[719] | 1 | include "ASM/ASM.ma". |
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| 2 | include "ASM/BitVectorTrie.ma". |
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| 3 | include "ASM/Arithmetic.ma". |
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| 4 | include "ASM/Fetch.ma". |
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| 5 | include "ASM/Status.ma". |
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| 6 | |
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[820] | 7 | definition assembly_preinstruction ≝ |
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| 8 | λA: Type[0]. |
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| 9 | λaddr_of: A → Byte. (* relative *) |
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| 10 | λpre: preinstruction A. |
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| 11 | match pre with |
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| 12 | [ ADD addr1 addr2 ⇒ |
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[757] | 13 | match addr2 return λx. bool_to_Prop (is_in ? [[registr;direct;indirect;data]] x) → ? with |
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[719] | 14 | [ REGISTER r ⇒ λ_.[ ([[false;false;true;false;true]]) @@ r ] |
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| 15 | | DIRECT b1 ⇒ λ_.[ ([[false;false;true;false;false;true;false;true]]); b1 ] |
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| 16 | | INDIRECT i1 ⇒ λ_. [ ([[false;false;true;false;false;true;true;i1]]) ] |
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| 17 | | DATA b1 ⇒ λ_. [ ([[false;false;true;false;false;true;false;false]]) ; b1 ] |
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| 18 | | _ ⇒ λK.match K in False with [ ] ] (subaddressing_modein … addr2) |
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| 19 | | ADDC addr1 addr2 ⇒ |
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[757] | 20 | match addr2 return λx. bool_to_Prop (is_in ? [[registr;direct;indirect;data]] x) → ? with |
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[719] | 21 | [ REGISTER r ⇒ λ_.[ ([[false;false;true;true;true]]) @@ r ] |
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| 22 | | DIRECT b1 ⇒ λ_.[ ([[false;false;true;true;false;true;false;true]]); b1 ] |
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| 23 | | INDIRECT i1 ⇒ λ_. [ ([[false;false;true;true;false;true;true;i1]]) ] |
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| 24 | | DATA b1 ⇒ λ_. [ ([[false;false;true;true;false;true;false;false]]) ; b1 ] |
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| 25 | | _ ⇒ λK.match K in False with [ ] ] (subaddressing_modein … addr2) |
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| 26 | | ANL addrs ⇒ |
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| 27 | match addrs with |
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| 28 | [ inl addrs ⇒ match addrs with |
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| 29 | [ inl addrs ⇒ let 〈addr1,addr2〉 ≝ addrs in |
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[757] | 30 | match addr2 return λx. bool_to_Prop (is_in ? [[registr;direct;indirect;data]] x) → ? with |
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[719] | 31 | [ REGISTER r ⇒ λ_.[ ([[false;true;false;true;true]]) @@ r ] |
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| 32 | | DIRECT b1 ⇒ λ_.[ ([[false;true;false;true;false;true;false;true]]); b1 ] |
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| 33 | | INDIRECT i1 ⇒ λ_. [ ([[false;true;false;true;false;true;true;i1]]) ] |
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| 34 | | DATA b1 ⇒ λ_. [ ([[false;true;false;true;false;true;false;false]]) ; b1 ] |
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| 35 | | _ ⇒ λK.match K in False with [ ] ] (subaddressing_modein … addr2) |
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| 36 | | inr addrs ⇒ let 〈addr1,addr2〉 ≝ addrs in |
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| 37 | let b1 ≝ |
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| 38 | match addr1 return λx. bool_to_Prop (is_in ? [[direct]] x) → ? with |
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| 39 | [ DIRECT b1 ⇒ λ_.b1 |
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| 40 | | _ ⇒ λK.match K in False with [ ] ] (subaddressing_modein … addr1) in |
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| 41 | match addr2 return λx. bool_to_Prop (is_in ? [[acc_a;data]] x) → ? with |
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| 42 | [ ACC_A ⇒ λ_.[ ([[false;true;false;true;false;false;true;false]]) ; b1 ] |
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| 43 | | DATA b2 ⇒ λ_. [ ([[false;true;false;true;false;false;true;true]]) ; b1 ; b2 ] |
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| 44 | | _ ⇒ λK.match K in False with [ ] ] (subaddressing_modein … addr2) |
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| 45 | ] |
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| 46 | | inr addrs ⇒ let 〈addr1,addr2〉 ≝ addrs in |
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| 47 | match addr2 return λx. bool_to_Prop (is_in ? [[bit_addr;n_bit_addr]] x) → ? with |
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| 48 | [ BIT_ADDR b1 ⇒ λ_.[ ([[true;false;false;false;false;false;true;false]]) ; b1 ] |
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| 49 | | N_BIT_ADDR b1 ⇒ λ_. [ ([[true;false;true;true;false;false;false;false]]) ; b1 ] |
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| 50 | | _ ⇒ λK.match K in False with [ ] ] (subaddressing_modein … addr2)] |
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| 51 | | CLR addr ⇒ |
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| 52 | match addr return λx. bool_to_Prop (is_in ? [[acc_a;carry;bit_addr]] x) → ? with |
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| 53 | [ ACC_A ⇒ λ_. |
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| 54 | [ ([[true; true; true; false; false; true; false; false]]) ] |
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| 55 | | CARRY ⇒ λ_. |
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| 56 | [ ([[true; true; false; false; false; false; true; true]]) ] |
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| 57 | | BIT_ADDR b1 ⇒ λ_. |
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| 58 | [ ([[true; true; false; false; false; false; true; false]]) ; b1 ] |
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| 59 | | _ ⇒ λK.match K in False with [ ] ] (subaddressing_modein … addr) |
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| 60 | | CPL addr ⇒ |
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| 61 | match addr return λx. bool_to_Prop (is_in ? [[acc_a;carry;bit_addr]] x) → ? with |
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| 62 | [ ACC_A ⇒ λ_. |
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| 63 | [ ([[true; true; true; true; false; true; false; false]]) ] |
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| 64 | | CARRY ⇒ λ_. |
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| 65 | [ ([[true; false; true; true; false; false; true; true]]) ] |
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| 66 | | BIT_ADDR b1 ⇒ λ_. |
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| 67 | [ ([[true; false; true; true; false; false; true; false]]) ; b1 ] |
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| 68 | | _ ⇒ λK.match K in False with [ ] ] (subaddressing_modein … addr) |
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| 69 | | DA addr ⇒ |
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| 70 | [ ([[true; true; false; true; false; true; false; false]]) ] |
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| 71 | | DEC addr ⇒ |
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[757] | 72 | match addr return λx. bool_to_Prop (is_in ? [[acc_a;registr;direct;indirect]] x) → ? with |
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[719] | 73 | [ ACC_A ⇒ λ_. |
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| 74 | [ ([[false; false; false; true; false; true; false; false]]) ] |
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| 75 | | REGISTER r ⇒ λ_. |
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| 76 | [ ([[false; false; false; true; true]]) @@ r ] |
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| 77 | | DIRECT b1 ⇒ λ_. |
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| 78 | [ ([[false; false; false; true; false; true; false; true]]); b1 ] |
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| 79 | | INDIRECT i1 ⇒ λ_. |
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| 80 | [ ([[false; false; false; true; false; true; true; i1]]) ] |
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| 81 | | _ ⇒ λK.match K in False with [ ] ] (subaddressing_modein … addr) |
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[820] | 82 | | DJNZ addr1 addr2 ⇒ |
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| 83 | let b2 ≝ addr_of addr2 in |
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[757] | 84 | match addr1 return λx. bool_to_Prop (is_in ? [[registr;direct]] x) → ? with |
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[719] | 85 | [ REGISTER r ⇒ λ_. |
