| 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 ≝ λp:params.λglobals.genv_t (joint_function p globals). |
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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 | coercion sem_state_params_to_state nocomposites: |
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| 37 | ∀p : sem_state_params.Type[0] ≝ state on _p : sem_state_params to Type[0]. |
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| 38 | |
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| 39 | record state_pc (semp : sem_state_params) : Type[0] ≝ |
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| 40 | { st_no_pc :> state semp |
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| 41 | ; pc : cpointer |
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| 42 | }. |
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| 43 | |
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| 44 | definition set_m: ∀p. bemem → state p → state p ≝ |
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| 45 | λp,m,st. mk_state p (st_frms ?…st) (sp … st) (isp … st) (carry … st) (regs … st) m. |
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| 46 | |
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| 47 | definition set_regs: ∀p:sem_state_params. regsT p → state p → state p ≝ |
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| 48 | λp,regs,st. mk_state p (st_frms … st) (sp … st) (isp … st) (carry … st) regs (m … st). |
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| 49 | |
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| 50 | definition set_sp: ∀p. ? → state p → state p ≝ |
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| 51 | λp,sp,st. mk_state … (st_frms … st) sp (isp … st) (carry … st) (regs … st) (m … st). |
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| 52 | |
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| 53 | definition set_isp: ∀p. ? → state p → state p ≝ |
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| 54 | λp,isp,st. mk_state … (st_frms … st) (sp … st) isp (carry … st) (regs … st) (m … st). |
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| 55 | |
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| 56 | definition set_carry: ∀p. beval → state p → state p ≝ |
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| 57 | λp,carry,st. mk_state … (st_frms … st) (sp … st) (isp … st) carry (regs … st) (m … st). |
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| 58 | |
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| 59 | definition set_pc: ∀p. ? → state_pc p → state_pc p ≝ |
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| 60 | λp,pc,st. mk_state_pc … (st_no_pc … st) pc. |
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| 61 | |
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| 62 | definition set_no_pc: ∀p. ? → state_pc p → state_pc p ≝ |
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| 63 | λp,s,st. mk_state_pc … s (pc … st). |
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| 64 | |
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| 65 | definition set_frms: ∀p:sem_state_params. framesT p → state p → state p ≝ |
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| 66 | λp,frms,st. mk_state … frms (sp … st) (isp … st) (carry … st) (regs … st) (m … st). |
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| 67 | |
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| 68 | axiom BadProgramCounter : String. |
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| 69 | |
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| 70 | definition function_of_block : |
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| 71 | ∀pars : params. |
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| 72 | ∀globals. |
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| 73 | genv pars globals → |
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| 74 | block → |
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| 75 | res (joint_internal_function pars globals) ≝ |
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| 76 | λpars,globals,ge,b. |
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| 77 | do def ← opt_to_res ? [MSG BadProgramCounter] (find_funct_ptr … ge b) ; |
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| 78 | match def with |
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| 79 | [ Internal def' ⇒ OK … def' |
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| 80 | | External _ ⇒ Error … [MSG BadProgramCounter]]. |
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| 81 | |
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| 82 | (* this can replace graph_fetch function and lin_fetch_function *) |
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| 83 | definition fetch_function: |
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| 84 | ∀pars : params. |
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| 85 | ∀globals. |
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| 86 | genv pars globals → |
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| 87 | cpointer → |
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| 88 | res (joint_internal_function pars globals) ≝ |
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| 89 | λpars,globals,ge,p.function_of_block pars globals ge (pblock p). |
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| 90 | |
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| 91 | inductive step_flow (p : unserialized_params) (F : Type[0]) : possible_flows → Type[0] ≝ |
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| 92 | | Redirect : ∀lbls.(Σl.In ? lbls l) → step_flow p F (Labels lbls) (* used for goto-like flow alteration *) |
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| 93 | | Init : Z → F → call_args p → call_dest p → step_flow p F Call (* call a function with given id, then proceed *) |
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| 94 | | Proceed : ∀flows.step_flow p F flows. (* go to implicit successor *) |
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| 95 | |
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| 96 | inductive fin_step_flow (p : unserialized_params) (F : Type[0]) : possible_flows → Type[0] ≝ |
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| 97 | | FRedirect : ∀lbls.(Σl.In ? lbls l) → fin_step_flow p F (Labels lbls) |
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| 98 | | FTailInit : Z → F → call_args p → fin_step_flow p F Call |
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| 99 | | FEnd1 : fin_step_flow p F (Labels [ ]) (* end flow *) |
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| 100 | | FEnd2 : fin_step_flow p F Call. (* end flow *) |
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| 101 | |
