| 1 | include "basics/lists/list.ma". |
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| 2 | include "common/Globalenvs.ma". |
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| 3 | include "common/IO.ma". |
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| 4 | include "common/SmallstepExec.ma". |
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| 5 | include "joint/BEMem.ma". |
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| 6 | include "joint/Joint_paolo.ma". |
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| 7 | include "ASM/I8051bis.ma". |
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| 8 | |
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| 9 | (* CSC: external functions never fail (??) and always return something of the |
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| 10 | size of one register, both in the frontend and in the backend. |
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| 11 | Is this reasonable??? In OCaml it always return a list, but in the frontend |
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| 12 | only the head is kept (or Undef if the list is empty) ??? *) |
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| 13 | |
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| 14 | definition genv ≝ λglobals.λp:params. genv_t (joint_function globals p). |
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| 15 | definition cpointer ≝ Σp.ptype p = Code. |
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| 16 | definition xpointer ≝ Σp.ptype p = XData. |
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| 17 | unification hint 0 ≔ ⊢ cpointer ≡ Sig pointer (λp.ptype p = Code). |
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| 18 | unification hint 0 ≔ ⊢ xpointer ≡ Sig pointer (λp.ptype p = XData). |
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| 19 | |
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| 20 | record sem_state_params : Type[1] ≝ |
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| 21 | { framesT: Type[0] |
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| 22 | ; empty_framesT: framesT |
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| 23 | ; regsT : Type[0] |
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| 24 | ; empty_regsT: xpointer → regsT (* Stack pointer *) |
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| 25 | }. |
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| 26 | |
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| 27 | record state (semp: sem_state_params): Type[0] ≝ |
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| 28 | { st_frms: framesT semp |
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| 29 | ; sp: xpointer |
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| 30 | ; isp: xpointer |
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| 31 | ; carry: beval |
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| 32 | ; regs: regsT semp |
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| 33 | ; m: bemem |
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| 34 | }. |
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| 35 | |
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| 36 | record state_pc (semp : sem_state_params) : Type[0] ≝ |
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| 37 | { st_no_pc :> state semp |
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| 38 | ; pc : cpointer |
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| 39 | }. |
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| 40 | |
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| 41 | definition set_m: ∀p. bemem → state p → state p ≝ |
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| 42 | λp,m,st. mk_state p (st_frms ?…st) (sp … st) (isp … st) (carry … st) (regs … st) m. |
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| 43 | |
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| 44 | definition set_regs: ∀p:sem_state_params. regsT p → state p → state p ≝ |
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| 45 | λp,regs,st. mk_state p (st_frms … st) (sp … st) (isp … st) (carry … st) regs (m … st). |
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| 46 | |
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| 47 | definition set_sp: ∀p. ? → state p → state p ≝ |
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| 48 | λp,sp,st. mk_state … (st_frms … st) sp (isp … st) (carry … st) (regs … st) (m … st). |
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| 49 | |
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| 50 | definition set_isp: ∀p. ? → state p → state p ≝ |
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| 51 | λp,isp,st. mk_state … (st_frms … st) (sp … st) isp (carry … st) (regs … st) (m … st). |
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| 52 | |
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| 53 | definition set_carry: ∀p. beval → state p → state p ≝ |
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| 54 | λp,carry,st. mk_state … (st_frms … st) (sp … st) (isp … st) carry (regs … st) (m … st). |
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| 55 | |
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| 56 | definition set_pc: ∀p. ? → state_pc p → state_pc p ≝ |
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| 57 | λp,pc,st. mk_state_pc … (st_no_pc … st) pc. |
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| 58 | |
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| 59 | definition set_no_pc: ∀p. ? → state_pc p → state_pc p ≝ |
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| 60 | λp,s,st. mk_state_pc … s (pc … st). |
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| 61 | |
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| 62 | definition set_frms: ∀p:sem_state_params. framesT p → state p → state p ≝ |
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| 63 | λp,frms,st. mk_state … frms (sp … st) (isp … st) (carry … st) (regs … st) (m … st). |
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| 64 | |
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| 65 | axiom BadProgramCounter : String. |
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| 66 | |
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| 67 | definition function_of_block : |
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| 68 | ∀pars : params. |
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| 69 | ∀globals. |
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| 70 | genv globals pars → |
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| 71 | block → |
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| 72 | res (joint_internal_function … pars) ≝ |
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| 73 | λpars,blobals,ge,b. |
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| 74 | do def ← opt_to_res ? [MSG BadProgramCounter] (find_funct_ptr … ge b) ; |
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| 75 | match def with |
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| 76 | [ Internal def' ⇒ OK … def' |
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| 77 | | External _ ⇒ Error … [MSG BadProgramCounter]]. |
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| 78 | |