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| 86 | [ ([[true; true; false; true; true]]) @@ r ; b2 ] |
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| 87 | | DIRECT b1 ⇒ λ_. |
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| 88 | [ ([[true; true; false; true; false; true; false; true]]); b1; b2 ] |
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| 89 | | _ ⇒ λK.match K in False with [ ] ] (subaddressing_modein … addr1) |
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| 90 | | JC addr ⇒ |
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[820] | 91 | let b1 ≝ addr_of addr in |
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| 92 | [ ([[false; true; false; false; false; false; false; false]]); b1 ] |
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[719] | 93 | | JNC addr ⇒ |
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[820] | 94 | let b1 ≝ addr_of addr in |
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| 95 | [ ([[false; true; false; true; false; false; false; false]]); b1 ] |
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[719] | 96 | | JZ addr ⇒ |
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[820] | 97 | let b1 ≝ addr_of addr in |
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| 98 | [ ([[false; true; true; false; false; false; false; false]]); b1 ] |
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[719] | 99 | | JNZ addr ⇒ |
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[820] | 100 | let b1 ≝ addr_of addr in |
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| 101 | [ ([[false; true; true; true; false; false; false; false]]); b1 ] |
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[719] | 102 | | JB addr1 addr2 ⇒ |
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[820] | 103 | let b2 ≝ addr_of addr2 in |
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[719] | 104 | match addr1 return λx. bool_to_Prop (is_in ? [[bit_addr]] x) → ? with |
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| 105 | [ BIT_ADDR b1 ⇒ λ_. |
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| 106 | [ ([[false; false; true; false; false; false; false; false]]); b1; b2 ] |
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| 107 | | _ ⇒ λK.match K in False with [ ] ] (subaddressing_modein … addr1) |
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| 108 | | JNB addr1 addr2 ⇒ |
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[820] | 109 | let b2 ≝ addr_of addr2 in |
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[719] | 110 | match addr1 return λx. bool_to_Prop (is_in ? [[bit_addr]] x) → ? with |
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| 111 | [ BIT_ADDR b1 ⇒ λ_. |
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| 112 | [ ([[false; false; true; true; false; false; false; false]]); b1; b2 ] |
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| 113 | | _ ⇒ λK.match K in False with [ ] ] (subaddressing_modein … addr1) |
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| 114 | | JBC addr1 addr2 ⇒ |
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[820] | 115 | let b2 ≝ addr_of addr2 in |
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[719] | 116 | match addr1 return λx. bool_to_Prop (is_in ? [[bit_addr]] x) → ? with |
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| 117 | [ BIT_ADDR b1 ⇒ λ_. |
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| 118 | [ ([[false; false; false; true; false; false; false; false]]); b1; b2 ] |
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| 119 | | _ ⇒ λK.match K in False with [ ] ] (subaddressing_modein … addr1) |
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| 120 | | CJNE addrs addr3 ⇒ |
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[820] | 121 | let b3 ≝ addr_of addr3 in |
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[719] | 122 | match addrs with |
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| 123 | [ inl addrs ⇒ let 〈addr1,addr2〉 ≝ addrs in |
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| 124 | match addr2 return λx. bool_to_Prop (is_in ? [[direct;data]] x) → ? with |
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| 125 | [ DIRECT b1 ⇒ λ_. |
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| 126 | [ ([[true; false; true; true; false; true; false; true]]); b1; b3 ] |
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| 127 | | DATA b1 ⇒ λ_. |
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| 128 | [ ([[true; false; true; true; false; true; false; false]]); b1; b3 ] |
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| 129 | | _ ⇒ λK.match K in False with [ ] ] (subaddressing_modein … addr2) |
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| 130 | | inr addrs ⇒ let 〈addr1,addr2〉 ≝ addrs in |
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| 131 | let b2 ≝ |
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| 132 | match addr2 return λx. bool_to_Prop (is_in ? [[data]] x) → ? with |
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| 133 | [ DATA b2 ⇒ λ_. b2 |
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| 134 | | _ ⇒ λK.match K in False with [ ] ] (subaddressing_modein … addr2) in |
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[757] | 135 | match addr1 return λx. bool_to_Prop (is_in ? [[registr;indirect]] x) → list Byte with |
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[820] | 136 | [ REGISTER r ⇒ λ_. |
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[719] | 137 | [ ([[true; false; true; true; true]]) @@ r; b2; b3 ] |
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| 138 | | INDIRECT i1 ⇒ λ_. |
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| 139 | [ ([[true; false; true; true; false; true; true; i1]]); b2; b3 ] |
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[820] | 140 | | _ ⇒ λK.match K in False with [ ] ] (subaddressing_modein … addr1) |
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| 141 | ] |
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| 142 | | DIV addr1 addr2 ⇒ |
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| 143 | [ ([[true;false;false;false;false;true;false;false]]) ] |
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[719] | 144 | | INC addr ⇒ |
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[757] | 145 | match addr return λx. bool_to_Prop (is_in ? [[acc_a;registr;direct;indirect;dptr]] x) → ? with |
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[719] | 146 | [ ACC_A ⇒ λ_. |
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| 147 | [ ([[false;false;false;false;false;true;false;false]]) ] |
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| 148 | | REGISTER r ⇒ λ_. |
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| 149 | [ ([[false;false;false;false;true]]) @@ r ] |
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| 150 | | DIRECT b1 ⇒ λ_. |
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| 151 | [ ([[false; false; false; false; false; true; false; true]]); b1 ] |
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| 152 | | INDIRECT i1 ⇒ λ_. |
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| 153 | [ ([[false; false; false; false; false; true; true; i1]]) ] |
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| 154 | | DPTR ⇒ λ_. |
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| 155 | [ ([[true;false;true;false;false;false;true;true]]) ] |
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| 156 | | _ ⇒ λK.match K in False with [ ] ] (subaddressing_modein … addr) |
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| 157 | | MOV addrs ⇒ |
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| 158 | match addrs with |
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| 159 | [ inl addrs ⇒ |
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| 160 | match addrs with |
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| 161 | [ inl addrs ⇒ |
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| 162 | match addrs with |
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| 163 | [ inl addrs ⇒ |
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| 164 | match addrs with |
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| 165 | [ inl addrs ⇒ |
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| 166 | match addrs with |
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| 167 | [ inl addrs ⇒ let 〈addr1,addr2〉 ≝ addrs in |
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[757] | 168 | match addr2 return λx. bool_to_Prop (is_in ? [[registr;direct;indirect;data]] x) → ? with |
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[719] | 169 | [ REGISTER r ⇒ λ_.[ ([[true;true;true;false;true]]) @@ r ] |
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| 170 | | DIRECT b1 ⇒ λ_.[ ([[true;true;true;false;false;true;false;true]]); b1 ] |
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| 171 | | INDIRECT i1 ⇒ λ_. [ ([[true;true;true;false;false;true;true;i1]]) ] |
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| 172 | | DATA b1 ⇒ λ_. [ ([[false;true;true;true;false;true;false;false]]) ; b1 ] |
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| 173 | | _ ⇒ λK.match K in False with [ ] ] (subaddressing_modein … addr2) |
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| 174 | | inr addrs ⇒ let 〈addr1,addr2〉 ≝ addrs in |