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| 102 | record more_sem_unserialized_params |
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| 103 | (uns_pars : unserialized_params) |
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| 104 | (F : list ident → Type[0]) : Type[1] ≝ |
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| 105 | { st_pars :> sem_state_params (* automatic coercion has issues *) |
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| 106 | ; acca_store_ : acc_a_reg uns_pars → beval → regsT st_pars → res (regsT st_pars) |
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| 107 | ; acca_retrieve_ : regsT st_pars → acc_a_reg uns_pars → res beval |
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| 108 | ; acca_arg_retrieve_ : regsT st_pars → acc_a_arg uns_pars → res beval |
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| 109 | ; accb_store_ : acc_b_reg uns_pars → beval → regsT st_pars → res (regsT st_pars) |
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| 110 | ; accb_retrieve_ : regsT st_pars → acc_b_reg uns_pars → res beval |
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| 111 | ; accb_arg_retrieve_ : regsT st_pars → acc_b_arg uns_pars → res beval |
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| 112 | ; dpl_store_ : dpl_reg uns_pars → beval → regsT st_pars → res (regsT st_pars) |
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| 113 | ; dpl_retrieve_ : regsT st_pars → dpl_reg uns_pars → res beval |
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| 114 | ; dpl_arg_retrieve_ : regsT st_pars → dpl_arg uns_pars → res beval |
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| 115 | ; dph_store_ : dph_reg uns_pars → beval → regsT st_pars → res (regsT st_pars) |
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| 116 | ; dph_retrieve_ : regsT st_pars → dph_reg uns_pars → res beval |
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| 117 | ; dph_arg_retrieve_ : regsT st_pars → dph_arg uns_pars → res beval |
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| 118 | ; snd_arg_retrieve_ : regsT st_pars → snd_arg uns_pars → res beval |
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| 119 | ; pair_reg_move_ : regsT st_pars → pair_move uns_pars → res (regsT st_pars) |
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| 120 | ; fetch_ra: state st_pars → res ((state st_pars) × cpointer) |
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| 121 | |
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| 122 | ; allocate_local : localsT uns_pars → regsT st_pars → regsT st_pars |
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| 123 | (* Paolo: save_frame separated from call_setup to factorize tailcall code *) |
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| 124 | ; save_frame: cpointer → call_dest uns_pars → state st_pars → res (state st_pars) |
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| 125 | (*CSC: setup_call returns a res only because we can call a function with the wrong number and |
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| 126 | type of arguments. To be fixed using a dependent type *) |
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| 127 | ; setup_call : nat → paramsT … uns_pars → call_args uns_pars → |
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| 128 | state st_pars → res (state st_pars) |
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| 129 | ; fetch_external_args: external_function → state st_pars → |
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| 130 | res (list val) |
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| 131 | ; set_result: list val → call_dest uns_pars → state st_pars → res (state st_pars) |
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| 132 | ; call_args_for_main: call_args uns_pars |
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| 133 | ; call_dest_for_main: call_dest uns_pars |
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| 134 | |
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| 135 | (* from now on, parameters that use the type of functions *) |
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| 136 | ; read_result: ∀globals.genv_t (fundef (F globals)) → call_dest uns_pars → state st_pars → res (list beval) |
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| 137 | (* change of pc must be left to *_flow execution *) |
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| 138 | ; eval_ext_seq: ∀globals.genv_t (fundef (F globals)) → ext_seq uns_pars → |
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| 139 | F globals → state st_pars → IO io_out io_in (state st_pars) |
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| 140 | ; eval_ext_tailcall : ∀globals.genv_t (fundef (F globals)) → ext_tailcall uns_pars → |
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| 141 | F globals → state st_pars → IO io_out io_in ((fin_step_flow uns_pars (F globals) Call)×(state st_pars)) |
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| 142 | ; eval_ext_call: ∀globals.genv_t (fundef (F globals)) → |
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| 143 | ext_call uns_pars → state st_pars → |
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| 144 | IO io_out io_in ((step_flow uns_pars (F globals) Call)×(state st_pars)) |
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| 145 | ; pop_frame: ∀globals.genv_t (fundef (F globals)) → F globals → state st_pars → res (state st_pars) |
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| 146 | (* do something more in some op2 calculations (e.g. mark a register for correction |
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| 147 | with spilled_no in ERTL) *) |
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| 148 | ; post_op2 : ∀globals.genv_t (fundef (F globals)) → |
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| 149 | Op2 → acc_a_reg uns_pars → acc_a_arg uns_pars → snd_arg uns_pars → |
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| 150 | state st_pars → state st_pars |
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| 151 | }. |
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| 152 | |
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| 153 | (*coercion msu_pars_to_ss_pars nocomposites : |
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| 154 | ∀p,F.∀msup : more_sem_unserialized_params p F.sem_state_params |
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| 155 | ≝ st_pars |
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| 156 | on _msup : more_sem_unserialized_params ?? to sem_state_params.*) |
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| 157 | |
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| 158 | |
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| 159 | definition helper_def_retrieve : |