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| 79 | (* this can replace graph_fetch function and lin_fetch_function *) |
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| 80 | definition fetch_function: |
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| 81 | ∀pars : params. |
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| 82 | ∀globals. |
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| 83 | genv globals pars → |
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| 84 | cpointer → |
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| 85 | res (joint_internal_function … pars) ≝ |
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| 86 | λpars,globals,ge,p.function_of_block pars globals ge (pblock p). |
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| 87 | |
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| 88 | inductive step_flow (p : params) (globals : list ident) (labels : list label) : Type[0] ≝ |
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| 89 | | Redirect : (Σl.In ? labels l) → step_flow p globals labels (* used for goto-like flow alteration *) |
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| 90 | | Init : Z → joint_internal_function globals p → call_args p → call_dest p → step_flow p globals labels (* call a function with given id, then proceed *) |
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| 91 | | Proceed : step_flow p globals labels. (* go to implicit successor *) |
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| 92 | |
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| 93 | definition step_flow_cons : ∀p,globals,l,lbls. |
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| 94 | step_flow p globals lbls → step_flow p globals (l :: lbls) ≝ |
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| 95 | λp,globals,l1,l2,flow.match flow with |
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| 96 | [ Redirect l ⇒ Redirect … «l, ?» |
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| 97 | | Init id f args dest ⇒ Init … id f args dest |
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| 98 | | Proceed ⇒ Proceed ??? |
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| 99 | ]. cases l /2 by or_intror/ qed. |
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| 100 | coercion step_flow_c : ∀p,globals,l1,l2.∀flow : step_flow p globals l2.step_flow p globals (l1::l2) ≝ |
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| 101 | step_flow_cons on _flow : step_flow ??? to step_flow ?? (cons ???). |
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| 102 | |
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| 103 | definition step_flow_append_l : ∀p,globals,l1,l2. |
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| 104 | step_flow p globals l1 → step_flow p globals (l1 @ l2) ≝ |
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| 105 | λp,globals,l1,l2,flow.match flow with |
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| 106 | [ Redirect l ⇒ Redirect … «l, ?» |
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| 107 | | Init id f args dest ⇒ Init … id f args dest |
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| 108 | | Proceed ⇒ Proceed ??? |
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| 109 | ]. cases l /2 by Exists_append_l/ qed. |
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| 110 | coercion step_flow_l : ∀p,globals,l1,l2.∀flow : step_flow p globals l1.step_flow p globals (l1@l2) ≝ |
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| 111 | step_flow_append_l on _flow : step_flow ??? to step_flow ?? (append ???). |
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| 112 | |
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| 113 | definition step_flow_append_r : ∀p,globals,l1,l2. |
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| 114 | step_flow p globals l2 → step_flow p globals (l1 @ l2) ≝ |
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| 115 | λp,globals,l1,l2,flow.match flow with |
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| 116 | [ Redirect l ⇒ Redirect … «l, ?» |
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| 117 | | Init id f args dest ⇒ Init … id f args dest |
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| 118 | | Proceed ⇒ Proceed ??? |
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| 119 | ]. cases l /2 by Exists_append_r/ qed. |
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| 120 | coercion step_flow_r : ∀p,globals,l1,l2.∀flow : step_flow p globals l2.step_flow p globals (l1@l2) ≝ |
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| 121 | step_flow_append_r on _flow : step_flow ??? to step_flow ?? (append ???). |
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| 122 | |
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| 123 | inductive fin_step_flow (p : params) (globals : list ident) (labels : list label): Type[0] ≝ |
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| 124 | | FRedirect : (Σl.In ? labels l) → fin_step_flow p globals labels |
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| 125 | | FTailInit : Z → joint_internal_function globals p → call_args p → fin_step_flow p globals labels |
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| 126 | | FEnd : fin_step_flow p globals labels. (* end flow *) |
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| 127 | |
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| 128 | definition fin_step_flow_cons : ∀p,globals,l,lbls. |
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| 129 | fin_step_flow p globals lbls → fin_step_flow p globals (l :: lbls) ≝ |
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| 130 | λp,globals,l1,l2,flow.match flow with |
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| 131 | [ FRedirect l ⇒ FRedirect … «l, ?» |
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| 132 | | FTailInit id f args ⇒ FTailInit … id f args |
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| 133 | | FEnd ⇒ FEnd ??? |
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| 134 | ]. cases l /2 by or_intror/ qed. |
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| 135 | coercion fin_step_flow_c : ∀p,globals,l1,l2.∀flow : fin_step_flow p globals l2.fin_step_flow p globals (l1::l2) ≝ |
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| 136 | fin_step_flow_cons on _flow : fin_step_flow ??? to fin_step_flow ?? (cons ???). |
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| 137 | |
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| 138 | definition fin_step_flow_append_l : ∀p,globals,l1,l2. |
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| 139 | fin_step_flow p globals l1 → fin_step_flow p globals (l1@l2) ≝ |
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| 140 | λp,globals,l1,l2,flow.match flow with |
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| 141 | [ FRedirect l ⇒ FRedirect … «l, ?» |
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| 142 | | FTailInit id f args ⇒ FTailInit … id f args |
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| 143 | | FEnd ⇒ FEnd ??? |
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| 144 | ]. cases l /2 by Exists_append_l/ qed. |
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| 145 | coercion fin_step_flow_l : ∀p,globals,l1,l2.∀flow : fin_step_flow p globals l1.fin_step_flow p globals (l1@l2) ≝ |