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[757] | 175 | match addr1 return λx. bool_to_Prop (is_in ? [[registr;indirect]] x) → ? with |
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[719] | 176 | [ REGISTER r ⇒ λ_. |
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| 177 | match addr2 return λx. bool_to_Prop (is_in ? [[acc_a;direct;data]] x) → ? with |
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| 178 | [ ACC_A ⇒ λ_.[ ([[true;true;true;true;true]]) @@ r ] |
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| 179 | | DIRECT b1 ⇒ λ_.[ ([[true;false;true;false;true]]) @@ r; b1 ] |
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| 180 | | DATA b1 ⇒ λ_. [ ([[false;true;true;true;true]]) @@ r; b1 ] |
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| 181 | | _ ⇒ λK.match K in False with [ ] ] (subaddressing_modein … addr2) |
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| 182 | | INDIRECT i1 ⇒ λ_. |
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| 183 | match addr2 return λx. bool_to_Prop (is_in ? [[acc_a;direct;data]] x) → ? with |
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| 184 | [ ACC_A ⇒ λ_.[ ([[true;true;true;true;false;true;true;i1]]) ] |
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| 185 | | DIRECT b1 ⇒ λ_.[ ([[true;false;true;false;false;true;true;i1]]); b1 ] |
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| 186 | | DATA b1 ⇒ λ_. [ ([[false;true;true;true;false;true;true;i1]]) ; b1 ] |
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| 187 | | _ ⇒ λK.match K in False with [ ] ] (subaddressing_modein … addr2) |
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| 188 | | _ ⇒ λK.match K in False with [ ] ] (subaddressing_modein … addr1)] |
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| 189 | | inr addrs ⇒ let 〈addr1,addr2〉 ≝ addrs in |
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| 190 | let b1 ≝ |
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| 191 | match addr1 return λx. bool_to_Prop (is_in ? [[direct]] x) → ? with |
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| 192 | [ DIRECT b1 ⇒ λ_. b1 |
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| 193 | | _ ⇒ λK.match K in False with [ ] ] (subaddressing_modein … addr1) in |
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[757] | 194 | match addr2 return λx. bool_to_Prop (is_in ? [[acc_a;registr;direct;indirect;data]] x) → ? with |
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[719] | 195 | [ ACC_A ⇒ λ_.[ ([[true;true;true;true;false;true;false;true]]); b1] |
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| 196 | | REGISTER r ⇒ λ_.[ ([[true;false;false;false;true]]) @@ r; b1 ] |
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| 197 | | DIRECT b2 ⇒ λ_.[ ([[true;false;false;false;false;true;false;true]]); b1; b2 ] |
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| 198 | | INDIRECT i1 ⇒ λ_. [ ([[true;false;false;false;false;true;true;i1]]); b1 ] |
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| 199 | | DATA b2 ⇒ λ_. [ ([[false;true;true;true;false;true;false;true]]); b1; b2 ] |
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| 200 | | _ ⇒ λK.match K in False with [ ] ] (subaddressing_modein … addr2)] |
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| 201 | | inr addrs ⇒ let 〈addr1,addr2〉 ≝ addrs in |
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| 202 | match addr2 return λx. bool_to_Prop (is_in ? [[data16]] x) → ? with |
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| 203 | [ DATA16 w ⇒ λ_. |
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[938] | 204 | let b1_b2 ≝ split ? 8 8 w in |
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| 205 | let b1 ≝ \fst b1_b2 in |
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| 206 | let b2 ≝ \fst b1_b2 in |
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[719] | 207 | [ ([[true;false;false;true;false;false;false;false]]); b1; b2] |
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| 208 | | _ ⇒ λK.match K in False with [ ] ] (subaddressing_modein … addr2)] |
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| 209 | | inr addrs ⇒ let 〈addr1,addr2〉 ≝ addrs in |
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| 210 | match addr2 return λx. bool_to_Prop (is_in ? [[bit_addr]] x) → ? with |
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| 211 | [ BIT_ADDR b1 ⇒ λ_. |
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| 212 | [ ([[true;false;true;false;false;false;true;false]]); b1 ] |
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| 213 | | _ ⇒ λK.match K in False with [ ] ] (subaddressing_modein … addr2)] |
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| 214 | | inr addrs ⇒ let 〈addr1,addr2〉 ≝ addrs in |
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| 215 | match addr1 return λx. bool_to_Prop (is_in ? [[bit_addr]] x) → ? with |
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| 216 | [ BIT_ADDR b1 ⇒ λ_. |
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| 217 | [ ([[true;false;false;true;false;false;true;false]]); b1 ] |
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| 218 | | _ ⇒ λK.match K in False with [ ] ] (subaddressing_modein … addr1)] |
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| 219 | | MOVX addrs ⇒ |
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| 220 | match addrs with |
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| 221 | [ inl addrs ⇒ let 〈addr1,addr2〉 ≝ addrs in |
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| 222 | match addr2 return λx. bool_to_Prop (is_in ? [[ext_indirect;ext_indirect_dptr]] x) → ? with |
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| 223 | [ EXT_INDIRECT i1 ⇒ λ_. |
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| 224 | [ ([[true;true;true;false;false;false;true;i1]]) ] |
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| 225 | | EXT_INDIRECT_DPTR ⇒ λ_. |
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| 226 | [ ([[true;true;true;false;false;false;false;false]]) ] |
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| 227 | | _ ⇒ λK.match K in False with [ ] ] (subaddressing_modein … addr2) |
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| 228 | | inr addrs ⇒ let 〈addr1,addr2〉 ≝ addrs in |
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| 229 | match addr1 return λx. bool_to_Prop (is_in ? [[ext_indirect;ext_indirect_dptr]] x) → ? with |
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| 230 | [ EXT_INDIRECT i1 ⇒ λ_. |
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| 231 | [ ([[true;true;true;true;false;false;true;i1]]) ] |
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| 232 | | EXT_INDIRECT_DPTR ⇒ λ_. |
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| 233 | [ ([[true;true;true;true;false;false;false;false]]) ] |
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| 234 | | _ ⇒ λK.match K in False with [ ] ] (subaddressing_modein … addr1)] |
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| 235 | | MUL addr1 addr2 ⇒ |
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| 236 | [ ([[true;false;true;false;false;true;false;false]]) ] |
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| 237 | | NOP ⇒ |
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| 238 | [ ([[false;false;false;false;false;false;false;false]]) ] |
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| 239 | | ORL addrs ⇒ |
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| 240 | match addrs with |
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| 241 | [ inl addrs ⇒ |
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| 242 | match addrs with |
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| 243 | [ inl addrs ⇒ let 〈addr1,addr2〉 ≝ addrs in |
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[757] | 244 | match addr2 return λx. bool_to_Prop (is_in ? [[registr;data;direct;indirect]] x) → ? with |
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[719] | 245 | [ REGISTER r ⇒ λ_.[ ([[false;true;false;false;true]]) @@ r ] |
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| 246 | | DIRECT b1 ⇒ λ_.[ ([[false;true;false;false;false;true;false;true]]); b1 ] |
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| 247 | | INDIRECT i1 ⇒ λ_. [ ([[false;true;false;false;false;true;true;i1]]) ] |
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| 248 | | DATA b1 ⇒ λ_. [ ([[false;true;false;false;false;true;false;false]]) ; b1 ] |
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| 249 | | _ ⇒ λK.match K in False with [ ] ] (subaddressing_modein … addr2) |
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| 250 | | inr addrs ⇒ let 〈addr1,addr2〉 ≝ addrs in |
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| 251 | let b1 ≝ |
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| 252 | match addr1 return λx. bool_to_Prop (is_in ? [[direct]] x) → ? with |
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| 253 | [ DIRECT b1 ⇒ λ_. b1 |
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| 254 | | _ ⇒ λK.match K in False with [ ] ] (subaddressing_modein … addr1) in |
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| 255 | match addr2 return λx. bool_to_Prop (is_in ? [[acc_a;data]] x) → ? with |
