_relative_jump ????); |
---|
| 1115 | <EQppc in fetch_many_assm; |
---|
| 1116 | @pair_elim #result #flags #sub16_refl |
---|
[2032] | 1117 | @pair_elim #upper #lower #vsplit_refl |
---|
[2018] | 1118 | cases (eq_bv ???) normalize nodelta |
---|
| 1119 | [1,3,5,7,9,11,13,15,17,19,21,23,25,27: |
---|
| 1120 | >EQppc in ⊢ (% → ?); #fetch_many_assm %{1} |
---|
| 1121 | whd in ⊢ (??%?); |
---|
| 1122 | <(fetch_many_singleton … fetch_many_assm) -fetch_many_assm whd in ⊢ (??%?); |
---|
| 1123 | (* XXX: work on the left hand side *) |
---|
| 1124 | @(if_then_else_replace ???????? p) normalize nodelta |
---|
| 1125 | [1,3,5,7,9,11,13,15,17,19,21,23,25,27: |
---|
| 1126 | cases daemon |
---|
| 1127 | ] |
---|
| 1128 | (* XXX: switch to the right hand side *) |
---|
| 1129 | normalize nodelta >EQs -s >EQticks -ticks |
---|
| 1130 | whd in ⊢ (??%%); |
---|
| 1131 | (* XXX: finally, prove the equality using sigma commutation *) |
---|
| 1132 | @split_eq_status try % |
---|
| 1133 | cases daemon |
---|
| 1134 | |2,4,6,8,10,12,14,16,18,20,22,24,26,28: |
---|
| 1135 | >EQppc |
---|
| 1136 | * @(pose … (add 16 ??)) #intermediate_pc #EQintermediate_pc #fetch_refl |
---|
| 1137 | * @(pose … (add 16 ??)) #intermediate_pc' #EQintermediate_pc' #fetch_refl' |
---|
| 1138 | * @(pose … (add 16 ??)) #intermediate_pc'' #EQintermediate_pc'' #fetch_refl'' |
---|
| 1139 | #fetch_many_assm whd in fetch_many_assm; %{2} |
---|
| 1140 | change with (execute_1 ?? = ?) |
---|
| 1141 | @(pose … (execute_1 ? (status_of_pseudo_status …))) |
---|
| 1142 | #status_after_1 #EQstatus_after_1 |
---|
| 1143 | <(?: ? = status_after_1) |
---|
| 1144 | [3,6,9,12,15,18,21,24,27,30,33,36,39,42: |
---|
| 1145 | >EQstatus_after_1 in ⊢ (???%); |
---|
| 1146 | whd in ⊢ (???%); |
---|
| 1147 | [1: <fetch_refl in ⊢ (???%); |
---|
| 1148 | |2: <fetch_refl in ⊢ (???%); |
---|
| 1149 | |3: <fetch_refl in ⊢ (???%); |
---|
| 1150 | |4: <fetch_refl in ⊢ (???%); |
---|
| 1151 | |5: <fetch_refl in ⊢ (???%); |
---|
| 1152 | |6: <fetch_refl in ⊢ (???%); |
---|
| 1153 | |7: <fetch_refl in ⊢ (???%); |
---|
| 1154 | |8: <fetch_refl in ⊢ (???%); |
---|
| 1155 | |9: <fetch_refl in ⊢ (???%); |
---|
| 1156 | |10: <fetch_refl in ⊢ (???%); |
---|
| 1157 | |11: <fetch_refl in ⊢ (???%); |
---|
| 1158 | |12: <fetch_refl in ⊢ (???%); |
---|
| 1159 | |13: <fetch_refl in ⊢ (???%); |
---|
| 1160 | |14: <fetch_refl in ⊢ (???%); |
---|
| 1161 | ] |
---|
| 1162 | whd in ⊢ (???%); |
---|
| 1163 | @(if_then_else_replace ???????? p) |
---|
| 1164 | [1,3,5,7,9,11,13,15,17,19,21,23,25,27: |
---|
| 1165 | cases daemon |
---|
| 1166 | |2,4,6,8,10,12,14,16,18,20,22,24,26,28: |
---|
| 1167 | normalize nodelta |
---|
| 1168 | whd in match (addr_of_relative ????); |
---|
| 1169 | >set_clock_mk_Status_commutation |
---|
| 1170 | [9,10: |
---|
| 1171 | (* XXX: demodulation not working in this case *) |
---|
| 1172 | >program_counter_set_arg_1 in ⊢ (???%); |
---|
| 1173 | >program_counter_set_program_counter in ⊢ (???%); |
---|
| 1174 | |*: |
---|
| 1175 | /demod/ |
---|
| 1176 | ] |
---|
| 1177 | whd in ⊢ (???%); |
---|