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| 146 | fin_step_flow_append_l on _flow : fin_step_flow ??? to fin_step_flow ?? (append ???). |
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| 147 | |
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| 148 | definition fin_step_flow_append_r : ∀p,globals,l1,l2. |
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| 149 | fin_step_flow p globals l2 → fin_step_flow p globals (l1@l2) ≝ |
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| 150 | λp,globals,l1,l2,flow.match flow with |
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| 151 | [ FRedirect l ⇒ FRedirect … «l, ?» |
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| 152 | | FTailInit id f args ⇒ FTailInit … id f args |
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| 153 | | FEnd ⇒ FEnd ??? |
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| 154 | ]. cases l /2 by Exists_append_r/ qed. |
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| 155 | coercion fin_step_flow_r : ∀p,globals,l1,l2.∀flow : fin_step_flow p globals l2.fin_step_flow p globals (l1@l2) ≝ |
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| 156 | fin_step_flow_append_r on _flow : fin_step_flow ??? to fin_step_flow ?? (append ???). |
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| 157 | |
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| 158 | record more_sem_unserialized_params (uns_pars : unserialized_params) : Type[1] ≝ |
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| 159 | { st_pars :> sem_state_params |
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| 160 | ; acca_store_ : acc_a_reg uns_pars → beval → regsT st_pars → res (regsT st_pars) |
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| 161 | ; acca_retrieve_ : regsT st_pars → acc_a_reg uns_pars → res beval |
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| 162 | ; acca_arg_retrieve_ : regsT st_pars → acc_a_arg uns_pars → res beval |
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| 163 | ; accb_store_ : acc_b_reg uns_pars → beval → regsT st_pars → res (regsT st_pars) |
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| 164 | ; accb_retrieve_ : regsT st_pars → acc_b_reg uns_pars → res beval |
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| 165 | ; accb_arg_retrieve_ : regsT st_pars → acc_b_arg uns_pars → res beval |
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| 166 | ; dpl_store_ : dpl_reg uns_pars → beval → regsT st_pars → res (regsT st_pars) |
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| 167 | ; dpl_retrieve_ : regsT st_pars → dpl_reg uns_pars → res beval |
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| 168 | ; dpl_arg_retrieve_ : regsT st_pars → dpl_arg uns_pars → res beval |
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| 169 | ; dph_store_ : dph_reg uns_pars → beval → regsT st_pars → res (regsT st_pars) |
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| 170 | ; dph_retrieve_ : regsT st_pars → dph_reg uns_pars → res beval |
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| 171 | ; dph_arg_retrieve_ : regsT st_pars → dph_arg uns_pars → res beval |
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| 172 | ; snd_arg_retrieve_ : regsT st_pars → snd_arg uns_pars → res beval |
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| 173 | ; pair_reg_move_ : regsT st_pars → pair_move uns_pars → res (regsT st_pars) |
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| 174 | ; fetch_ra: state st_pars → res ((state st_pars) × cpointer) |
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| 175 | |
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| 176 | ; allocate_local : localsT uns_pars → regsT st_pars → regsT st_pars |
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| 177 | (* Paolo: save_frame separated from call_setup to factorize tailcall code *) |
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| 178 | ; save_frame: cpointer → call_dest uns_pars → state st_pars → framesT st_pars |
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| 179 | (*CSC: setup_call returns a res only because we can call a function with the wrong number and |
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| 180 | type of arguments. To be fixed using a dependent type *) |
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| 181 | ; setup_call : nat → paramsT … uns_pars → call_args uns_pars → |
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| 182 | state st_pars → res (state st_pars) |
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| 183 | ; fetch_external_args: external_function → state st_pars → |
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| 184 | res (list val) |
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| 185 | ; set_result: list val → state st_pars → res (state st_pars) |
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| 186 | ; call_args_for_main: call_args uns_pars |
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| 187 | ; call_dest_for_main: call_dest uns_pars |
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| 188 | }. |
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| 189 | |
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| 190 | |
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| 191 | definition helper_def_retrieve : |
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| 192 | ∀X : ? → ? → Type[0]. |
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| 193 | (∀up.∀p:more_sem_unserialized_params up. regsT p → X up p → res beval) → |
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| 194 | ∀up.∀p : more_sem_unserialized_params up.state p → X up p → res beval ≝ |
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| 195 | λX,f,up,p,st.f ? p (regs … st). |
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| 196 | |
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| 197 | definition helper_def_store : |
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| 198 | ∀X : ? → ? → Type[0]. |
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| 199 | (∀up.∀p : more_sem_unserialized_params up.X up p → beval → regsT p → res (regsT p)) → |
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| 200 | ∀up.∀p : more_sem_unserialized_params up.X up p → beval → state p → res (state p) ≝ |
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| 201 | λX,f,up,p,x,v,st.! r ← f ? p x v (regs … st) ; return set_regs … r st. |
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| 202 | |
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| 203 | definition acca_retrieve ≝ helper_def_retrieve ? acca_retrieve_. |
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| 204 | definition acca_store ≝ helper_def_store ? acca_store_. |
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| 205 | definition acca_arg_retrieve ≝ helper_def_retrieve ? acca_arg_retrieve_. |
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| 206 | definition accb_store ≝ helper_def_store ? accb_store_. |
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| 207 | definition accb_retrieve ≝ helper_def_retrieve ? accb_retrieve_. |
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| 208 | definition accb_arg_retrieve ≝ helper_def_retrieve ? accb_arg_retrieve_. |
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| 209 | definition dpl_store ≝ helper_def_store ? dpl_store_. |