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| 256 | [ ACC_A ⇒ λ_. |
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| 257 | [ ([[false;true;false;false;false;false;true;false]]); b1 ] |
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| 258 | | DATA b2 ⇒ λ_. |
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| 259 | [ ([[false;true;false;false;false;false;true;true]]); b1; b2 ] |
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| 260 | | _ ⇒ λK.match K in False with [ ] ] (subaddressing_modein … addr2)] |
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| 261 | | inr addrs ⇒ let 〈addr1,addr2〉 ≝ addrs in |
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| 262 | match addr2 return λx. bool_to_Prop (is_in ? [[bit_addr;n_bit_addr]] x) → ? with |
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| 263 | [ BIT_ADDR b1 ⇒ λ_. |
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| 264 | [ ([[false;true;true;true;false;false;true;false]]); b1 ] |
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| 265 | | N_BIT_ADDR b1 ⇒ λ_. |
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| 266 | [ ([[true;false;true;false;false;false;false;false]]); b1 ] |
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| 267 | | _ ⇒ λK.match K in False with [ ] ] (subaddressing_modein … addr2)] |
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| 268 | | POP addr ⇒ |
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| 269 | match addr return λx. bool_to_Prop (is_in ? [[direct]] x) → ? with |
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| 270 | [ DIRECT b1 ⇒ λ_. |
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| 271 | [ ([[true;true;false;true;false;false;false;false]]) ; b1 ] |
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| 272 | | _ ⇒ λK.match K in False with [ ] ] (subaddressing_modein … addr) |
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| 273 | | PUSH addr ⇒ |
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| 274 | match addr return λx. bool_to_Prop (is_in ? [[direct]] x) → ? with |
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| 275 | [ DIRECT b1 ⇒ λ_. |
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| 276 | [ ([[true;true;false;false;false;false;false;false]]) ; b1 ] |
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| 277 | | _ ⇒ λK.match K in False with [ ] ] (subaddressing_modein … addr) |
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| 278 | | RET ⇒ |
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| 279 | [ ([[false;false;true;false;false;false;true;false]]) ] |
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| 280 | | RETI ⇒ |
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| 281 | [ ([[false;false;true;true;false;false;true;false]]) ] |
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| 282 | | RL addr ⇒ |
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| 283 | [ ([[false;false;true;false;false;false;true;true]]) ] |
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| 284 | | RLC addr ⇒ |
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| 285 | [ ([[false;false;true;true;false;false;true;true]]) ] |
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| 286 | | RR addr ⇒ |
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| 287 | [ ([[false;false;false;false;false;false;true;true]]) ] |
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| 288 | | RRC addr ⇒ |
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| 289 | [ ([[false;false;false;true;false;false;true;true]]) ] |
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| 290 | | SETB addr ⇒ |
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| 291 | match addr return λx. bool_to_Prop (is_in ? [[carry;bit_addr]] x) → ? with |
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| 292 | [ CARRY ⇒ λ_. |
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| 293 | [ ([[true;true;false;true;false;false;true;true]]) ] |
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| 294 | | BIT_ADDR b1 ⇒ λ_. |
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| 295 | [ ([[true;true;false;true;false;false;true;false]]); b1 ] |
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| 296 | | _ ⇒ λK.match K in False with [ ] ] (subaddressing_modein … addr) |
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| 297 | | SUBB addr1 addr2 ⇒ |
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[757] | 298 | match addr2 return λx. bool_to_Prop (is_in ? [[registr;direct;indirect;data]] x) → ? with |
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[719] | 299 | [ REGISTER r ⇒ λ_. |
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| 300 | [ ([[true;false;false;true;true]]) @@ r ] |
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| 301 | | DIRECT b1 ⇒ λ_. |
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| 302 | [ ([[true;false;false;true;false;true;false;true]]); b1] |
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| 303 | | INDIRECT i1 ⇒ λ_. |
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| 304 | [ ([[true;false;false;true;false;true;true;i1]]) ] |
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| 305 | | DATA b1 ⇒ λ_. |
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| 306 | [ ([[true;false;false;true;false;true;false;false]]); b1] |
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| 307 | | _ ⇒ λK.match K in False with [ ] ] (subaddressing_modein … addr2) |
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| 308 | | SWAP addr ⇒ |
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| 309 | [ ([[true;true;false;false;false;true;false;false]]) ] |
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| 310 | | XCH addr1 addr2 ⇒ |
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[757] | 311 | match addr2 return λx. bool_to_Prop (is_in ? [[registr;direct;indirect]] x) → ? with |
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[719] | 312 | [ REGISTER r ⇒ λ_. |
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| 313 | [ ([[true;true;false;false;true]]) @@ r ] |
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| 314 | | DIRECT b1 ⇒ λ_. |
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| 315 | [ ([[true;true;false;false;false;true;false;true]]); b1] |
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| 316 | | INDIRECT i1 ⇒ λ_. |
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| 317 | [ ([[true;true;false;false;false;true;true;i1]]) ] |
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| 318 | | _ ⇒ λK.match K in False with [ ] ] (subaddressing_modein … addr2) |
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| 319 | | XCHD addr1 addr2 ⇒ |
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| 320 | match addr2 return λx. bool_to_Prop (is_in ? [[indirect]] x) → ? with |
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| 321 | [ INDIRECT i1 ⇒ λ_. |
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| 322 | [ ([[true;true;false;true;false;true;true;i1]]) ] |
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| 323 | | _ ⇒ λK.match K in False with [ ] ] (subaddressing_modein … addr2) |
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| 324 | | XRL addrs ⇒ |
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| 325 | match addrs with |
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| 326 | [ inl addrs ⇒ let 〈addr1,addr2〉 ≝ addrs in |
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[757] | 327 | match addr2 return λx. bool_to_Prop (is_in ? [[data;registr;direct;indirect]] x) → ? with |
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[719] | 328 | [ REGISTER r ⇒ λ_. |
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| 329 | [ ([[false;true;true;false;true]]) @@ r ] |
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| 330 | | DIRECT b1 ⇒ λ_. |
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| 331 | [ ([[false;true;true;false;false;true;false;true]]); b1] |
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| 332 | | INDIRECT i1 ⇒ λ_. |
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| 333 | [ ([[false;true;true;false;false;true;true;i1]]) ] |
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| 334 | | DATA b1 ⇒ λ_. |
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| 335 | [ ([[false;true;true;false;false;true;false;false]]); b1] |
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| 336 | | _ ⇒ λK.match K in False with [ ] ] (subaddressing_modein … addr2) |
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| 337 | | inr addrs ⇒ let 〈addr1,addr2〉 ≝ addrs in |
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| 338 | let b1 ≝ |
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| 339 | match addr1 return λx. bool_to_Prop (is_in ? [[direct]] x) → ? with |
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| 340 | [ DIRECT b1 ⇒ λ_. b1 |
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| 341 | | _ ⇒ λK.match K in False with [ ] ] (subaddressing_modein … addr1) in |
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| 342 | match addr2 return λx. bool_to_Prop (is_in ? [[acc_a;data]] x) → ? with |
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| 343 | [ ACC_A ⇒ λ_. |
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| 344 | [ ([[false;true;true;false;false;false;true;false]]); b1 ] |