| 1178 | change with (add ???) in match (\snd (half_add ???)); |
---|
| 1179 | >(?: add ? intermediate_pc (sign_extension (bitvector_of_nat ? 2)) = intermediate_pc') |
---|
| 1180 | [2,4,6,8,10,12,14,16,18,20,22,24,26,28: |
---|
| 1181 | >bitvector_of_nat_sign_extension_equivalence |
---|
| 1182 | [1,3,5,7,9,11,13,15,17,19,21,23,25,27: |
---|
| 1183 | >EQintermediate_pc' % |
---|
| 1184 | |*: |
---|
| 1185 | repeat @le_S_S @le_O_n |
---|
| 1186 | ] |
---|
| 1187 | ] |
---|
| 1188 | % |
---|
| 1189 | ] |
---|
| 1190 | |1,4,7,10,13,16,19,22,25,28,31,34,37,40: |
---|
| 1191 | skip |
---|
| 1192 | ] |
---|
| 1193 | -status_after_1 |
---|
| 1194 | @(pose … (execute_1 ? (mk_PreStatus …))) |
---|
| 1195 | #status_after_1 #EQstatus_after_1 |
---|
| 1196 | <(?: ? = status_after_1) |
---|
| 1197 | [3,6,9,12,15,18,21,24,27,30,33,36,39,42: |
---|
| 1198 | >EQstatus_after_1 in ⊢ (???%); |
---|
| 1199 | whd in ⊢ (???%); |
---|
| 1200 | (* XXX: matita bug with patterns across multiple goals *) |
---|
| 1201 | [1: <fetch_refl'' in ⊢ (???%); |
---|
| 1202 | |2: <fetch_refl' in ⊢ (???%); |
---|
| 1203 | |3: <fetch_refl'' in ⊢ (???%); |
---|
| 1204 | |4: <fetch_refl' in ⊢ (???%); |
---|
| 1205 | |5: <fetch_refl'' in ⊢ (???%); |
---|
| 1206 | |6: <fetch_refl' in ⊢ (???%); |
---|
| 1207 | |7: <fetch_refl'' in ⊢ (???%); |
---|
| 1208 | |8: <fetch_refl' in ⊢ (???%); |
---|
| 1209 | |9: <fetch_refl'' in ⊢ (???%); |
---|
| 1210 | |10: <fetch_refl' in ⊢ (???%); |
---|
| 1211 | |11: <fetch_refl'' in ⊢ (???%); |
---|
| 1212 | |12: <fetch_refl' in ⊢ (???%); |
---|
| 1213 | |13: <fetch_refl'' in ⊢ (???%); |
---|
| 1214 | |14: <fetch_refl' in ⊢ (???%); |
---|
| 1215 | ] |
---|
| 1216 | whd in ⊢ (???%); |
---|
| 1217 | [9,10: |
---|
| 1218 | |*: |
---|
| 1219 | /demod/ |
---|
| 1220 | ] % |
---|
| 1221 | |1,4,7,10,13,16,19,22,25,28,31,34,37,40: |
---|
| 1222 | skip |
---|
| 1223 | ] |
---|
| 1224 | -status_after_1 whd in ⊢ (??%?); |
---|
| 1225 | (* XXX: switch to the right hand side *) |
---|
| 1226 | normalize nodelta >EQs -s >EQticks -ticks |
---|
| 1227 | whd in ⊢ (??%%); |
---|
| 1228 | (* XXX: finally, prove the equality using sigma commutation *) |
---|
| 1229 | @split_eq_status try % |
---|
| 1230 | [3,11,19,27,36,53,61: |
---|
| 1231 | >program_counter_set_program_counter >set_clock_mk_Status_commutation |
---|
| 1232 | [5: >program_counter_set_program_counter ] |
---|
| 1233 | >EQaddr_of normalize nodelta |
---|
| 1234 | whd in ⊢ (??%?); >EQlookup_labels normalize nodelta |
---|
| 1235 | >EQcm % |
---|
| 1236 | |7,15,23,31,45,57,65: |
---|
| 1237 | >set_clock_mk_Status_commutation >program_counter_set_program_counter |
---|
| 1238 | whd in ⊢ (??%?); normalize nodelta |
---|
| 1239 | >EQppc in fetch_many_assm; #fetch_many_assm |
---|
| 1240 | [5: |
---|
| 1241 | >program_counter_set_arg_1 >program_counter_set_program_counter |
---|
| 1242 | ] |
---|
| 1243 | <(eq_bv_eq … fetch_many_assm) >EQintermediate_pc'' |
---|
| 1244 | <bitvector_of_nat_sign_extension_equivalence |
---|
| 1245 | [1,3,5,7,9,11,13: |
---|
| 1246 | whd in ⊢ (???%); cases (half_add ???) normalize // |