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| 210 | definition dpl_retrieve ≝ helper_def_retrieve ? dpl_retrieve_. |
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| 211 | definition dpl_arg_retrieve ≝ helper_def_retrieve ? dpl_arg_retrieve_. |
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| 212 | definition dph_store ≝ helper_def_store ? dph_store_. |
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| 213 | definition dph_retrieve ≝ helper_def_retrieve ? dph_retrieve_. |
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| 214 | definition dph_arg_retrieve ≝ helper_def_retrieve ? dph_arg_retrieve_. |
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| 215 | definition snd_arg_retrieve ≝ helper_def_retrieve ? snd_arg_retrieve_. |
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| 216 | definition pair_reg_move : ?→?→?→?→? ≝ |
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| 217 | λup.λp : more_sem_unserialized_params up.λst : state p.λpm : pair_move up. |
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| 218 | ! r ← pair_reg_move_ ? p (regs ? st) pm; |
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| 219 | return set_regs ? r st. |
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| 220 | |
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| 221 | |
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| 222 | axiom BadPointer : String. |
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| 223 | |
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| 224 | (* this is preamble to all calls (including tail ones). The optional argument in |
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| 225 | input tells the function whether it has to save the frame for internal |
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| 226 | calls. |
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| 227 | the first element of the triple is the entry point of the function if |
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| 228 | it is an internal one, or false in case of an external one. |
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| 229 | The actual update of the pc is left to later, as it depends on |
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| 230 | serialization and on whether the call is a tail one. *) |
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| 231 | definition eval_call_block: |
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| 232 | ∀globals.∀p : params.∀p':more_sem_unserialized_params p.∀lbls. |
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| 233 | genv globals p → state p' → block → call_args p → call_dest p → |
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| 234 | IO io_out io_in ((step_flow p globals lbls)×(state p')) ≝ |
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| 235 | λglobals,p,p',lbls,ge,st,b,args,dest. |
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| 236 | ! fd ← (opt_to_res ? [MSG BadPointer] (find_funct_ptr … ge b) : IO ? io_in ?); |
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| 237 | match fd with |
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| 238 | [ Internal fn ⇒ |
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| 239 | return 〈Init … (block_id b) fn args dest, st〉 |
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| 240 | | External fn ⇒ |
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| 241 | ! params ← fetch_external_args … p' fn st : IO ???; |
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| 242 | ! evargs ← check_eventval_list params (sig_args (ef_sig fn)) : IO ???; |
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| 243 | ! evres ← do_io (ef_id fn) evargs (proj_sig_res (ef_sig fn)); |
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| 244 | (* CSC: XXX bug here; I think I should split it into Byte-long |
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| 245 | components; instead I am making a singleton out of it. To be |
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| 246 | fixed once we fully implement external functions. *) |
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| 247 | let vs ≝ [mk_val ? evres] in |
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| 248 | ! st ← set_result … p' vs st : IO ???; |
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| 249 | return 〈Proceed ???, st〉 |
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| 250 | ]. |
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| 251 | |
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| 252 | axiom FailedStore: String. |
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| 253 | |
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| 254 | definition push: ∀p.state p → beval → res (state p) ≝ |
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| 255 | λp,st,v. |
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| 256 | let isp' ≝ isp ? st in |
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| 257 | do m ← opt_to_res ? (msg FailedStore) (bestorev (m … st) isp' v); |
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| 258 | let isp'' ≝ shift_pointer … isp' [[false;false;false;false;false;false;false;true]] in |
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| 259 | return set_m … m (set_isp … isp'' st). |
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| 260 | normalize elim (isp p st) // |
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| 261 | qed. |
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| 262 | |
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| 263 | definition pop: ∀p. state p → res ((state p ) × beval) ≝ |
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| 264 | λp,st. |
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| 265 | let isp' ≝ isp ? st in |
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| 266 | let isp'' ≝ neg_shift_pointer ? isp' [[false;false;false;false;false;false;false;true]] in |
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| 267 | let ist ≝ set_isp … isp'' st in |
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| 268 | do v ← opt_to_res ? (msg FailedStore) (beloadv (m ? st) isp''); |
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| 269 | OK ? 〈ist,v〉. |
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| 270 | normalize elim (isp p st) // |
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| 271 | qed. |
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| 272 | |
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| 273 | definition save_ra : ∀p. state p → cpointer → res (state p) ≝ |
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| 274 | λp,st,l. |
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| 275 | let 〈addrl,addrh〉 ≝ address_of_code_pointer l in |
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| 276 | ! st' ← push … st addrl; |
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| 277 | push … st' addrh. |
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| 278 | |
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| 279 | definition load_ra : ∀p.state p → res ((state p) × cpointer) ≝ |
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| 280 | λp,st. |
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| 281 | do 〈st',addrh〉 ← pop … st; |