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| 160 | ∀X : ? → ? → ? → Type[0]. |
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| 161 | (∀up,F.∀p:more_sem_unserialized_params up F. regsT (st_pars up F p) → X up F p → res beval) → |
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| 162 | ∀up,F.∀p : more_sem_unserialized_params up F.state (st_pars up F p) → X up F p → res beval ≝ |
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| 163 | λX,f,up,F,p,st.f ?? p (regs … st). |
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| 164 | |
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| 165 | definition helper_def_store : |
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| 166 | ∀X : ? → ? → ? → Type[0]. |
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| 167 | (∀up,F.∀p : more_sem_unserialized_params up F.X up F p → beval → regsT (st_pars … p) → res (regsT (st_pars … p))) → |
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| 168 | ∀up,F.∀p : more_sem_unserialized_params up F.X up F p → beval → state (st_pars … p) → res (state (st_pars … p)) ≝ |
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| 169 | λX,f,up,F,p,x,v,st.! r ← f ?? p x v (regs … st) ; return set_regs … r st. |
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| 170 | |
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| 171 | definition acca_retrieve ≝ helper_def_retrieve ? acca_retrieve_. |
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| 172 | definition acca_store ≝ helper_def_store ? acca_store_. |
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| 173 | definition acca_arg_retrieve ≝ helper_def_retrieve ? acca_arg_retrieve_. |
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| 174 | definition accb_store ≝ helper_def_store ? accb_store_. |
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| 175 | definition accb_retrieve ≝ helper_def_retrieve ? accb_retrieve_. |
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| 176 | definition accb_arg_retrieve ≝ helper_def_retrieve ? accb_arg_retrieve_. |
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| 177 | definition dpl_store ≝ helper_def_store ? dpl_store_. |
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| 178 | definition dpl_retrieve ≝ helper_def_retrieve ? dpl_retrieve_. |
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| 179 | definition dpl_arg_retrieve ≝ helper_def_retrieve ? dpl_arg_retrieve_. |
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| 180 | definition dph_store ≝ helper_def_store ? dph_store_. |
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| 181 | definition dph_retrieve ≝ helper_def_retrieve ? dph_retrieve_. |
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| 182 | definition dph_arg_retrieve ≝ helper_def_retrieve ? dph_arg_retrieve_. |
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| 183 | definition snd_arg_retrieve ≝ helper_def_retrieve ? snd_arg_retrieve_. |
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| 184 | definition pair_reg_move ≝ |
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| 185 | λup,F.λp : more_sem_unserialized_params up F.λst : state (st_pars … p).λpm : pair_move up. |
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| 186 | ! r ← pair_reg_move_ ?? p (regs ? st) pm; |
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| 187 | return set_regs ? r st. |
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| 188 | |
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| 189 | |
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| 190 | axiom BadPointer : String. |
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| 191 | |
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| 192 | (* this is preamble to all calls (including tail ones). The optional argument in |
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| 193 | input tells the function whether it has to save the frame for internal |
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| 194 | calls. |
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| 195 | the first element of the triple is the entry point of the function if |
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| 196 | it is an internal one, or false in case of an external one. |
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| 197 | The actual update of the pc is left to later, as it depends on |
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| 198 | serialization and on whether the call is a tail one. *) |
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| 199 | definition eval_call_block: |
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| 200 | ∀p,F.∀p':more_sem_unserialized_params p F.∀globals. |
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| 201 | genv_t (fundef (F globals)) → state (st_pars ?? p') → block → call_args p → call_dest p → |
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| 202 | IO io_out io_in ((step_flow p (F globals) Call)×(state (st_pars ?? p'))) ≝ |
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| 203 | λp,F,p',globals,ge,st,b,args,dest. |
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| 204 | ! fd ← (opt_to_res ? [MSG BadPointer] (find_funct_ptr ? ge b) : IO ? io_in ?); |
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| 205 | match fd with |
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| 206 | [ Internal fd ⇒ |
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| 207 | return 〈Init ?? (block_id b) fd args dest, st〉 |
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| 208 | | External fn ⇒ |
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| 209 | ! params ← fetch_external_args … p' fn st : IO ???; |
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| 210 | ! evargs ← check_eventval_list params (sig_args (ef_sig fn)) : IO ???; |
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| 211 | ! evres ← do_io (ef_id fn) evargs (proj_sig_res (ef_sig fn)); |
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| 212 | (* CSC: XXX bug here; I think I should split it into Byte-long |
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| 213 | components; instead I am making a singleton out of it. To be |
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| 214 | fixed once we fully implement external functions. *) |
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| 215 | let vs ≝ [mk_val ? evres] in |
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| 216 | ! st ← set_result … p' vs dest st : IO ???; |
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| 217 | return 〈Proceed ???, st〉 |
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| 218 | ]. |
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| 219 | |
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| 220 | axiom FailedStore: String. |