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| 345 | | DATA b2 ⇒ λ_. |
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| 346 | [ ([[false;true;true;false;false;false;true;true]]); b1; b2 ] |
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[820] | 347 | | _ ⇒ λK.match K in False with [ ] ] (subaddressing_modein … addr2)] |
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| 348 | ]. |
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[719] | 349 | |
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[820] | 350 | definition assembly1 ≝ |
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| 351 | λi: instruction. |
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| 352 | match i with |
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| 353 | [ ACALL addr ⇒ |
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| 354 | match addr return λx. bool_to_Prop (is_in ? [[addr11]] x) → ? with |
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| 355 | [ ADDR11 w ⇒ λ_. |
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[938] | 356 | let v1_v2 ≝ split ? 3 8 w in |
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| 357 | let v1 ≝ \fst v1_v2 in |
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| 358 | let v2 ≝ \snd v1_v2 in |
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[820] | 359 | [ (v1 @@ [[true; false; false; false; true]]) ; v2 ] |
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| 360 | | _ ⇒ λK.match K in False with [ ] ] (subaddressing_modein … addr) |
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| 361 | | AJMP addr ⇒ |
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| 362 | match addr return λx. bool_to_Prop (is_in ? [[addr11]] x) → ? with |
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| 363 | [ ADDR11 w ⇒ λ_. |
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[938] | 364 | let v1_v2 ≝ split ? 3 8 w in |
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| 365 | let v1 ≝ \fst v1_v2 in |
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| 366 | let v2 ≝ \snd v1_v2 in |
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[820] | 367 | [ (v1 @@ [[false; false; false; false; true]]) ; v2 ] |
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| 368 | | _ ⇒ λK.match K in False with [ ] ] (subaddressing_modein … addr) |
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| 369 | | JMP adptr ⇒ |
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| 370 | [ ([[false;true;true;true;false;false;true;true]]) ] |
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| 371 | | LCALL addr ⇒ |
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| 372 | match addr return λx. bool_to_Prop (is_in ? [[addr16]] x) → ? with |
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| 373 | [ ADDR16 w ⇒ λ_. |
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[938] | 374 | let b1_b2 ≝ split ? 8 8 w in |
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| 375 | let b1 ≝ \fst b1_b2 in |
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| 376 | let b2 ≝ \snd b1_b2 in |
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[820] | 377 | [ ([[false;false;false;true;false;false;true;false]]); b1; b2 ] |
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| 378 | | _ ⇒ λK.match K in False with [ ] ] (subaddressing_modein … addr) |
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| 379 | | LJMP addr ⇒ |
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| 380 | match addr return λx. bool_to_Prop (is_in ? [[addr16]] x) → ? with |
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| 381 | [ ADDR16 w ⇒ λ_. |
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[938] | 382 | let b1_b2 ≝ split ? 8 8 w in |
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| 383 | let b1 ≝ \fst b1_b2 in |
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| 384 | let b2 ≝ \snd b1_b2 in |
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[820] | 385 | [ ([[false;false;false;false;false;false;true;false]]); b1; b2 ] |
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| 386 | | _ ⇒ λK.match K in False with [ ] ] (subaddressing_modein … addr) |
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| 387 | | MOVC addr1 addr2 ⇒ |
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| 388 | match addr2 return λx. bool_to_Prop (is_in ? [[acc_dptr;acc_pc]] x) → ? with |
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| 389 | [ ACC_DPTR ⇒ λ_. |
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| 390 | [ ([[true;false;false;true;false;false;true;true]]) ] |
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| 391 | | ACC_PC ⇒ λ_. |
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| 392 | [ ([[true;false;false;false;false;false;true;true]]) ] |
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| 393 | | _ ⇒ λK.match K in False with [ ] ] (subaddressing_modein … addr2) |
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| 394 | | SJMP addr ⇒ |
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| 395 | match addr return λx. bool_to_Prop (is_in ? [[relative]] x) → ? with |
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| 396 | [ RELATIVE b1 ⇒ λ_. |
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| 397 | [ ([[true;false;false;false;false;false;false;false]]); b1 ] |
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| 398 | | _ ⇒ λK.match K in False with [ ] ] (subaddressing_modein … addr) |
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| 399 | | RealInstruction instr ⇒ |
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| 400 | assembly_preinstruction [[ relative ]] |
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| 401 | (λx. |
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| 402 | match x return λs. bool_to_Prop (is_in ? [[ relative ]] s) → ? with |
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| 403 | [ RELATIVE r ⇒ λ_. r |
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| 404 | | _ ⇒ λabsd. ⊥ |
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| 405 | ] (subaddressing_modein … x)) instr |
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| 406 | ]. |
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| 407 | cases absd |
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| 408 | qed. |
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| 409 | |
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[842] | 410 | definition is_relative_jump ≝ |
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| 411 | λi: preinstruction Identifier. |
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| 412 | match i with |
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| 413 | [ JC _ ⇒ True |
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| 414 | | JNC _ ⇒ True |
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| 415 | | JB _ _ ⇒ True |
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| 416 | | JNB _ _ ⇒ True |
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| 417 | | JBC _ _ ⇒ True |
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| 418 | | JZ _ ⇒ True |
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| 419 | | JNZ _ ⇒ True |
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| 420 | | CJNE _ _ ⇒ True |
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| 421 | | DJNZ _ _ ⇒ True |
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| 422 | | _ ⇒ False |
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| 423 | ]. |
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[719] | 424 | |
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[842] | 425 | definition pseudo_instruction_is_relative_jump: pseudo_instruction → Prop ≝ |
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| 426 | λi. |
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| 427 | match i with |
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| 428 | [ Instruction j ⇒ is_relative_jump j |
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| 429 | | _ ⇒ False ]. |
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| 430 | |
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[832] | 431 | inductive jump_length: Type[0] ≝ |
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| 432 | | short_jump: jump_length |
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| 433 | | medium_jump: jump_length |
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| 434 | | long_jump: jump_length. |
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| 435 | |
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[907] | 436 | definition jump_expansion_policy ≝ BitVectorTrie jump_length 16. |
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[832] | 437 | |
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[907] | 438 | definition find_right_call: Word → Word → nat × (option jump_length) ≝ |
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| 439 | (* medium call: 11 bits, only in "current segment" *) |
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| 440 | (* can this be done more efficiently with bit vector arithmetic? *) |
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| 441 | λpc.λaddress. |
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| 442 | let 〈p1, p2〉 ≝ split ? 5 11 address in |