---|
| 1247 | |2,4,6,8,10,12,14: |
---|
| 1248 | @assembly1_lt_128 |
---|
| 1249 | @le_S_S @le_O_n |
---|
| 1250 | ] |
---|
| 1251 | |*: |
---|
| 1252 | cases daemon |
---|
| 1253 | ] |
---|
| 1254 | ] |
---|
| 1255 | |4,5,6,7,8,36,37,38,39,40,41,50: (* INC, CLR, CPL, PUSH *) |
---|
| 1256 | (* XXX: work on the right hand side *) |
---|
[1975] | 1257 | lapply (subaddressing_modein ???) |
---|
| 1258 | <EQaddr normalize nodelta #irrelevant |
---|
| 1259 | try (>p normalize nodelta) |
---|
| 1260 | try (>p1 normalize nodelta) |
---|
[1984] | 1261 | (* XXX: switch to the left hand side *) |
---|
[2017] | 1262 | >EQP -P normalize nodelta |
---|
[1984] | 1263 | #sigma_increment_commutation #maps_assm #fetch_many_assm %{1} |
---|
| 1264 | whd in ⊢ (??%?); |
---|
| 1265 | <(fetch_many_singleton … fetch_many_assm) -fetch_many_assm whd in ⊢ (??%?); |
---|
| 1266 | (* XXX: work on the left hand side *) |
---|
[1975] | 1267 | [1,2,3,4,5: |
---|
| 1268 | generalize in ⊢ (??(???(?%))?); |
---|
| 1269 | |6,7,8,9,10,11: |
---|
| 1270 | generalize in ⊢ (??(???(?%))?); |
---|
| 1271 | |12: |
---|
| 1272 | generalize in ⊢ (??(???(?%))?); |
---|
| 1273 | ] |
---|
| 1274 | <EQaddr normalize nodelta #irrelevant |
---|
[1977] | 1275 | try @(jmpair_as_replace ?????????? p) |
---|
| 1276 | [10: normalize nodelta try @(jmpair_as_replace ?????????? p1) ] |
---|
[1984] | 1277 | (* XXX: switch to the right hand side *) |
---|
| 1278 | normalize nodelta >EQs -s >EQticks -ticks |
---|
[1975] | 1279 | whd in ⊢ (??%%); |
---|
[1984] | 1280 | (* XXX: finally, prove the equality using sigma commutation *) |
---|
[2017] | 1281 | try @split_eq_status try % whd in ⊢ (??%%); |
---|
[2023] | 1282 | cases daemon |
---|
[2017] | 1283 | |1,2,3,9,46,51,53,54,55: (* ADD, ADDC, SUBB, DEC, SWAP, POP, XCHD, RET, RETI *) |
---|
[1984] | 1284 | (* XXX: work on the right hand side *) |
---|
[1971] | 1285 | >p normalize nodelta |
---|
[1975] | 1286 | try (>p1 normalize nodelta) |
---|
[1984] | 1287 | (* XXX: switch to the left hand side *) |
---|
| 1288 | -instr_refl >EQP -P normalize nodelta |
---|
| 1289 | #sigma_increment_commutation #maps_assm #fetch_many_assm %{1} |
---|
| 1290 | whd in ⊢ (??%?); |
---|
| 1291 | <(fetch_many_singleton … fetch_many_assm) -fetch_many_assm whd in ⊢ (??%?); |
---|
| 1292 | (* XXX: work on the left hand side *) |
---|
[1971] | 1293 | @(pair_replace ?????????? p) |
---|
[1978] | 1294 | [1,3,5,7,9,11,13,15,17: |
---|
[2017] | 1295 | >set_clock_set_program_counter >set_clock_mk_Status_commutation |
---|
| 1296 | >set_program_counter_mk_Status_commutation >clock_set_program_counter |
---|
[1975] | 1297 | cases daemon |
---|
[1978] | 1298 | |14,16,18: |
---|
[1975] | 1299 | normalize nodelta |
---|
| 1300 | @(pair_replace ?????????? p1) |
---|
[2017] | 1301 | [1,3,5: |
---|
| 1302 | >set_clock_mk_Status_commutation |
---|
| 1303 | cases daemon |
---|
| 1304 | ] |
---|
[1975] | 1305 | ] |
---|
[1984] | 1306 | (* XXX: switch to the right hand side *) |
---|
| 1307 | normalize nodelta >EQs -s >EQticks -ticks |
---|
[1975] | 1308 | whd in ⊢ (??%%); |
---|