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| 221 | |
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| 222 | definition push: ∀p.state p → beval → res (state p) ≝ |
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| 223 | λp,st,v. |
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| 224 | let isp' ≝ isp ? st in |
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| 225 | do m ← opt_to_res ? (msg FailedStore) (bestorev (m … st) isp' v); |
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| 226 | let isp'' ≝ shift_pointer … isp' [[false;false;false;false;false;false;false;true]] in |
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| 227 | return set_m … m (set_isp … isp'' st). |
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| 228 | normalize elim (isp p st) #p #H @H |
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| 229 | qed. |
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| 230 | |
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| 231 | definition pop: ∀p. state p → res ((state p ) × beval) ≝ |
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| 232 | λp,st. |
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| 233 | let isp' ≝ isp ? st in |
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| 234 | let isp'' ≝ neg_shift_pointer ? isp' [[false;false;false;false;false;false;false;true]] in |
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| 235 | let ist ≝ set_isp … isp'' st in |
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| 236 | do v ← opt_to_res ? (msg FailedStore) (beloadv (m ? st) isp''); |
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| 237 | OK ? 〈ist,v〉. |
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| 238 | normalize elim (isp p st) #p #H @H |
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| 239 | qed. |
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| 240 | |
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| 241 | definition save_ra : ∀p. state p → cpointer → res (state p) ≝ |
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| 242 | λp,st,l. |
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| 243 | let 〈addrl,addrh〉 ≝ address_of_code_pointer l in |
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| 244 | ! st' ← push … st addrl; |
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| 245 | push … st' addrh. |
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| 246 | |
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| 247 | definition load_ra : ∀p.state p → res ((state p) × cpointer) ≝ |
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| 248 | λp,st. |
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| 249 | do 〈st',addrh〉 ← pop … st; |
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| 250 | do 〈st'',addrl〉 ← pop … st'; |
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| 251 | do pr ← code_pointer_of_address 〈addrh, addrl〉; |
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| 252 | return 〈st'', pr〉. |
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| 253 | |
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| 254 | (* parameters that are defined by serialization *) |
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| 255 | record more_sem_params (pp : params) : Type[1] ≝ |
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| 256 | { msu_pars :> more_sem_unserialized_params pp (joint_internal_function pp) |
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| 257 | ; offset_of_point : code_point pp → option offset (* can overflow *) |
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| 258 | ; point_of_offset : offset → code_point pp |
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| 259 | ; point_of_offset_of_point : |
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| 260 | ∀pt.opt_All ? (eq ? pt) (option_map ?? point_of_offset (offset_of_point pt)) |
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| 261 | ; offset_of_point_of_offset : |
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| 262 | ∀o.offset_of_point (point_of_offset o) = Some ? o |
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| 263 | }. |
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| 264 | |
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| 265 | (* |
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| 266 | coercion ms_pars_to_msu_pars nocomposites : |
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| 267 | ∀p : params.∀msp : more_sem_params p.more_sem_unserialized_params p (λglobals.joint_internal_function globals p) |
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| 268 | ≝ msu_pars |
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| 269 | on _msp : more_sem_params ? to more_sem_unserialized_params ??. |
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| 270 | |
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| 271 | definition ss_pars_of_ms_pars ≝ |
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| 272 | λp.λpp : more_sem_params p. |
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| 273 | st_pars … (msu_pars … pp). |
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| 274 | coercion ms_pars_to_ss_pars nocomposites : |
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| 275 | ∀p : params.∀msp : more_sem_params p.sem_state_params ≝ |
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| 276 | ss_pars_of_ms_pars on _msp : more_sem_params ? to sem_state_params.*) |
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| 277 | |
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| 278 | axiom CodePointerOverflow : String. |
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| 279 | |
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| 280 | definition pointer_of_point : ∀p.more_sem_params p → |
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| 281 | cpointer→ code_point p → res cpointer ≝ |
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| 282 | λp,msp,ptr,pt. |
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| 283 | ! o ← opt_to_res ? [MSG CodePointerOverflow] (offset_of_point ? msp pt) ; |
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| 284 | return «mk_pointer (pblock ptr) o, ?». |
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| 285 | elim ptr #ptr' #EQ <EQ % qed. |
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| 286 | |
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| 287 | definition point_of_pointer : |
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| 288 | ∀p.more_sem_params p → cpointer → code_point p ≝ |
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| 289 | λp,msp,ptr.point_of_offset p msp (poff ptr). |
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| 290 | |
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| 291 | lemma point_of_pointer_of_point : |