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| 443 | let 〈a1, a2〉 ≝ split ? 5 11 pc in |
---|
| 444 | if eq_bv ? p1 a1 then (* we're in the same segment *) |
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| 445 | 〈2, Some ? medium_jump〉 |
---|
| 446 | else |
---|
| 447 | 〈3, Some ? long_jump〉. |
---|
| 448 | |
---|
| 449 | definition distance ≝ |
---|
| 450 | λx.λy.if gtb x y then x - y else y - x. |
---|
| 451 | |
---|
| 452 | definition find_right_jump: Word → Word → nat × (option jump_length) ≝ |
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| 453 | (* short jump: 8 bits signed *) |
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| 454 | (* medium jump: 11 bits, forward only *) |
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| 455 | λpc.λaddress. |
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| 456 | let pn ≝ nat_of_bitvector ? pc in |
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| 457 | let pa ≝ nat_of_bitvector ? address in |
---|
[914] | 458 | if ltb (distance pn pa) 127 then |
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[907] | 459 | 〈2, Some ? short_jump〉 |
---|
| 460 | else |
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| 461 | find_right_call pc address. |
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| 462 | |
---|
| 463 | definition find_right_relative_jump: Word → (BitVectorTrie Word 16) → |
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| 464 | Identifier → nat × (option jump_length) ≝ |
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| 465 | λpc.λlabels.λjmp. |
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| 466 | match lookup_opt ? ? jmp labels with |
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| 467 | [ None ⇒ 〈2, Some ? short_jump〉 |
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| 468 | | Some a ⇒ find_right_jump pc a ]. |
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| 469 | |
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| 470 | definition jep_relative: Word → (BitVectorTrie Word 16) → preinstruction Identifier → ? ≝ |
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| 471 | λpc.λlabels.λi. |
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| 472 | match i with |
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| 473 | [ JC jmp ⇒ find_right_relative_jump pc labels jmp |
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| 474 | | JNC jmp ⇒ find_right_relative_jump pc labels jmp |
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| 475 | | JB baddr jmp ⇒ find_right_relative_jump pc labels jmp |
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| 476 | | JZ jmp ⇒ find_right_relative_jump pc labels jmp |
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| 477 | | JNZ jmp ⇒ find_right_relative_jump pc labels jmp |
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| 478 | | JBC baddr jmp ⇒ find_right_relative_jump pc labels jmp |
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| 479 | | JNB baddr jmp ⇒ find_right_relative_jump pc labels jmp |
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| 480 | | CJNE addr jmp ⇒ find_right_relative_jump pc labels jmp |
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| 481 | | DJNZ addr jmp ⇒ find_right_relative_jump pc labels jmp |
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| 482 | | _ ⇒ 〈length ? (assembly_preinstruction ? (λx.zero ?) i), None …〉 ]. |
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| 483 | |
---|
| 484 | definition jump_expansion_policy_internal: pseudo_assembly_program → |
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| 485 | (BitVectorTrie Word 16) → jump_expansion_policy → |
---|
| 486 | ((BitVectorTrie Word 16) × jump_expansion_policy × bool)≝ |
---|
| 487 | λprogram.λlabels.λpolicy. |
---|
| 488 | let 〈pc, new_labels, new_policy, changed〉 ≝ |
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| 489 | foldl ? ? (λacc.λi:labelled_instruction. |
---|
| 490 | let 〈label, instr〉 ≝ i in |
---|
| 491 | let 〈pc,labels,policy,c0〉 ≝ acc in |
---|
| 492 | let 〈c1,new_labels〉 ≝ match label with |
---|
| 493 | [ None ⇒ 〈c0,labels〉 |
---|
| 494 | | Some l ⇒ |
---|
| 495 | match update ? ? pc l labels with |
---|
| 496 | [ None ⇒ 〈c0,labels〉 |
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| 497 | | Some x ⇒ 〈true, x〉 ] ] in |
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| 498 | let 〈pc_delta, jmp_len〉 ≝ match instr with |
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| 499 | [ Call c ⇒ |
---|
| 500 | match lookup_opt ? ? c new_labels with |
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| 501 | [ None ⇒ 〈2, Some ? medium_jump〉 |
---|
| 502 | | Some c_addr ⇒ find_right_call pc c_addr ] |
---|
| 503 | | Jmp j ⇒ |
---|
| 504 | match lookup_opt ? ? j new_labels with |
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| 505 | [ None ⇒ 〈2, Some ? short_jump〉 |
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| 506 | | Some j_addr ⇒ find_right_jump pc j_addr ] |
---|
| 507 | | Instruction i ⇒ jep_relative pc new_labels i |
---|
[920] | 508 | | Mov _ _ ⇒ 〈3, None …〉 |
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[907] | 509 | | Cost _ ⇒ 〈0, None …〉 |
---|
| 510 | | Comment _ ⇒ 〈0, None …〉 ] in |
---|
| 511 | let 〈new_pc,ignore〉 ≝ add_16_with_carry pc (bitvector_of_nat ? pc_delta) false in |
---|
| 512 | match jmp_len with |
---|
| 513 | [ None ⇒ 〈new_pc, new_labels, policy, c1〉 |
---|
| 514 | | Some j ⇒ |
---|
| 515 | match update ? ? pc j policy with |
---|
| 516 | [ None ⇒ 〈new_pc, new_labels, policy, c1〉 |
---|
| 517 | | Some x ⇒ 〈new_pc, new_labels, x, true〉 ] ] |
---|
| 518 | ) 〈zero ?, labels, policy, false〉 (\snd program) in |
---|
| 519 | 〈labels, policy, changed〉. |
---|
| 520 | |
---|
[842] | 521 | definition expand_relative_jump_internal: |
---|
| 522 | (Identifier → Word) → jump_length → Identifier → Word → ([[relative]] → preinstruction [[relative]]) → |
---|
| 523 | option (list instruction) |
---|
| 524 | ≝ |
---|
| 525 | λlookup_labels,jmp_len.λjmp:Identifier.λpc,i. |
---|
[832] | 526 | match jmp_len with |
---|
[842] | 527 | [ short_jump ⇒ |
---|
| 528 | let lookup_address ≝ lookup_labels jmp in |
---|
| 529 | let 〈result, flags〉 ≝ sub_16_with_carry pc lookup_address false in |
---|
| 530 | let 〈upper, lower〉 ≝ split ? 8 8 result in |
---|
| 531 | if eq_bv ? upper (zero 8) then |
---|
| 532 | let address ≝ RELATIVE lower in |
---|
| 533 | Some ? [ RealInstruction (i address) ] |
---|
| 534 | else |
---|
| 535 | None ? |
---|
| 536 | | medium_jump ⇒ None … |
---|
[832] | 537 | | long_jump ⇒ |
---|
[842] | 538 | Some ? |
---|
| 539 | [ RealInstruction (i (RELATIVE (bitvector_of_nat ? 2))); |
---|
[832] | 540 | SJMP (RELATIVE (bitvector_of_nat ? 3)); (* LJMP size? *) |
---|
[842] | 541 | LJMP (ADDR16 (lookup_labels jmp)) |
---|
[832] | 542 | ] |
---|
| 543 | ]. |
---|
| 544 | @ I |
---|
| 545 | qed. |
---|
[825] | 546 | |
---|
[842] | 547 | definition expand_relative_jump: (Identifier → Word) → jump_length → Word → preinstruction Identifier → option (list instruction) ≝ |
---|
| 548 | λlookup_labels. |
---|
[832] | 549 | λjmp_len: jump_length. |
---|
[842] | 550 | λpc. |
---|
[832] | 551 | λi: preinstruction Identifier. |
---|
| 552 | let rel_jmp ≝ RELATIVE (bitvector_of_nat ? 2) in |
---|
| 553 | match i with |
---|
[842] | 554 | [ JC jmp ⇒ expand_relative_jump_internal lookup_labels jmp_len jmp pc (JC ?) |
---|
| 555 | | JNC jmp ⇒ expand_relative_jump_internal lookup_labels jmp_len jmp pc (JNC ?) |
---|
| 556 | | JB baddr jmp ⇒ expand_relative_jump_internal lookup_labels jmp_len jmp pc (JB ? baddr) |
---|
| 557 | | JZ jmp ⇒ expand_relative_jump_internal lookup_labels jmp_len jmp pc (JZ ?) |
---|
| 558 | | JNZ jmp ⇒ expand_relative_jump_internal lookup_labels jmp_len jmp pc (JNZ ?) |
---|
| 559 | | JBC baddr jmp ⇒ expand_relative_jump_internal lookup_labels jmp_len jmp pc (JBC ? baddr) |
---|
| 560 | | JNB baddr jmp ⇒ expand_relative_jump_internal lookup_labels jmp_len jmp pc (JNB ? baddr) |
---|
| 561 | | CJNE addr jmp ⇒ expand_relative_jump_internal lookup_labels jmp_len jmp pc (CJNE ? addr) |
---|
| 562 | | DJNZ addr jmp ⇒ expand_relative_jump_internal lookup_labels jmp_len jmp pc (DJNZ ? addr) |
---|
[832] | 563 | | ADD arg1 arg2 ⇒ Some ? [ ADD ? arg1 arg2 ] |
---|
| 564 | | ADDC arg1 arg2 ⇒ Some ? [ ADDC ? arg1 arg2 ] |
---|
| 565 | | SUBB arg1 arg2 ⇒ Some ? [ SUBB ? arg1 arg2 ] |
---|
| 566 | | INC arg ⇒ Some ? [ INC ? arg ] |
---|
| 567 | | DEC arg ⇒ Some ? [ DEC ? arg ] |
---|
| 568 | | MUL arg1 arg2 ⇒ Some ? [ MUL ? arg1 arg2 ] |
---|
| 569 | | DIV arg1 arg2 ⇒ Some ? [ DIV ? arg1 arg2 ] |
---|
| 570 | | DA arg ⇒ Some ? [ DA ? arg ] |
---|
| 571 | | ANL arg ⇒ Some ? [ ANL ? arg ] |
---|
| 572 | | ORL arg ⇒ Some ? [ ORL ? arg ] |
---|
| 573 | | XRL arg ⇒ Some ? [ XRL ? arg ] |
---|
| 574 | | CLR arg ⇒ Some ? [ CLR ? arg ] |
---|
| 575 | | CPL arg ⇒ Some ? [ CPL ? arg ] |
---|
| 576 | | RL arg ⇒ Some ? [ RL ? arg ] |
---|
| 577 | | RR arg ⇒ Some ? [ RR ? arg ] |
---|
| 578 | | RLC arg ⇒ Some ? [ RLC ? arg ] |
---|
| 579 | | RRC arg ⇒ Some ? [ RRC ? arg ] |
---|
| 580 | | SWAP arg ⇒ Some ? [ SWAP ? arg ] |
---|
| 581 | | MOV arg ⇒ Some ? [ MOV ? arg ] |
---|
| 582 | | MOVX arg ⇒ Some ? [ MOVX ? arg ] |
---|
| 583 | | SETB arg ⇒ Some ? [ SETB ? arg ] |
---|
| 584 | | PUSH arg ⇒ Some ? [ PUSH ? arg ] |
---|