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| 282 | do 〈st'',addrl〉 ← pop … st'; |
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| 283 | do pr ← code_pointer_of_address 〈addrh, addrl〉; |
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| 284 | return 〈st'', pr〉. |
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| 285 | |
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| 286 | (* parameters that need full params to have type of functions, |
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| 287 | but are still independent of serialization *) |
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| 288 | record more_sem_genv_params (pp : params) : Type[1] ≝ |
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| 289 | { msu_pars :> more_sem_unserialized_params pp |
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| 290 | ; read_result: ∀globals.genv globals pp → state msu_pars → res (list beval) |
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| 291 | (* change of pc must be left to *_flow execution *) |
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| 292 | ; exec_extended: ∀globals.genv globals pp → ∀s : ext_step pp. |
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| 293 | state msu_pars → |
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| 294 | IO io_out io_in ((step_flow pp globals (ext_step_labels … s))× (state msu_pars)) |
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| 295 | ; exec_fin_extended: ∀globals.genv globals pp → ∀s : ext_fin_stmt pp. |
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| 296 | state msu_pars → |
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| 297 | IO io_out io_in ((fin_step_flow pp globals (ext_fin_stmt_labels … s))×(state msu_pars)) |
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| 298 | ; pop_frame: ∀globals.genv globals pp → state msu_pars → res (state msu_pars) |
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| 299 | }. |
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| 300 | |
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| 301 | (* parameters that are defined by serialization *) |
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| 302 | record more_sem_params (pp : params) : Type[1] ≝ |
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| 303 | { msg_pars :> more_sem_genv_params pp |
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| 304 | ; offset_of_point : code_point pp → offset |
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| 305 | ; point_of_offset : offset → option (code_point pp) |
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| 306 | ; point_of_offset_of_point : ∀pt.point_of_offset (offset_of_point pt) = Some ? pt |
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| 307 | ; offset_of_point_of_offset : ∀o.opt_All ? (eq ? o) (! pt ← point_of_offset o ; return offset_of_point pt) |
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| 308 | }. |
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| 309 | |
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| 310 | definition pointer_of_point : ∀p.more_sem_params p → |
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| 311 | cpointer→ code_point p → cpointer ≝ |
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| 312 | λp,msp,ptr,pt. |
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| 313 | mk_pointer Code (pblock ptr) ? (offset_of_point p msp pt). |
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| 314 | [ elim ptr #ptr' #EQ <EQ @pok |
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| 315 | | %] qed. |
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| 316 | |
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| 317 | axiom BadOffsetForCodePoint : String. |
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| 318 | |
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| 319 | definition point_of_pointer : |
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| 320 | ∀p.more_sem_params p → cpointer → res (code_point p) ≝ |
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| 321 | λp,msp,ptr.opt_to_res … (msg BadOffsetForCodePoint) |
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| 322 | (point_of_offset p msp (poff ptr)). |
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| 323 | |
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| 324 | lemma point_of_pointer_of_point : |
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| 325 | ∀p,msp.∀ptr : cpointer.∀pt.point_of_pointer p msp (pointer_of_point p msp ptr pt) = return pt. |
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| 326 | #p #msp #ptr #pt normalize |
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| 327 | >point_of_offset_of_point % |
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| 328 | qed. |
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| 329 | |
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| 330 | lemma pointer_of_point_block : |
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| 331 | ∀p,msp,ptr,pt.pblock (pointer_of_point p msp ptr pt) = pblock ptr. |
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| 332 | / by refl/ |
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| 333 | qed. |
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| 334 | |
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| 335 | lemma pointer_of_point_uses_block : |
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| 336 | ∀p,msp.∀ptr1,ptr2 : cpointer.∀pt.pblock ptr1 = pblock ptr2 → pointer_of_point p msp ptr1 pt = pointer_of_point p msp ptr2 pt. |
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| 337 | #p #msp ** #ty1 #bl1 #H1 #o1 #EQ1 |
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| 338 | ** #ty2 #bl2 #H2 #o2 #EQ2 |
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| 339 | #pt #EQ3 destruct normalize // |
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| 340 | qed. |
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| 341 | |
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| 342 | lemma pointer_of_point_of_pointer : |
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| 343 | ∀p,msp.∀ptr1,ptr2 : cpointer.∀pt. |
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| 344 | pblock ptr1 = pblock ptr2 → point_of_pointer p msp ptr1 = OK … pt → |
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| 345 | pointer_of_point p msp ptr2 pt = ptr1. |
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| 346 | #p #msp ** #ty1 #bl1 #H1 #o1 #EQ1 |
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| 347 | ** #ty2 #bl2 #H2 #o2 #EQ2 #pt #EQ |
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| 348 | destruct |
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| 349 | lapply (offset_of_point_of_offset p msp o1) |
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| 350 | normalize |
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| 351 | elim (point_of_offset ???) normalize [* #ABS destruct(ABS)] |
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| 352 | #pt' #EQ #EQ' destruct % |
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| 353 | qed. |
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| 354 | |
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| 355 | |
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| 356 | axiom ProgramCounterOutOfCode : String. |