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| 292 | ∀p,msp.∀ptr1,ptr2 : cpointer.∀pt. |
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| 293 | pointer_of_point p msp ptr1 pt = return ptr2 → |
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| 294 | point_of_pointer p msp ptr2 = pt. |
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| 295 | #p #msp #ptr1 #ptr2 #pt normalize |
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| 296 | lapply (point_of_offset_of_point p msp pt) |
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| 297 | cases (offset_of_point ???) normalize |
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| 298 | [ * #ABS destruct(ABS) |
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| 299 | | #o #EQ1 #EQ2 destruct % |
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| 300 | ] |
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| 301 | qed. |
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| 302 | |
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| 303 | lemma pointer_of_point_block : |
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| 304 | ∀p,msp,ptr1,ptr2,pt. |
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| 305 | pointer_of_point p msp ptr1 pt = return ptr2 → |
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| 306 | pblock ptr2 = pblock ptr1. |
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| 307 | #p #msp #ptr1 #ptr2 #pt normalize |
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| 308 | cases (offset_of_point ???) normalize |
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| 309 | [ #ABS destruct(ABS) |
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| 310 | | #o #EQ destruct(EQ) % |
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| 311 | ] |
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| 312 | qed. |
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| 313 | |
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| 314 | lemma pointer_of_point_uses_block : |
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| 315 | ∀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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| 316 | #p #msp ** #b1 #o1 #EQ1 |
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| 317 | ** #b2 #o2 #EQ2 |
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| 318 | #pt #EQ3 destruct normalize // |
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| 319 | qed. |
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| 320 | |
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| 321 | lemma pointer_of_point_of_pointer : |
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| 322 | ∀p,msp.∀ptr1,ptr2 : cpointer. |
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| 323 | pblock ptr1 = pblock ptr2 → |
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| 324 | pointer_of_point p msp ptr1 (point_of_pointer p msp ptr2) = return ptr2. |
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| 325 | #p #msp ** #b1 #o1 #EQ1 |
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| 326 | ** #b2 #o2 #EQ2 |
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| 327 | #EQ3 destruct |
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| 328 | normalize >offset_of_point_of_offset normalize % |
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| 329 | qed. |
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| 330 | |
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| 331 | axiom ProgramCounterOutOfCode : String. |
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| 332 | axiom PointNotFound : String. |
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| 333 | axiom LabelNotFound : String. |
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| 334 | |
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| 335 | definition fetch_statement: ∀p : params.∀ msp : more_sem_params p.∀globals. |
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| 336 | genv p globals → cpointer → |
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| 337 | res ((joint_internal_function p globals) × (joint_statement p globals)) ≝ |
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| 338 | λp,msp,globals,ge,ptr. |
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| 339 | let pt ≝ point_of_pointer ? msp ptr in |
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| 340 | ! fn ← fetch_function … ge ptr ; |
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| 341 | ! stmt ← opt_to_res … (msg ProgramCounterOutOfCode) (stmt_at … (joint_if_code … fn) pt); |
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| 342 | return 〈fn, stmt〉. |
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| 343 | |
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| 344 | definition pointer_of_label : ∀p : params.∀ msp : more_sem_params p.∀globals. |
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| 345 | genv p globals → cpointer → label → res cpointer ≝ |
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| 346 | λp,msp,globals,ge,ptr,lbl. |
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| 347 | ! fn ← fetch_function … ge ptr ; |
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| 348 | ! pt ← opt_to_res … [MSG LabelNotFound ; CTX ? lbl] |
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| 349 | (point_of_label … (joint_if_code … fn) lbl) ; |
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| 350 | pointer_of_point p msp ptr pt. |
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| 351 | |
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| 352 | definition succ_pc : ∀p : params.∀ msp : more_sem_params p. |
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| 353 | cpointer → succ p → res cpointer ≝ |
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| 354 | λp,msp,ptr,nxt. |
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| 355 | let curr ≝ point_of_pointer p msp ptr in |
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| 356 | pointer_of_point p msp ptr (point_of_succ p curr nxt). |
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| 357 | |
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| 358 | record sem_params : Type[1] ≝ |
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| 359 | { spp :> params |
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| 360 | ; more_sem_pars :> more_sem_params spp |
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| 361 | }. |
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| 362 | |
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| 363 | (* definition msu_pars_of_s_pars : |
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| 364 | ∀p : sem_params.more_sem_unserialized_params (spp p) (λglobals.joint_internal_function globals (spp p)) |
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| 365 | ≝ λp : sem_params. |