| 585 | | POP arg ⇒ Some ? [ POP ? arg ] |
---|
| 586 | | XCH arg1 arg2 ⇒ Some ? [ XCH ? arg1 arg2 ] |
---|
| 587 | | XCHD arg1 arg2 ⇒ Some ? [ XCHD ? arg1 arg2 ] |
---|
| 588 | | RET ⇒ Some ? [ RET ? ] |
---|
| 589 | | RETI ⇒ Some ? [ RETI ? ] |
---|
| 590 | | NOP ⇒ Some ? [ RealInstruction (NOP ?) ] |
---|
| 591 | ]. |
---|
| 592 | |
---|
| 593 | definition expand_pseudo_instruction: ? → ? → Word → jump_length → pseudo_instruction → option (list instruction) ≝ |
---|
[825] | 594 | λlookup_labels. |
---|
| 595 | λlookup_datalabels. |
---|
[832] | 596 | λpc. |
---|
| 597 | λjmp_len. |
---|
| 598 | λi. |
---|
| 599 | match i with |
---|
| 600 | [ Cost cost ⇒ Some ? [ ] |
---|
| 601 | | Comment comment ⇒ Some ? [ ] |
---|
| 602 | | Call call ⇒ |
---|
| 603 | match jmp_len with |
---|
| 604 | [ short_jump ⇒ None ? |
---|
| 605 | | medium_jump ⇒ |
---|
| 606 | let 〈ignore, address〉 ≝ split ? 5 11 (lookup_labels call) in |
---|
| 607 | let 〈fst_5, rest〉 ≝ split ? 5 11 pc in |
---|
| 608 | if eq_bv ? ignore fst_5 then |
---|
| 609 | let address ≝ ADDR11 address in |
---|
| 610 | Some ? ([ ACALL address ]) |
---|
| 611 | else |
---|
| 612 | None ? |
---|
| 613 | | long_jump ⇒ |
---|
| 614 | let address ≝ ADDR16 (lookup_labels call) in |
---|
| 615 | Some ? [ LCALL address ] |
---|
| 616 | ] |
---|
| 617 | | Mov d trgt ⇒ |
---|
| 618 | let address ≝ DATA16 (lookup_datalabels trgt) in |
---|
| 619 | Some ? [ RealInstruction (MOV ? (inl ? ? (inl ? ? (inr ? ? 〈DPTR, address〉))))] |
---|
[842] | 620 | | Instruction instr ⇒ expand_relative_jump lookup_labels jmp_len pc instr |
---|
[832] | 621 | | Jmp jmp ⇒ |
---|
| 622 | match jmp_len with |
---|
| 623 | [ short_jump ⇒ |
---|
| 624 | let lookup_address ≝ lookup_labels jmp in |
---|
| 625 | let 〈result, flags〉 ≝ sub_16_with_carry pc lookup_address false in |
---|
| 626 | let 〈upper, lower〉 ≝ split ? 8 8 result in |
---|
| 627 | if eq_bv ? upper (zero 8) then |
---|
| 628 | let address ≝ RELATIVE lower in |
---|
| 629 | Some ? [ SJMP address ] |
---|
| 630 | else |
---|
| 631 | None ? |
---|
| 632 | | medium_jump ⇒ |
---|
| 633 | let address ≝ lookup_labels jmp in |
---|
| 634 | let 〈fst_5_addr, rest_addr〉 ≝ split ? 5 11 address in |
---|
| 635 | let 〈fst_5_pc, rest_pc〉 ≝ split ? 5 11 pc in |
---|
| 636 | if eq_bv ? fst_5_addr fst_5_pc then |
---|
| 637 | let address ≝ ADDR11 rest_addr in |
---|
| 638 | Some ? ([ AJMP address ]) |
---|
| 639 | else |
---|
| 640 | None ? |
---|
| 641 | | long_jump ⇒ |
---|
| 642 | let address ≝ ADDR16 (lookup_labels jmp) in |
---|
| 643 | Some ? [ LJMP address ] |
---|
| 644 | ] |
---|
| 645 | ]. |
---|
[825] | 646 | @ I |
---|
| 647 | qed. |
---|
| 648 | |
---|
[914] | 649 | let rec jump_expansion_internal (n: nat) (program: pseudo_assembly_program) |
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| 650 | (old_labels: BitVectorTrie Word 16) (old_policy: BitVectorTrie jump_length 16) |
---|
| 651 | on n: jump_expansion_policy ≝ |
---|
| 652 | match n with |
---|
| 653 | [ O ⇒ old_policy |
---|
| 654 | | S n' ⇒ |
---|
| 655 | let 〈new_labels, new_policy, ch〉 ≝ |
---|
| 656 | jump_expansion_policy_internal program old_labels old_policy in |
---|
| 657 | jump_expansion_internal n' program new_labels new_policy ]. |
---|
[987] | 658 | |
---|
[989] | 659 | (**************************************** START OF POLICY ABSTRACTION ********************) |
---|
| 660 | |
---|
[987] | 661 | definition policy_type ≝ Word → jump_length. |
---|
| 662 | |
---|
| 663 | definition jump_expansion': pseudo_assembly_program → policy_type ≝ |
---|
| 664 | λprogram.λpc. |
---|
[914] | 665 | let policy ≝ jump_expansion_internal (length ? (\snd program)) program (Stub ? ?) (Stub ? ?) in |
---|
| 666 | lookup ? ? pc policy long_jump. |
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| 667 | |
---|
[993] | 668 | definition assembly_1_pseudoinstruction_safe ≝ |
---|
[913] | 669 | λprogram: pseudo_assembly_program. |
---|
[987] | 670 | λjump_expansion: policy_type. |
---|
[922] | 671 | λppc: Word. |
---|
[913] | 672 | λpc: Word. |
---|
[832] | 673 | λlookup_labels. |
---|
| 674 | λlookup_datalabels. |
---|
| 675 | λi. |
---|
[987] | 676 | let expansion ≝ jump_expansion ppc in |
---|
[836] | 677 | match expand_pseudo_instruction lookup_labels lookup_datalabels pc expansion i with |
---|
[832] | 678 | [ None ⇒ None ? |
---|
[836] | 679 | | Some pseudos ⇒ |
---|
| 680 | let mapped ≝ map ? ? assembly1 pseudos in |
---|
| 681 | let flattened ≝ flatten ? mapped in |
---|
[922] | 682 | let pc_len ≝ length ? flattened in |
---|
| 683 | Some ? (〈pc_len, flattened〉) |
---|
[832] | 684 | ]. |
---|
[913] | 685 | |
---|
[993] | 686 | definition construct_costs_safe ≝ |
---|
[832] | 687 | λprogram. |
---|
[987] | 688 | λjump_expansion: policy_type. |
---|
[922] | 689 | λpseudo_program_counter: nat. |
---|
[832] | 690 | λprogram_counter: nat. |
---|
| 691 | λcosts: BitVectorTrie Word 16. |
---|
| 692 | λi. |
---|
| 693 | match i with |
---|
[840] | 694 | [ Cost cost ⇒ |
---|
[832] | 695 | let program_counter_bv ≝ bitvector_of_nat ? program_counter in |
---|
| 696 | Some ? 〈program_counter, (insert ? ? program_counter_bv cost costs)〉 |
---|
| 697 | | _ ⇒ |
---|
| 698 | let pc_bv ≝ bitvector_of_nat ? program_counter in |
---|
[922] | 699 | let ppc_bv ≝ bitvector_of_nat ? pseudo_program_counter in |
---|
[993] | 700 | let lookup_labels ≝ λx.pc_bv in |
---|
| 701 | let lookup_datalabels ≝ λx.zero ? in |
---|
[836] | 702 | let pc_delta_assembled ≝ |
---|
[993] | 703 | assembly_1_pseudoinstruction_safe program jump_expansion ppc_bv pc_bv |
---|
[836] | 704 | lookup_labels lookup_datalabels i |
---|
| 705 | in |
---|
| 706 | match pc_delta_assembled with |
---|
[832] | 707 | [ None ⇒ None ? |
---|
[836] | 708 | | Some pc_delta_assembled ⇒ |
---|
| 709 | let 〈pc_delta, assembled〉 ≝ pc_delta_assembled in |
---|
[837] | 710 | Some ? 〈pc_delta + program_counter, costs〉 |
---|
[832] | 711 | ] |
---|
| 712 | ]. |
---|
| 713 | |
---|
[985] | 714 | (* This establishes the correspondence between pseudo program counters and |
---|
| 715 | program counters. It is at the heart of the proof. *) |
---|
| 716 | (*CSC: code taken from build_maps *) |
---|
[987] | 717 | definition sigma00: pseudo_assembly_program → policy_type → list ? → option (nat × (nat × (BitVectorTrie Word 16))) ≝ |
---|
| 718 | λinstr_list. |
---|
| 719 | λjump_expansion: policy_type. |
---|
| 720 | λl:list labelled_instruction. |
---|
[985] | 721 | foldl ?? |
---|
| 722 | (λt,i. |
---|
[832] | 723 | match t with |
---|
| 724 | [ None ⇒ None ? |
---|
[985] | 725 | | Some ppc_pc_map ⇒ |
---|
| 726 | let 〈ppc,pc_map〉 ≝ ppc_pc_map in |
---|
| 727 | let 〈program_counter, sigma_map〉 ≝ pc_map in |
---|
| 728 | let 〈label, i〉 ≝ i in |
---|
[993] | 729 | match construct_costs_safe instr_list jump_expansion ppc program_counter (Stub …) i with |
---|
[832] | 730 | [ None ⇒ None ? |
---|
[985] | 731 | | Some pc_ignore ⇒ |
---|
| 732 | let 〈pc,ignore〉 ≝ pc_ignore in |
---|
| 733 | Some … 〈S ppc,〈pc, insert ? ? (bitvector_of_nat ? ppc) (bitvector_of_nat ? pc) sigma_map〉〉 ] |
---|
| 734 | ]) (Some ? 〈0, 〈0, (Stub ? ?)〉〉) l. |
---|
| 735 | |
---|
[987] | 736 | definition sigma0: pseudo_assembly_program → policy_type → option (nat × (nat × (BitVectorTrie Word 16))) |
---|
| 737 | ≝ λprog.λjump_expansion.sigma00 prog jump_expansion (\snd prog). |
---|
[985] | 738 | |
---|
[987] | 739 | definition tech_pc_sigma00: pseudo_assembly_program → policy_type → list labelled_instruction → option (nat × nat) ≝ |
---|
| 740 | λprogram,jump_expansion,instr_list. |
---|
| 741 | match sigma00 program jump_expansion instr_list with |
---|
[985] | 742 | [ None ⇒ None … |
---|
| 743 | | Some result ⇒ |
---|
| 744 | let 〈ppc,pc_sigma_map〉 ≝ result in |
---|
| 745 | let 〈pc,map〉 ≝ pc_sigma_map in |
---|
| 746 | Some … 〈ppc,pc〉 ]. |
---|
| 747 | |
---|
[987] | 748 | definition sigma_safe: pseudo_assembly_program → policy_type → option (Word → Word) ≝ |
---|
| 749 | λinstr_list,jump_expansion. |
---|
| 750 | match sigma0 instr_list jump_expansion with |
---|
[832] | 751 | [ None ⇒ None ? |
---|
| 752 | | Some result ⇒ |
---|
[985] | 753 | let 〈ppc,pc_sigma_map〉 ≝ result in |
---|
| 754 | let 〈pc, sigma_map〉 ≝ pc_sigma_map in |
---|
[832] | 755 | if gtb pc (2^16) then |
---|
| 756 | None ? |
---|
| 757 | else |
---|
[985] | 758 | Some ? (λx.lookup ?? x sigma_map (zero …)) ]. |
---|
[832] | 759 | |
---|
[985] | 760 | (* stuff about policy *) |
---|
| 761 | |
---|
[987] | 762 | definition policy_ok ≝ λjump_expansion,p. sigma_safe p jump_expansion ≠ None …. |
---|
[985] | 763 | |
---|
[987] | 764 | definition policy ≝ λp. Σjump_expansion:policy_type. policy_ok jump_expansion p. |
---|
| 765 | |
---|
| 766 | lemma eject_policy: ∀p. policy p → policy_type. |
---|
| 767 | #p #pol @(eject … pol) |
---|
| 768 | qed. |
---|
| 769 | |
---|
| 770 | coercion eject_policy nocomposites: ∀p.∀pol:policy p. policy_type ≝ eject_policy on _pol:(policy ?) to policy_type. |
---|
| 771 | |
---|
| 772 | definition sigma: ∀p:pseudo_assembly_program. policy p → Word → Word ≝ |
---|
| 773 | λp,policy. |
---|
| 774 | match sigma_safe p (eject … policy) return λr:option (Word → Word). r ≠ None … → Word → Word with |
---|
[985] | 775 | [ None ⇒ λabs. ⊥ |
---|
[987] | 776 | | Some r ⇒ λ_.r] (sig2 … policy). |
---|
[993] | 777 | cases abs /2/ |
---|
[985] | 778 | qed. |
---|
| 779 | |
---|