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| 357 | axiom PointNotFound : String. |
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| 358 | axiom LabelNotFound : String. |
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| 359 | |
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| 360 | definition fetch_statement: ∀p : params.∀ msp : more_sem_params p.∀globals. |
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| 361 | genv globals p → cpointer → res (joint_statement p globals) ≝ |
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| 362 | λp,msp,globals,ge,ptr. |
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| 363 | ! pt ← point_of_pointer ? msp ptr ; |
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| 364 | ! fn ← fetch_function … ge ptr ; |
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| 365 | opt_to_res … (msg ProgramCounterOutOfCode) (stmt_at … (joint_if_code … fn) pt). |
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| 366 | |
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| 367 | definition pointer_of_label_in_block : ∀p : params.∀ msp : more_sem_params p.∀globals. |
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| 368 | genv globals p → block → label → res cpointer ≝ |
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| 369 | λp,msp,globals,ge,b,lbl. |
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| 370 | ! fn ← function_of_block … ge b ; |
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| 371 | ! pt ← opt_to_res … [MSG LabelNotFound ; CTX ? lbl] |
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| 372 | (point_of_label … (joint_if_code … fn) lbl) ; |
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| 373 | return (mk_pointer Code (mk_block Code (block_id b)) ? (offset_of_point p msp pt) : Σp.?). // qed. |
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| 374 | |
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| 375 | definition pointer_of_label : ∀p : params.∀ msp : more_sem_params p.∀globals. |
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| 376 | genv globals p → cpointer → label → res cpointer ≝ |
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| 377 | λp,msp,globals,ge,ptr. |
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| 378 | pointer_of_label_in_block p msp globals ge (pblock ptr). |
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| 379 | |
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| 380 | definition succ_pc : ∀p : params.∀ msp : more_sem_params p. |
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| 381 | cpointer → succ p → res cpointer ≝ |
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| 382 | λp,msp,ptr,nxt. |
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| 383 | ! curr ← point_of_pointer p msp ptr ; |
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| 384 | return pointer_of_point p msp ptr (point_of_succ p curr nxt). |
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| 385 | |
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| 386 | record sem_params : Type[1] ≝ |
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| 387 | { spp :> params |
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| 388 | ; more_sem_pars :> more_sem_params spp |
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| 389 | }. |
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| 390 | |
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| 391 | (* definition address_of_label: ∀globals. ∀p:sem_params. |
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| 392 | genv globals p → pointer → label → res address ≝ |
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| 393 | λglobals,p,ge,ptr,l. |
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| 394 | do newptr ← pointer_of_label … p ? ge … ptr l ; |
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| 395 | OK … (address_of_code_pointer newptr). *) |
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| 396 | |
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| 397 | definition goto: ∀globals. ∀p:sem_params. |
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| 398 | genv globals p → label → state p → block → res (state_pc p) ≝ |
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| 399 | λglobals,p,ge,l,st,b. |
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| 400 | ! newpc ← pointer_of_label_in_block ? p … ge b l ; |
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| 401 | return mk_state_pc ? st newpc. |
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| 402 | |
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| 403 | (* |
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| 404 | definition empty_state: ∀p. more_sem_params p → state p ≝ |
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| 405 | mk_state … (empty_framesT …) |
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| 406 | *) |
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| 407 | |
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| 408 | definition next : ∀p : sem_params.succ p → state p → cpointer → res (state_pc p) ≝ |
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| 409 | λp,l,st,pc. |
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| 410 | ! newpc ← succ_pc ? p … pc l ; |
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| 411 | return mk_state_pc … st newpc. |
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| 412 | |
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| 413 | axiom MissingSymbol : String. |
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| 414 | axiom FailedLoad : String. |
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| 415 | axiom BadFunction : String. |
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| 416 | axiom SuccessorNotProvided : String. |
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| 417 | |
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| 418 | (* the optional point must be given only for calls *) |
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| 419 | definition eval_step : |
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| 420 | ∀globals.∀p:sem_params. genv globals p → state p → |
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| 421 | ∀s:joint_step p globals. |
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| 422 | IO io_out io_in ((step_flow p globals (step_labels … s))×(state p)) ≝ |
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| 423 | λglobals,p,ge,st,seq. |
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| 424 | match seq return λx.IO ?? ((step_flow ?? (step_labels … x) × ?)) with |
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| 425 | [ extension c ⇒ |
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| 426 | exec_extended … ge c st |
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| 427 | | COST_LABEL cl ⇒ |
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| 428 | return 〈Proceed ???, st〉 |
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| 429 | | COMMENT c ⇒ |
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| 430 | return 〈Proceed ???, st〉 |
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| 431 | | LOAD dst addrl addrh ⇒ |
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| 432 | ! vaddrh ← dph_arg_retrieve … st addrh ; |