[1984] | 1309 | (* XXX: finally, prove the equality using sigma commutation *) |
---|
[2017] | 1310 | try @split_eq_status try % |
---|
[2023] | 1311 | cases daemon |
---|
[2017] | 1312 | |10,42,43,44,45,49,52,56: (* MUL *) |
---|
[1984] | 1313 | (* XXX: work on the right hand side *) |
---|
| 1314 | (* XXX: switch to the left hand side *) |
---|
| 1315 | -instr_refl >EQP -P normalize nodelta |
---|
| 1316 | #sigma_increment_commutation #maps_assm #fetch_many_assm %{1} |
---|
| 1317 | whd in ⊢ (??%?); |
---|
| 1318 | <(fetch_many_singleton … fetch_many_assm) -fetch_many_assm whd in ⊢ (??%?); |
---|
| 1319 | (* XXX: work on the left hand side *) |
---|
| 1320 | (* XXX: switch to the right hand side *) |
---|
| 1321 | normalize nodelta >EQs -s >EQticks -ticks |
---|
[1975] | 1322 | whd in ⊢ (??%%); |
---|
[1984] | 1323 | (* XXX: finally, prove the equality using sigma commutation *) |
---|
[1975] | 1324 | cases daemon |
---|
[2017] | 1325 | |11,12: (* DIV *) |
---|
[1984] | 1326 | (* XXX: work on the right hand side *) |
---|
[1975] | 1327 | normalize nodelta in p; |
---|
| 1328 | >p normalize nodelta |
---|
[1984] | 1329 | (* XXX: switch to the left hand side *) |
---|
| 1330 | -instr_refl >EQP -P normalize nodelta |
---|
| 1331 | #sigma_increment_commutation #maps_assm #fetch_many_assm %{1} |
---|
| 1332 | whd in ⊢ (??%?); |
---|
| 1333 | <(fetch_many_singleton … fetch_many_assm) -fetch_many_assm whd in ⊢ (??%?); |
---|
[1975] | 1334 | @(pose … (nat_of_bitvector 8 ?)) #pose_assm #pose_refl |
---|
[1984] | 1335 | >(?: pose_assm = 0) normalize nodelta |
---|
[1975] | 1336 | [2,4: |
---|
| 1337 | <p >pose_refl |
---|
| 1338 | cases daemon |
---|
| 1339 | |1,3: |
---|
[1984] | 1340 | (* XXX: switch to the right hand side *) |
---|
| 1341 | >EQs -s >EQticks -ticks |
---|
[1975] | 1342 | whd in ⊢ (??%%); |
---|
[1984] | 1343 | (* XXX: finally, prove the equality using sigma commutation *) |
---|
[1975] | 1344 | @split_eq_status try % |
---|
| 1345 | cases daemon |
---|
| 1346 | ] |
---|
[2017] | 1347 | |13,14,15: (* DA *) |
---|
[1984] | 1348 | (* XXX: work on the right hand side *) |
---|
[1975] | 1349 | >p normalize nodelta |
---|
| 1350 | >p1 normalize nodelta |
---|
| 1351 | try (>p2 normalize nodelta |
---|
| 1352 | try (>p3 normalize nodelta |
---|
| 1353 | try (>p4 normalize nodelta |
---|
| 1354 | try (>p5 normalize nodelta)))) |
---|
[1984] | 1355 | (* XXX: switch to the left hand side *) |
---|
| 1356 | -instr_refl >EQP -P normalize nodelta |
---|
| 1357 | #sigma_increment_commutation #maps_assm #fetch_many_assm %{1} |
---|
| 1358 | whd in ⊢ (??%?); |
---|
| 1359 | <(fetch_many_singleton … fetch_many_assm) -fetch_many_assm whd in ⊢ (??%?); |
---|
| 1360 | (* XXX: work on the left hand side *) |
---|
[1975] | 1361 | @(pair_replace ?????????? p) |
---|
| 1362 | [1,3,5: |
---|
[2017] | 1363 | /demod/ |
---|
[1975] | 1364 | cases daemon |
---|
| 1365 | |2,4,6: |
---|
| 1366 | @(if_then_else_replace ???????? p1) |
---|
| 1367 | [1,3,5: |
---|
| 1368 | cases daemon |
---|
| 1369 | |2,4: |
---|
| 1370 | normalize nodelta |
---|