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| 366 | msu_pars … (more_sem_pars p). |
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| 367 | coercion s_pars_to_msu_pars nocomposites : |
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| 368 | ∀p : sem_params.more_sem_unserialized_params (spp p) (λglobals.joint_internal_function globals (spp p)) ≝ |
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| 369 | msu_pars_of_s_pars |
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| 370 | on p : sem_params to more_sem_unserialized_params ??. |
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| 371 | |
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| 372 | definition ss_pars_of_s_pars : |
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| 373 | ∀p : sem_params.sem_state_params |
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| 374 | ≝ λp : sem_params. |
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| 375 | st_pars … (msu_pars … (more_sem_pars p)). |
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| 376 | coercion s_pars_to_ss_pars nocomposites : |
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| 377 | ∀p : sem_params.sem_state_params ≝ |
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| 378 | ss_pars_of_s_pars |
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| 379 | on _p : sem_params to sem_state_params. |
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| 380 | |
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| 381 | definition ms_pars_of_s_pars : |
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| 382 | ∀p : sem_params.more_sem_params (spp p) |
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| 383 | ≝ more_sem_pars. |
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| 384 | coercion s_pars_to_ms_pars nocomposites : |
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| 385 | ∀p : sem_params.more_sem_params (spp p) ≝ |
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| 386 | ms_pars_of_s_pars |
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| 387 | on p : sem_params to more_sem_params ?.*) |
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| 388 | |
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| 389 | (* definition address_of_label: ∀globals. ∀p:sem_params. |
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| 390 | genv globals p → pointer → label → res address ≝ |
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| 391 | λglobals,p,ge,ptr,l. |
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| 392 | do newptr ← pointer_of_label … p ? ge … ptr l ; |
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| 393 | OK … (address_of_code_pointer newptr). *) |
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| 394 | |
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| 395 | definition goto: ∀globals.∀p : sem_params. |
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| 396 | genv p globals → label → state p → cpointer → res (state_pc p) ≝ |
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| 397 | λglobals,p,ge,l,st,b. |
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| 398 | ! newpc ← pointer_of_label ? p … ge b l ; |
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| 399 | return mk_state_pc ? st newpc. |
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| 400 | |
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| 401 | (* |
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| 402 | definition empty_state: ∀p. more_sem_params p → state p ≝ |
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| 403 | mk_state … (empty_framesT …) |
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| 404 | *) |
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| 405 | |
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| 406 | definition next : ∀p : sem_params.succ p → state p → cpointer → res (state_pc p) ≝ |
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| 407 | λp,l,st,pc. |
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| 408 | ! newpc ← succ_pc ? p … pc l ; |
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| 409 | return mk_state_pc … st newpc. |
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| 410 | |
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| 411 | axiom MissingSymbol : String. |
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| 412 | axiom FailedLoad : String. |
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| 413 | axiom BadFunction : String. |
|---|
| 414 | axiom SuccessorNotProvided : String. |
|---|
| 415 | |
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| 416 | definition eval_seq_no_pc : |
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| 417 | ∀p:sem_params.∀globals. genv p globals → joint_internal_function p globals → |
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| 418 | state p → ∀s:joint_seq p globals. |
|---|
| 419 | IO io_out io_in (state p) ≝ |
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| 420 | λp,globals,ge,curr_fn,st,seq. |
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| 421 | match seq return λx.IO ??? with |
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| 422 | [ extension_seq c ⇒ |
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| 423 | eval_ext_seq … ge c curr_fn st |
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| 424 | | LOAD dst addrl addrh ⇒ |
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| 425 | ! vaddrh ← dph_arg_retrieve … st addrh ; |
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| 426 | ! vaddrl ← dpl_arg_retrieve … st addrl; |
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| 427 | ! vaddr ← pointer_of_address 〈vaddrl,vaddrh〉; |
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| 428 | ! v ← opt_to_res … (msg FailedLoad) (beloadv (m … st) vaddr); |
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| 429 | acca_store p … dst v st |
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| 430 | | STORE addrl addrh src ⇒ |
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| 431 | ! vaddrh ← dph_arg_retrieve … st addrh; |
|---|
| 432 | ! vaddrl ← dpl_arg_retrieve … st addrl; |
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| 433 | ! vaddr ← pointer_of_address 〈vaddrl,vaddrh〉; |
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| 434 | ! v ← acca_arg_retrieve … st src; |
|---|
| 435 | ! m' ← opt_to_res … (msg FailedStore) (bestorev (m … st) vaddr v); |
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| 436 | return set_m … m' st |
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| 437 | | ADDRESS ident prf ldest hdest ⇒ |
|---|
| 438 | let addr ≝ opt_safe ? (find_symbol … ge ident) ? in |
|---|
| 439 | ! 〈laddr,haddr〉 ← address_of_pointer (mk_pointer addr zero_offset) ; |