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| 433 | ! vaddrl ← dpl_arg_retrieve … st addrl; |
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| 434 | ! vaddr ← pointer_of_address 〈vaddrl,vaddrh〉; |
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| 435 | ! v ← opt_to_res … (msg FailedLoad) (beloadv (m … st) vaddr); |
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| 436 | ! st ← acca_store p … dst v st ; |
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| 437 | return 〈Proceed ???, st〉 |
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| 438 | | STORE addrl addrh src ⇒ |
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| 439 | ! vaddrh ← dph_arg_retrieve … st addrh; |
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| 440 | ! vaddrl ← dpl_arg_retrieve … st addrl; |
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| 441 | ! vaddr ← pointer_of_address 〈vaddrl,vaddrh〉; |
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| 442 | ! v ← acca_arg_retrieve … st src; |
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| 443 | ! m' ← opt_to_res … (msg FailedStore) (bestorev (m … st) vaddr v); |
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| 444 | return 〈Proceed ???, set_m … m' st〉 |
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| 445 | | COND src ltrue ⇒ |
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| 446 | ! v ← acca_retrieve … st src; |
|---|
| 447 | ! b ← bool_of_beval v; |
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| 448 | if b then |
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| 449 | return 〈Redirect ??? ltrue, st〉 |
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| 450 | else |
|---|
| 451 | return 〈Proceed ???, st〉 |
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| 452 | | ADDRESS ident prf ldest hdest ⇒ |
|---|
| 453 | let addr ≝ opt_safe ? (find_symbol … ge ident) ? in |
|---|
| 454 | ! 〈laddr,haddr〉 ← address_of_pointer (mk_pointer (block_region addr) addr ? zero_offset) ; |
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| 455 | ! st' ← dpl_store … ldest laddr st; |
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| 456 | ! st'' ← dph_store … hdest haddr st'; |
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| 457 | return 〈Proceed ???, st''〉 |
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| 458 | | OP1 op dacc_a sacc_a ⇒ |
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| 459 | ! v ← acca_retrieve … st sacc_a; |
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| 460 | ! v ← Byte_of_val v; |
|---|
| 461 | let v' ≝ BVByte (op1 eval op v) in |
|---|
| 462 | ! st ← acca_store … dacc_a v' st; |
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| 463 | return 〈Proceed ???, st〉 |
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| 464 | | OP2 op dacc_a sacc_a src ⇒ |
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| 465 | ! v1 ← acca_arg_retrieve … st sacc_a; |
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| 466 | ! v1 ← Byte_of_val v1; |
|---|
| 467 | ! v2 ← snd_arg_retrieve … st src; |
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| 468 | ! v2 ← Byte_of_val v2; |
|---|
| 469 | ! carry ← bool_of_beval (carry … st); |
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| 470 | let 〈v',carry〉 ≝ op2 eval carry op v1 v2 in |
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| 471 | let v' ≝ BVByte v' in |
|---|
| 472 | let carry ≝ beval_of_bool carry in |
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| 473 | ! st' ← acca_store … dacc_a v' st; |
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| 474 | let st'' ≝ set_carry … carry st' in |
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| 475 | return 〈Proceed ???, st''〉 |
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| 476 | | CLEAR_CARRY ⇒ |
|---|
| 477 | let st' ≝ set_carry … BVfalse st in |
|---|
| 478 | return 〈Proceed ???, st'〉 |
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| 479 | | SET_CARRY ⇒ |
|---|
| 480 | let st' ≝ set_carry … BVtrue st in |
|---|
| 481 | return 〈Proceed ???, st'〉 |
|---|
| 482 | | OPACCS op dacc_a_reg dacc_b_reg sacc_a_reg sacc_b_reg ⇒ |
|---|
| 483 | ! v1 ← acca_arg_retrieve … st sacc_a_reg; |
|---|
| 484 | ! v1 ← Byte_of_val v1; |
|---|
| 485 | ! v2 ← accb_arg_retrieve … st sacc_b_reg; |
|---|
| 486 | ! v2 ← Byte_of_val v2; |
|---|
| 487 | let 〈v1',v2'〉 ≝ opaccs eval op v1 v2 in |
|---|
| 488 | let v1' ≝ BVByte v1' in |
|---|
| 489 | let v2' ≝ BVByte v2' in |
|---|
| 490 | ! st' ← acca_store … dacc_a_reg v1' st; |
|---|
| 491 | ! st'' ← accb_store … dacc_b_reg v2' st'; |
|---|
| 492 | return 〈Proceed ???, st''〉 |
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| 493 | | POP dst ⇒ |
|---|
| 494 | ! 〈st',v〉 ← pop p st; |
|---|
| 495 | ! st'' ← acca_store p p dst v st'; |
|---|
| 496 | return 〈Proceed ???, st''〉 |
|---|
| 497 | | PUSH src ⇒ |
|---|
| 498 | ! v ← acca_arg_retrieve … st src; |
|---|
| 499 | ! st ← push … st v; |
|---|
| 500 | return 〈Proceed ???, st〉 |
|---|
| 501 | | MOVE dst_src ⇒ |
|---|
| 502 | ! st ← pair_reg_move … st dst_src ; |
|---|
| 503 | return 〈Proceed ???, st〉 |
|---|
| 504 | | CALL_ID id args dest ⇒ |
|---|
| 505 | ! b ← opt_to_res … [MSG MissingSymbol; CTX ? id] (find_symbol … ge id) : IO ???; |
|---|
| 506 | eval_call_block … ge st b args dest |
|---|
| 507 | ]. |
|---|
| 508 | [ cases addr // |
|---|
| 509 | | (* TODO: to prove *) |
|---|
| 510 | elim daemon |
|---|
| 511 | | %1 % |
|---|
| 512 | ] qed. |
|---|
| 513 | |
|---|
| 514 | definition eval_fin_step : ∀globals: list ident.∀p:sem_params. genv globals p → |
|---|
| 515 | state p → ∀s : joint_fin_step … p globals. |
|---|
| 516 | IO io_out io_in ((fin_step_flow p globals (fin_step_labels … s))×(state p)) ≝ |
|---|
| 517 | λglobals,p,ge,st,s. |
|---|
| 518 | match s return λx.IO ?? ((fin_step_flow ?? (fin_step_labels … x)) × ?) with |
|---|
| 519 | [ GOTO l ⇒ return 〈FRedirect ??? l, st〉 |
|---|
| 520 | | RETURN ⇒ return 〈FEnd ???, st〉 |
|---|
| 521 | | extension_fin c ⇒ exec_fin_extended … ge c st |
|---|
| 522 | ]. %1 % qed. |
|---|
| 523 | |
|---|
| 524 | |
|---|
| 525 | definition do_call : ∀globals: list ident.∀p:sem_params. genv globals p → |
|---|
| 526 | state p → Z → joint_internal_function globals p → call_args p → |
|---|
| 527 | res (state_pc p) ≝ |
|---|
| 528 | λglobals,p,ge,st,id,fn,args. |
|---|
| 529 | ! st' ← setup_call … (joint_if_stacksize … fn) (joint_if_params … fn) |
|---|
| 530 | args st ; |
|---|
| 531 | let regs ≝ foldr ?? (allocate_local p p) (regs … st) (joint_if_locals … fn) in |
|---|
| 532 | let l' ≝ joint_if_entry … fn in |
|---|
| 533 | let st' ≝ set_regs p regs st in |
|---|
| 534 | let pointer_in_fn ≝ mk_pointer Code (mk_block Code id) ? (mk_offset 0) in |
|---|
| 535 | let pc ≝ pointer_of_point ? p … pointer_in_fn l' in |
|---|
| 536 | return mk_state_pc ? st' pc. % qed. |
|---|
| 537 | |
|---|
| 538 | (* The pointer provided is the one to the *next* instruction. |
|---|
| 539 | The boolean tells wether a flow changement has occurred (i.e. |
|---|
| 540 | a non Proceed cmd was issued). Used in linking block evaluation |
|---|
| 541 | with regular one *) |
|---|
| 542 | definition eval_step_flow : |
|---|
| 543 | ∀globals.∀p:sem_params.∀lbls.genv globals p → |
|---|
| 544 | state p → cpointer → step_flow p globals lbls → |
|---|
| 545 | res (bool × (state_pc p)) ≝ |
|---|
| 546 | λglobals,p,lbls,ge,st,nxt,cmd. |