[987] | 780 | example sigma_0: ∀p,pol. sigma p pol (bitvector_of_nat ? 0) = bitvector_of_nat ? 0. |
---|
[985] | 781 | cases daemon. |
---|
| 782 | qed. |
---|
| 783 | |
---|
[993] | 784 | (* MAIN AXIOM HERE, HIDDEN USING cases daemon *) |
---|
| 785 | definition assembly_1_pseudoinstruction: |
---|
| 786 | ∀program:pseudo_assembly_program.∀pol: policy program. |
---|
| 787 | ∀ppc:Word.∀lookup_labels,lookup_datalabels,pi. |
---|
| 788 | lookup_labels = (λx. sigma program pol (address_of_word_labels_code_mem (\snd program) x)) → |
---|
| 789 | lookup_datalabels = (λx. lookup ?? x (construct_datalabels (\fst program)) (zero ?)) → |
---|
| 790 | \fst (fetch_pseudo_instruction (\snd program) ppc) = pi → |
---|
| 791 | Σres:(nat × (list Byte)). |
---|
| 792 | let 〈len,code〉 ≝ res in |
---|
| 793 | sigma program pol (\snd (half_add ? ppc (bitvector_of_nat ? 1))) = |
---|
| 794 | bitvector_of_nat … (nat_of_bitvector … (sigma program pol ppc) + len) |
---|
| 795 | ≝ λprogram: pseudo_assembly_program. |
---|
| 796 | λpol: policy program. |
---|
| 797 | λppc: Word. |
---|
| 798 | λlookup_labels. |
---|
| 799 | λlookup_datalabels. |
---|
| 800 | λpi. |
---|
| 801 | λprf1,prf2,prf3. |
---|
| 802 | match assembly_1_pseudoinstruction_safe program pol ppc (sigma program pol ppc) lookup_labels lookup_datalabels pi with |
---|
| 803 | [ None ⇒ let dummy ≝ 〈0,[ ]〉 in dummy |
---|
| 804 | | Some res ⇒ res ]. |
---|
| 805 | [ @⊥ elim pi in p [*] |
---|
| 806 | try (#ARG1 #ARG2 #ARG3 #abs) try (#ARG1 #ARG2 #abs) try (#ARG1 #abs) try #abs |
---|
| 807 | generalize in match (jmeq_to_eq ??? abs) -abs; #abs whd in abs:(??%?); try destruct(abs) |
---|
| 808 | whd in abs:(??match % with [_ ⇒ ? | _ ⇒ ?]?); |
---|
| 809 | (* WRONG HERE, NEEDS LEMMA SAYING THAT THE POLICY DOES NOT RETURN MEDIUM! *) |
---|
| 810 | cases daemon |
---|
| 811 | | cases res in p ⊢ %; -res; #len #code #EQ normalize nodelta; |
---|
| 812 | (* THIS SHOULD BE TRUE INSTEAD *) |
---|
| 813 | cases daemon] |
---|
| 814 | qed. |
---|
| 815 | |
---|
| 816 | (* MAIN AXIOM HERE, HIDDEN USING cases daemon *) |
---|
| 817 | definition construct_costs': |
---|
| 818 | ∀program. policy program → nat → nat → ? → ? → |
---|
| 819 | Σres:(nat × (BitVectorTrie Word 16)). True |
---|
| 820 | ≝ |
---|
| 821 | λprogram.λpol: policy program.λppc,pc,costs,i. |
---|
| 822 | match construct_costs_safe program pol ppc pc costs i with |
---|
| 823 | [ None ⇒ let dummy ≝ 〈0, Stub ??〉 in dummy |
---|
| 824 | | Some res ⇒ res ]. |
---|
| 825 | [ cases daemon |
---|
| 826 | | %] |
---|
| 827 | qed. |
---|
| 828 | |
---|
| 829 | definition construct_costs ≝ |
---|
| 830 | λprogram,pol,ppc,pc,costs,i. eject … (construct_costs' program pol ppc pc costs i). |
---|
| 831 | |
---|
[985] | 832 | axiom construct_costs_sigma: |
---|
[993] | 833 | ∀p.∀pol:policy p.∀ppc,pc,costs,i. |
---|
[987] | 834 | bitvector_of_nat ? pc = sigma p pol (bitvector_of_nat ? ppc) → |
---|
[993] | 835 | bitvector_of_nat ? (\fst (construct_costs p pol ppc pc costs i)) = sigma p pol (bitvector_of_nat 16 (S ppc)). |
---|
[985] | 836 | |
---|
| 837 | axiom tech_pc_sigma00_append_Some: |
---|
[993] | 838 | ∀program.∀pol:policy program.∀prefix,costs,label,i,ppc,pc. |
---|
[987] | 839 | tech_pc_sigma00 program pol prefix = Some … 〈ppc,pc〉 → |
---|
[993] | 840 | tech_pc_sigma00 program pol (prefix@[〈label,i〉]) = Some … 〈S ppc,\fst (construct_costs program pol … ppc pc costs i)〉. |
---|
[985] | 841 | |
---|
[989] | 842 | definition build_maps: |
---|
| 843 | ∀pseudo_program.∀pol:policy pseudo_program. |
---|
| 844 | Σres:((BitVectorTrie Word 16) × (BitVectorTrie Word 16)). |
---|
| 845 | let 〈labels,costs〉 ≝ res in |
---|
| 846 | ∀id. occurs_exactly_once id (\snd pseudo_program) → |
---|
| 847 | lookup ?? id labels (zero …) = sigma pseudo_program pol (address_of_word_labels_code_mem (\snd pseudo_program) id) |
---|
[993] | 848 | ≝ |
---|
[987] | 849 | λpseudo_program.λpol:policy pseudo_program. |
---|
[985] | 850 | let result ≝ |
---|
| 851 | foldl_strong |
---|
| 852 | (option Identifier × pseudo_instruction) |
---|
| 853 | (λpre. Σres:((BitVectorTrie Word 16) × (nat × (nat × (BitVectorTrie Word 16)))). |
---|
| 854 | let 〈labels,ppc_pc_costs〉 ≝ res in |
---|
| 855 | let 〈ppc',pc_costs〉 ≝ ppc_pc_costs in |
---|
| 856 | let 〈pc',costs〉 ≝ pc_costs in |
---|
[993] | 857 | And ( And ( |
---|
| 858 | And (bitvector_of_nat ? pc' = sigma pseudo_program pol (bitvector_of_nat ? ppc')) (*∧*) |
---|
| 859 | (ppc' = length … pre)) (*∧ *) |
---|
| 860 | (tech_pc_sigma00 pseudo_program (eject … pol) pre = Some ? 〈ppc',pc'〉)) (*∧*) |
---|
| 861 | (∀id. occurs_exactly_once id pre → |
---|
| 862 | lookup ?? id labels (zero …) = sigma pseudo_program pol (address_of_word_labels_code_mem pre id))) |
---|
[985] | 863 | (\snd pseudo_program) |
---|
| 864 | (λprefix,i,tl,prf,t. |
---|
| 865 | let 〈labels, ppc_pc_costs〉 ≝ t in |
---|
| 866 | let 〈ppc, pc_costs〉 ≝ ppc_pc_costs in |
---|
| 867 | let 〈pc,costs〉 ≝ pc_costs in |
---|
| 868 | let 〈label, i'〉 ≝ i in |
---|
| 869 | let labels ≝ |
---|
| 870 | match label with |
---|
| 871 | [ None ⇒ labels |
---|
| 872 | | Some label ⇒ |
---|
| 873 | let program_counter_bv ≝ bitvector_of_nat ? pc in |
---|
[993] | 874 | insert ? ? label program_counter_bv labels] |
---|
[985] | 875 | in |
---|
[993] | 876 | let construct ≝ construct_costs pseudo_program pol ppc pc costs i' in |
---|
| 877 | 〈labels, 〈S ppc,construct〉〉 |
---|
[985] | 878 | ) 〈(Stub ? ?), 〈0, 〈0, Stub ? ?〉〉〉 |
---|
| 879 | in |
---|
| 880 | let 〈labels, ppc_pc_costs〉 ≝ result in |
---|
| 881 | let 〈ppc,pc_costs〉 ≝ ppc_pc_costs in |
---|
| 882 | let 〈pc, costs〉 ≝ pc_costs in |
---|
| 883 | 〈labels, costs〉. |
---|
[993] | 884 | [2: whd generalize in match (sig2 … t) >p >p1 >p2 >p3 * * * #IHn1 #IH0 #IH1 #IH2 |
---|
| 885 | generalize in match (refl … construct); cases construct in ⊢ (???% → %) #PC #CODE #JMEQ % [% [%]] |
---|
| 886 | [ <(construct_costs_sigma … costs i1 IHn1) change with (? = ?(\fst construct)) >JMEQ % |
---|
[985] | 887 | | >length_append <IH0 normalize; -IHn1; (*CSC: otherwise it diverges!*) // |
---|
[993] | 888 | | >(tech_pc_sigma00_append_Some … costs … IH1) change with (Some … 〈S ppc,\fst construct〉 = ?) >JMEQ % |
---|
[985] | 889 | | #id normalize nodelta; -labels1; cases label; normalize nodelta |
---|
| 890 | [ #K <address_of_word_labels_code_mem_None [2:@K] @IH2 -IHn1; (*CSC: otherwise it diverges!*) // |
---|
| 891 | | #l #H generalize in match (occurs_exactly_once_Some ???? H) in ⊢ ?; |
---|
| 892 | generalize in match (refl … (eq_bv ? l id)); cases (eq_bv … l id) in ⊢ (???% → %) |
---|
| 893 | [ #EQ #_ <(eq_bv_eq … EQ) >lookup_insert_hit >address_of_word_labels_code_mem_Some_hit |
---|
| 894 | <IH0 [@IHn1 | <(eq_bv_eq … EQ) in H #H @H] |
---|
| 895 | | #EQ change with (occurs_exactly_once ?? → ?) #K >lookup_insert_miss [2: -IHn1; /2/] |
---|
| 896 | <(address_of_word_labels_code_mem_Some_miss … EQ … H) @IH2 -IHn1; //]]] |
---|
[993] | 897 | |3: whd % [% [%]] // [>sigma_0//] #id normalize in ⊢ (% → ?) #abs @⊥ // |
---|
| 898 | | generalize in match (sig2 … result) in ⊢ ?; |
---|
| 899 | normalize nodelta in p ⊢ %; -result; >p in ⊢ (match % with [_ ⇒ ?] → ?) |
---|
| 900 | normalize nodelta; >p1 normalize nodelta; >p2; normalize nodelta; * #_; #H @H] |
---|
[985] | 901 | qed. |
---|
| 902 | |
---|
[993] | 903 | definition assembly: |
---|
| 904 | ∀p:pseudo_assembly_program. policy p → list Byte × (BitVectorTrie Identifier 16) ≝ |
---|
| 905 | λp.let 〈preamble, instr_list〉 ≝ p in |
---|
| 906 | λpol. |
---|
| 907 | let 〈labels,costs〉 ≝ build_maps 〈preamble,instr_list〉 pol in |
---|
[985] | 908 | let datalabels ≝ construct_datalabels preamble in |
---|
| 909 | let lookup_labels ≝ λx. lookup ? ? x labels (zero ?) in |
---|
| 910 | let lookup_datalabels ≝ λx. lookup ? ? x datalabels (zero ?) in |
---|
[993] | 911 | let result ≝ |
---|
| 912 | foldl_strong |
---|
| 913 | (option Identifier × pseudo_instruction) |
---|
| 914 | (λpre. Σpc_ppc_code:(Word × (Word × (list Byte))). |
---|
| 915 | let 〈pc,ppc_code〉 ≝ pc_ppc_code in |
---|
| 916 | let 〈ppc,code〉 ≝ ppc_code in |
---|
| 917 | ∀ppc'. |
---|
| 918 | let 〈pi,newppc〉 ≝ fetch_pseudo_instruction instr_list ppc' in |
---|
| 919 | let 〈len,assembledi〉 ≝ |
---|
| 920 | assembly_1_pseudoinstruction 〈preamble,instr_list〉 pol ppc' lookup_labels lookup_datalabels pi ??? in |
---|
| 921 | True) |
---|
| 922 | instr_list |
---|
| 923 | (λprefix,hd,tl,prf,pc_ppc_code. |
---|
| 924 | let 〈pc, ppc_code〉 ≝ pc_ppc_code in |
---|
| 925 | let 〈ppc, code〉 ≝ ppc_code in |
---|
| 926 | let 〈pc_delta, program〉 ≝ assembly_1_pseudoinstruction 〈preamble,instr_list〉 pol ppc lookup_labels lookup_datalabels (\snd hd) ??? in |
---|
| 927 | let 〈new_pc, flags〉 ≝ add_16_with_carry pc (bitvector_of_nat ? pc_delta) false in |
---|
| 928 | let new_ppc ≝ \snd (half_add ? ppc (bitvector_of_nat ? 1)) in |
---|
| 929 | 〈new_pc, 〈new_ppc, (code @ program)〉〉) |
---|
| 930 | 〈(zero ?), 〈(zero ?), [ ]〉〉 |
---|
[985] | 931 | in |
---|
[993] | 932 | 〈\snd (\snd result), costs〉. |
---|
| 933 | [2,5: % |
---|
| 934 | |*: cases daemon ] |
---|
| 935 | qed. |
---|
[832] | 936 | |
---|
[820] | 937 | definition assembly_unlabelled_program: assembly_program → option (list Byte × (BitVectorTrie Identifier 16)) ≝ |
---|
[993] | 938 | λp. Some ? (〈foldr ? ? (λi,l. assembly1 i @ l) [ ] p, Stub …〉). |
---|