[3378] | 1 | include "Common.ma". |
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| 2 | |
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| 3 | inductive instr: Type[0] := |
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| 4 | | Iconst: nat → instr |
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| 5 | | Ivar: option ident → instr |
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| 6 | | Isetvar: option ident → instr |
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| 7 | | Iadd: instr |
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| 8 | | Isub: instr |
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[3379] | 9 | | Ijmp: nat → instr |
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| 10 | | Ibne: nat → instr |
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| 11 | | Ibge: nat → instr |
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[3378] | 12 | | Ihalt: instr |
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[3379] | 13 | | Iio: instr |
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| 14 | | Icall: fname → instr |
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[3378] | 15 | | Iret: fname → instr. |
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| 16 | |
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| 17 | definition programT ≝ fname → list instr. |
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| 18 | |
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| 19 | definition fetch: list instr → nat → option instr ≝ λl,n. nth_opt ? n l. |
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| 20 | |
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| 21 | definition stackT: Type[0] ≝ list nat. |
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| 22 | |
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| 23 | definition vmstate ≝ λS:storeT. (list instr) × nat × (stackT × S). |
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| 24 | |
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[3379] | 25 | definition pc: ∀S. vmstate S → nat ≝ λS,s. \snd (\fst s). |
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| 26 | |
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| 27 | inductive vmstep (p: programT) (S: storeT) : vmstate S → vmstate S → Prop := |
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[3378] | 28 | | vmstep_const: ∀c,pc,stk,s,n. fetch c pc = Some … (Iconst n) → |
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| 29 | vmstep … |
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| 30 | 〈c, pc, stk, s〉 |
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| 31 | 〈c, 1 + pc, n :: stk, s〉 |
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| 32 | | vmstep_var: ∀c,pc,stk,s,x. fetch c pc = Some … (Ivar x) → |
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| 33 | vmstep … |
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| 34 | 〈c, pc, stk, s〉 |
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| 35 | 〈c, 1 + pc, get … s x :: stk, s〉 |
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| 36 | | vmstep_setvar: ∀c,pc,stk,s,x,n. fetch c pc = Some … (Isetvar x) → |
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| 37 | vmstep … |
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| 38 | 〈c, pc, n :: stk, s〉 |
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| 39 | 〈c, 1 + pc, stk, set … s x n〉 |
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| 40 | | vmstep_add: ∀c,pc,stk,s,n1,n2. fetch c pc = Some … Iadd → |
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| 41 | vmstep … |
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| 42 | 〈c, pc, n2 :: n1 :: stk, s〉 |
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| 43 | 〈c, 1 + pc, (n1 + n2) :: stk, s〉 |
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| 44 | | vmstep_sub: ∀c,pc,stk,s,n1,n2. fetch c pc = Some … Isub → |
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| 45 | vmstep … |
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| 46 | 〈c, pc, n2 :: n1 :: stk, s〉 |
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| 47 | 〈c, 1 + pc, (n1 - n2) :: stk, s〉 |
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[3379] | 48 | | vmstep_bne: ∀c,pc,stk,s,ofs,n1,n2. fetch c pc = Some … (Ibne ofs) → |
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[3378] | 49 | let pc' ≝ if eqb n1 n2 then 1 + pc else 1 + pc + ofs in |
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| 50 | vmstep … |
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| 51 | 〈c, pc, n2 :: n1 :: stk, s〉 |
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| 52 | 〈c, pc', stk, s〉 |
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[3379] | 53 | | vmstep_bge: ∀c,pc,stk,s,ofs,n1,n2. fetch c pc = Some … (Ibge ofs) → |
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[3378] | 54 | let pc' ≝ if ltb n1 n2 then 1 + pc else 1 + pc + ofs in |
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| 55 | vmstep … |
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| 56 | 〈c, pc, n2 :: n1 :: stk, s〉 |
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| 57 | 〈c, pc', stk, s〉 |
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[3379] | 58 | | vmstep_branch: ∀c,pc,stk,s,ofs. fetch c pc = Some … (Ijmp ofs) → |
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[3378] | 59 | let pc' ≝ 1 + pc + ofs in |
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[3379] | 60 | vmstep … |
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| 61 | 〈c, pc, stk, s〉 |
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| 62 | 〈c, 1 + pc + ofs, stk, s〉 |
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| 63 | | vmstep_io: ∀c,pc,stk,s. fetch c pc = Some … Iio → |
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| 64 | vmstep … |
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| 65 | 〈c, pc, stk, s〉 |
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| 66 | 〈c, 1 + pc, stk, s〉. |
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[3378] | 67 | |
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[3379] | 68 | definition emitterT ≝ nat → nat → option label. |
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| 69 | |
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| 70 | definition vmlstep: ∀p: programT. ∀S: storeT. ∀emit: emitterT. |
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| 71 | vmstate S → vmstate S → list label → Prop ≝ |
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| 72 | λp,S,emitter,s1,s2,ll. ∀l. |
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| 73 | vmstep p S s1 s2 ∧ ll = [l] ∧ emitter (pc … s1) (pc … s2) = Some … l. |
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| 74 | |
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[3378] | 75 | (* |
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| 76 | Definition star_vm (lbl: Type) (c: code (instr_vm lbl)) := star (trans_vm lbl c). |
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| 77 | |
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| 78 | Definition term_vm_lbl (lbl: Type) (c: code (instr_vm lbl)) (s_init s_fin: store) (trace: list lbl) := |
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| 79 | exists pc, |
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| 80 | code_at c pc = Some (Ihalt lbl) /\ |
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| 81 | star_vm lbl c (0, nil, s_init) (pc, nil, s_fin) trace. |
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| 82 | |
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| 83 | Definition term_vm (c: code_vm) (s_init s_fin: store):= |
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| 84 | exists pc, |
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| 85 | code_at c pc = Some (Ihalt False) /\ |
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| 86 | star_vm False c (0, nil, s_init) (pc, nil, s_fin) nil. |
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| 87 | |
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| 88 | Definition term_vml (c: code_vml) (s_init s_fin: store) (trace: list label) := |
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| 89 | exists pc, |
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| 90 | code_at c pc = Some (Ihalt label) /\ |
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| 91 | star_vm label c (0, nil, s_init) (pc, nil, s_fin) trace. |
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| 92 | *) |
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