|---|
| 547 | match cmd with |
|---|
| 548 | [ Redirect l ⇒ |
|---|
| 549 | ! st ← goto … ge l st (pblock nxt) ; return 〈true, st〉 |
|---|
| 550 | | Init id fn args dest ⇒ |
|---|
| 551 | let st' ≝ set_frms … (save_frame … nxt dest st) st in |
|---|
| 552 | ! st ← do_call ?? ge st' id fn args ; |
|---|
| 553 | return 〈true, st〉 |
|---|
| 554 | | Proceed ⇒ |
|---|
| 555 | return 〈false, mk_state_pc ? st nxt〉 |
|---|
| 556 | ]. |
|---|
| 557 | |
|---|
| 558 | definition eval_fin_step_flow : ∀globals: list ident.∀p:sem_params.∀lbls. genv globals p → |
|---|
| 559 | state p → block → fin_step_flow p globals lbls → res (state_pc p) ≝ |
|---|
| 560 | λglobals,p,lbls,ge,st,b,cmd. |
|---|
| 561 | match cmd with |
|---|
| 562 | [ FRedirect l ⇒ goto … ge l st b |
|---|
| 563 | | FTailInit id fn args ⇒ |
|---|
| 564 | do_call … ge st id fn args |
|---|
| 565 | | FEnd ⇒ |
|---|
| 566 | ! 〈st',ra〉 ← fetch_ra … st ; |
|---|
| 567 | ! st'' ← pop_frame … ge st; |
|---|
| 568 | return mk_state_pc ? st'' ra |
|---|
| 569 | ]. |
|---|
| 570 | |
|---|
| 571 | definition eval_statement : |
|---|
| 572 | ∀globals.∀p:sem_params.genv globals p → |
|---|
| 573 | state_pc p → joint_statement p globals → |
|---|
| 574 | IO io_out io_in (bool × (state_pc p)) ≝ |
|---|
| 575 | λglobals,p,ge,st,stmt. |
|---|
| 576 | match stmt with |
|---|
| 577 | [ sequential s nxt ⇒ |
|---|
| 578 | ! 〈flow, st'〉 ← eval_step … ge st s ; |
|---|
| 579 | ! nxtptr ← succ_pc ? p (pc … st) nxt ; |
|---|
| 580 | eval_step_flow … ge st' nxtptr flow |
|---|
| 581 | | final s ⇒ |
|---|
| 582 | ! 〈flow, st'〉 ← eval_fin_step … ge st s ; |
|---|
| 583 | ! st ← eval_fin_step_flow … ge st' (pblock … (pc … st)) flow ; |
|---|
| 584 | return 〈true, st〉 |
|---|
| 585 | ]. |
|---|
| 586 | |
|---|
| 587 | definition eval_state_flag : ∀globals: list ident.∀p:sem_params. genv globals p → |
|---|
| 588 | state_pc p → IO io_out io_in (bool × (state_pc p)) ≝ |
|---|
| 589 | λglobals,p,ge,st. |
|---|
| 590 | ! s ← fetch_statement ? p … ge (pc … st) : IO ???; |
|---|
| 591 | eval_statement … ge st s. |
|---|
| 592 | |
|---|
| 593 | definition eval_state : ∀globals: list ident.∀p:sem_params. genv globals p → |
|---|
| 594 | state_pc p → IO io_out io_in (state_pc p) ≝ |
|---|
| 595 | λglobals,p,ge,st. |
|---|
| 596 | ! 〈flag,st'〉 ← eval_state_flag … ge st ; |
|---|
| 597 | return st'. |
|---|
| 598 | |
|---|
| 599 | (* Paolo: what if in an intermediate language main finishes with an external |
|---|
| 600 | tailcall? Maybe it should rely on an FEnd flow command issued, but that's |
|---|
| 601 | not static... *) |
|---|
| 602 | definition is_final: ∀globals:list ident. ∀p: sem_params. |
|---|
| 603 | genv globals p → cpointer → state_pc p → option int ≝ |
|---|
| 604 | λglobals,p,ge,exit,st.res_to_opt ? ( |
|---|
| 605 | do s ← fetch_statement ? p … ge (pc … st); |
|---|
| 606 | match s with |
|---|
| 607 | [ final s' ⇒ |
|---|
| 608 | match s' with |
|---|
| 609 | [ RETURN ⇒ |
|---|
| 610 | do 〈st,ra〉 ← fetch_ra … st; |
|---|
| 611 | if eq_pointer ra exit then |
|---|
| 612 | do vals ← read_result … ge st ; |
|---|
| 613 | Word_of_list_beval vals |
|---|
| 614 | else |
|---|
| 615 | Error ? [ ] |
|---|
| 616 | | _ ⇒ Error ? [ ] |
|---|
| 617 | ] |
|---|
| 618 | | _ ⇒ Error ? [ ] |
|---|
| 619 | ]). |
|---|
| 620 | |
|---|
| 621 | record evaluation_parameters : Type[1] ≝ |
|---|
| 622 | { globals: list ident |
|---|
| 623 | ; sparams:> sem_params |
|---|
| 624 | ; exit: cpointer |
|---|
| 625 | ; genv2: genv globals sparams |
|---|
| 626 | }. |
|---|
| 627 | |
|---|
| 628 | (* Paolo: with structured traces, eval need not emit labels. However, this |
|---|
| 629 | changes trans_system. For now, just putting a dummy thing for |
|---|
| 630 | the transition. *) |
|---|
| 631 | definition joint_exec: trans_system io_out io_in ≝ |
|---|
| 632 | mk_trans_system … evaluation_parameters (λG. state_pc G) |
|---|
| 633 | (λG.is_final (globals G) G (genv2 G) (exit G)) |
|---|
| 634 | (λG,st.! 〈flag,st'〉 ← eval_state_flag (globals G) G (genv2 G) st ; return 〈E0, st'〉). |
|---|
| 635 | |
|---|
| 636 | definition make_global : |
|---|
| 637 | ∀pars: sem_params. |
|---|
| 638 | joint_program pars → evaluation_parameters |
|---|
| 639 | ≝ |
|---|
| 640 | λpars. |
|---|
| 641 | (* Invariant: a -1 block is unused in common/Globalenvs *) |
|---|
| 642 | let b ≝ mk_block Code (-1) in |
|---|
| 643 | let ptr ≝ mk_pointer Code b ? (mk_offset 0) in |
|---|
| 644 | (λp. mk_evaluation_parameters |
|---|
| 645 | (prog_var_names … p) |
|---|
| 646 | (mk_sem_params … pars) |
|---|
| 647 | ptr |
|---|
| 648 | (globalenv_noinit … p) |
|---|
| 649 | ). |
|---|
| 650 | % qed. |
|---|
| 651 | |
|---|
| 652 | axiom ExternalMain: String. |
|---|
| 653 | |
|---|
| 654 | definition make_initial_state : |
|---|
| 655 | ∀pars: sem_params. |
|---|
| 656 | ∀p: joint_program … pars. res (state_pc pars) ≝ |
|---|
| 657 | λpars,p. |
|---|
| 658 | let sem_globals ≝ make_global pars p in |
|---|
| 659 | let ge ≝ genv2 sem_globals in |
|---|
| 660 | let m ≝ alloc_mem … p in |
|---|
| 661 | let 〈m,spb〉 ≝ alloc … m 0 external_ram_size XData in |
|---|
| 662 | let 〈m,ispb〉 ≝ alloc … m 0 internal_ram_size XData in |
|---|
| 663 | let dummy_pc ≝ mk_pointer Code (mk_block Code (-1)) ? (mk_offset 0) in |
|---|
| 664 | let spp ≝ mk_pointer XData spb ? (mk_offset external_ram_size) in |
|---|
| 665 | let ispp ≝ mk_pointer XData ispb ? (mk_offset 47) in |
|---|
| 666 | let main ≝ prog_main … p in |
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| 667 | let st0 ≝ mk_state pars (empty_framesT …) spp ispp BVfalse (empty_regsT … spp) m in |
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| 668 | (* use exit sem_globals as ra and call_dest_for_main as dest *) |
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| 669 | let st0' ≝ set_frms ? (save_frame … (exit sem_globals) (call_dest_for_main … pars) st0) st0 in |
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| 670 | let st_pc0 ≝ mk_state_pc ? st0' dummy_pc in |
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| 671 | ! main_block ← opt_to_res … [MSG MissingSymbol; CTX ? main] (find_symbol … ge main) ; |
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| 672 | ! main_fd ← opt_to_res ? [MSG BadPointer] (find_funct_ptr … ge main_block) ; |
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| 673 | match main_fd with |
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| 674 | [ Internal fn ⇒ |
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| 675 | do_call ?? ge st_pc0 (block_id main_block) fn (call_args_for_main … pars) |
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| 676 | | External _ ⇒ Error … [MSG ExternalMain] (* External main not supported: why? *) |
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| 677 | ]. [5: cases ispb * |6: cases spb * ] (* without try it fails! *) try // |
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| 678 | qed. |
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| 679 | |
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| 680 | definition joint_fullexec : |
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| 681 | ∀pars:sem_params.fullexec io_out io_in ≝ |
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| 682 | λpars.mk_fullexec ??? joint_exec (make_global pars) (make_initial_state pars). |
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