| 1371 | @(pair_replace ?????????? p2) |
---|
| 1372 | [1,3: |
---|
| 1373 | cases daemon |
---|
| 1374 | |2,4: |
---|
| 1375 | normalize nodelta >p3 normalize nodelta |
---|
| 1376 | >p4 normalize nodelta try >p5 |
---|
| 1377 | ] |
---|
| 1378 | ] |
---|
[1984] | 1379 | (* XXX: switch to the right hand side *) |
---|
| 1380 | normalize nodelta >EQs -s >EQticks -ticks |
---|
| 1381 | whd in ⊢ (??%%); |
---|
| 1382 | (* XXX: finally, prove the equality using sigma commutation *) |
---|
| 1383 | @split_eq_status try % |
---|
| 1384 | cases daemon |
---|
[1975] | 1385 | ] |
---|
[2017] | 1386 | |33,34,35,48: (* ANL, ORL, XRL, MOVX *) |
---|
[1984] | 1387 | (* XXX: work on the right hand side *) |
---|
| 1388 | cases addr #addr' normalize nodelta |
---|
[1978] | 1389 | [1,3: |
---|
[1984] | 1390 | cases addr' #addr'' normalize nodelta |
---|
[1975] | 1391 | ] |
---|
[1984] | 1392 | @pair_elim #lft #rgt #lft_rgt_refl >lft_rgt_refl normalize nodelta |
---|
| 1393 | (* XXX: switch to the left hand side *) |
---|
| 1394 | -instr_refl >EQP -P normalize nodelta |
---|
| 1395 | #sigma_increment_commutation #maps_assm #fetch_many_assm %{1} |
---|
| 1396 | whd in ⊢ (??%?); |
---|
| 1397 | <(fetch_many_singleton … fetch_many_assm) -fetch_many_assm whd in ⊢ (??%?); |
---|
| 1398 | (* XXX: work on the left hand side *) |
---|
| 1399 | (* XXX: switch to the right hand side *) |
---|
| 1400 | normalize nodelta >EQs -s >EQticks -ticks |
---|
[1975] | 1401 | whd in ⊢ (??%%); |
---|
[1984] | 1402 | (* XXX: finally, prove the equality using sigma commutation *) |
---|
[1975] | 1403 | cases daemon |
---|
[2017] | 1404 | |47: (* MOV *) |
---|
[1984] | 1405 | (* XXX: work on the right hand side *) |
---|
| 1406 | cases addr -addr #addr normalize nodelta |
---|
| 1407 | [1: |
---|
| 1408 | cases addr #addr normalize nodelta |
---|
| 1409 | [1: |
---|
| 1410 | cases addr #addr normalize nodelta |
---|
| 1411 | [1: |
---|
| 1412 | cases addr #addr normalize nodelta |
---|
| 1413 | [1: |
---|
| 1414 | cases addr #addr normalize nodelta |
---|
| 1415 | ] |
---|
| 1416 | ] |
---|
| 1417 | ] |
---|
| 1418 | ] |
---|
| 1419 | cases addr #lft #rgt normalize nodelta |
---|
| 1420 | (* XXX: switch to the left hand side *) |
---|
| 1421 | >EQP -P normalize nodelta |
---|
| 1422 | #sigma_increment_commutation #maps_assm #fetch_many_assm %{1} |
---|
| 1423 | whd in ⊢ (??%?); |
---|
| 1424 | <(fetch_many_singleton … fetch_many_assm) -fetch_many_assm whd in ⊢ (??%?); |
---|
| 1425 | (* XXX: work on the left hand side *) |
---|
| 1426 | (* XXX: switch to the right hand side *) |
---|
| 1427 | normalize nodelta >EQs -s >EQticks -ticks |
---|
| 1428 | whd in ⊢ (??%%); |
---|
| 1429 | (* XXX: finally, prove the equality using sigma commutation *) |
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| 1430 | cases daemon |
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[1985] | 1431 | ] |
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[1971] | 1432 | qed. |
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[2047] | 1433 | *) |
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