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| 440 | ! st' ← dpl_store … ldest laddr st; |
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| 441 | dph_store … hdest haddr st' |
|---|
| 442 | | OP1 op dacc_a sacc_a ⇒ |
|---|
| 443 | ! v ← acca_retrieve … st sacc_a; |
|---|
| 444 | ! v ← Byte_of_val v; |
|---|
| 445 | let v' ≝ BVByte (op1 eval op v) in |
|---|
| 446 | acca_store … dacc_a v' st |
|---|
| 447 | | OP2 op dacc_a sacc_a src ⇒ |
|---|
| 448 | ! v1 ← acca_arg_retrieve … st sacc_a; |
|---|
| 449 | ! v1 ← Byte_of_val v1; |
|---|
| 450 | ! v2 ← snd_arg_retrieve … st src; |
|---|
| 451 | ! v2 ← Byte_of_val v2; |
|---|
| 452 | ! carry ← bool_of_beval (carry … st); |
|---|
| 453 | let 〈v',carry〉 ≝ op2 eval carry op v1 v2 in |
|---|
| 454 | let v' ≝ BVByte v' in |
|---|
| 455 | let carry ≝ beval_of_bool carry in |
|---|
| 456 | ! st' ← acca_store … dacc_a v' st; |
|---|
| 457 | return set_carry … carry (post_op2 … p … ge op dacc_a sacc_a src st') |
|---|
| 458 | | CLEAR_CARRY ⇒ |
|---|
| 459 | return set_carry … BVfalse st |
|---|
| 460 | | SET_CARRY ⇒ |
|---|
| 461 | return set_carry … BVtrue st |
|---|
| 462 | | OPACCS op dacc_a_reg dacc_b_reg sacc_a_reg sacc_b_reg ⇒ |
|---|
| 463 | ! v1 ← acca_arg_retrieve … st sacc_a_reg; |
|---|
| 464 | ! v1 ← Byte_of_val v1; |
|---|
| 465 | ! v2 ← accb_arg_retrieve … st sacc_b_reg; |
|---|
| 466 | ! v2 ← Byte_of_val v2; |
|---|
| 467 | let 〈v1',v2'〉 ≝ opaccs eval op v1 v2 in |
|---|
| 468 | let v1' ≝ BVByte v1' in |
|---|
| 469 | let v2' ≝ BVByte v2' in |
|---|
| 470 | ! st' ← acca_store … dacc_a_reg v1' st; |
|---|
| 471 | accb_store … dacc_b_reg v2' st' |
|---|
| 472 | | POP dst ⇒ |
|---|
| 473 | ! 〈st',v〉 ← pop p st; |
|---|
| 474 | acca_store … p dst v st' |
|---|
| 475 | | PUSH src ⇒ |
|---|
| 476 | ! v ← acca_arg_retrieve … st src; |
|---|
| 477 | push … st v |
|---|
| 478 | | MOVE dst_src ⇒ |
|---|
| 479 | pair_reg_move … st dst_src |
|---|
| 480 | | CALL_ID id args dest ⇒ |
|---|
| 481 | ! b ← opt_to_res … [MSG MissingSymbol; CTX ? id] (find_symbol … ge id) : IO ???; |
|---|
| 482 | ! 〈flow, st'〉 ← eval_call_block … ge st b args dest ; |
|---|
| 483 | return st' |
|---|
| 484 | | extension_call s ⇒ |
|---|
| 485 | !〈flow, st'〉 ← eval_ext_call … ge s st ; |
|---|
| 486 | return st' |
|---|
| 487 | | _ ⇒ return st |
|---|
| 488 | ]. |
|---|
| 489 | (* TODO: to prove *) |
|---|
| 490 | elim daemon |
|---|
| 491 | qed. |
|---|
| 492 | |
|---|
| 493 | definition eval_seq_pc : |
|---|
| 494 | ∀p:sem_params.∀globals. genv p globals → state p → |
|---|
| 495 | ∀s:joint_seq p globals. |
|---|
| 496 | IO io_out io_in (step_flow p ? (step_flows … s)) ≝ |
|---|
| 497 | λp,g,ge,st,s.match s return λx : joint_seq ??.IO ?? (step_flow ?? (step_flows … x)) with |
|---|
| 498 | [ CALL_ID id args dest ⇒ |
|---|
| 499 | ! b ← opt_to_res \ldots [MSG MissingSymbol; CTX ? id] (find_symbol … ge id) : IO ???; |
|---|
| 500 | ! 〈flow, st'〉 ← eval_call_block … ge st b args dest ; |
|---|
| 501 | return flow |
|---|
| 502 | | extension_call s ⇒ |
|---|
| 503 | !〈flow, st'〉 ← eval_ext_call … ge s st ; |
|---|
| 504 | return flow |
|---|
| 505 | | _ ⇒ return Proceed ??? |
|---|
| 506 | ]. |
|---|
| 507 | |
|---|
| 508 | definition eval_step : |
|---|
| 509 | ∀p:sem_params.∀globals. genv p globals → |
|---|
| 510 | joint_internal_function p globals → state p → |
|---|
| 511 | ∀s:joint_step p globals. |
|---|
| 512 | IO io_out io_in ((step_flow p ? (step_flows … s))×(state p)) ≝ |
|---|
| 513 | λp,globals,ge,curr_fn,st,s. |
|---|
| 514 | match s return λx.IO ?? ((step_flow ?? (step_flows … x))×?) with |
|---|
| 515 | [ step_seq s ⇒ |
|---|
| 516 | ! flow ← eval_seq_pc ?? ge st s ; |
|---|
| 517 | ! st' ← eval_seq_no_pc ?? ge curr_fn st s ; |
|---|
| 518 | return 〈flow,st'〉 |
|---|
| 519 | | COND src ltrue ⇒ |
|---|
| 520 | ! v ← acca_retrieve … st src; |
|---|
| 521 | ! b ← bool_of_beval v; |
|---|
| 522 | if b then |
|---|
| 523 | return 〈Redirect ??? ltrue, st〉 |
|---|
| 524 | else |
|---|
| 525 | return 〈Proceed ???, st〉 |
|---|
| 526 | ]. |
|---|
| 527 | %1 % qed. |
|---|
| 528 | |
|---|
| 529 | definition eval_fin_step_no_pc : ∀p:sem_params.∀globals. genv p globals → |
|---|
| 530 | (* current function *) joint_internal_function p globals → state p → ∀s : joint_fin_step p. |
|---|
| 531 | IO io_out io_in (state p) ≝ |
|---|
| 532 | λp,globals,ge,curr_fn,st,s. |
|---|
| 533 | match s return λx.IO ??? with |
|---|
| 534 | [ tailcall c ⇒ |
|---|
| 535 | !〈flow,st'〉 ← eval_ext_tailcall … ge c curr_fn st ; |
|---|
| 536 | return st' |
|---|
| 537 | | _ ⇒ return st |
|---|
| 538 | ]. |
|---|
| 539 | |
|---|
| 540 | definition eval_fin_step_pc : |
|---|
| 541 | ∀p:sem_params.∀globals. genv p globals → joint_internal_function p globals → state p → |
|---|
| 542 | ∀s:joint_fin_step p. |
|---|
| 543 | IO io_out io_in (fin_step_flow p ? (fin_step_flows … s)) ≝ |
|---|
| 544 | λp,g,ge,curr_fn,st,s. |
|---|
| 545 | match s return λx.IO ?? (fin_step_flow ?? (fin_step_flows … x)) with |
|---|
| 546 | [ tailcall c ⇒ |
|---|
| 547 | !〈flow,st'〉 ← eval_ext_tailcall … ge c curr_fn st ; |
|---|
| 548 | return flow |
|---|
| 549 | | GOTO l ⇒ return FRedirect … l |
|---|
| 550 | | RETURN ⇒ return FEnd1 ?? |
|---|
| 551 | ]. %1 % qed. |
|---|
| 552 | |
|---|
| 553 | definition do_call : ∀p:sem_params.∀globals: list ident. genv p globals → |
|---|
| 554 | state p → Z → joint_internal_function p globals → call_args p → |
|---|
| 555 | res (state_pc p) ≝ |
|---|
| 556 | λp,globals,ge,st,id,fn,args. |
|---|
| 557 | ! st' ← setup_call … (joint_if_stacksize … fn) (joint_if_params … fn) |
|---|
| 558 | args st ; |
|---|
| 559 | let regs ≝ foldr ?? (allocate_local … p) (regs … st) (joint_if_locals … fn) in |
|---|
| 560 | let l' ≝ joint_if_entry … fn in |
|---|
| 561 | let st' ≝ set_regs p regs st in |
|---|
| 562 | let pointer_in_fn ≝ mk_pointer (mk_block Code id) (mk_offset (bv_zero …)) in |
|---|
| 563 | ! pc ← pointer_of_point ? p … pointer_in_fn l' ; |
|---|
| 564 | return mk_state_pc ? st' pc. % qed. |
|---|
| 565 | |
|---|
| 566 | (* The pointer provided is the one to the *next* instruction. *) |
|---|
| 567 | definition eval_step_flow : |
|---|
| 568 | ∀p:sem_params.∀globals.∀flows.genv p globals → |
|---|
| 569 | state p → cpointer → step_flow p ? flows → res (state_pc p) ≝ |
|---|
| 570 | λp,globals,flows,ge,st,nxt,cmd. |
|---|
| 571 | match cmd with |
|---|
| 572 | [ Redirect _ l ⇒ |
|---|
| 573 | goto … ge l st nxt |
|---|
| 574 | | Init id fn args dest ⇒ |
|---|
| 575 | ! st' ← save_frame … nxt dest st ; |
|---|
| 576 | do_call ?? ge st' id fn args |
|---|
| 577 | | Proceed _ ⇒ |
|---|
| 578 | return mk_state_pc ? st nxt |
|---|
| 579 | ]. |
|---|
| 580 | |
|---|
| 581 | definition eval_fin_step_flow : ∀p:sem_params.∀globals: list ident.∀flows. genv p globals → |
|---|
| 582 | state p → cpointer → fin_step_flow p ? flows → res (state_pc p) ≝ |
|---|
| 583 | λp,globals,lbls,ge,st,curr,cmd. |
|---|
| 584 | match cmd with |
|---|
| 585 | [ FRedirect _ l ⇒ goto … ge l st curr |
|---|
| 586 | | FTailInit id fn args ⇒ |
|---|
| 587 | do_call … ge st id fn args |
|---|
| 588 | | _ ⇒ |
|---|
| 589 | ! 〈st',ra〉 ← fetch_ra … st ; |
|---|
| 590 | ! fn ← fetch_function … ge curr ; |
|---|
| 591 | ! st'' ← pop_frame … ge fn st'; |
|---|
| 592 | return mk_state_pc ? st'' ra |
|---|
| 593 | ]. |
|---|
| 594 | |
|---|
| 595 | definition eval_statement : |
|---|
| 596 | ∀globals.∀p:sem_params.genv p globals → |
|---|
| 597 | state_pc p → joint_internal_function p globals → joint_statement p globals → |
|---|
| 598 | IO io_out io_in (state_pc p) ≝ |
|---|
| 599 | λglobals,p,ge,st,curr_fn,stmt. |
|---|
| 600 | match stmt with |
|---|
| 601 | [ sequential s nxt ⇒ |
|---|
| 602 | ! 〈flow,st'〉 ← eval_step … ge curr_fn st s ; |
|---|
| 603 | ! nxtptr ← succ_pc ? p (pc … st) nxt ; |
|---|
| 604 | eval_step_flow … ge st' nxtptr flow |
|---|
| 605 | | final s ⇒ |
|---|
| 606 | ! st' ← eval_fin_step_no_pc … ge curr_fn st s ; |
|---|
| 607 | ! flow ← eval_fin_step_pc … ge curr_fn st s ; |
|---|
| 608 | eval_fin_step_flow … ge st' (pc … st) flow |
|---|
| 609 | ]. |
|---|
| 610 | |
|---|
| 611 | definition eval_state : ∀globals: list ident.∀p:sem_params. genv p globals → |
|---|
| 612 | state_pc p → IO io_out io_in (state_pc p) ≝ |
|---|
| 613 | λglobals,p,ge,st. |
|---|
| 614 | ! 〈fn,s〉 ← fetch_statement ? p … ge (pc … st) : IO ???; |
|---|
| 615 | eval_statement … ge st fn s. |
|---|
| 616 | |
|---|
| 617 | (* Paolo: what if in an intermediate language main finishes with an external |
|---|
| 618 | tailcall? Maybe it should rely on an FEnd flow command issued, but that's |
|---|
| 619 | not static... *) |
|---|
| 620 | definition is_final: ∀globals:list ident. ∀p: sem_params. |
|---|
| 621 | genv p globals → cpointer → state_pc p → option int ≝ |
|---|
| 622 | λglobals,p,ge,exit,st.res_to_opt ? ( |
|---|
| 623 | do 〈fn,s〉 ← fetch_statement ? p … ge (pc … st); |
|---|
| 624 | match s with |
|---|
| 625 | [ final s' ⇒ |
|---|
| 626 | match s' with |
|---|
| 627 | [ RETURN ⇒ |
|---|
| 628 | do 〈st',ra〉 ← fetch_ra … st; |
|---|
| 629 | if eq_pointer ra exit then |
|---|
| 630 | do vals ← read_result … ge (joint_if_result … fn) st' ; |
|---|
| 631 | Word_of_list_beval vals |
|---|
| 632 | else |
|---|
| 633 | Error ? [ ] |
|---|
| 634 | | _ ⇒ Error ? [ ] |
|---|
| 635 | ] |
|---|
| 636 | | _ ⇒ Error ? [ ] |
|---|
| 637 | ]). |
|---|
| 638 | |
|---|
| 639 | (* |
|---|
| 640 | record evaluation_parameters : Type[1] ≝ |
|---|
| 641 | { globals: list ident |
|---|
| 642 | ; sparams:> sem_params |
|---|
| 643 | ; exit: cpointer |
|---|
| 644 | ; genv2: genv globals sparams |
|---|
| 645 | }. |
|---|
| 646 | |
|---|
| 647 | (* Paolo: with structured traces, eval need not emit labels. However, this |
|---|
| 648 | changes trans_system. For now, just putting a dummy thing for |
|---|
| 649 | the transition. *) |
|---|
| 650 | definition joint_exec: trans_system io_out io_in ≝ |
|---|
| 651 | mk_trans_system … evaluation_parameters (λG. state_pc G) |
|---|
| 652 | (λG.is_final (globals G) G (genv2 G) (exit G)) |
|---|
| 653 | (λG,st.! 〈flag,st'〉 ← eval_state_flag (globals G) G (genv2 G) st ; return 〈E0, st'〉). |
|---|
| 654 | |
|---|
| 655 | definition make_global : |
|---|
| 656 | ∀pars: sem_params. |
|---|
| 657 | joint_program pars → evaluation_parameters |
|---|
| 658 | ≝ |
|---|
| 659 | λpars. |
|---|
| 660 | (* Invariant: a -1 block is unused in common/Globalenvs *) |
|---|
| 661 | let b ≝ mk_block Code (-1) in |
|---|
| 662 | let ptr ≝ mk_pointer Code b ? (mk_offset 0) in |
|---|
| 663 | (λp. mk_evaluation_parameters |
|---|
| 664 | (prog_var_names … p) |
|---|
| 665 | (mk_sem_params … pars) |
|---|
| 666 | ptr |
|---|
| 667 | (globalenv_noinit … p) |
|---|
| 668 | ). |
|---|
| 669 | % qed. |
|---|
| 670 | |
|---|
| 671 | axiom ExternalMain: String. |
|---|
| 672 | |
|---|
| 673 | definition make_initial_state : |
|---|
| 674 | ∀pars: sem_params. |
|---|
| 675 | ∀p: joint_program … pars. res (state_pc pars) ≝ |
|---|
| 676 | λpars,p. |
|---|
| 677 | let sem_globals ≝ make_global pars p in |
|---|
| 678 | let ge ≝ genv2 sem_globals in |
|---|
| 679 | let m ≝ alloc_mem … p in |
|---|
| 680 | let 〈m,spb〉 ≝ alloc … m 0 external_ram_size XData in |
|---|
| 681 | let 〈m,ispb〉 ≝ alloc … m 0 internal_ram_size XData in |
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| 682 | let dummy_pc ≝ mk_pointer Code (mk_block Code (-1)) ? (mk_offset 0) in |
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| 683 | let spp ≝ mk_pointer XData spb ? (mk_offset external_ram_size) in |
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| 684 | let ispp ≝ mk_pointer XData ispb ? (mk_offset 47) in |
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| 685 | let main ≝ prog_main … p in |
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| 686 | let st0 ≝ mk_state pars (empty_framesT …) spp ispp BVfalse (empty_regsT … spp) m in |
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| 687 | (* use exit sem_globals as ra and call_dest_for_main as dest *) |
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| 688 | let st0' ≝ set_frms ? (save_frame … (exit sem_globals) (call_dest_for_main … pars) st0) st0 in |
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| 689 | let st_pc0 ≝ mk_state_pc ? st0' dummy_pc in |
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| 690 | ! main_block ← opt_to_res … [MSG MissingSymbol; CTX ? main] (find_symbol … ge main) ; |
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| 691 | ! main_fd ← opt_to_res ? [MSG BadPointer] (find_funct_ptr … ge main_block) ; |
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| 692 | match main_fd with |
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| 693 | [ Internal fn ⇒ |
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| 694 | do_call ?? ge st_pc0 (block_id main_block) fn (call_args_for_main … pars) |
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| 695 | | External _ ⇒ Error … [MSG ExternalMain] (* External main not supported: why? *) |
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| 696 | ]. [5: cases ispb * |6: cases spb * ] (* without try it fails! *) try // |
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| 697 | qed. |
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| 698 | |
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| 699 | definition joint_fullexec : |
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| 700 | ∀pars:sem_params.fullexec io_out io_in ≝ |
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| 701 | λpars.mk_fullexec ??? joint_exec (make_global pars) (make_initial_state pars). |
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| 702 | *) |
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